The construction and application of a simpli ed pore ...

Scientia Iranica C (2016) 23(3), 1184{1194

Sharif University of TechnologyScientia Iranica

Transactions C: Chemistry and Chemical Engineeringwww.scientiairanica.com

Research Note

The construction and application of a simpli�ed porenetwork model based on computerized tomography

Y.T. Xiea;�, Z.H. Chenb and Z.M. Dub

a. State Key Lab of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China.b. School of Oil & Natural Gas Engineering, Southwest Petroleum University, Chengdu, China.

Received 11 April 2015; received in revised form 1 October 2015; accepted 2 February 2016

KEYWORDSPore network model;Flow capacity;Non-linear ow;Computerizedtomography.

Abstract. A simpli�ed pore network model, which divided pore structure into cubelattices, was developed based on the digital core extracted from micro computerizedtomography (�-CT) in this study. It rolled the complex topology and connectivity of porestructure into adjacent cubes. The static property of each cube was determined by thestatistic CT data. The connectivity of adjacent cubes and ow regime were determined bythe capillary pressure di�erence which is a function of tunnel size, interfacial tension, wetcontact angle, and external pressure gradient. In this simpli�ed pore network model, the ow capacity properties are determined by number and size distribution, mobile tunnels,and uid viscosity. The ow velocity and sweep e�ciency are non-linear as mobile tunnelsincrease nonlinearly with increasing driving force before all tunnels start owing. Thecritical pressure gradient that changed the non-linear ow to linear ow was performed asthe threshold pressure gradient. The dynamic mobile performance of Oil In Place (OIP) isdetermined by the number of mobile tunnels and their diameter distribution for di�erentpressure gradients. The relationship of microscopic sweep e�ciency, water cut, and pressuregradient to oil recovery can be quanti�ed by ow simulation in this pore network model.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

The formation ow capacity is a crucial factor inwell productivity and ultimate oil �eld developmente�ciency from a theoretical seepage perspective [1].Flow capacity depends on the rock permeability and uid viscosity. Small core samples are usually drilledfrom a full diameter core obtained from the targetpayzone in the reservoir. The samples are used inlaboratory experiments after a series of proceduressuch as washing, drying, and saturating. The in-situ absolute permeability under di�erent overburdenpressures and the relative permeability performance

*. Corresponding author. Tel.: +86 13438353246;Fax: +86 028 83033316E-mail address: [email protected] (Y.T. Xie)

under di�erent phase saturations are measured in core ooding experiments via changes in temperature, pres-sure, and uid saturation. These evaluation methodsmay not be suitable for heavy oil reservoir [2]. Mostof the formation in heavy oil reservoirs is weaklyconsolidated and may even be unconsolidated. Itis di�cult to obtain a standard complete cylindricalcore from the target layer using the routine coringbarrel. In the small core drilling process, the rockskeleton structure su�ers structure damage due tothe vibration in the sample drilling process. Liquidnitrogen is typically used to freeze loose rock, but thevolume expansion of the ice formed from the connatewater can change the micro-structure in porous media.During the core washing, drying, and uid saturationprocesses, the lead sheath or heat shrinkable sleeve usedto maintain the loose core integrity cannot guarantee

Y.T. Xie et al./Scientia Iranica, Transactions C: Chemistry and ... 23 (2016) 1184{1194 1185

that the inner structure remains intact [3-5]. Forcore analysis experiments, a con�ning pressure, 1-1.5 MPa, greater than the in ow pressure is neededto maintain seal in core surface and inner wall ofcore tank [6]. The radial deformation, caused bysealing procedure, in combination with the internalrock skeleton structure damage, caused by uid dis-placement, leads to erroneous analysis of experimentalresults.

Meanwhile, the development of computationalmethods to analyze the 3-dimensional (3D) structure ofpore networks has made signi�cant advances with theadvent of X-ray micro computerized tomography (�-CT) which allows for the visualization of the internalstructure of a rock sample at the micron scale [7-11]. There are no obstacles to obtaining high qualityimages of the spatial microscopic structure of unconsol-idated rock samples without causing any damage [12].Petrophysical properties such as sound speed, electricalproperties, nuclear magnetic resonance response, and ow characteristics that are usually derived from lab-oratory experiments can now be simulated using CTimages [13-14].

