Research ArticleNumerical Well Testing Interpretation Model and Applicationsin Crossflow Double-Layer Reservoirs by Polymer Flooding

Haiyang Yu1 Hui Guo1 Youwei He1 Hainan Xu1 Lei Li1 Tiantian Zhang2 Bo Xian3

Song Du4 and Shiqing Cheng1

1 MOE Key Laboratory of Petroleum Engineering China University of Petroleum Beijing 102249 China2Department of Petroleum Engineering University of Texas at Austin Austin TX 78712 USA3 Research Institute of Exploration and Development PetroChina Korla 841000 China4Department of Petroleum Engineering Texas AampM University College Station TX 77843 USA

Correspondence should be addressed to Haiyang Yu haiyangyuutexasedu

Received 19 May 2014 Revised 13 June 2014 Accepted 13 June 2014 Published 26 June 2014

Academic Editor Wei Wan

Copyright copy 2014 Haiyang Yu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This work presents numerical well testing interpretation model and analysis techniques to evaluate formation by using pressuretransient data acquired with logging tools in crossflow double-layer reservoirs by polymer flooding A well testing model isestablished based on rheology experiments and by considering shear diffusion convection inaccessible pore volume (IPV)permeability reduction wellbore storage effect and skin factors The type curves were then developed based on this model andparameter sensitivity is analyzed Our research shows that the type curves have five segments with different flow status (I) wellborestorage section (II) intermediate flow section (transient section) (III) mid-radial flow section (IV) crossflow section (from lowpermeability layer to high permeability layer) and (V) systematic radial flow section The polymer flooding field tests prove thatour model can accurately determine formation parameters in crossflow double-layer reservoirs by polymer flooding Moreoverformation damage caused by polymer flooding can also be evaluated by comparison of the interpreted permeability with initiallayered permeability before polymer flooding Comparison of the analysis of numerical solution based on flow mechanism withobserved polymer flooding field test data highlights the potential for the application of this interpretation method in formationevaluation and enhanced oil recovery (EOR)

1 Introduction

Over the past several decades many EOR methods wereresearched in laboratories and oilfields to improve oil recov-ery for example polymer flooding [1] surfactant flooding[2] alkali-surfactant-polymer (ASP) flooding [3] nanopar-ticles [4 5] low salinity water flooding [6] and CO

2[7

8] However polymer flooding is most commonly appliedin oilfields especially hydrolyzed polyacrylamide (HPAM)polymer flooding because of its low cost and high efficiency[9] The oil recovery of polymer flooding is enhanced mainlyby increasing sweep efficiency [10]

Conventional pressure transient test has historically beenthe main application of permeability and skin estimation inoilfields by using a pressure gauge positioned at a fixed depth

in a well The pressure test of multilayered reservoir wasstudied from the 1960s however the research on the indi-vidual production of multilayered reservoir was not carriedout due to the restriction of testing tools and technology Apercolation model of multilayered reservoir was derived in1961 and the wellbore pressure and production of individuallayers were also deduced [11] This model considered that theinterlayer had different parameters but neglected thewellborestorage effect In 1978 a new model was further developedto get the wellbore pressure solution in real space for mul-tilayered reservoir by using Stehfest algorithm [12] It tookthe wellbore storage and skin factor into account whereasit ignored the crossflow of wellbore pressure response Fromthe 1980s to 1990s many researchers interpreted well testingdata by analysis of measured wellbore pressure and stratified

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 890874 11 pageshttpdxdoiorg1011552014890874

2 The Scientific World Journal

flow rate With the help of multilayer testing techniquesthe expression of pressure solution was established throughthe relationship between wellbore pressure and stratifiedflow rate of multilayered reservoir [13 14] The well testingmodel of crossflow double-layer reservoir was put forwardin 1985 [15] which was further investigated by theoreticalstudy of flow mechanics [16] However the type curves ofcrossflow double-layer reservoirs were not established Theproblem of interlayered crossflow in a stratified reservoir wasmathematically simplified by employing a semipermeablewall model [17] Based on the former research the dynamicmodel and exact solution of bottom hole pressure were pro-posed Most researches on well testing and fluid percolationin double-layer reservoirs were based on analysis methodto get the analytic solution of bottom hole pressure (BHP)In recent years the numerical methods were employed tostudy well testing problems of multilayered reservoir withthe help of rapid development of computer technology[18ndash21]

HPAM polymer solution is one kind of non-Newtonianfluids and its viscosity is a significant parameter usedto establish well testing interpretation model for polymerflooding Many researches on the rheological behavior ofpolymer solution simply consider polymer as power lawfluid and using constant power exponent model to representthe percolation of polymer solution in reservoirs [22ndash25]which is unable to meet the actual demands of our oilfieldsFor crossflow double-layer reservoirs by polymer floodingthere exist not only shear effect and viscoelastic effect butalso physic-chemical interaction during polymer solutionpercolating in porous medium whereas the constant powerexponent viscosity model ignores diffusion and convectionof polymer during transport in porous medium Meanwhilethe adsorption of polymers in the porous medium results inIPV [1 6 26 27] and permeability reduction [28ndash31] whichalso needs to be taken into account

At present well testing models and techniques in double-layer reservoirs by water flooding become mature andcommercial software can be used for reservoir evaluationhowever well testing models and interpretation methods inreservoirs with crossflow by polymer flooding are still lessThe purpose of this study is to establish well testing inter-pretation method that can be applied in crossflow double-layer reservoir by polymer flooding by considering sheardiffusion convection IPV permeability reduction wellborestorage effect and skin factors Moreover field test data arefurther interpreted by this method for formation evaluationand EOR

2 Polymer Rheology in Porous Medium

21 Materials A proprietary HPAM used for polymer flood-ing was supplied by CNPC The degree of hydrolysis is 25andmolecular weight ofHPAM is 4050The formation brinesused in this study were prepared with salts of NaCl MgCl

2

CaCl2 and Na

2SO4 and the synthetic brine composition

is listed in Table 1 The total salinity the sum of the ionicconcentration is 43 wt (43000 ppm or 4295 gL)

Table 1 Synthetic brine composition

Total salinity NaCl MgCl2 CaCl2 Na2SO4

43 wt 344wt 018 wt 064wt 004wt

22 Rheological Model Polymer solution was assumed tobehave as pseudoplastic non-Newtonian fluid As discussedabove the power law model [32] or Carreau model [33]cannot accurately illustrate rheological behavior of the poly-mer used in our case In this study polymer shear-thinningbehavior was simulated by use of Meter equation [34]

120583119901= 120583infin

+

1205830

119901minus 120583infin

1 + (12057412057412

)119875119886minus1

= (120583119908+

1205830

119901minus 120583119908

1 + (12057412057412

)119875119886minus1)

(1)

where 120583119901is apparent viscosity of polymer solution 120583

infinis

viscosity of polymer solution at infinite shear rate which issimplified as brine viscosity (120583

119908) and satisfied the accuracy

in this study since polymer concentration is relatively lowand its viscosity at infinite shear rate is pretty close to brineviscosity 120574

12is the shear rate at which apparent viscosity is

the average of 120583infin

and 1205830

119901 120574 is the effective shear rate 119875

119886is a

fitting parameter (usually 10 lt 119875119886lt 18) 1205830

119901is the viscosity

at very low shear rate which is calculated by modified Flory-Huggins equation [35]

1205830

119901= 120583119908[1 + (119860

1119862119901+ 11986021198622

119901+ 11986031198623

119901) 119862

SPSEP] (2)

where 1198601 1198602 and 119860

3are fitting parameters obtained from

matching experimental data 119862119901is polymer concentration

119862SPSEP represents the effect of salinity and hardness on polymer

viscositySince temperature significantly affects rheological behav-

ior of polymer and the effect of pressure on polymer vis-cosity is negligible compared with temperature the polymersolutions were prepared by mechanical stirring at 75∘C tosimulate reservoir temperature The tested polymer con-centrations range from 100mgL (01 gL or 001 wt) to4000mgL (the polymer concentrations in our field tests arebetween 1600mgL and 2500mgL)The polymer rheologicalmeasurement was carried out by Haake RS6000 rheometermade in Germany The viscosity of polymer solutions withdifferent concentrations was measured at 75∘C to get thefitting numbers of 119860

1 1198602 and 119860

3 shown in Figure 1 and

Table 2 The measurements were performed under 001 sminus1shear rate since 1205830

119901is the viscosity at very low shear rate

119875119886and 120574

12are functions of 120583

0

119901(or polymer concen-

tration) the expressions are provided by CNPC based ontheir former research shown in the following equationsrespectively

119875119886= 1182(120583

0

119901)00341

(3)

12057412

= 3762(1205830

119901)minus1365

+ 00341 (4)

The Scientific World Journal 3

Table 2 Characteristics of polymer solutions

120583119908 (mPasdots) 119860

1 (gL)minus1 119860

2 (gL)minus2 119860

3 (gL)minus3 119862

1199010 (gL) 119863 (cm2s)

05 0642 0201 0931 1750 00246

0

10

20

30

40

50

60

0 05 1 15 2 25 3 35 4 45Cp (gL)

Visc

osity

(mPmiddot

s)

Figure 1 Relationship between polymer viscosity (1205830119901) and polymer

concentration (119862119901) at 75∘C under 001 sminus1 shear rate

The relationship between effective shear rate 120574 and seepagevelocity is shown in the following [36]

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870120601

(5)

