Course:- 28117Class:- 289013

HERIOT-WATT UNIVERSITYDEPARTMENT OF PETROLEUM ENGINEERING

Examination for the Degree ofMEng in Petroleum Engineering

Reservoir Engineering 1

Tuesday 6th January 199809.30 - 13.30

NOTES FOR CANDIDATES

1. This is a Closed Book Examination.

2. 15 minutes reading time is provided from 09.15 - 09.30.

3. Examination Papers will be marked anonymously. See separate instructions forcompletion of Script Book front covers and attachment of loose pages. Do not writeyour name on any loose pages which are submitted as part of your answer.

4. This Paper consists of 3 Sections:- A, B and C.

5. Section A:- Attempt all QuestionsSections B & C:- Attempt 4 numbered Questions with at least 1 Question from

each Section

6. Section A:- 20% of marksSection B / C:- 80% of marks

Marks for Questions and parts are indicated in [brackets]

7. This Examination represents 100% of the Class assessment.

8 State clearly any assumptions used and intermediate calculations made in numericalquestions. No marks can be given for an incorrect answer if the method ofcalculation is not presented.

9. Answers must be written in separate, coloured books as follows:-

Section A:- BlueSection B:- GreenSection C:- Yellow

SECTION A

A1 Define:-

(i) Gas formation-volume factor(ii) Oil formation-volume factor(iii) Total formation-volume factor(iv) Solution gas-oil ratio

[2]

A2 Explain briefly what you understand by:-

(i) Compositional model description for the characterisation of areservoir fluid.

(ii) Black oil description for the characterisation of a reservoir fluid.[3]

A3 Draw the pressure - temperature phase diagram for a gas condensatereservoir indicating the following:-

(i) Bubble point and dew point lines(ii) Critical point(iii) Cricondentherm(iv) Lines of constant proportion of liquid-gas(v) Region of retrograde condensation.

[3]

A4 Derive an equation for the average permeability, resulting from radialcircular flow into a well from layers of different permeabilities andthicknesses.

From where would such an average be obtained ?[3]

A5 List the rock properties that should be determined in a rock-mechanical-oriented, special core analysis programme.

[3]

A6 Describe the nature of a partially communicating fault and how pressuredata may be used to identify the transmissibility index of such features.

[3]

A7 Explain the difference between a steady-state and a semi-steady-stateproductivity index.

[3]

SECTION B

B8(a) Methane is a significant component in reservoir fluids.

Using a sketch for a binary of methane and n-decane (C10), illustratethe impact of methane on the critical point loci of C1-C10 binarymixtures.

What is the significance of this diagram ?[6]

(b) A wet gas is producing at 40,000 SCF/STB, from a reservoir which hasbeen estimated from petrophysics to have a volume of 1.1 x 1010 cu ft.and has a pressure of 3,000 psia and a temperature of 250°F

The composition of the producing gas is given below:-

Component (MW) Composition (Mole fraction)Gas Condensate

Methane (16.04) 0.84 -Ethane (30.07) 0.07 -Propane (44.09) 0.05 0.16N-butane (58.12) 0.02 0.34N-pentane (72.15) 0.02 0.31Hexane (86.17) - 0.10Heptane plus (114.2) - 0.09(equivalent to octane)

(i) What is the composition of the reservoir gas?

(ii) What are the reserves of gas and condensate at 3,000 psia?

(iii) How much gas will have been produced, when the pressure hasdropped to 2,000 psia?

[14]

R = 10.72cu ft.psi/lb mole.°R1lb mole = 379.4 SCF1bbl = 5.615cu ft

B9(a) You have been given a PVT report for an oil sample.

List the procedures and calculations you would take to determine:-

(i) The bubble point pressure at reservoir temperature(ii) The solution gas-oil ratios and the oil formation volume factors

above the bubble point and below the bubble point.[10]

(b) A laboratory cell, contained 290cc of reservoir liquid at its bubble pointof 2100 psia at 145°F. 21cc of mercury were removed from the cell andthe pressure dropped to 1700 psia. Mercury was then re-injected atconstant temperature and pressure and 0.153 SCF of gas was removedleaving 270cc of liquid in the cell. The process was repeated reducingthe pressure to 14.7 psia and the temperature to 60°F. Then 0.45 SCF ofgas was removed and 207.5cc of liquid remained in the cell.

