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ENPE523 Practise Midterm Exam Name: _______________________ ID: _______________________ Please Note: 1. Closed book exam.

No textbooks, notes, or information sheets (except for exam formula sheet) permitted in exam. 2. Individual exam ⎯ no interactions with other students are allowed during the exam. 3. Non-programmable calculators are permitted. 4. Exam duration: 1800-2000 (120 minutes). 5. Back of pages can be used as scrap paper or extra paper for your work if needed.

Indicate if your solution to a question if it continues on the back of the page. 6. Units are required as part of the answer.

Question

Grade

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5

Total

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Question 1 (10 Marks) Multiple Choice A. Which of the following is not a primary drive mechanism: (a) natural water drive (b) gas cap expansion (c) sedimentation drive (d) solution gas drive (e) oil expansion Answer:______ B. The effective porosity: (a) is greater than the total porosity (b) is the total pore volume in rock divided by rock volume (c) can never exceed 0.48 (d) is the fluid communicating pore volume divided by the rock volume (e) is always equal to the vugular porosity Answer:______ C. Which is not a mechanism for fluid motion in an oil reservoir: (a) pressure difference (b) formation re-compaction (c) capillary pressure (d) gravity drainage (e) oil phase viscosity Answer:______ D. The tortuosity is: (a) the square of the ratio of the flow path length to the sample length (b) is always less than or equal to 1 (c) depends only on the grain size (d) the square of the ratio of the sample length to the flow path length (e) equals 42 Answer:______ E. In an oil-water system, which of the following is not a reason why the effective permeability of the oil phase is less than the absolute permeability: (a) adverse capillary forces cause water to plug a channel because the pressure gradient is

insufficient to push the interface through a pore constriction (b) trapping of clustered globules (c) viscosity of oil is less than viscosity of water (d) the water phase flow interferes with the flow of the oil phase (e) immobilized drops of water plug some pore channels Answer:______ F. The retrograde regions are: (a) inside the two-phase region and in one of them, as the temperature and pressure is raised, the

amount of the liquid phase remains constant (b) inside the two-phase region and in one of them, as the pressure is raised, the amount of the

liquid phase drops (c) inside the two-phase region and in one of them, as the pressure is raised, the amount of the

liquid phase rises

No answers provided for multiple choice

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(d) adjacent but outside the two-phase region and in one of them, as the pressure is raised, the amount of the liquid phase drops

(e) inside the two-phase region and in one of them, as the viscosity is raised, the amount of the liquid phase drops Answer:______

G. The porosity-permeability transform refers to: (a) strictly the effective permeability and pore space (b) porosity at a given location and the permeability at a different location (c) relationship defined by the Kozeny-Corey equation (d) three-phase relative permeabilities (e) relationship between absolute permeability and porosity Answer:______ H. Drainage refers to: (a) the process where the non-wetting phase is displaced from the reservoir rock by a rise in the

pressure of the nonwetting phase and the wetting phase saturation falls (b) the process where the wetting phase saturation is raised because the wetting phase is

displacing a nonwetting phase (c) the process where the wetting phase is displaced from the reservoir rock by a rise in the

pressure of the nonwetting phase and the wetting phase saturation rises (d) the process where the wetting phase is displaced from the reservoir rock by a rise in the

pressure of the nonwetting phase and the wetting phase saturation falls (e) the process where the wetting phase saturation is raised because the nonwetting phase is

displacing a wetting phase Answer:______ I. Stone’s models can be used to generate: (a) relative permeabilities of gas and liquid phases as a function of the absolute permeability of

the reservoir rock (b) relative permeabilities of gas and liquid phases as a function of the saturations of each phase (c) the oil and water effective permeabilities but only at critical gas saturation (d) the relative permeabilities for multiple gas phase systems (e) the permeability of a component in a fluid Answer:______ J. ( )mNBoi +1 represents: (a) oil volume in reservoir (expressed at reservoir conditions) (b) original gas (both free and dissolved) volume in reservoir (expressed at reservoir conditions) (c) total free gas volume in reservoir (expressed at standard conditions) (d) original hydrocarbon pore volume (oil and both free and dissolved gas) volume in reservoir