V =119876

2120587119903ℎ (6)

where 119899 is the bulk power law index in the range of 0 to 1 1198621015840is tortuosity coefficient 120601 is porosity 119870 is permeability 119876 isflow rate of injected polymer solutionℎ is reservoir thickness119903 is radial distance V is Darcy velocity

By considering IPV and permeability reduction caused bypolymer flooding (5) is changed to

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870119901120601119901

(7)

where 119870119901is effective permeability 119870

119901= 119870119877

119896 119877119896being

permeability reduction coefficient 120601119901is effective porosity

120601119901= 120601(1 minus IPV)During transport in porousmedium polymer concentra-

tion is also affected by convection and diffusion Thus poly-mer concentration by considering convection and diffusionis shown in the following [37]

119862119901(119903 119905) =

1198621199010

2minus1198621199010

2erf [119903 minus 119881119905

2radic119863119905] (8)

where 1198621199010

is initial polymer concentration 119863 is diffusioncoefficient

There are several shear-thinning rheological modelsdeveloped for polymer solutions The model used in this

study can accurately match the apparent viscosity of theproprietary HPAM polymer provided by CNPC over a widerange of injected velocity especially when polymer solutionspass through the perforation

3 Well Testing Modeling Methodology

The percolation of polymer flooding in crossflow double-layer reservoir is sketched in Figure 2 Crossflow occurs inthe interlayer and fluids can transport from low permeabilityzone to high permeability zone when polymer solutions areinjected into the reservoir The hypotheses are as follows(1) polymer solutions and reservoir brines are miscible(2) properties of polymer solutions are the same in eachlayer (3) fluids flow satisfies Darcyrsquos law (4) each layer ishomogeneous but formation properties for example layerthickness permeability skin factor and compressibility aredifferent between two layers (5) gravity effect is negligible (6)the initial pressure of each layer is the same 119901

119894 (7) reservoir

rocks and fluids are compressible (8) process of polymertransportation is isothermal (9) crossflow of interlayer ispseudosteady state

Based on the rheologicalmodel and hypotheses discussedabove the well testing interpretation model in crossflowdouble-layer reservoir by polymer flooding is established byconsidering shear diffusion convection IPV permeabilityreduction wellbore storage effect and different layered skinfactors

(i) percolation equation

1198701199011ℎ1

120597

120597119903(119903

1

120583119901

1205971199011

120597119903) + 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990111198621199051ℎ1

1205971199011

120597119905

1198701199012ℎ2

120597

120597119903(119903

1

120583119901

1205971199012

120597119903) minus 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990121198621199052ℎ2

1205971199012

120597119905

(9)

(ii) internal boundary conditions

wellbore storage effect

119902119861 = 119862119889119901119908119891

119889119905minus (

1198701199011ℎ1

120583119901

1199031205971199011

120597119903+1198701199012ℎ2

120583119901

1199031205971199012

120597119903)

100381610038161003816100381610038161003816100381610038161003816119903=119903119908

skin factor

119901119908(119905) = (119901

1minus 11990411199031205971199011

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

= (1199012minus 11990421199031205971199012

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

(10)

(iii) external boundary condition (infinite boundary)

1199011(infin 119905) = 119901

2(infin 119905) = 119901

119894 (11)

4 The Scientific World Journal

q

q1

q2

h1 k1

h2 k2

Ct1

Ct2

1206011

1206012

Figure 2 Sketch of polymer flooding in crossflow double-layerreservoir

(iv) initial condition

1199011(119903 0) = 119901

2(119903 0) = 119901

119894 (12)

where 1199011and 119901

2are reservoir pressure of each layer

1198701199011

and 1198701199012

are effective layered permeability ℎ1

and ℎ2are layer thickness 119862

1199051and 119862

1199052are total

layered compressibility 1206011199011

and 1206011199012

are porosity 119862 iswellbore storage coefficient 119904

1and 1199042are skin factor

119901119908119891

is BHP 119901119894is initial reservoir pressure 119886 is flow-

rate exchange coefficientDimensionless parameters are involved after solving themodel and obtaining BHP

119901119908119863119895

=

sum2

119895=1(119896119901ℎ)119895

1842 times 10minus3119902120583119901119861(119901119908119891119895

minus 119901119894) (119895 = 1 2)

119905119863=

36sum2

119895=1(119896119901ℎ)119895

sum2

119895=1(120601119901119862119905ℎ)1198951205831199011199032119908

119905

119862119863=

119862

21205871199032119908sum2

119895=1(120601119901119862119905ℎ)119895

(13)

where 119901119908119863

is dimensionless BHP 119905119863is dimensionless time

119862119863is dimensionless wellbore storage coefficient 120583

119901is the

viscosity of the first grid which expresses the rheologybehavior of fluid near wellbore

Three new parameters are then proposed in order toeffectively analyze parameters sensitivity and interpret fieldtest data

120594 =1198701199011ℎ1

1198701199011ℎ1+ 1198701199012ℎ2

120596 =

12060111990111198621199051ℎ1

12060111990111198621199051ℎ1+ 12060111990121198621199052ℎ2

120582 =1198861199032

1199081198701199012ℎ2

1198701199011ℎ1+ 1198701199012ℎ2

(14)

where 120594 is formation coefficient ratio 120596 is storativity ratio 120582is interporosity flow coefficient

4 Type Curves and Sensitivity Analysis

Based on dimensionless BHP and dimensionless BHPderiva-tive the type curves of pressure and pressure derivativein log-log scale are obtained Sensitivity analysis is furtherinvestigated

41 Type Curves Type curves of well testing in crossflowdouble-layer reservoir by polymer flooding are shown inFigure 3 which shows that type curves have five flow seg-ments (I) wellbore storage section where pressure andpressure derivative curves are superposed reflecting the pres-sure response characteristics during well storage stage (II)intermediate flow section (transient section) that describesthe pressure response from pure wellbore storage stage tomid-radial flow stage within internal region and there is aldquoconvexityrdquo (III) mid-radial flow section where fluids flowof individual layer achieves plane radial flow before crossflowhappens showing a horizontal period of pressure derivativeline (IV) crossflow section where fluids in low permeabilitylayer transport through interlayer into high permeabilitylayer and there is a ldquoconcaverdquo and (V) systematic radial flowsection where the whole system presents plane radial flowover time and the pressure curve lightly turns upward dueto the influence of the non-Newtonian fluid properties ofpolymer solution

The comparison of type curves in double-layer reservoirby polymer flooding with and without crossflow is demon-strated in Figure 4 It is obvious that there exists a ldquoconcaverdquo(section IV) in the crossflow double-layer reservoir which isformed by the fluids percolation from low permeability layerinto high permeability layer resulting in crossflow throughthe interlayer After crossflow is developed over time theldquoconcaverdquo will vanish and curves will overlap when pressuresof each layer achieve equilibrium In systematic radial flowsection (V) the BHP in crossflow reservoir is lower thanthat in noncrossflow reservoir since crossflow reduces theflow resistance (equal to systematic permeability enhanced)however the BHP derivative is the same with value of 05

42 Sensitivity Analysis The effects of different parameterson type curves are investigated including interporosity flowcoefficient ratio of formation coefficient storativity ratioinitial polymer concentration and IPV

421 Interporosity Flow Coefficient The influence of inter-porosity flow coefficient (120582) on type curves in crossflowdouble-layer reservoir by polymer flooding is shown inFigure 5 Smaller 120582 indicates fewer fluids transport throughinterlayer which depends on the permeability difference andBHP difference between two layers Smaller permeabilitydifference or BHP difference results in small 119886 and 120582 Theldquoconcaverdquo appears delayed with smaller interporosity flowcoefficient since it needs more time for the fluids in crossflowsection (IV) to achieve equilibrium After that individuallayer reaches the plane radial flow and BHP derivative curvechanges to horizontal indicating fluids flow achieves system-atic radial flow section (V)The time of ldquoconcaverdquo appearance

The Scientific World Journal 5

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

I

II IIIIV

V

log

pw

D)

log(

(p

998400 wD)

Figure 3 Type curves of well testing in crossflow double-layerreservoir by polymer flooding

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

Without crossflowCrossflow

log

pw

D)

log(

(p

998400 wD)

Figure 4 Type curves of well testing in double-layer reservoir bypolymer flooding with and without crossflow

can qualitatively evaluate formation heterogeneity since itis influenced by layered permeability difference it appearsearlier in heterogeneous formation and it appears later inrelative homogenous formation

422 Formation Coefficient Ratio Figure 6 represents theeffect of formation coefficient ratio (120594) on type curves incrossflow double-layer reservoir by polymer flooding Itshows that 120594 only affects the crossflow section (IV) thesmaller 120594 is the shallower the ldquoconcaverdquo becomes and vice

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120582 = 10minus4

120582 = 10minus5120582 = 10minus6

120582 = 10minus7

log

pw

D)

log(

(p

998400 wD)

Figure 5 Effect of interporosity flow coefficient (120582) on type curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

x = 07

x = 08

x = 09

log

pw

D)

log(

(p

998400 wD)

Figure 6 Effect of formation coefficient ratio (120594) on type curves

versa For reservoirs with fixed value of layer permeabilitysmaller 120594 means smaller difference of layer thickness andthe ldquoconcaverdquo becomes shallower as permeability differencedecreases

