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G11RE Reservoir Engineering

Institute of GeoEnergy Engineering

G11RE

RESERVOIR ENGINEERING

  1. Attempt ALL questions. Total 100 marks.
  2. For descriptive questions provide the answers in your own words and adhere to the word limits shown. Any additional words will not be marked. Equations, numbers or figures are not counted as words.
  3. For calculation questions clearly state any assumptions and include all intermediate steps.
  4. Symbols have their usual meaning.

Question 1

A major international energy company has discovered an oil field in offshore Senegal.

Based on a full appraisal of the field the probabilistic representation of the reserves is:

P90: 500 MMstb

P50: 700 MMstb P10: 1000 MMstb.

A commercial analysis has been carried out and relevant government licenses have been obtained. Only small amounts of oil have been produced from formation tests.

Discuss how much of the reserves the company can quote as proved.

(3 marks)

(Word Limit: 90)

Question 2

For a sandstone reservoir the oil and water pressure distributions have been determined as shown in Figure 2.1. Additionally, for a representative core plug the airmercury capillary pressure curve has been measured as shown in Figure 2.2. Estimate the height of the transition zone.

(6 marks)

G11RE Reservoir Engineering img1

Figure 2.1 – Oil and water pressure distributions.

G11RE Reservoir Engineering img2

Figure 2.2 – Air mercury capillary pressure curve.

Question 3

Describe the objectives of the flash and differential liberation tests. Discuss how conditions in these tests compare with conditions in the reservoir during production.

(5 marks)

(Word Limit:150)

Question 4

  1. Using a sketch of the relevant pressure-temperature phase diagram discuss development of a gas condensate reservoir by natural depletion and the potential drawbacks of this recovery mechanism, including the effect of the production rate.
  2. Using a sketch of the corresponding changes in the pressure-temperature phase diagram discuss how so-called gas cycling may improve recovery from a gas condensate reservoir.
  3. Discuss whether the black oil model may be used in simulating the development of a gas condensate reservoir.

(10 marks)

(Word Limit: 300)

Question 5

A section of a water-wet oil reservoir consists of three horizontal layers in which a water injector and a producer have been drilled, as sketched in Figure 5.1. The horizontal permeability k2 of the middle layer is about three times larger than the horizontal permeabilities k1 and k3 of the top and bottom layers. The water density is significantly larger than the oil density. The wells have been completed over the full height of the reservoir section.

G11RE Reservoir Engineering img3

Figure 5.1 – Vertical cross-section of layered reservoir.

Consider a base case water flood scenario for which the vertical permeability is of the same order of magnitude as the horizontal permeabilities, while the oil and water viscosities are approximately the same.

Discuss and sketch the expected water saturation profiles, including three relevant saturation contour lines, in the section between the wells (a) before and (b) after water breakthrough for cases i), ii) and iii) below. Compare the breakthrough times for the various cases.

  1. For the base case scenario.
  2. For the base case scenario, but with the oil viscosity much larger than the water viscosity.
  • For the base case scenario, but with the vertical permeability several orders of magnitude smaller than the horizontal permeabilities.

(12 marks)

(Word limit 360)

Question 6

  1. Discuss how rock compression affects oil and gas recovery and how it is incorporated in the material balance equation.
  2. Name three natural drive mechanisms, or stages of drive mechanisms, for which rock compressibility in an oil reservoir may be neglected and explain why this is the case.

(6 marks)

(Word Limit: 180)

Question 7

An oil field has been discovered in a water depth of 100 meters. Seismic interpretations revealed that the reservoir is divided into two sections by a fault (Figure 7.1). Discovery Well 1 was drilled in the western flank of the structure where no traces of hydrocarbon were found. Discovery Well 2 was drilled on the opposite side of the fault (eastern flank). The mud-log analysis and well log interpretations revealed that the eastern flank contains commercially producible volumes of hydrocarbons. Despite the presence of the fault, it is assumed that an aquifer is present that is continuous across the reservoir.

G11RE Reservoir Engineering img4

Figure 7.1 – Reservoir cross-section (not to scale)

In Well 1 a single pressure measurement was performed. At a depth of 5,500 ft (TVDSS) the pressure was measured as 2,534.7 psia. From the well logs run in Well 2, an oil-water contact (OWC) was detected at 5,700 ft. A well test program performed early during the appraisal stage on Well 2 produced oil with a constant flowrate of 7,000 stb/d and a corresponding gas flowrate of 10 MMscf/d. Two pressures were also measured in Well 2 as shown in Table 7.1.