Determine:-

(i) Bo and Rs at the bubble point.(ii) Bo, Bt, Bg, Rs and z at 1,700 psia and 145°F(iii) B t at 2100 psia and 145°F

[10]

B10 Using field examples, describe the various rock-mechanical phenomenawhich can be activated in producing reservoirs, and explain the impact ofthese phenomena on reservoir development and management strategies.

[20]

B11(a) For low permeability rocks, the measured permeability of the rock, using

gas as the fluid is more than it is using a liquid.

Comment briefly on this and how the permeability of a rock can beobtained using gas as the fluid.

[4]

(b) The system below represents the common arrangement for measuring thepermeability of a core plug using a gas.

Derive an equation to calculate the gas permeabilities of a rock using theabove system.

[6]

(c) What is the free water level?

Explain briefly why, because of capillary pressure, it is possible to havewater saturations of large values, up to 100%, above the oil-water contactand above layers with lower water saturations.

[4]

(d) Capillary pressure data are obtained from core samples which represent asmall part of the reservoir. Leverett derived a “J” Function using thePoiseuille equation for laminar flow:-

q

r PL

= πµ

4

8∆

to relate Capillary pressure (Pc), to Permeability (k), and Porosity (ø).

Derive the 'J' function and comment on one of its limiting assumptions.[6]

B12(a) Identify the various elements in the material balance equation below:-

( ) [ ( ) ]

[( ) ] ( )

( ) ( )

N N B NB B NR N N R G

G G B GB W W B

NB m pc S c

SW B G B

p o oi g si p s ps

pc g gi e p w

oif wc w

wcinj w inj g

− = − − − − −

− − − − −

+ +−

− +1

1∆

with a line above the symbols of the equation e.g.

( ) infW W B net water luxe p w− =[3]

(b) Simplify the material balance equation above so that it can be used for anundersaturated reservoir without waterdrive and water production.

Modify the simplified equation so that it can be used to express therecovery at the bubble point in terms of the effective compressibility ofthe reservoir system..

[4]

(c) To predict the performance of a solution gas drive reservoir we requireboth the instantaneous gas-oil ratio equation and an equation to expressthe average oil saturation.

Derive the instantaneous gas-oil ratio equation and use the equation toexplain briefly the shape of the producing GOR of a depletion typereservoir from a pressure above the bubble point to one significantlybelow the bubble point pressure.

[6]

(d) Tarner’s method and Tracy's modification of Tarner's method use theMaterial Balance equation, the Instantaneous GOR equation and theSaturation equation to predict oil production as a function of pressure fora solution gas drive reservoir from the bubble point pressure.

Describe briefly, in a step by step procedure, the application of one ofthese methods.

[7]

SECTION C

C13 A tight formation of horizontal permeability, ky, equal to 0.5md andthickness, h, of 150ft is to be developed for oil production. The choicelies between horizontal wells or vertical wells with hydraulic fracturing.The rock mechanics suggest that an infinite-conductivity fracture of half-length, xf, equal to 300ft will be feasible.

Determine the length of a horizontal well, L, which will have acomparable semi-steady-state productivity index (PI) to the fractured,vertical well.

Additional Well Data:-

Formation vertical permeability, kz = 0.01mdOil viscosity, µ0 = 1.5cpOil formation volume factor, B0 = 1.25Wellbore radius, rw = 0.3ftEquivalent cylindrical external radius of reservoir drainage compartment, re = 10,000ft.

[20]

C14 A particular formation has been shown to be amenable to acid treatmentwhich can increase the rock permeability from the intrinsic value of 5mdto an improved value of 17md due to its effect on interstitial clay.

In a formation of 80ft thickness and 20% porosity, estimate how much thewell productivity index will be increased if 1000bbl of acid are injectedinto the formation, assuming piston displacement of connate water andoil to a residual saturation of 0.35.

Additional reservoir data:-

Connate water saturation, Swc = 0.25Oil formation volume factor, B0 = 1.2Oil viscosity, µ0 = 0.8cpDrainage area external radius, re = 5000ftWellbore radius, rw = 0.3ft

[20]

C15 Discuss how the wireline formation tester can give information ondynamic aquifer effects and indicate where other phenomena can givesimilar pressure-depth plots to those associated with a dynamic aquifer.