423 Storativity Ratio The effect of storativity ratio (120596) ontype curves in crossflow double-layer reservoir by polymerflooding is shown in Figure 7 The width and depth ofthe ldquoconcaverdquo are influenced by 120596 the ldquoconcaverdquo graduallybecomes narrower and shallower when 120596 increases and viceversa Individual layers respectively reach their radial flow

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

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2 The Scientific World Journal

flow rate With the help of multilayer testing techniquesthe expression of pressure solution was established throughthe relationship between wellbore pressure and stratifiedflow rate of multilayered reservoir [13 14] The well testingmodel of crossflow double-layer reservoir was put forwardin 1985 [15] which was further investigated by theoreticalstudy of flow mechanics [16] However the type curves ofcrossflow double-layer reservoirs were not established Theproblem of interlayered crossflow in a stratified reservoir wasmathematically simplified by employing a semipermeablewall model [17] Based on the former research the dynamicmodel and exact solution of bottom hole pressure were pro-posed Most researches on well testing and fluid percolationin double-layer reservoirs were based on analysis methodto get the analytic solution of bottom hole pressure (BHP)In recent years the numerical methods were employed tostudy well testing problems of multilayered reservoir withthe help of rapid development of computer technology[18ndash21]

HPAM polymer solution is one kind of non-Newtonianfluids and its viscosity is a significant parameter usedto establish well testing interpretation model for polymerflooding Many researches on the rheological behavior ofpolymer solution simply consider polymer as power lawfluid and using constant power exponent model to representthe percolation of polymer solution in reservoirs [22ndash25]which is unable to meet the actual demands of our oilfieldsFor crossflow double-layer reservoirs by polymer floodingthere exist not only shear effect and viscoelastic effect butalso physic-chemical interaction during polymer solutionpercolating in porous medium whereas the constant powerexponent viscosity model ignores diffusion and convectionof polymer during transport in porous medium Meanwhilethe adsorption of polymers in the porous medium results inIPV [1 6 26 27] and permeability reduction [28ndash31] whichalso needs to be taken into account

At present well testing models and techniques in double-layer reservoirs by water flooding become mature andcommercial software can be used for reservoir evaluationhowever well testing models and interpretation methods inreservoirs with crossflow by polymer flooding are still lessThe purpose of this study is to establish well testing inter-pretation method that can be applied in crossflow double-layer reservoir by polymer flooding by considering sheardiffusion convection IPV permeability reduction wellborestorage effect and skin factors Moreover field test data arefurther interpreted by this method for formation evaluationand EOR

2 Polymer Rheology in Porous Medium

21 Materials A proprietary HPAM used for polymer flood-ing was supplied by CNPC The degree of hydrolysis is 25andmolecular weight ofHPAM is 4050The formation brinesused in this study were prepared with salts of NaCl MgCl

2

CaCl2 and Na

2SO4 and the synthetic brine composition

is listed in Table 1 The total salinity the sum of the ionicconcentration is 43 wt (43000 ppm or 4295 gL)

Table 1 Synthetic brine composition

Total salinity NaCl MgCl2 CaCl2 Na2SO4

43 wt 344wt 018 wt 064wt 004wt

22 Rheological Model Polymer solution was assumed tobehave as pseudoplastic non-Newtonian fluid As discussedabove the power law model [32] or Carreau model [33]cannot accurately illustrate rheological behavior of the poly-mer used in our case In this study polymer shear-thinningbehavior was simulated by use of Meter equation [34]

120583119901= 120583infin

+

1205830

119901minus 120583infin

1 + (12057412057412

)119875119886minus1

= (120583119908+

1205830

119901minus 120583119908

1 + (12057412057412

)119875119886minus1)

(1)

where 120583119901is apparent viscosity of polymer solution 120583

infinis

viscosity of polymer solution at infinite shear rate which issimplified as brine viscosity (120583

119908) and satisfied the accuracy

in this study since polymer concentration is relatively lowand its viscosity at infinite shear rate is pretty close to brineviscosity 120574

12is the shear rate at which apparent viscosity is

the average of 120583infin

and 1205830

119901 120574 is the effective shear rate 119875

119886is a

fitting parameter (usually 10 lt 119875119886lt 18) 1205830

119901is the viscosity

at very low shear rate which is calculated by modified Flory-Huggins equation [35]

1205830

119901= 120583119908[1 + (119860

1119862119901+ 11986021198622

119901+ 11986031198623

119901) 119862

SPSEP] (2)

where 1198601 1198602 and 119860

3are fitting parameters obtained from

matching experimental data 119862119901is polymer concentration

119862SPSEP represents the effect of salinity and hardness on polymer

viscositySince temperature significantly affects rheological behav-

ior of polymer and the effect of pressure on polymer vis-cosity is negligible compared with temperature the polymersolutions were prepared by mechanical stirring at 75∘C tosimulate reservoir temperature The tested polymer con-centrations range from 100mgL (01 gL or 001 wt) to4000mgL (the polymer concentrations in our field tests arebetween 1600mgL and 2500mgL)The polymer rheologicalmeasurement was carried out by Haake RS6000 rheometermade in Germany The viscosity of polymer solutions withdifferent concentrations was measured at 75∘C to get thefitting numbers of 119860

1 1198602 and 119860

3 shown in Figure 1 and

Table 2 The measurements were performed under 001 sminus1shear rate since 1205830

119901is the viscosity at very low shear rate

119875119886and 120574

12are functions of 120583

0

119901(or polymer concen-

tration) the expressions are provided by CNPC based ontheir former research shown in the following equationsrespectively

119875119886= 1182(120583

0

119901)00341

(3)

12057412

= 3762(1205830

119901)minus1365

+ 00341 (4)

The Scientific World Journal 3

Table 2 Characteristics of polymer solutions

120583119908 (mPasdots) 119860

1 (gL)minus1 119860

2 (gL)minus2 119860

3 (gL)minus3 119862

1199010 (gL) 119863 (cm2s)

05 0642 0201 0931 1750 00246

0

10

20

30

40

50

60

0 05 1 15 2 25 3 35 4 45Cp (gL)

Visc

osity

(mPmiddot

s)

Figure 1 Relationship between polymer viscosity (1205830119901) and polymer

concentration (119862119901) at 75∘C under 001 sminus1 shear rate

The relationship between effective shear rate 120574 and seepagevelocity is shown in the following [36]

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870120601

(5)

V =119876

2120587119903ℎ (6)

where 119899 is the bulk power law index in the range of 0 to 1 1198621015840is tortuosity coefficient 120601 is porosity 119870 is permeability 119876 isflow rate of injected polymer solutionℎ is reservoir thickness119903 is radial distance V is Darcy velocity

By considering IPV and permeability reduction caused bypolymer flooding (5) is changed to

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870119901120601119901

(7)

where 119870119901is effective permeability 119870

119901= 119870119877

119896 119877119896being

permeability reduction coefficient 120601119901is effective porosity

120601119901= 120601(1 minus IPV)During transport in porousmedium polymer concentra-

tion is also affected by convection and diffusion Thus poly-mer concentration by considering convection and diffusionis shown in the following [37]

119862119901(119903 119905) =

1198621199010

2minus1198621199010

2erf [119903 minus 119881119905

2radic119863119905] (8)

where 1198621199010

is initial polymer concentration 119863 is diffusioncoefficient

There are several shear-thinning rheological modelsdeveloped for polymer solutions The model used in this

study can accurately match the apparent viscosity of theproprietary HPAM polymer provided by CNPC over a widerange of injected velocity especially when polymer solutionspass through the perforation

3 Well Testing Modeling Methodology

The percolation of polymer flooding in crossflow double-layer reservoir is sketched in Figure 2 Crossflow occurs inthe interlayer and fluids can transport from low permeabilityzone to high permeability zone when polymer solutions areinjected into the reservoir The hypotheses are as follows(1) polymer solutions and reservoir brines are miscible(2) properties of polymer solutions are the same in eachlayer (3) fluids flow satisfies Darcyrsquos law (4) each layer ishomogeneous but formation properties for example layerthickness permeability skin factor and compressibility aredifferent between two layers (5) gravity effect is negligible (6)the initial pressure of each layer is the same 119901

119894 (7) reservoir

rocks and fluids are compressible (8) process of polymertransportation is isothermal (9) crossflow of interlayer ispseudosteady state

Based on the rheologicalmodel and hypotheses discussedabove the well testing interpretation model in crossflowdouble-layer reservoir by polymer flooding is established byconsidering shear diffusion convection IPV permeabilityreduction wellbore storage effect and different layered skinfactors

(i) percolation equation

1198701199011ℎ1

120597

120597119903(119903

1

120583119901

1205971199011

120597119903) + 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990111198621199051ℎ1

1205971199011

120597119905

1198701199012ℎ2

120597

120597119903(119903

1

120583119901

1205971199012

120597119903) minus 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990121198621199052ℎ2

1205971199012

120597119905

(9)

(ii) internal boundary conditions

wellbore storage effect

119902119861 = 119862119889119901119908119891

119889119905minus (

1198701199011ℎ1

120583119901

1199031205971199011

120597119903+1198701199012ℎ2

120583119901

1199031205971199012

120597119903)

100381610038161003816100381610038161003816100381610038161003816119903=119903119908

skin factor

119901119908(119905) = (119901

1minus 11990411199031205971199011

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

= (1199012minus 11990421199031205971199012

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

(10)

(iii) external boundary condition (infinite boundary)

1199011(infin 119905) = 119901

2(infin 119905) = 119901

119894 (11)