(expressed at standard conditions) (e) original hydrocarbon pore volume (oil and both free and dissolved gas) volume in reservoir

(expressed at reservoir conditions) Answer:______

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Question 2 (30 Marks) The material balance states that the changes in the oil, water, and gas volumes must sum to zero. In equation form, this is given by:

( ) ( ) ( ) wpegspppsigi

oioiopoi BWWBRNNRNNR

BNmBNmBBNNNB −=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−−+−+−−

(a) Which term or terms represents the change in free gas volume in reservoir at time t

(expressed at reservoir conditions) ? (b) If the above material balance equation was modified to include cumulative gas injected, GI,

which term would be modified and state final form of this term ? (c) In an oil reservoir where there is no gas cap, no water drive, no water production, no active

gas injection, what does the material balance equation reduce to ?

( ) gspppsigi

oioi BRNNRNNR

BNmBNmB

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−−+−

( ) ( ) ( ) wpegspppIsigi

oioiopoi BWWBRNNRNGNR

BNmBNmBBNNNB −=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−−++−+−−

( ) ( )[ ] 0=−−−−−− gspppsiopoi BRNNRNNRBNNNB

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(d) For a given reservoir, the initial reservoir pressure is 4200 kPa and the PVT and production data is given versus pressure and time in the following Table. The porosity is 0.3 and initial water saturation is 0.2.

Time, Years P, kPa Rs Bo Bg Np, Mm3 Rp

0 4200 52 1.11 0.010 0 62 2 3400 47 1.10 0.012 15 57

(i) Is there a gas cap in this reservoir ? How can you tell this ?

Since Rp > Rs, yes there is a gas cap.

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Question 3 (20 Marks) The oil-water relative permeability curve for a given reservoir is given in the following Table. The water and oil viscosities are 1 and 3 cP, respectively.

Sw krA krB 0.2100000 0.0000000 1.0000000 0.2310714 0.0000008 0.8804812 0.2521428 0.0000130 0.7715315 0.2732143 0.0000659 0.6725691 0.2942857 0.0002082 0.5830237 0.3153571 0.0005084 0.5023360 0.3364286 0.0010542 0.4299582 0.3575000 0.0019531 0.3653545 0.3785715 0.0033319 0.3080007 0.3999999 0.0053371 0.2573857 0.4207143 0.0081346 0.2130103 0.4417857 0.0119099 0.1743886 0.4628571 0.0168680 0.1410480 0.4839286 0.0232333 0.1125295 0.5050000 0.0312500 0.0883883 0.5260714 0.0411816 0.0681944 0.5471429 0.0533111 0.0515325 0.5682143 0.0679413 0.0380033 0.5892857 0.0853941 0.0272237 0.6103572 0.1060114 0.0188276 0.6314286 0.1301541 0.0124670 0.6525000 0.1582032 0.0078125 0.6735715 0.1905587 0.0045549 0.6946429 0.2276404 0.0024063 0.7157143 0.2698875 0.0011019 0.7367857 0.3177590 0.0004026 0.7578571 0.3717331 0.0000974 0.7789286 0.4323077 0.0000086 0.8000000 0.5000000 0.0000000

(a) Which curve (A and B) is water and which one is oil ?

A = ________________ B = ________________ (b) What is the connate water saturation ? (c) What is the residual oil saturation ? (d) What is the approximate value of the water saturation at the crossover point ?

Water Oil

0.21

0.20

~0.54

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(e) Does the data suggest the reservoir rock is water or oil wet ? (f) At Sw = 0.4, what is the mobility ratio ? (g) At Sw = 0.4, what is the fractional flow to water and to oil ? (h) If the OOIP in the reservoir is estimated to be 100 million m3, what is the maximum

recoverable oil from the reservoir given the relative permeability data above ?