Why is it important to know if dynamic aquifer effects are present?[20]

End of Paper

Course:- 28117Class:- 289013

HERIOT-WATT UNIVERSITYDEPARTMENT OF PETROLEUM ENGINEERING

Examination for the Degree ofMEng in Petroleum Engineering

Reservoir Engineering 1

Friday 8 January 199909.30 - 13.30

NOTES FOR CANDIDATES

1. This is a Closed Book Examination.

2. 15 minutes reading time is provided from 09.15 - 09.30.

3. Examination Papers will be marked anonymously. See separateinstructions for completion of Script Book front covers and attachmentof loose pages. Do not write your name on any loose pages which aresubmitted as part of your answer.

4. This Paper consists of 3 Sections:- A, B and C.

5. Section A:- Attempt all QuestionsSections B & C:- Attempt 4 numbered Questions with at least

1 Question from each Section

6. Section A:- 20% of marksSection B / C:- 80% of marks

Marks for Questions and parts are indicated in [brackets]

7. This Examination represents 100% of the Class assessment.

8 State clearly any assumptions used and intermediate calculations madein numerical questions. No marks can be given for an incorrect answerif the method of calculation is not presented.

9. Answers must be written in separate, coloured books as follows:-

Section A:- BlueSection B:- GreenSection C:- Yellow

SECTION A

A1 Define:

(i) The gas formation volume factor(ii) The oil formation-volume factor(iii) The total formation volume factor(iv) The solution gas-oil ratio

[2]

A2 Derive an equation in terms of equilibrium ratios and composition topredict liquid and vapour ratios and compositions resulting from theflash separation of a reservoir fluid. Explain briefly the application ofthe equation when the reservoir fluid composition, temperature, and thepressure of the separation are known.

[3]

A3 Derive the instantaneous gas-oil ratio equation and plot the shape ofthe producing GOR versus pressure for a solution gas drive reservoir

[3]

A4 With the aid of a diagram, comment on the fluid pressure gradients in anoil reservoir with a gas cap with a supporting aquifer for a normallypressured reservoir. Illustrate the gradient for an overpressuredreservoir.

[3]

A5 Briefly describe how the permeability sensitivity of rocks to stress canbe measured in the laboratory, and draw a graphical, normalised,representation of the results you would expect to see for sandstoneswith high, medium and low permeabilties measured at ambientconditions.

[3]

A6 Discuss the common mechanisms of formation damage occurring duringdrilling.

[3]

A7 Discuss the concept of a critical rate in coning situations.[3]

SECTION B

B8(a) Draw a Pressure-Temperature phase diagram to illustrate the phase

behaviour of a gas condensate fluid. [2]

(b) Explain briefly gas cycling with reference to gas condensate reservoirs.[3]

(c) A wet gas reservoir is producing gas and condensate with thecompositions given below at a gas-oil ratio of 25,000 SCF/STB. Theaverage reservoir temperature is 260˚F and the initial reservoir pressureis 8520 psia.

The pore volume of the reservoir is considered to be 9.5 x 108 cu ft andthe average water saturation is 19%.

(i) Calculate the composition of the reservoir fluid

(ii) Calculate the inplace reserves in SCF of gas and STBcondensate of the reservoir at the original pressure.

(iii) Calculate the production of gas and condensate when thereservoir pressure has declined to 4260psia.

[15]

1bbl = 5.615 cu ft0˚F = 460˚ R1lb mole = 379.4 SCFR = 10.73 psi cu ft/lb mole° R

Composition of Produced Fluids (Mole fraction)

Gas Condensate

C1 Methane 0.890 --C3 Propane 0.075 0.215C5 n-Pentane 0.035 0.620C8 Octane -- 0.165

Attachments

B9(a) After natural water drive or injected water drive residual oil is left

within that part of the rock contacted by the water. Comment brieflywith the aid of a sketch why this might be.

[5]

(b) Miscible gas injection can be used to recover the residual oil after awater flood. Explain briefly what miscible gas injection is and why insome cases gas injected is alternated with water injection in a WAG(water alternating gas ) process.

[5]

(c) An edge water drive reservoir extends to a radius of 8,000 ft. Sealingfaults are such that the water influx only forms part of a full radialsystem as the sketch below illustrates. The supporting aquifer extendsto a radius of 40,000ft. Over the first two years of production thepressure decline is expected to be as follows:

Time( months) 0 6 12 18 24Pressure(psia) 4640 4630 4612 4584 4448

After the first 6 month period 23,200 bbls. of water were estimated tohave influxed from the aquifer.