Pore scale modelling is another method to de-scribe internal rock structure and study multiphase ow and transport in porous media. It was �rstintroduced by Fatt in the 1950s in his tubes networkmodel [15]. To simplify operations, he replaced thethree-dimensional network by a two-dimensional net-work. Within that model, he calculated the capillarypressure curve and obtained pore size distribution.Since then, many scholars have put lots of e�orts on theconstruction and application of pore network model.Percolation theory was used to describe multiphase ow properties [16-17]. Micro model experimentswere used for parameters adjustment. Permeability,wettability, interfacial area, dissolution rate, rela-tive permeability, mass transfer coe�cient, and manyother physical properties have been predicted [18-25].Geometry, spatial correlation, and other topologicalcharacteristics have been discussed in description ofthe pore space. Matching geometric parameters withavailable experiments to build a regular network modelor directly modeling the random topology of the porespace were two mainstreams in 1990s [26-28]. Both ofthem faced limitation; regular network model is limitedin prediction because the coordination of data withexperiments is non-unique and essential features of thepore space are missing; while, random network modelswould have similar ow properties if the grain sizedistributions inferred from thin section analysis weresimilar to each other [29].

Reconstruction of pore network from �-CT-scanning images has been studied [30-34]. Com-putational Fluid Dynamics (CFD) method was thedirect method in pore-scale modeling to simulate the

uid ow by solving the Navier-Stokes equations in2000s [35]. The dimensions of CT images were morethan 1000� 1000� 1000 voxels. A pore network basedon these images, without simpli�cation, represents alarge data set which requires a large amount of memoryin CFD application [36]. Due to irregular uid-solidboundaries and the deformability of uid- uid inter-faces, direct models are computationally expensive andmay not be suitable for studying uid ow [37]. Withthe introduction of more sophisticated seepage theoriesin conventional reservoirs and more unconventionalreservoirs being developed, non-linear ow phenomenaand their governing mechanisms are receiving increasedattention. The pore network modeling technologybased on �-CT image post-processing has gradually be-come one of the main technologies and methods used inthe oil industry [38]. Reconstructing the pore structurefrom �-CT scan images more accurately, modeling thepore network more reasonably, and simulating the uid ow of the pore network more e�ciently continue to bethe main objectives in this �eld.

This study aimed at developing a pore networkthat characterized reservoir rocks more e�ciently andsimulated the uid ow process dominated by thecombined e�ects of capillary pressure, viscous forces,and driving pressure within the pore networks. Highresolution CT scan was conducted on the core samplesobtained from the target layer. The pore spatiallocation and the pore structure parameters were ex-tracted. Connectivity of each pair of adjacent cubeswas investigated under certain condition. A Cartesiancoordinate overlapped the sample unit and it wasdivided into 1000 � 1000 � 1000 blocks. The porosityof each block was calculated from the size and locationof each pore. Oil and water two-phase hydrodynamicbalance was checked in each connected tunnel todetermine the ow ability. The multi-pipe Poiseulle'slaw and Darcy's equation were applied to calculate thee�ective permeability that indicated the ow capacityof this scan rock sample. The dynamic e�ective ow parameters and the non-linear ow mechanismwere studied through applying the above proceduresin di�erent external pressure gradients and di�erent oiland water saturations. The methodology may then beapplied to oil development processes such as studyingthe ow properties and non-linear ow mechanismsfor di�erent external pressure gradients and di�erentwater saturations. This will help to validate the 3Ddescription of irreducible oil and to predict the changesin the recoverable reserves.

2. Procedures of modelling

2.1. Obtaining the digital coreData applied in this pore network model was originallybased on �-CT scan of actual rock samples from Bohai

1186 Y.T. Xie et al./Scientia Iranica, Transactions C: Chemistry and ... 23 (2016) 1184{1194

Bay with a resolution of approximately 10 �m. Di�er-ent mineral types and subject thicknesses in rock werere ected by the X-ray in variable energy attenuation.The intensity of X-ray was measured after it penetratedthe rock sample and then the absorption coe�cient wascalculated. The two-dimensional (2D) micro-structureof matrix and pores in a rock slice was extractedfrom 2D images and then the 3D micro-structure wasreconstructed by image processing algorithms of theprojection slices in the same direction. Each 3D porewas described by the maximum ball method. Then, thesize and spatial location of each pore were compiledinto data sets. The data sets associated with themicroscopic pore structure in the rock sample are theso-called digital core.

2.2. Model description2.2.1. Model constructionThe rock model was constructed by stacked particleswith di�erent sizes, shapes, and contact relationships.The diameters and connectivity of the inside tunnelnetwork were variously dependent on particle sizes.The status of both ow regime and ow rate dependson the balance between capillary pressure di�erencewhich is a function of tunnel size, interfacial tension,wet contact angle, and external pressure gradient.