4 The Scientific World Journal

q

q1

q2

h1 k1

h2 k2

Ct1

Ct2

1206011

1206012

Figure 2 Sketch of polymer flooding in crossflow double-layerreservoir

(iv) initial condition

1199011(119903 0) = 119901

2(119903 0) = 119901

119894 (12)

where 1199011and 119901

2are reservoir pressure of each layer

1198701199011

and 1198701199012

are effective layered permeability ℎ1

and ℎ2are layer thickness 119862

1199051and 119862

1199052are total

layered compressibility 1206011199011

and 1206011199012

are porosity 119862 iswellbore storage coefficient 119904

1and 1199042are skin factor

119901119908119891

is BHP 119901119894is initial reservoir pressure 119886 is flow-

rate exchange coefficientDimensionless parameters are involved after solving themodel and obtaining BHP

119901119908119863119895

=

sum2

119895=1(119896119901ℎ)119895

1842 times 10minus3119902120583119901119861(119901119908119891119895

minus 119901119894) (119895 = 1 2)

119905119863=

36sum2

119895=1(119896119901ℎ)119895

sum2

119895=1(120601119901119862119905ℎ)1198951205831199011199032119908

119905

119862119863=

119862

21205871199032119908sum2

119895=1(120601119901119862119905ℎ)119895

(13)

where 119901119908119863

is dimensionless BHP 119905119863is dimensionless time

119862119863is dimensionless wellbore storage coefficient 120583

119901is the

viscosity of the first grid which expresses the rheologybehavior of fluid near wellbore

Three new parameters are then proposed in order toeffectively analyze parameters sensitivity and interpret fieldtest data

120594 =1198701199011ℎ1

1198701199011ℎ1+ 1198701199012ℎ2

120596 =

12060111990111198621199051ℎ1

12060111990111198621199051ℎ1+ 12060111990121198621199052ℎ2

120582 =1198861199032

1199081198701199012ℎ2

1198701199011ℎ1+ 1198701199012ℎ2

(14)

where 120594 is formation coefficient ratio 120596 is storativity ratio 120582is interporosity flow coefficient

4 Type Curves and Sensitivity Analysis

Based on dimensionless BHP and dimensionless BHPderiva-tive the type curves of pressure and pressure derivativein log-log scale are obtained Sensitivity analysis is furtherinvestigated

41 Type Curves Type curves of well testing in crossflowdouble-layer reservoir by polymer flooding are shown inFigure 3 which shows that type curves have five flow seg-ments (I) wellbore storage section where pressure andpressure derivative curves are superposed reflecting the pres-sure response characteristics during well storage stage (II)intermediate flow section (transient section) that describesthe pressure response from pure wellbore storage stage tomid-radial flow stage within internal region and there is aldquoconvexityrdquo (III) mid-radial flow section where fluids flowof individual layer achieves plane radial flow before crossflowhappens showing a horizontal period of pressure derivativeline (IV) crossflow section where fluids in low permeabilitylayer transport through interlayer into high permeabilitylayer and there is a ldquoconcaverdquo and (V) systematic radial flowsection where the whole system presents plane radial flowover time and the pressure curve lightly turns upward dueto the influence of the non-Newtonian fluid properties ofpolymer solution

The comparison of type curves in double-layer reservoirby polymer flooding with and without crossflow is demon-strated in Figure 4 It is obvious that there exists a ldquoconcaverdquo(section IV) in the crossflow double-layer reservoir which isformed by the fluids percolation from low permeability layerinto high permeability layer resulting in crossflow throughthe interlayer After crossflow is developed over time theldquoconcaverdquo will vanish and curves will overlap when pressuresof each layer achieve equilibrium In systematic radial flowsection (V) the BHP in crossflow reservoir is lower thanthat in noncrossflow reservoir since crossflow reduces theflow resistance (equal to systematic permeability enhanced)however the BHP derivative is the same with value of 05

42 Sensitivity Analysis The effects of different parameterson type curves are investigated including interporosity flowcoefficient ratio of formation coefficient storativity ratioinitial polymer concentration and IPV

421 Interporosity Flow Coefficient The influence of inter-porosity flow coefficient (120582) on type curves in crossflowdouble-layer reservoir by polymer flooding is shown inFigure 5 Smaller 120582 indicates fewer fluids transport throughinterlayer which depends on the permeability difference andBHP difference between two layers Smaller permeabilitydifference or BHP difference results in small 119886 and 120582 Theldquoconcaverdquo appears delayed with smaller interporosity flowcoefficient since it needs more time for the fluids in crossflowsection (IV) to achieve equilibrium After that individuallayer reaches the plane radial flow and BHP derivative curvechanges to horizontal indicating fluids flow achieves system-atic radial flow section (V)The time of ldquoconcaverdquo appearance

The Scientific World Journal 5

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

I

II IIIIV

V

log

pw

D)

log(

(p

998400 wD)

Figure 3 Type curves of well testing in crossflow double-layerreservoir by polymer flooding

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

Without crossflowCrossflow

log

pw

D)

log(

(p

998400 wD)

Figure 4 Type curves of well testing in double-layer reservoir bypolymer flooding with and without crossflow

can qualitatively evaluate formation heterogeneity since itis influenced by layered permeability difference it appearsearlier in heterogeneous formation and it appears later inrelative homogenous formation

422 Formation Coefficient Ratio Figure 6 represents theeffect of formation coefficient ratio (120594) on type curves incrossflow double-layer reservoir by polymer flooding Itshows that 120594 only affects the crossflow section (IV) thesmaller 120594 is the shallower the ldquoconcaverdquo becomes and vice

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120582 = 10minus4

120582 = 10minus5120582 = 10minus6

120582 = 10minus7

log

pw

D)

log(

(p

998400 wD)

Figure 5 Effect of interporosity flow coefficient (120582) on type curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

x = 07

x = 08

x = 09

log

pw

D)

log(

(p

998400 wD)

Figure 6 Effect of formation coefficient ratio (120594) on type curves

versa For reservoirs with fixed value of layer permeabilitysmaller 120594 means smaller difference of layer thickness andthe ldquoconcaverdquo becomes shallower as permeability differencedecreases

423 Storativity Ratio The effect of storativity ratio (120596) ontype curves in crossflow double-layer reservoir by polymerflooding is shown in Figure 7 The width and depth ofthe ldquoconcaverdquo are influenced by 120596 the ldquoconcaverdquo graduallybecomes narrower and shallower when 120596 increases and viceversa Individual layers respectively reach their radial flow

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

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The Scientific World Journal 3

Table 2 Characteristics of polymer solutions

120583119908 (mPasdots) 119860

1 (gL)minus1 119860

2 (gL)minus2 119860

3 (gL)minus3 119862

1199010 (gL) 119863 (cm2s)

05 0642 0201 0931 1750 00246

0

10

20

30

40

50

60

0 05 1 15 2 25 3 35 4 45Cp (gL)

Visc

osity

(mPmiddot

s)

Figure 1 Relationship between polymer viscosity (1205830119901) and polymer

concentration (119862119901) at 75∘C under 001 sminus1 shear rate

The relationship between effective shear rate 120574 and seepagevelocity is shown in the following [36]

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870120601

(5)

V =119876

2120587119903ℎ (6)

where 119899 is the bulk power law index in the range of 0 to 1 1198621015840is tortuosity coefficient 120601 is porosity 119870 is permeability 119876 isflow rate of injected polymer solutionℎ is reservoir thickness119903 is radial distance V is Darcy velocity

By considering IPV and permeability reduction caused bypolymer flooding (5) is changed to

120574 =3119899 + 1

119899 + 1

104V

radic81198621015840119870119901120601119901

(7)

where 119870119901is effective permeability 119870

119901= 119870119877

119896 119877119896being

permeability reduction coefficient 120601119901is effective porosity

120601119901= 120601(1 minus IPV)During transport in porousmedium polymer concentra-

tion is also affected by convection and diffusion Thus poly-mer concentration by considering convection and diffusionis shown in the following [37]

119862119901(119903 119905) =

1198621199010

2minus1198621199010

2erf [119903 minus 119881119905

2radic119863119905] (8)

where 1198621199010

is initial polymer concentration 119863 is diffusioncoefficient

There are several shear-thinning rheological modelsdeveloped for polymer solutions The model used in this

study can accurately match the apparent viscosity of theproprietary HPAM polymer provided by CNPC over a widerange of injected velocity especially when polymer solutionspass through the perforation

3 Well Testing Modeling Methodology

The percolation of polymer flooding in crossflow double-layer reservoir is sketched in Figure 2 Crossflow occurs inthe interlayer and fluids can transport from low permeabilityzone to high permeability zone when polymer solutions areinjected into the reservoir The hypotheses are as follows(1) polymer solutions and reservoir brines are miscible(2) properties of polymer solutions are the same in eachlayer (3) fluids flow satisfies Darcyrsquos law (4) each layer ishomogeneous but formation properties for example layerthickness permeability skin factor and compressibility aredifferent between two layers (5) gravity effect is negligible (6)the initial pressure of each layer is the same 119901

119894 (7) reservoir

rocks and fluids are compressible (8) process of polymertransportation is isothermal (9) crossflow of interlayer ispseudosteady state

Based on the rheologicalmodel and hypotheses discussedabove the well testing interpretation model in crossflowdouble-layer reservoir by polymer flooding is established byconsidering shear diffusion convection IPV permeabilityreduction wellbore storage effect and different layered skinfactors