The properties common to the oil reservoir and the adjoining aquifer areas follows:

permeability k = 120 milli darcieswater viscosity µw = 0.8 cpporosity ∅ = 0.2effective water compressibility = 1 x 10 -6 psi-1

(i) Calculate the average thickness of the aquifer sands.

(ii) The cumulative water influx after 12, 18 and 24 months.

The Hurst & van Everdingen equation for a full radial flow system is:[10]

W cR h pWe o D= 1 119 2. φ ∆

where

We = cumulative water influx (bbls)∆p = pressure drop(psi)WD = dimensionless water influxc = compressibility of the aquifer (psi-1)Ro = radius of the oil reservoir (ft)h = average thickness of the aquifer sands. (ft)Ø = porosity

Charts are supplied of dimensionless water influx WD versusdimensionless time tD (see 2 attachments)

where

tktcRD

w o

= 2 309 2.µ φ

t = time ( years)k = permeability (millidarcies)µw = viscosity (cp)

Aquifer Radius 40,000ft

Oil Reservoir Radius 8,000ftAngle - 135º

B10(a) Describe briefly the drive mechanisms associated with producing an

undersaturated oil reservoir, without a supporting aquifer, down to apressure well below the bubble point.

[6]

(b) Explain briefly why surface samples from a wet gas or condensatereservoir can be unrepresentative if collected too early after a shutdown or major well disturbance. What suggestions would you give toget more representative samples.

[4]

(c) Table 1 gives the results for a constant mass study on an oil sample. Inthe test the volume of live oil was measured as a function of pressure.The temperature was maintained at the reservoir temperature of 220 ˚F.

In another test a sample of the same oil in a PVT cell,at its bubble pointand at 220 ˚F was passed through a two stage separator at 500 psigand 160 ˚F and 0 psig and 60 ˚F. 38 cc of oil were removed from thePVT cell and 28.34 cc of oil were collected from the final separator. Atotal amount of 3492 cc of gas at 60˚F and 0 psig were collected fromboth stages of the separation process.

In a further test a differential liberation procedure was carried out on asample of the oil at 220 ˚F and the volumes of oil remaining andstandard volumes of gas liberated at each stage were recorded. Theresults are presented in Table 2.

From the results of these tests assuming separator conditions of 500psig and 160 ˚F and 0 psig and 60 ˚F determine:

(i) The bubble point pressure of the reservoir fluid at 220 ˚F

(ii) The oil formation volume factor at 4400 psig and 3925 psig.

(iii) The solution gas to oil ratio at 4400 psig and 3925 psig.

(iv) The oil formation volume factor and solution gas to oil ratio youwould use for reservoir calculations at 1605 psig.

(v) The total formation volume factor at 3300 psig.[10]

Table 1 Constant Mass Study of Reservoir fluid at 220 ºF

Pressure (psig) 5500 5000 4500 4350 4173 4000 3800 3675

Volume of 193.00 194.97 196.08 196.42 196.81 197.21 197.68 198.00Oil in Cell (cc)

Pressure (psig) 3643 3594 3493 3446 3293 3146 2954 2713

Volume of 198.46 199.21 200.85 201.66 204.67 208.00 213.29 221.82Oil in Cell (cc)

Pressure (psig) 2453 2186 1968 1769 1580 1344

Volume of 234.39 252.81 274.35 302.11 339.97 415.31Oil in Cell (cc)

Table 2 Differential test at 220 ºF

Pressure (psig) Cumulative Gas Produced Volume of Oilin Cell cc @ 60 º F & 0 psig (cc at pressure)

Bubble point pressure 0 177.25

2924 698 171.13

2265 1440 164.75

1605 2051 159.50

1095 2537 154.88

420 3322 147.13

0 3996 135.50

@60ºF 125.00

B11(a) In reserve estimates what do you understand by Proven, Probable and

Possible reserves.[6]

(b) A well penetrates an oil reservoir from which core samples have beencollected and capillary pressure curves generated using the air-mercurymethod. The capillary pressure data for the specific rock types aregiven in the attached figure. The lowest 100% Sw saturation level wasfound at the bottom of the well in rock A as indicated.