2.2.2. Model assumptions� There was no absolutely dead end tunnel in the rock;

� The size and connectivity of a tunnel depended onparticle size;

� There was no rock deformation during the produc-tion period;

� The surface of rock tunnels was completely waterwet;

� All tunnels were initially saturated with water;

� The inside tunnel network was saturated with waterand oil;

� The ow was assumed to be laminar.

2.2.3. Flow processThe external pressure gradient arises either from buoy-ancy due to the density di�erence between oil andwater or from the pressure drawdown of productionwell. If the external pressure gradient is higher thanthe threshold pressure in the largest tunnel in thepore network, the uid initially starts owing throughthat tunnel. With increase in driving pressure, uidstarts owing in the smaller tunnel. As a result,the volumetric sweep e�ciency in the pore networkincreases and the ow capacity of rock is enhanced.Therefore, the apparent ow velocity, which is thefunction of ow section area, is non-linear since the owsection area increases as more tunnels are involved.

2.2.4. Saturation historyDuring the hydrocarbon accumulation period, sometunnels were gradually displaced by the oil with lighterdensity under the action of buoyancy. Meanwhile,the others were still saturated with water since thebuoyancy was less than the threshold pressure. The oildisplaced by water in each tunnel obeyed the sequenceof resistance from small to large. At the end ofwater ooding, all pores were saturated with water,completely.

2.3. Construction of digital coreThe setting of CT-scanning resolution a�ects the imageclarity and the accuracy of pore structure identi�ca-tion. With higher resolution setting, the intensityand penetrability of X-ray will be higher and stronger.Improper resolution setting may bring in overexpo-sure or underexposure that result in poor imaging ofpore structure inside a rock sample. The grain size-distribution of target rock sample ranges from 20 to300 �m, then the scanning resolution should be set at10 �m.

After CT-scanning of the rock sample, a three-dimensional Cartesian coordinate system, correspond-ing to the in-situ ow direction in the reservoir, iscreated. The diameter of core plug is 2.5 cm. Toexclude the impact of cutting process on inner porestructure, the center of scanning area is placed at thecore of the rock sample and the scanning area is setas a cube with 1 cm of length of edge. Based onthe 10 �m scanning resolution and 1 cm length ofthe scanning area, the digital core unit is divided into1000 � 1000 � 1000 blocks. The edge length of eachcube is 10 �m (Figure 1).

The porosity of the digital core is de�ned as theratio of identi�ed pore volume to the total volume ofscanning area. The porosity of each block is based onthe size and location of each recognized pore in thedigital core (Figure 2). Equivalent sphere should beused to identify the radius and location of each porefrom each 2D scanning image. Eq. (1) is applied tocalculate porosity of the 3D digital core. The thresholdof pore color is determined by the digital core porosity�tted with rock porosity from experiment.

The connectivity between blocks i� 1 and i+ 1 is

Figure 1. Block system of the digital core.


Figure 2. Porosity in the blocks.

Figure 3. Connection between blocks.

Figure 4. Flow status in a tunnel of varying diameters.

determined by the radius of a cylinder whose volume isequal to block i (Figure 3). If the porosity of block i isgreater than 0, blocks i�1 and i+1 will be connected.If the porosity of block i� 1 is equal to the porosity ofblock i+ 1, the radius of the cylinder-connected blocksi � 1 and i + 1 will be the same at each end, whichmeans there is no ow resistance between blocks i� 1and i+ 1.

Otherwise, the radius of the cylinder-connectedblocks i � 1 and i + 1 will be di�erent at each end.The ow resistance can be calculated by Eq. (5). Thecapillary pressure di�erence is the resistance in a waterwet tunnel of varying sizes (Figure 4). Only when the

driving pressure gradient overcomes the ow resistancewill the uid start owing.

2.4. Flow parameters calculationBased on the geometry of each tunnel in the blocksystem of the digital core, the porosity of the porenetwork unit is de�ned as:

� =Pni=1 �r

2i �i�L

�L=

nXi=1

�r2i �i: (1)

The total ow rate of all tunnels in cross-section isexpressed, using Poiseulle's law, as:

q =�8�

nXi=1

�ar4

�

�i

�P�L

: (2)

Substituting Eq. (2) into Darcy's equation, the perme-ability of the pore network unit can be expressed as:

K =qA��L�P

=�8�Pni=1

�ar4

�

�i

�P�L

A��L�P

=�8

nXi=1

r4i�i: (3)