(i) percolation equation

1198701199011ℎ1

120597

120597119903(119903

1

120583119901

1205971199011

120597119903) + 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990111198621199051ℎ1

1205971199011

120597119905

1198701199012ℎ2

120597

120597119903(119903

1

120583119901

1205971199012

120597119903) minus 119886

1198701199012ℎ2

120583119901

(1199012minus 1199011) = 12060111990121198621199052ℎ2

1205971199012

120597119905

(9)

(ii) internal boundary conditions

wellbore storage effect

119902119861 = 119862119889119901119908119891

119889119905minus (

1198701199011ℎ1

120583119901

1199031205971199011

120597119903+1198701199012ℎ2

120583119901

1199031205971199012

120597119903)

100381610038161003816100381610038161003816100381610038161003816119903=119903119908

skin factor

119901119908(119905) = (119901

1minus 11990411199031205971199011

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

= (1199012minus 11990421199031205971199012

120597119903)

10038161003816100381610038161003816100381610038161003816119903=119903119908

(10)

(iii) external boundary condition (infinite boundary)

1199011(infin 119905) = 119901

2(infin 119905) = 119901

119894 (11)

4 The Scientific World Journal

q

q1

q2

h1 k1

h2 k2

Ct1

Ct2

1206011

1206012

Figure 2 Sketch of polymer flooding in crossflow double-layerreservoir

(iv) initial condition

1199011(119903 0) = 119901

2(119903 0) = 119901

119894 (12)

where 1199011and 119901

2are reservoir pressure of each layer

1198701199011

and 1198701199012

are effective layered permeability ℎ1

and ℎ2are layer thickness 119862

1199051and 119862

1199052are total

layered compressibility 1206011199011

and 1206011199012

are porosity 119862 iswellbore storage coefficient 119904

1and 1199042are skin factor

119901119908119891

is BHP 119901119894is initial reservoir pressure 119886 is flow-

rate exchange coefficientDimensionless parameters are involved after solving themodel and obtaining BHP

119901119908119863119895

=

sum2

119895=1(119896119901ℎ)119895

1842 times 10minus3119902120583119901119861(119901119908119891119895

minus 119901119894) (119895 = 1 2)

119905119863=

36sum2

119895=1(119896119901ℎ)119895

sum2

119895=1(120601119901119862119905ℎ)1198951205831199011199032119908

119905

119862119863=

119862

21205871199032119908sum2

119895=1(120601119901119862119905ℎ)119895

(13)

where 119901119908119863

is dimensionless BHP 119905119863is dimensionless time

119862119863is dimensionless wellbore storage coefficient 120583

119901is the

viscosity of the first grid which expresses the rheologybehavior of fluid near wellbore

Three new parameters are then proposed in order toeffectively analyze parameters sensitivity and interpret fieldtest data

120594 =1198701199011ℎ1

1198701199011ℎ1+ 1198701199012ℎ2

120596 =

12060111990111198621199051ℎ1

12060111990111198621199051ℎ1+ 12060111990121198621199052ℎ2

120582 =1198861199032

1199081198701199012ℎ2

1198701199011ℎ1+ 1198701199012ℎ2

(14)

where 120594 is formation coefficient ratio 120596 is storativity ratio 120582is interporosity flow coefficient

4 Type Curves and Sensitivity Analysis

Based on dimensionless BHP and dimensionless BHPderiva-tive the type curves of pressure and pressure derivativein log-log scale are obtained Sensitivity analysis is furtherinvestigated

41 Type Curves Type curves of well testing in crossflowdouble-layer reservoir by polymer flooding are shown inFigure 3 which shows that type curves have five flow seg-ments (I) wellbore storage section where pressure andpressure derivative curves are superposed reflecting the pres-sure response characteristics during well storage stage (II)intermediate flow section (transient section) that describesthe pressure response from pure wellbore storage stage tomid-radial flow stage within internal region and there is aldquoconvexityrdquo (III) mid-radial flow section where fluids flowof individual layer achieves plane radial flow before crossflowhappens showing a horizontal period of pressure derivativeline (IV) crossflow section where fluids in low permeabilitylayer transport through interlayer into high permeabilitylayer and there is a ldquoconcaverdquo and (V) systematic radial flowsection where the whole system presents plane radial flowover time and the pressure curve lightly turns upward dueto the influence of the non-Newtonian fluid properties ofpolymer solution

The comparison of type curves in double-layer reservoirby polymer flooding with and without crossflow is demon-strated in Figure 4 It is obvious that there exists a ldquoconcaverdquo(section IV) in the crossflow double-layer reservoir which isformed by the fluids percolation from low permeability layerinto high permeability layer resulting in crossflow throughthe interlayer After crossflow is developed over time theldquoconcaverdquo will vanish and curves will overlap when pressuresof each layer achieve equilibrium In systematic radial flowsection (V) the BHP in crossflow reservoir is lower thanthat in noncrossflow reservoir since crossflow reduces theflow resistance (equal to systematic permeability enhanced)however the BHP derivative is the same with value of 05

42 Sensitivity Analysis The effects of different parameterson type curves are investigated including interporosity flowcoefficient ratio of formation coefficient storativity ratioinitial polymer concentration and IPV

421 Interporosity Flow Coefficient The influence of inter-porosity flow coefficient (120582) on type curves in crossflowdouble-layer reservoir by polymer flooding is shown inFigure 5 Smaller 120582 indicates fewer fluids transport throughinterlayer which depends on the permeability difference andBHP difference between two layers Smaller permeabilitydifference or BHP difference results in small 119886 and 120582 Theldquoconcaverdquo appears delayed with smaller interporosity flowcoefficient since it needs more time for the fluids in crossflowsection (IV) to achieve equilibrium After that individuallayer reaches the plane radial flow and BHP derivative curvechanges to horizontal indicating fluids flow achieves system-atic radial flow section (V)The time of ldquoconcaverdquo appearance

The Scientific World Journal 5

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

I

II IIIIV

V

log

pw

D)

log(

(p

998400 wD)

Figure 3 Type curves of well testing in crossflow double-layerreservoir by polymer flooding

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

Without crossflowCrossflow

log

pw

D)

log(

(p

998400 wD)

Figure 4 Type curves of well testing in double-layer reservoir bypolymer flooding with and without crossflow

can qualitatively evaluate formation heterogeneity since itis influenced by layered permeability difference it appearsearlier in heterogeneous formation and it appears later inrelative homogenous formation

422 Formation Coefficient Ratio Figure 6 represents theeffect of formation coefficient ratio (120594) on type curves incrossflow double-layer reservoir by polymer flooding Itshows that 120594 only affects the crossflow section (IV) thesmaller 120594 is the shallower the ldquoconcaverdquo becomes and vice

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120582 = 10minus4

120582 = 10minus5120582 = 10minus6

120582 = 10minus7

log

pw

D)

log(

(p

998400 wD)

Figure 5 Effect of interporosity flow coefficient (120582) on type curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

x = 07

x = 08

x = 09

log

pw

D)

log(

(p

998400 wD)

Figure 6 Effect of formation coefficient ratio (120594) on type curves

versa For reservoirs with fixed value of layer permeabilitysmaller 120594 means smaller difference of layer thickness andthe ldquoconcaverdquo becomes shallower as permeability differencedecreases

423 Storativity Ratio The effect of storativity ratio (120596) ontype curves in crossflow double-layer reservoir by polymerflooding is shown in Figure 7 The width and depth ofthe ldquoconcaverdquo are influenced by 120596 the ldquoconcaverdquo graduallybecomes narrower and shallower when 120596 increases and viceversa Individual layers respectively reach their radial flow

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

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4 The Scientific World Journal

q

q1

q2

h1 k1

h2 k2

Ct1

Ct2

1206011

1206012

Figure 2 Sketch of polymer flooding in crossflow double-layerreservoir

(iv) initial condition

1199011(119903 0) = 119901

2(119903 0) = 119901

119894 (12)

where 1199011and 119901

2are reservoir pressure of each layer

1198701199011

and 1198701199012

are effective layered permeability ℎ1

and ℎ2are layer thickness 119862

1199051and 119862

1199052are total

layered compressibility 1206011199011

and 1206011199012

are porosity 119862 iswellbore storage coefficient 119904

1and 1199042are skin factor

119901119908119891

is BHP 119901119894is initial reservoir pressure 119886 is flow-

rate exchange coefficientDimensionless parameters are involved after solving themodel and obtaining BHP

119901119908119863119895

=

sum2

119895=1(119896119901ℎ)119895

1842 times 10minus3119902120583119901119861(119901119908119891119895

minus 119901119894) (119895 = 1 2)

119905119863=

36sum2

119895=1(119896119901ℎ)119895

sum2

119895=1(120601119901119862119905ℎ)1198951205831199011199032119908

119905

119862119863=

119862

21205871199032119908sum2

119895=1(120601119901119862119905ℎ)119895

(13)

where 119901119908119863

is dimensionless BHP 119905119863is dimensionless time

119862119863is dimensionless wellbore storage coefficient 120583

119901is the

viscosity of the first grid which expresses the rheologybehavior of fluid near wellbore

Three new parameters are then proposed in order toeffectively analyze parameters sensitivity and interpret fieldtest data

120594 =1198701199011ℎ1

1198701199011ℎ1+ 1198701199012ℎ2

120596 =

12060111990111198621199051ℎ1

12060111990111198621199051ℎ1+ 12060111990121198621199052ℎ2

120582 =1198861199032

1199081198701199012ℎ2

1198701199011ℎ1+ 1198701199012ℎ2

(14)

where 120594 is formation coefficient ratio 120596 is storativity ratio 120582is interporosity flow coefficient