Oil-wet

o

w

oo

ww

o

o

w

w

o

w

kk

LPAkLPAk

qqM

λλ

µµ

µ

µ==

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

==

M = (0.0053371/1)/(0.2573857/3) = 0.06221

wbS

o

w

w

rw

o

ro

w

w

o

owow

aekkkkqqf

−+=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

=+

=

µµ

µµµµ1

1

1

1

1

11

1

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛+=

10053371.0

32573857.01

1wf = 0.005856

Recoverable Oil = (RF) (OOIP)

wc

orwwc

SSSRF

−−−

=1

1

Recoverable Oil = 74.7 million m3

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Question 4 (20 Marks) In preparation for a sandpack experiment, the absolute permeability of sand is determined by flowing water at 20 cc/min continuously through it. The sand (density equal to 2640 kg/m3) is held in a 3 m long vertical tube with diameter equal to 10 cm. Water flows from the top of the tube and its pressure there is 1.1 atm. The viscosity of the water is 1 cP, its density is 1000 kg/m3, and its surface tension is 65 mN/m. (a) If the porosity of the sandpack is 0.33, what is the mass of sand required to fill the tube ? (b) What is the permeability of the sand in Darcy’s ? (c) If the target water saturation in the sand was to be 0.3, how much water, in m3, should be

added to the sandpack ? (d) The sandpack is initially saturated with water and then it is allowed to flow out at the bottom

of the sandpack. (i) What is the wetting fluid and what is the nonwetting fluid ? (ii) Is imbibition or drainage occurring ?

RV = (1-0.33)(3 m)(π/4)(0.10m)2 Mass sand = (2640)(RV) = 41.67 kg

gkAq ρµ

=

k = (20 cc/min)(1m3/1000000cc)(1min/60s)(0.001)/(1000)(9.81)A

= 4.33 D

Sw = 0.3 = Vw/PV PV = (0.33)(3 m)(π/4)(0.10m)2 Vw = 0.3 PV = 0.002333 m3

Wetting = water Nonwetting = air

Since Sw going down, drainage is occurring

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(e) The capillary pressure for this sand is given in the following Figure.

(i) Determine an estimate for Swc.

(ii) What is the capillary pressure after the sandpack reaches an average water saturation equal to 0.3 ?

(iii) What is the equivalent capillary rise for this capillary pressure ?

(iv) If the contact angle is estimated to be 30°, what is the approximate curvature of the air-water interfaces in the pores ?

(v) If the contact angle is estimated to be 30°, determine an estimate for the average pore radius ?

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Water Saturation

Cap

illar

y Pr

essu

re, k

Pa

_

From inspection, Swc ~ 0.23

Sw = 0.3, so get Pcap ~ 5.5 kPa

Sw = 0.3, so get Pcap ~ 5.5 kPa

( )gP

hairw

cap

ρρ −= = 0.56 m

Curvature = Pcap / σ = 5500 / 0.065 = 84615 m-1

Curvature = 84615 m-1 = rθcos2

so get r = 2.05e-5 m

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Question 5 (20 Marks) (a) On the following diagram, label the cricondentherm, cricondenbar, bubble point line, dew

point line, liquid region, vapour region, and two-phase region. On the right are schematics of a container holding the fluid mixture at various temperatures and pressures. Match letters (A, B, C, and D) to the pictures (you can write letter on line at left side of each schematic).

(b) For a single component, draw the vapour-liquid P-T diagram on the following Figure.

Indicate the critical point and where two-phases would occur. (c) For water, name a pressure and temperature where two fluid phases simultaneously exist.

T

P

T

P D

C

B

A

Vapour (Mixture)

Liquid Mixture

Liquid+Vapour

Liquid+Vapour CP

B

C

A

D

CP

Boiling point, 100°C and 1 atm

Two Phases

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(d) The steam zone in a thermal oil recovery process contains water at saturation conditions and

methane at total pressure equal to 2 MPa. The mole fraction of water in the vapour phase is equal to 0.6.

(i) What is the partial pressure of methane in the vapour phase ?

(ii) If the K-value for methane is equal to 13.4, what is the mole fraction of methane in the liquid phase ?

Partial pressure of methane = (0.4)(2) = 0.8 MPa

yCH4 = 0.4 K-value = y CH4/x CH4 = 13.4 xCH4 = y CH4/13.4 = 0.4/13.4 = 0.02985