The relationship between porosity and permeability isgiven as:

K ='8

nXi=1

� r�

�2

i: (4)

The capillary pressure between each pair of connectedblocks is given as:

�Pc = 2�ow cos �ow�

1r1� 1r2

�: (5)

2.5. Flow capacity evaluationFor the underground reservoir, the pressure gradientincreases gradually from 0 to a steady value with theincreased well production. For pore network model,the capillary pressure was calculated by Eq. (5) for eachpair of connected blocks in ascending order. The blocksthat have a capillary pressure lower than the drivingpressure but have not been displaced are identi�ed.The driving pressure increases and the searching pro-cess is repeated until no more blocks can be displaced.This is the process of pressure propagation in the porenetwork model.

The curve for the number of mobile tunnels canbe obtained using the number of all the involved blocksfor di�erent driving pressures.

The e�ective permeability of each phase is cal-culated by Eq. (3) based on the size of all mobiletunnels saturated with the given phase. Based on


microscopic oil-water two phase displacement process,sweep e�ciency under di�erent pressure gradients ande�ective permeability at variable water saturation canbe determined.

Applying Eq. (2) can get the ow velocity in porenetwork model. The ow velocity in one pore networkunit is converted to apparent ow velocity in a rocksample (dividing ow velocity by cross-sectional area)for analysis of the relationship between the apparent ow velocity and the external pressure gradient. Therelation of ow velocity to pressure gradient is nonlin-ear before all the tunnels start owing. The thresholdpressure gradient and the initial pressure gradient ofthe linear ow were determined when all the tunnels inthe pore network were mobile.

The pore volume percentage in the mobile areaand its contribution to oil recovery were calculatedfor di�erent driving pressures. The additional drivingpressure gradient required to increase the recoveryfactor was predicted based on the amount of reservesavailable at each pressure gradient level. Water ood-ing process in pore network model was simulated byincreasing driving pressure. The simulated results ofhow oil recovery changed with water cut increase canbe used to evaluate the EOR potential. Based onparallel-pipe ow principle { the ow velocity in thepipe is proportional to the square of pipe diameter{ the elapsed time to reach a given recovery factorcorresponding to a particular pressure gradient can becalculated.

3. Case study and discussion

3.1. Geometric characteristicsThe data of digital core based on CT-scanning of targetlayer rock sample shows that there is a reciprocalrelationship between number of tunnels and tunneldiameter (Figure 5). The relationship between the pore

Figure 5. Tunnel diameter distribution.

Figure 6. Distribution of tunnel volume.

volume and tunnel diameter resembles a skewed normaldistribution (Figure 6), which agrees with core labexperiments. Many core particle size tests show thatthe size of mineral particles in rock sample is roughlynormally distributed and the number of particles isexponentially distributed.

Controlled by lithology of parent rocks, depositionand diagenesis, reservoir formation is heterogeneousand anisotropic. The size, space form, and connectivityof pores in porous media are complex to describemathematically. Applying statistics from digital corecan be used as an alternative method. The statisticsof digital core show that there are more small poresthan large ones in the rock, but the total volume issmaller. Medium size pores own the largest numberand occupy most of the volume of the rock sample.All these characteristics will a�ect the storage and owcapacity of a reservoir.

3.2. Flow properties and ow regimeBased on the method described in Section 2 andthe statistics of digital core from CT-scanning, thepore network model of rock sample has been builtusing the percolation theory described in Section 2to calculate the ow capacity and simulate the owprocess in the pore network model. The pore networksimulation shows that the number of mobile tunnelsand the microscopic sweep e�ciency start at zeroand increase with higher driving pressure gradients(Figures 7 and 8). Tunnels with larger diameter turnto mobile more easily than smaller ones that have ahigher resistance. As a result, the ow is non linearin porous media like rocks that are characterized byvariable pore size and connectivity. Figure 9 showsthat the permeability gradually increases with increasein the pressure gradient. It plateaus at the absolutepermeability if no more tunnels can become mobile andcontribute to the ow capacity in the porous networkas the driving pressure increases. Figure 10 shows


Figure 7. Ratio of mobile tunnels.

Figure 8. Volumetric sweep e�ciency.

Figure 9. E�ective permeability.

that the apparent ow velocity changes from standstillthrough a non-linear regime to a linear ow regime asthe driving pressure gradient is increased.

3.3. Recoverable reserves during pressuredepletion

The in-situ pressure continuously decreases with thepressure decrease propagating from the drawdown

Figure 10. Non-linear ow mechanism.