4 Type Curves and Sensitivity Analysis

Based on dimensionless BHP and dimensionless BHPderiva-tive the type curves of pressure and pressure derivativein log-log scale are obtained Sensitivity analysis is furtherinvestigated

41 Type Curves Type curves of well testing in crossflowdouble-layer reservoir by polymer flooding are shown inFigure 3 which shows that type curves have five flow seg-ments (I) wellbore storage section where pressure andpressure derivative curves are superposed reflecting the pres-sure response characteristics during well storage stage (II)intermediate flow section (transient section) that describesthe pressure response from pure wellbore storage stage tomid-radial flow stage within internal region and there is aldquoconvexityrdquo (III) mid-radial flow section where fluids flowof individual layer achieves plane radial flow before crossflowhappens showing a horizontal period of pressure derivativeline (IV) crossflow section where fluids in low permeabilitylayer transport through interlayer into high permeabilitylayer and there is a ldquoconcaverdquo and (V) systematic radial flowsection where the whole system presents plane radial flowover time and the pressure curve lightly turns upward dueto the influence of the non-Newtonian fluid properties ofpolymer solution

The comparison of type curves in double-layer reservoirby polymer flooding with and without crossflow is demon-strated in Figure 4 It is obvious that there exists a ldquoconcaverdquo(section IV) in the crossflow double-layer reservoir which isformed by the fluids percolation from low permeability layerinto high permeability layer resulting in crossflow throughthe interlayer After crossflow is developed over time theldquoconcaverdquo will vanish and curves will overlap when pressuresof each layer achieve equilibrium In systematic radial flowsection (V) the BHP in crossflow reservoir is lower thanthat in noncrossflow reservoir since crossflow reduces theflow resistance (equal to systematic permeability enhanced)however the BHP derivative is the same with value of 05

42 Sensitivity Analysis The effects of different parameterson type curves are investigated including interporosity flowcoefficient ratio of formation coefficient storativity ratioinitial polymer concentration and IPV

421 Interporosity Flow Coefficient The influence of inter-porosity flow coefficient (120582) on type curves in crossflowdouble-layer reservoir by polymer flooding is shown inFigure 5 Smaller 120582 indicates fewer fluids transport throughinterlayer which depends on the permeability difference andBHP difference between two layers Smaller permeabilitydifference or BHP difference results in small 119886 and 120582 Theldquoconcaverdquo appears delayed with smaller interporosity flowcoefficient since it needs more time for the fluids in crossflowsection (IV) to achieve equilibrium After that individuallayer reaches the plane radial flow and BHP derivative curvechanges to horizontal indicating fluids flow achieves system-atic radial flow section (V)The time of ldquoconcaverdquo appearance

The Scientific World Journal 5

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

I

II IIIIV

V

log

pw

D)

log(

(p

998400 wD)

Figure 3 Type curves of well testing in crossflow double-layerreservoir by polymer flooding

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

Without crossflowCrossflow

log

pw

D)

log(

(p

998400 wD)

Figure 4 Type curves of well testing in double-layer reservoir bypolymer flooding with and without crossflow

can qualitatively evaluate formation heterogeneity since itis influenced by layered permeability difference it appearsearlier in heterogeneous formation and it appears later inrelative homogenous formation

422 Formation Coefficient Ratio Figure 6 represents theeffect of formation coefficient ratio (120594) on type curves incrossflow double-layer reservoir by polymer flooding Itshows that 120594 only affects the crossflow section (IV) thesmaller 120594 is the shallower the ldquoconcaverdquo becomes and vice

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120582 = 10minus4

120582 = 10minus5120582 = 10minus6

120582 = 10minus7

log

pw

D)

log(

(p

998400 wD)

Figure 5 Effect of interporosity flow coefficient (120582) on type curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

x = 07

x = 08

x = 09

log

pw

D)

log(

(p

998400 wD)

Figure 6 Effect of formation coefficient ratio (120594) on type curves

versa For reservoirs with fixed value of layer permeabilitysmaller 120594 means smaller difference of layer thickness andthe ldquoconcaverdquo becomes shallower as permeability differencedecreases

423 Storativity Ratio The effect of storativity ratio (120596) ontype curves in crossflow double-layer reservoir by polymerflooding is shown in Figure 7 The width and depth ofthe ldquoconcaverdquo are influenced by 120596 the ldquoconcaverdquo graduallybecomes narrower and shallower when 120596 increases and viceversa Individual layers respectively reach their radial flow

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

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The Scientific World Journal 5

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

I

II IIIIV

V

log

pw

D)

log(

(p

998400 wD)

Figure 3 Type curves of well testing in crossflow double-layerreservoir by polymer flooding

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

Without crossflowCrossflow

log

pw

D)

log(

(p

998400 wD)

Figure 4 Type curves of well testing in double-layer reservoir bypolymer flooding with and without crossflow

can qualitatively evaluate formation heterogeneity since itis influenced by layered permeability difference it appearsearlier in heterogeneous formation and it appears later inrelative homogenous formation

422 Formation Coefficient Ratio Figure 6 represents theeffect of formation coefficient ratio (120594) on type curves incrossflow double-layer reservoir by polymer flooding Itshows that 120594 only affects the crossflow section (IV) thesmaller 120594 is the shallower the ldquoconcaverdquo becomes and vice

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120582 = 10minus4

120582 = 10minus5120582 = 10minus6

120582 = 10minus7

log

pw

D)

log(

(p

998400 wD)

Figure 5 Effect of interporosity flow coefficient (120582) on type curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

x = 07

x = 08

x = 09

log

pw

D)

log(

(p

998400 wD)

Figure 6 Effect of formation coefficient ratio (120594) on type curves

versa For reservoirs with fixed value of layer permeabilitysmaller 120594 means smaller difference of layer thickness andthe ldquoconcaverdquo becomes shallower as permeability differencedecreases

423 Storativity Ratio The effect of storativity ratio (120596) ontype curves in crossflow double-layer reservoir by polymerflooding is shown in Figure 7 The width and depth ofthe ldquoconcaverdquo are influenced by 120596 the ldquoconcaverdquo graduallybecomes narrower and shallower when 120596 increases and viceversa Individual layers respectively reach their radial flow

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

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Navigation and Observation

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DistributedSensor Networks

International Journal of

6 The Scientific World Journal

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

120596 = 001

120596 = 003

120596 = 006

120596 = 01

log

pw

D)

log(

(p

998400 wD)

Figure 7 Effect of storativity ratio (120596) on type curves

after the crossflow segment ends indicating systematic radialflow section (V)

424 Initial Polymer Concentration Theeffect of initial poly-mer concentration (119862

1199010) on type curves in crossflow double-

layer reservoir by polymer flooding is shown in Figure 8which indicate that the crossflow section (IV) appears laterand BHP derivative curve in systematic radial flow section(V) turns more upward by increasing 119862

1199010 Since viscosity

is increased for higher 1198621199010 there is more flow resistance

for fluids to transport through interlayer resulting in delayof crossflow section (IV) appearance and greater amplitudeof BHP derivative curve in systematic radial flow section(V) Consider 119862

0= 0mgL expressed as water flooding

which is Newtonian fluid with constant viscosity Furtherinvestigation indicates that the effect of polymer rheology ontype curve section (V) is dramatically reduced by crossflowwhichmeans the pressure curve andpressure derivative curveof polymer flooding are similar to those of water flooding insection (V) and this phenomenon is also proved by field testdata However the slope of type curves in one-layer reservoirwith homogenous thickness by polymer flooding is muchlarger than that of water flooding

425 Inaccessible Pore Volume Figure 9 represents the effectof IPV on type curves in crossflow double-layer reservoirby polymer flooding The crossflow section (IV) appearsearlier for reservoir with bigger IPV Bigger IPVmeans lowereffective porosity and the fluid velocity is higher for thereservoir with fixed flow rate of polymer injected resultingin earlier appearance of the crossflow section (IV) andsystematic radial flow section (V) However the effect of IPVon well testing type curves is unremarkable moreover theIPV caused by polymer flooding in oilfields is usually lessthan 015 so the effect of IPV can be negligible during well

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

C0 = 0 mgLC0 = 500 mgL

C0 = 1000 mgLC0 = 2000 mgL

log

pw

D)

log(

(p

998400 wD)

Figure 8 Effect of initial polymer concentration (1198621199010) on type

curves

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

IPV = 01

IPV = 02

IPV = 03

IPV = 04

log

pw

D)

log(

(p

998400 wD)

Figure 9 Effect of IPV on type curves

testing interpretation Unlike other parameters the effect ofIPV on type curves is listed here only for theoretical analysis

426 Wellbore Storage Coefficient The effect of wellborestorage coefficient on type curves in crossflow double-layerreservoir by polymer flooding is shown in Figure 10 Thedepth of the ldquoconcaverdquo and ldquoconvexityrdquo is influenced by 119862however it does not affect the width The crossflow section(IV) and systematic radial flow section (V) gradually appearearlier with 120596 increases meanwhile the mid-radial flowsection (III) is shortened

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

The Scientific World Journal 7

102

101

100

10minus1

10minus2

10minus2 100 102 104 106 108

log(tDCD)

10minus3

10minus4

C = 01 m3MPaC = 05 m3MPaC = 1 m3MPa

log

pw

D)

log(

(p

998400 wD)