(i) Determine the free water level and indicate it on the diagram.[2]

(ii) Construct the water saturation profile on the saturation heightdiagram.

[7]

(iii) Estimate the oil -in place per unit cross section area over thereservoir thickness.

[5]

Data

The specific gravities of water and oil relative to water density at 60 ˚F are1.03 & 0.8 respectively. The density of water at 60˚F is 62.4 lbm/cu.ft.

Air/mercury capillary pressure = 10 x capillary pressure water/ oil.1 bbl = 5.615 cu. ft

1 lbf = 1 lbm x g.psi = lbf / sq inch

B12 You have been appointed as the engineering manager of a reservoir.Given that you appreciate the importance of allowing for the activationof rock mechanical phenomena ( stress-sensitivity) in the managementof the reservoir, explain how you would screen the reservoir for stress -sensitivity at the reservoir scale by listing and describing:

(a) the relevant rock mechanical phenomena to be considered, and their impact on reservoir performance

[9](b) the data set required to conduct the screening process

[9]

(c) the software tools necessary[2]

Section C

C13 A “super well” has been devised for high permeability reservoirs inwhich individual vertical wells are drilled in two concentric circles asshown in the diagram. Each ring has the same number of wells butstaggered in position as shown. Yaxley has given an expression for theDietz shape factor for a well in a triangular drainage area, also shown asa diagram. Sketch the approximate shape of the well drainage areas forthe “super well” configuration and show how Yaxley’s formula maybe used to obtain the productivity index of the wells in the inner andouter rings.

CA

rr

r

A

e

o

o

o

=

−

+

4

4 34

22

γ πθ

θ

π πθθ

exp ln lnsin

whereA r re e= =θ

ππ θ

2 22 2

or

Derive the Hawkins equation for the damage skin factor in an open-hole completion. Supposing the skin factor, S , has been measured in atransient well test what additional information could be used toestimate the depth of damage, ra , and hence the damage zonepermeability, ka .

[20]

Closed OuterBoundary

16 Well "Super Well" in a Large Circular Reservoir

C14 A two layer reservoir is produced commingled as shown in the diagramand it is desired to balance the production by the use of variablechokes; here balanced production implies that the rate from a layer isproportional to its thickness i.e. q1 /h1 = q2 /h2 . This is the basis of“smart” wells used to optimise production behaviour. Each chokediameter may be continuously varied from fully open to closed. Givena vertical lift curve for the well i.e. a plot of bottom-hole flowingprerssure, pwf , versus well total flow-rate, q , where q = q1 + q2 ,show how the choke settings may be calculated to give maximumbalanced production. Assume that the choke performance is given byan equation of the form:

qi = Cch At 2∆p

ρ 1 − σ2

where∆p = pressure drop over chokeqi = flow-rate through deviceCch = discharge coefficient (constant)

At = throat area = πD2t /4

σ = DtDp

Dt = throat diameterDp = pipe diameter

[20]

C15 Describe the phenomenon of “supercharging” and the procedureswhich may be used to obtain a useful WFT survey in a low permeabilityreservoir

[20]

End of Paper

q

q = q1 + q

2

q1

p1

S1

Layer 1

Layer 2

k1 h1

p2

k2 h2S2q2

Balanced Production UsingVariable Chokes

Q14

0

1.0

1.1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.25

1.1

1.0

0.9

1.01.05

1.05

1.11.2

1.3

1.4

1.5

1.6 1.7

1.8 1.9

2.0 2.2

2.4

2.6

3.0

3.02.8

1.21.3

1.1

1.10.95

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

1 2 3 4 5 6 7 8

7 8 9 10 11 12 13 14 15

Compressibility of Natural Gases(Jan. 1, 1941)

BEHAVIOUR OF OIL FIELD HYDROCARBON SYSTEMS

Com

pres

sibi

lity

Fact

or, z

Pseudo Reduced Temperature

Pseudo Reduced Pressure, Pr

3.02.82.62.42.22.01.91.8

1.7

1.6

1.5

1.45

1.35

1.4

1.3

1.25

1.2

1.15

1.1

2.6 2.4

2.22.0 1.9

1.71.6 1.4

1.3

1.2

1.1

1.05

1.051.8

1.4

1.5

Pseudo Reduced Pressure, Pr