Figure 11. Maximum driven pressure gradient.

point to the remaining portions of the reservoir. From amicroscopic point of view, large tunnels become mobile�rst followed by smaller tunnels. At any moment,the recoverable reserve is the total amount of oil ineach mobile tunnel in the pore network. The dynamicmobile performance of Oil In Place (OIP) was studiedbased on the number of mobile tunnels and theirdiameter distribution for di�erent pressure gradients.Figure 11 shows that the pressure gradient requiredto achieve a given amount of recovery for di�erentmicroscopic volumetric sweep e�ciencies. A lowerpressure gradient is required to reach the same recoveryfactor for lower sweep e�ciencies, since the largertunnels have a higher oil content and lower resistanceto becoming mobile. As shown in Figure 12, a highermicroscopic sweep e�ciency is achieved if more smalltunnels are mobile at higher pressure gradients.

The microscopic mechanism can explain howreservoirs with a higher porosity and permeability canachieve a higher recovery using a lower productiondrawdown. In addition, the production rate dramati-


Figure 12. Minimum mobile tunnels.

cally decline in low-mobility reservoirs such as heavy oiland compact reservoirs. This is because the e�ective in-situ ow capacity in this kind of reservoir is lower thanthose in the laboratory. As a result, only larger tunnelsare mobile for lower sweep e�ciencies and mobile area.In this situation, oil recovery can be enhanced using themobility of smaller tunnels by applying higher pressuregradients through production well in�ll and an increasein production drawdown.

3.4. Recoverable reserves during waterdisplacement

The saturation and distribution of connate waterformed during hydrocarbon accumulation are depen-dent on the viscosity and density of oil and thediameters of tunnels of the rock. Oil initially satu-rates tunnels of larger diameter and good connectivity.Therefore, smaller tunnels with poor connectivity aresaturated with water. Initial oil migration simulationsshow that the saturation and distribution of connatewater vary based on oil viscosity and pore size (Fig-ure 13).

A higher oil viscosity leads to a higher initialwater saturation and a lower initial mobility of oil, asshown in Figure 14. The results of the simulations

Figure 14. Relative permeability (Kr) at di�erent oilviscosities.

show that oil and water coexist in the heterogeneousreservoir. There is initially connate water in heavy oilreservoir. This means that there is no uni�ed oil andwater contact surface and no piston-like displacementeven in this microscopic pore network. Connate waterwill be mobile and will be produced when the pressuregradient is greater than the resistance in the tunnels.This is governed by capillary pressure di�erence intunnels with varying diameters. During water ooding,the mobile water will �rst access the largest tunnel ina pore node with di�erent ow directions and tunneldiameters, then enter the second largest tunnel at ahigher pressure gradient. This dynamic process isquantitatively and visually simulated by the currentpore network model and the relationship between thewater cut and recovery is shown in Figure 15. In therock model unit, the largest tunnels are �rst displacedby water until the water cut reaches 0.1 and the oilrecovery is 0.19 which corresponds to the oil contentin the tunnels. As the pressure gradient increases, theoil in smaller mobile tunnels is displaced by water andmore oil is produced by water ooding, as shown in

Figure 13. Connate oil and water distribution for di�erent oil viscosities.


Figure 15. Period of recovery, decimal, during water cut.

Figure 15. The water cut increases to 0.2 and the oilrecovery increases to 0.28. The relationship betweenthe water cut and oil recovery is non-linear becausethe size distribution and connectivity in tunnels arenon-uniform. The residual oil saturation is 0.34 andthe water cut reaches 1.0. Therefore, it can beconcluded that the amount of oil stored in the non-mobile smaller tunnels at this pressure gradient issigni�cantly higher than that in larger ones. The oilrecovery can be enhanced by increasing the pressuregradient to improve the sweep e�ciency.

3.5. Performance of oil recoveryIn the current microscopic pore network model, thedimensionless production period is de�ned as the ratioof the end time of displacement in the smallest tunnelto the end time in the largest tunnel. Compared toa large-scale reservoir, the end time of displacementin the largest tunnel can be regarded as the period ofwater breakthrough into production well. Hence, theproduction period to reach a certain recovery can bebased on the dimensionless time.