Figure 10 Effect of wellbore storage coefficient (119862) on type curves

Table 3 Characteristics of crude oil under surface conditions

Density (gcm3 20∘C) Viscosity (mPasdots20∘C)

Viscosity (mPasdots55∘C)

0925sim0934 4075sim5336 4956sim5821

5 Field Tests Interpretation

Well testing data of field test was provided by CNPC Thendraw the BHP data with time in log-log scale Interpretthe data and perform history matching of type curvesto evaluate reservoir formation and calculate the averageformation pressure layered permeability layered skin factorand wellbore storage coefficient The interpretation results oflayered permeability and layered skin factor are significantfor oilfields since oil industry will adjust development planof production based on them If the layered permeability ismuch lower or the layered skin factor is much higher thanthose of before polymer flooding it indicates that polymerflooding leads to serious formation damage and specificmethods should be employed to reduce formation damageand improve production for example acidizing

51 Basic Properties of Oilfield The tectonic surface areais 33 km2 and structure amplitude is about 100m Theformation conditions and fluid properties are suitable forpolymer flooding meanwhile relatively low salinity and lowdivalent cation concentration are beneficial to maintainingsystematic viscoelasticity The characteristics of crude oilunder surface conditions and reservoir conditions are shownin Tables 3 and 4 respectively The pressure derivative curveof field test data was modified for curve smoothing by usingBourdetrsquos method [38]

Table 4 Characteristics of crude oil under reservoir conditions

Density(gcm3)

Viscosity(mPasdots)

Volumefactor

Saturationpressure(MPa)

Oil-gasratio

Acidnumber

08675 142 11038 1270 42 04sim116

52 Field Test One Well testing was based on injection fall-off processThe polymer solutions were injected into double-layer reservoirs with initial concentration of 1600mgL andthe reservoir thickness is 14mWell 5-227 performedpolymerflooding from Feb 1 2012 to May 7 2012 and then thepolymer injection was stopped and pressures were measuredIt took three days for well testing and polymer flooding wasperformed again since May 10 2012 Basic parameters of welland reservoir are shown in Table 5

The history matching curves and field testing data areshown in Figure 11 and the interpretation results are shownin Table 6 The permeability and skin factor of individuallayer acquired by interpreting field test data are consistentwith the actual situation of oilfield indicating that ourmodel can accurately interpret Field Test One and evaluateformation Meanwhile polymer flooding results in negligiblepermeability reduction or formation damage in this casesince the interpreted permeability and skin factors are nearlythe same as those of before polymer flooding

53 Field Test Two Well testing was also based on injec-tion fall-off process The polymer solutions were injectedinto double-layer reservoirs with initial concentration of1600mgL and the reservoir thickness is 21m Well 5-225(500 meters away from Well 5-227) performed polymerflooding from Feb 1 2012 to Apr 28 2012 and then thepolymer injection was stopped and pressures were measured(nine days before Field Test One) It took three days for welltesting and polymer floodingwas performed again sinceMay1 2012 Basic parameters of well and reservoir are shown inTable 7

The history matching curves and field testing data areshown in Figure 12 and the interpretation results are shownin Table 8 The occurrence of ldquoconcaverdquo is earlier than FieldTest One due to the bigger permeability difference betweentwo layers The skin factor of individual layer and layer1 permeability acquired by interpreting field test data areconsistent with the actual situation of oilfield which furtherprove that our model can accurately interpret Field Test Twoand evaluate formation Moreover the layer 2 permeabilityis 68mD and permeability reduction coefficient is 31 onaverage indicating formation was damaged by polymerflooding Blockage removal agent was further injected intothe reservoir and layer 2 permeability was increased to174mD resulting in 24 EOR of individual well

6 Conclusion

This work established well testing models for crossflowdouble-layer reservoirs by polymer flooding Type curvesof numerical well testing were obtained and field test data

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 The Scientific World Journal

102

101

100

10minus1

101 102 103 104 105

log(tDCD)

10minus2

log

pw

D)

log(

(p

998400 wD)

Figure 11 Field test data and history matching of type curves (FieldTest One Well 5-227)

Table 5 Basic parameters of well and reservoir for 5-227 field test

Injection rate 119902 (m3d) 100Layer 1 thickness ℎ

1(m) 8

Layer 2 thickness ℎ2(m) 6

Oil volume factor 1198610

11037Porosity 120601 03Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1592

Layer 2 permeability before polymerflooding mD 1466

Layer 1 skin factor before polymer flooding na 111Layer 2 skin factor before polymer flooding na 118

Table 6 Interpretation results of Field Test One (Well 5-227)

Average reservoir pressure MPa 1726Layer 1 permeability mD 1570Layer 2 permeability mD 1460Layer 1 skin factor na 113Layer 2 skin factor na 120Wellbore storage coefficient m3MPa 060

were further interpreted and history-matched The mainconclusions drawn from this study are as follows

(1) The model developed in this work by consideringIPV permeability reduction shear rate diffusion and

Table 7 Basic parameters of well and reservoir for 5-225 field test

Injection rate 119902 (m3d) 136Layer 1 thickness ℎ

1(m) 12

Layer 2 thickness ℎ2(m) 9

Oil volume factor 1198610

11037Porosity 120601 025Crude oil viscosity 120583

119900(mPasdots) 142

Brine viscosity 120583119908(mPasdots) 05

Temperature ∘C 75Total compressibility 119862

119905(1MPa) 00014

Well radius 119903119908(m) 01

Layer 1 permeability before polymerflooding mD 1352

Layer 2 permeability before polymerflooding mD 211

Layer 1 skin factor before polymer flooding na 249Layer 2 skin factor before polymer flooding na 037

Table 8 Interpretation results of Field Test Two (Well 5-225)

Average reservoir pressure MPa 1856Layer 1 permeability mD 1340Layer 2 permeability mD 68Layer 1 skin factor na 256Layer 2 skin factor na 198Wellbore storage coefficient m3MPa 054

convection can accurately demonstrate rheologicalbehavior of the proprietary HPAM polymer providedby CNPC over a wide range of injected velocityespecially when polymer solutions pass through theperforation

(2) Type curves have five sections with different flow sta-tus (I) wellbore storage section where pressure andpressure derivative curves are superposed reflectingthe pressure response characteristics during well stor-age stage (II) intermediate flow section (transientsection between wellbore storage section and mid-radial flow section) (III) mid-radial flow sectionwhere fluids flow of each layer achieves plane radialflow before crossflow occurs (IV) crossflow sectionwhere fluids in low permeability layer transportthrough interlayer into high permeability layer and(V) systematic radial flow section where the wholesystem presents plane radial flow over time

(3) The remarkable feature of the crossflow in type curvesis the occurrence of ldquoconcaverdquo The effect of polymerrheology on type curve section (V) is dramaticallyreduced by crossflow whichmeans the pressure curveand pressure derivative curve of polymer flooding aresimilar to those of water flooding in systematic radialflow section (V) Sensitivity analysis was performedto investigate the effect of different parameters on thetype curves including interporosity flow coefficient

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 9

log(tDCD)

102

101

100

10010minus1 101 102 103 10410minus1

log

pw

D)

log(

(p

998400 wD)

Figure 12 Field test data and history matching of type curves (FieldTest Two Well 5-225)

formation coefficient ratio storativity ratio initialpolymer concentration IPV and wellbore storagecoefficientThe influence of IPV on the well testing inpolymer flooding reservoirs can be neglected sincepolymer flooding usually results in unremarkableIPV

(4) Field tests were conducted in two wells of crossflowdouble-layer reservoirs by polymer floodingThe fieldtest data were interpreted and history-matched byemploying our well testing interpretation methodwhich indicated our model can accurately interpretfield test data and evaluate formation Moreoverformation damage caused by polymer flooding canalso be evaluated by comparison of the interpretedpermeability with initial layered permeability beforepolymer flooding If interpreted permeability is muchlower than initial permeability specific techniquesshould be employed to eliminate formation damageand enhance oil recovery

Annotation

ASP Alkali-surfactant-polymer119862 Wellbore storage coefficient1198621199010 Initial polymer concentration

119862119863 Dimensionless wellbore storage

coefficient119862119901 Polymer concentration

1198621015840 Tortuosity coefficient

119862119905 1198621199051 1198621199052 Total compressibility

119863 Diffusion coefficientEOR Enhanced oil recovery

HPAM Hydrolyzed polyacrylamideIPV Inaccessible pore volume119870 Permeability119870119901 1198701199011 1198701199012 Effective permeability

119901 1199011 1199012 Reservoir pressure

119901119894 Initial reservoir pressure

119901119908119863

Dimensionless BHP119876 Flow rate119877119896 Permeability reduction coefficient

119886 Flow-rate exchange coefficientℎ ℎ1 ℎ2 Reservoir thickness

119899 Bulk power law index119875119886 1198601 1198602 1198603 119862

SPSEP Fitting parameters

119901119908119891

BHP Bottom hole pressure119903 Radial distance1199041 1199042 Skin factor

119905119863 Dimensionless time

120601119901 1206011199011 1206011199012 Effective porosity

120594 Formation coefficient ratio120574 Effective shear rate12057412

Shear rate at which apparent vis-cosity is the average of 120583

infinand 120583

0

119901

120582 Interporosity flow coefficient120583119901 Apparent viscosity of polymer

solution1205830

119901 Viscosity of polymer solution at

low shear rate120583119908 Brine viscosity

120583infin Viscosity of polymer solution at

infinite shear rateV Darcy velocity120601 Porosity120596 Storativity ratio

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge financial support fromthe Science Foundation of China University of PetroleumBeijing (no YJRC-2013-41) the National Natural ScienceFoundation of China (no 51304223) and the National Sci-ence and Technology Major Projects (no 2011ZX05024-004-07)