Simulations were performed for three rock sam-ples with average permeability values of 193 mD,482 mD, and 1066 mD. The results show that therecovery will reach 0.37, 0.40, and 0.45 after 20production periods and will reach 0.52, 0.57, and0.63 after 40 production periods. Theoretically, theoil recovery could reach 0.80 in the dimensionlessproduction periods of 83, 102, and 132 for each rocksample, respectively (Figure 16). This shows that ahigher recovery can be achieved in a reservoir withhigher permeability and over a shorter production time.As development continues, the recovery increment willgradually slow down since the produced oil mainlycomes from smaller tunnels with poor connectivityduring pressure depletion and water ooding. In the

Figure 16. Maximum recovery at di�erent dimensionlessproduction period.

pay layer of the reservoir, it is a reasonable assumptionthat the in-situ pressure gradient due to production isgreater than buoyancy. Therefore, it is theoreticallypossible to recover 100% of the oil as each tunnel thathas been �lled with oil can be displaced with water.However, this is not the case in practice, because thedevelopment life cycle is limited due to technologicalconstraints, economical factors, the lease period, andother factors. The optimized production rate can beestimated using the proposed methodology based onthe development, cost, and pro�t targets.

4. Conclusions

1. As an alternative of laboratory core experiments,pore network model, based on micro ComputerizedTomography (�-CT), can be used to determineporosity, permeability, and ow capacity properties(relative permeability, ow velocity, sweep e�-ciency, etc.) of a rock sample;

2. The simpli�ed pore network model was built tocharacterize the pore structure of reservoir rockand simulate the transport in such porous media,more e�ciently. It rolls the complex topology andconnectivity of pore structure into adjacent cubes.The static property of each cube is determinedby the statistics of CT data. The connectivityand ow regime are determined by the capillarypressure di�erence of adjacent cubes. The pressuredi�erence is a function of tunnel size, interfacialtension, wet contact angle, and external pressuregradient;

3. In this simpli�ed pore network model, the ow ca-pacity properties are determined by the number andsize distribution, mobile tunnels, and uid viscosity.


The ow velocity and sweep e�ciency are non-linear as the mobile tunnels increase nonlinearlywith increase in driving force before all tunnels start owing. The critical pressure gradient that changedthe non-linear ow to linear ow was performed asthe threshold pressure gradient;

4. The dynamic mobile performance of Oil In Place(OIP) is determined by the number of mobiletunnels and their diameter distribution for di�erentpressure gradients. Higher microscopic sweep e�-ciency can be achieved as more small tunnels areavailable at higher pressure gradients;

5. Since oil and water coexist in the heterogeneousreservoir, there is no uni�ed oil and water contactsurface and no piston-like displacement even in mi-croscopic pore network. The relationship betweenthe water cut and oil recovery is non-linear becausethe size distribution and connectivity in tunnelsare non-uniform. However, oil recovery is roughlyproportional to the pressure gradient increment. Itcan be quanti�ed by ow simulation in this porenetwork model. The production period to reach acertain recovery can be based on the dimensionlesstime;

6. In further studies, speci�c micrometer-scale coreexperiments are needed to verify the method. More�tting methods are needed to improve the accuracyof simulation of pore network model.

Acknowledgment

The authors are grateful for the �nancial supportof Open Fund Project (No. CCL2013RCPS0235GNN)provided by the State Key Laboratory of O�shore OilExploitation of China.

Nomenclature

A Cross-sectional area of pore networkunit, cm2

a Tunnel cross-sectional area, cm2

K Permeability, �m2

N;n Area density of tunnels, m�2

q Volumetric ow rate, cm3/sr; r1; r2 Tunnel radius, cmSwc Connate water saturation, %�L Length of core and length of pore

network unit, cm�P;�Pd Displacement pressure, MPa�Pc Capillary pressure di�erence, MPa� Tunnel tortuosity, dimensionless� Porosity, %

�ow Oil-water interfacial tension, N/m�ow Wetting contact angle, angle� Viscosity, mPa.s

References

1. Aghaei, A. and Piri, M. \Direct pore-to-core up-scalingof displacement processes: Dynamic pore networkmodeling and experimentation", Journal of Hydrology,522, pp. 488-509 (2015).

2. Kaviani, D. and Jensen, J.L. \Reliable connectivityevaluation in conventional and heavy oil reservoirs: Acase study from Senlac heavy oil pool", In Proceed-ings of the Canadian Unconventional Resources andInternational Petroleum Conference, Alberta, Canada.SPE-137504-MS (2010).

3. Torabi, F., Zarivnyy, O. and Mosavat, N. \Developingnew Corey-based water/oil relative permeability cor-relations for heavy oil systems", In Proceedings of theSPE Heavy Oil Conference-Canada, Alberta, Canada.SPE-165445-MS (2013).

4. Mattax, C., Mckinley, R. and Clothier, A. \Core anal-ysis of unconsolidated and friable sands", Journal ofPetroleum Technology, 27(12), pp. 1423-1432 (1975).

5. Bretz, R.E., Specter, R.M. and Orr Jr, F.M. \E�ect ofpore structure on miscible displacement in laboratorycores", SPE Reservoir Engineering, 3(03), pp. 857-866(1988).

6. Musin, K., Khisamov, R. and Dinmuhamedov, R.\Solution to problem of evaluation of unconsolidatedheavy oil reservoirs in tatarstan", In SPE RussianOil and Gas Conference and Exhibition., Society ofPetroleum Engineers (2010).

7. Professional committee for standardization of oil andgas �eld development, The Oil and Gas Industry Stan-dard of the People's Republic of China-SY/T 5336-1996-Method of Core Routine Analysis, China nationalpetroleum corporation (1996).

8. Honarpour M.M., Cromwell V., Hatton D., et al.Reservoir Rock Descriptions Using Computed Tomog-raphy (CT). In SPE Annual Technical Conference andExhibition, Society of Petroleum Engineers (1985).

9. Pierret, A. and Moran, C. \Quanti�cation of orienta-tion of pore patterns in x-ray images of deformed clay",Microscopy Microanalysis Microstructures, 7, pp. 421-431 (1996).

10. Okabe, H. and Blunt, M.J. \Pore space reconstructionusing multiple-point statistics", Journal of PetroleumScience and Engineering, 46, pp. 121-137 (2005).

11. Maga~na, B.O., Dom��nguez, J.D., Ruelas, R., Tarquis,A.M., Gomez-Barba, L. and Andina, D. \Identi�cationof pore spaces in 3D CT soil images using PFCMpartitional clustering", Geoderma, 217-218, pp. 90-101 (2012).

12. Likos, W.J. \Quanti�cation of grain, pore, and uidmicrostructure of unsaturated sand from x-ray com-puted tomography images", Geothechnical TestingJournal, 35(6), pp. 911-923 (2012).


13. Elliott, J.C. and Dover, S.D. \X-ray micro-tomography", Journal of Microscopy, 126, pp. 211-213(1982).

14. Dvorkin, J., Fang, Q. and Derzhi, N. \Etudes incomputational rock physics: Alterations and bench-marking", Geophysics, 77(3), pp. D45-D52 (2012).

15. Youssef S., Rosenberg E., Kenter J., et al. \High res-olution CT and pore-network models to assess petro-physical properties of homogeneous and heterogeneouscarbonates", In SPE/EAGE Reservoir Characteriza-tion and Simulation Conference., Society of PetroleumEngineers (2007).

16. Fatt, I. \The network model of porous media I.Capillary pressure characteristics", Trans AIME, 207,pp. 144-159 (1956).

17. Koplik, J. \Creeping ow in two-dimensional net-works", Journal of Fluid Mechanics, 119, pp. 219-247(1982).

18. Wilkinson, D. and Willemsen, J.F. \Invasion percola-tion: A new form of percolation theory", Journal ofPhysics A: Mathematical and General, 16(14), p. 3365(1983).

19. Larsen, J.K., Bech, N. and Winter, A. \Three-phaseimmiscible WAG injection: Micromodel experimentsand network models", In SPE/DOE Improved OilRecovery Symposium., Society of Petroleum Engineers(2000).

20. Lenormand, R., Zarcone, C. and Sarr, A. \Mechanismsof the displacement of one uid by another in a networkof capillary ducts", Journal of Fluid Mechanics, 135,pp. 337-353 (1983).

21. Fenwick, D.H. and Blunt, M.J. \Three-dimensionalmodeling of three phase imbibition and drainage",Advances in Water Resources, 21(2), pp. 121-143(1998).

22. Thauvin, F. and Mohanty, K.K. \Network modeling ofnon-Darcy ow through porous media", Transport inPorous Media, 31(1), pp. 19-37 (1998).

23. Blunt, M.J. \Physically-based network modeling ofmultiphase ow in intermediate-wet porous media",Journal of Petroleum Science and Engineering, 20(3),pp. 117-125 (1998).

24. Fischer, U. and Celia, M.A. \Prediction of relativeand absolute permeabilities for gas and water fromsoil water retention curves using a pore-scale networkmodel", Water Resources Research, 35(4), pp. 1089-1100 (1999).

25. Man, H.N. and Jing, X.D. \Network modelling ofwettability and pore geometry e�ects on electrical re-sistivity and capillary pressure", Journal of PetroleumScience and Engineering, 24(2), pp. 255-267 (1999).