References

[1] B Y Jamaloei R Kharrat and F Torabi ldquoAnalysis and corre-lations of viscous fingering in low-tension polymer flooding inheavy oil reservoirsrdquo Energy and Fuels vol 24 no 12 pp 6384ndash6392 2010

[2] A Bera A Mandal and B B Guha ldquoSynergistic effect ofsurfactant and salt mixture on interfacial tension reductionbetween crude oil and water in enhanced oil recoveryrdquo Journalof Chemical amp Engineering Data vol 59 no 1 pp 89ndash96 2014

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 The Scientific World Journal

[3] R Farajzadeh A Ameri M J Faber D W Batenburg D WBoersma and J Bruining ldquoEffect of continuous trapped andflowing gas on performance of Alkaline Surfactant Polymer(ASP) floodingrdquo Industrial amp Engineering Chemistry Researchvol 52 no 38 pp 13839ndash13848 2012

[4] H Yu C Kotsmar K Y Yoon et al ldquoTransport and retention ofaqueous dispersions of paramagnetic nanoparticles in reservoirrocksrdquo in Proceedings of the 17th SPE Improved Oil RecoverySymposium (IOR rsquo10) pp 1027ndash1047 Tulsa Okla USA April2010

[5] T ZhangMMurphyH Yu et al ldquoInvestigation of nanoparticleadsorption during transport in porous mediardquo in Proceedings ofthe SPE Annual Technology Conference and Exibition Society ofPetroleum Engineers (SPE) New Orleans La USA 2013 SPEpaper no 166346

[6] B S Shiran and A Skauge ldquoEnhanced oil recovery (EOR)by combined low salinity waterpolymer floodingrdquo Energy andFuels vol 27 no 3 pp 1223ndash1235 2013

[7] G Ren H Zhang and Q P Nguyen ldquoEffect of surfactantpartitioning between CO

2and water on CO

2mobility con-

trol in hydrocarbon reservoirsrdquo SPE Paper 145102 Society ofPetroleum Engineers (SPE) Kuala Lumpur Malaysia 2011

[8] G Ren A W Sanders and Q P Nguyen ldquoNew method for thedetermination of surfactant solubility and partitioning betweenCO2and brinerdquo The Journal of Supercritical Fluids vol 91 pp

77ndash83 2014[9] N B Wyatt C M Gunther and M W Liberatore ldquoIncreasing

viscosity in entangled polyelectrolyte solutions by the additionof saltrdquo Polymer vol 52 no 11 pp 2437ndash2444 2011

[10] LW Lake Enhanced Oil Recovery Prentice Hall Boston MassUSA 1st edition 1996

[11] H C Lefkovits P Hazebroek E E Allen and C S MatthewsldquoA study of the behaviour of bounded reservoir composed ofstratified layersrdquo Society of Petroleum Engineers Journal vol 1no 1 pp 43ndash58 1961

[12] SM Tariq andH J Ramey ldquoDrawdown behavior of a well withstorage and skin effect communicating with layers of differentRadii and other characteristicsrdquo SPE Paper 7453 Society ofPetroleum Engineers (SPE) Houston Tex USA 1978

[13] F Kucuk M Karakas and L Ayestaran ldquoWell testing andanalysis techniques for layered reservoirsrdquo SPE FormationEvaluation vol 1 no 4 pp 342ndash354 1986

[14] F J Kuchuk P C Shah L Ayestaran and B NicholsonldquoApplication of multilayer testing and analysis a field caserdquoin Proceedings of the SPE Annual Technical Conference andExhibition SPE-15419-MS Society of Petroleum Engineers(SPE) New Orleans La USA October 1986

[15] D Bourdet and F Johnston ldquopressure behavior of layered reser-voirs with crossflowrdquo SPE paper 13628 Society of PetroleumEngineers (SPE) Bakersfield Calif USA 1985

[16] C A Ehlig-Economides and J Joseph ldquoA new test for determi-nation of individual layer properties in amultilayered reservoirrdquoSPE Formation Evaluation vol 2 no 3 pp 261ndash282 1987

[17] C-TGao ldquoSingle phase fluid flow in a stratified porousmediumwith crossflowrdquo Society of Petroleum Engineers Journal vol 24no 1 pp 97ndash106 1984

[18] R R Jackson R Banerjee and R K M Thambynayagam ldquoAnintegrated approach to interval pressure transient test analysisusing analytical and numerical methodsrdquo in Proceedings of the13thMiddle East Oil and Gas Show Conference SPE Paper 81515pp 765ndash773 Society of Petroleum Engineers Bahrain June2003

[19] MM Kamal Y Pan J L Landa andOOThomas ldquoNumericalwell testing a method to use transient testing results inreservoir simulationrdquo inProceedings of the SPEAnnual TechnicalConference and Exhibition (ATCE rsquo05) pp 1905ndash1917 October2005

[20] A Mijinyawa P Alamina and A Orekoya ldquoAn integratedapproach to well test analysis-use of numerical simulationfor complex reservoir systemsrdquo SPE paper 140617 Society ofPetroleum Engineers (SPE) Warri Nigeria 2010

[21] L Zhang J Guo and Q Liu ldquoA well test model for stress-sensitive andheterogeneous reservoirswith non-uniform thick-nessesrdquo Petroleum Science vol 7 no 4 pp 524ndash529 2010

[22] S K Veerabhadrappa J J Trivedi and E Kuru ldquoVisualconfirmation of the elasticity dependence of unstable secondarypolymer floodsrdquo Industrial and Engineering Chemistry Researchvol 52 no 18 pp 6234ndash6241 2013

[23] H Zhang R S Challa B Bai X Tang and J Wang ldquoUsingscreening test results to predict the effective viscosity of swollensuperabsorbent polymer particles extrusion through an openfracturerdquo Industrial andEngineeringChemistry Research vol 49no 23 pp 12284ndash12293 2010

[24] P V D Hoek H Mahani T Sorop et al ldquoApplication ofinjection fall-off analysis in polymer floodingrdquo in Proceedingsof the SPE EuropecEAGE Annual Conference and ExhibitionSPE-154376-MS Society of PetroleumEngineers (SPE) Copen-hagen Denmark June 2012

[25] J Jian Q Hou L Cheng W Liu J Li and Y Zhu ldquoRecentprogress and effects analysis of surfactant-polymer floodingfield tests in Chinardquo in Proceedings of the SPE Enhanced OilRecovery Conference SPE Paper 165213 Society of PetroleumEngineers (SPE) Kuala Lumpur Malaysia July 2013

[26] J Liu Y Guo J Hu et al ldquoDisplacement characters of combi-nation flooding systems consisting of gemini-nonionic mixedsurfactant and hydrophobically associating polyacrylamide forbohai offshoreoilfieldrdquoEnergy and Fuels vol 26 no 5 pp 2858ndash2864 2012

[27] J Shi AVaravei CHuhMDelshadK Sepehrnoori andX LildquoTransport model implementation and simulation of microgelprocesses for conformance and mobility control purposesrdquoEnergy amp Fuels vol 25 no 11 pp 5063ndash5075 2011

[28] L Ali and M A Barrufet ldquoProfile modification due to polymeradsorption in reservoir rocksrdquo Energy amp Fuels vol 8 no 6 pp1217ndash1222 1994

[29] N Lai X Qin Z Ye C Li K Chen and Y Zhang ldquoThe studyon permeability reduction performance of a hyperbranchedpolymer in high permeability porous mediumrdquo Journal ofPetroleum Science and Engineering vol 112 pp 198ndash205 2013

[30] A L Ogunberu and K Asghari Water Permeability Reductionunder Flow-Induced Polymer Adsorption SPE Paper 89855Society of Petroleum Engineers (SPE) Houston Tex USA2004

[31] R S Seright ldquoDisproportionate permeability reduction withpore-filling gelsrdquo SPE Journal vol 14 no 1 pp 5ndash13 2009

[32] P L Bondor G J Hirasaki and M J Tham ldquoMathematicalsimulation of polymer flooding in complex reservoirsrdquo Societyof Petroleum Engineers Journal vol 12 no 5 pp 369ndash382 1972

[33] P J Carreau Rheological equations for molecular networktheories [PhD dissertation] University of Wisconsin-MadisonMadison Wis USA 1968

[34] D M Mete and R B Bird ldquoTube flow of non-newtonianpolymer solutions part I Laminar flow and rheological modelrdquoAIChE Journal vol 10 no 6 pp 878ndash881 1964

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 11

[35] P G Flory Principles of Polymer Chemistry Cornell UniversityPress New York NY USA 1953

[36] X Wang ldquoDetermination of the main parameters in thenumerical simulation of polymer floodingrdquo Petrol ExplorationDevelopment vol 3 pp 69ndash76 1990

[37] J Wang Physic-Chemical Fluid Mechanics and Application inChemical EOR Petroleum Industry Press Beijing China 2008

[38] D Bourdet J A Ayoub and Y M Pirard ldquoUse of pressurederivative in well test interpretationrdquo SPE Journal vol 4 no 2pp 293ndash302 1989

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of