26. Lerdahl, T.R., Oren, P.E. and Bakke, S. \A predictivenetwork model for three-phase ow in porous media",In SPE/DOE Improved Oil Recovery Symposium., So-ciety of Petroleum Engineers (2000).

27. Jerauld, G.R. and Salter, S.J. \The e�ect of pore-structure on hysteresis in relative permeability andcapillary pressure: Pore-level modeling", Transport inPorous Media, 5(2), pp. 103-151 (1990).

28. Bryant, S.L., King, P.R. and Mellor, D.W. \Networkmodel evaluation of permeability and spatial correla-tion in a real random sphere packing", Transport inPorous Media, 11(1), pp. 53-70 (1993).

29. Hilpert, M. and Miller, C.T. \Pore-morphology-basedsimulation of drainage in totally wetting porous me-dia", Advances in Water Resources, 24(3), pp. 243-255(2001).

30. Dong, H. and Blunt, M.J. \Pore-network extractionfrom micro-computerized-tomography images", Phys-ical Review E Statistical Nonlinear & Soft MatterPhysics, 80(2), pp. 1957-1974(2009).

31. Delerue J.F., Perrier E., Yu Z.Y., et al. \New algo-rithms in 3d image analysis and their application tothe measurement of a spatialized pore size distributionin soils", Physics and Chemistry of the Earth, Part A:Solid Earth and Geodesy, 24(99), pp. 639-644 (1999).

32. Zhang X.H, Q. J, X. B. \Comparisons of static,quasi-static and dynamic 3D porous media scale net-work models for two-phase immiscible ow in porousmedia", New Trends in Fluid Mechanics Research,Springer Berlin Heidelberg, pp. 530-533 (2009).

33. Al-Kharusi, A.S. and Blunt, M.J. \Network extractionfrom sandstone and carbonate pore space images",Journal of Petroleum Science and Engineering, 56, pp.219-231 (2007).

34. Raoof, A. and Hassanizadeh, S.M. \A new methodfor generating pore-network models of porous media",Transport in Porous Media, 81, pp. 391-407 (2010).

35. Jiang, Z., Dijke, M.I.J.V., Wu, K., et al .\Stochasticpore network generation from 3D rock images", Trans-port in Porous Media, 94(2), pp. 1-23 (2011).

36. Schena G., Favretto S., Piller M., et al. \Pore spacecharacterisation and permeability prediction using fastnetwork extraction and pore throat conductance cal-culation", In 70th EAGE Conference and ExhibitionIncorporating SPE EUROPEC (2008).

37. Marcke, P.V., Verleye, B., Carmeliet, J., et al. \Animproved pore network model for the computation ofthe saturated permeability of porous rock", Transportin Porous Media, 85, pp. 451-476 (2010).

38. Aghaei, A. and Piri, M. \Direct pore-to-core up-scalingof displacement processes: Dynamic pore networkmodeling and experimentation", Journal of Hydrology,522, pp. 488-509 (2015).

Biographies

Yiting Xie was born in 1987. She is a PhD candidatein the Department of Petroleum and Nature GasInstitute at Southwest Petroleum University, Chengdu,China. She has worked as a part-time sta� member in


Titan-Petro Ltd. since 2013. She has been studyingporous media ow mechanism experiments and mathe-matic modeling, sand management production control,reservoir numerical simulation, and well productionoptimization for more than 6 years.

Zhaohui Chen was born in 1970. Dr. Chen istechnical director of Titan-Petro Ltd. and a reservoirengineer with more than 20 years of experience inresearch and oil/gas �eld development planning andreservoir evaluation. Also, he has assisted clientsto make the most pro�table reservoir developmentstrategy and worked on underbalanced drilling design,sand management production control, integrated ge-omechanical reservoir simulation, well production opti-mization, EOR, and geomechanical laboratory testing.

He has extensive experience in development of loosensand heavy oil reservoir and loosen sand multi-layer gasreservoirs.

Zhimin Du was born in 1953. She is the Professorof Petroleum and Nature Gas Institute and the formerpresident of Southwest Petroleum University, Chengdu,China. She received her BSc in Oil Production En-gineering from Southwest Petroleum Institute in 1978and was a fellow at Germany's Clausthal TechnicalUniversity from 1985 to 1988. Her research interestsinclude a broad area of topics in the theories andapplication of complex oil gas reservoirs development.Recently, she has been focusing on grid simulation andparallel computation of fractured oil reservoir based onunstructured hexahedral

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