Table 7.1 – Pressure measurements in Well 2.

TVDSS (ft)

Pressure (psia)

4,575.00

2,319

4,675.00

2,330

From the PVT analysis performed on fluid samples taken from both wells the data shown in Table 7.2 was obtained. Assume further that the average reservoir pressure and temperature are 2,500 psia and 120 °F, respectively.

Table 7.2 – Fluid properties.

Oil formation volume factor, Bo

1.45

rb/stb

Water formation volume factor, Bw

1.02

rb/stb

Solution gas-oil ratio, Rs

1,000

scf/stb

Gas specific gravity (surface conditions), g

0.7

Oil specific gravity (surface conditions), o

0.8

Water density (surface conditions), w

64.63

lb/ft3

i) Identify the gas-oil contact (GOC), if any. ii) In the absence of data regarding the strength of the aquifer, what advice would you give the production engineer to prevent fast decline in reservoir pressure?

(25 marks)

Question 8

A well in an oil reservoir with properties shown in Table 8.1 produces at a constant flow rate of 240.7 stm3/day. Figure 8.1 shows the bottomhole flowing pressures for the first 140 hours of production.

  1. Using the average reservoir pressure of 263.6 bar at time t = 80 hours, calculate the skin factor.
  2. Calculate the pressure at the external boundary of the reservoir at time (a) t = 10 hours and (b) t = 100 hours.

(11 marks)

Table 8.1 – Fluid and reservoir properties.

Oil formation volume factor, Bo

1.2

rm3/stm3

Oil viscosity, 

1.2 x 10-3

Pa s

Permeability, k

85.8

mD

Porosity, 

0.21

Compressibility, c

3.0 x 10-9

Pa-1

Net formation thickness, h

20

m

Wellbore radius, rw

0.15

m

External radius, re

325

m

Initial reservoir pressure, Pi

289.2

bar

G11RE Reservoir Engineering img5

Figure 8.1 – Bottomhole flowing pressure versus time.

Question 9(a)

A water drive oil reservoir is bounded at one edge by an aquifer, as sketched in Figure 9.1. Properties of the aquifer are given in Table 9.1.

Table 9.1 – Aquifer properties.

Aquifer length, L

40,000

ft

Permeability, k

300

mD

Effective aquifer compressibility, c

7.0 x 10-6

psi-1

Porosity, 

0.23

Water viscosity, w

0.8

cP

Over the first 4 years of production the pressure decline at the oil-water contact is considered to be as shown in Table 9.2. At the end of the first year, 50,000 bbls of water are estimated to have flowed in from the aquifer.

Table 9.2 – Pressure decline.

Time

(years)

Pressure

(psi)

0

6,500

1

6,475

2

6,425

3

6,350

4

6,250

  1. Calculate the cross-sectional area A between the aquifer and the reservoir.
  2. Briefly discuss an alternative calculation to confirm that the answer to i) is approximately correct. You do not have to carry out the calculation.
  3. Calculate the cumulative water influx at the end of years 2 and 4.

(14 marks)

G11RE Reservoir Engineering img6

Figure 9.1 – Sketch of reservoir-aquifer geometry.

Question 9(b)

Discuss the step-by-step procedure that Havlena and Odeh proposed to calculate the aquifer influx constant B from the form of the material balance equation shown in Figure 9.2 below. Indicate the data required for this equation and their sources. Discuss also the significance for the aquifer if B varies during the life of the reservoir.

(8 marks)

(Word Limit: 400)

G11RE Reservoir Engineering img7

Figure 9.2 – Graph of material balance equation.

Unit Conversion Tables

1. ALPHABETICAL LIST OF UNITS

To convert from

To

Multiply by

acre

meter2(m2)

4.046873E+03

atm

MPa

1.013250E-01

atmosphere

pascal (Pa)

1.013250E+05

bar

pascal (Pa)

1.000000E+05

bar

MPa

1.000000E-01

barrel

meter3

1.589873E-01

bbl/day

meter3/day

1.589873E-01

centimeter of mercury (0°C)

pascal (Pa)

1.333220E+03

centimeter of water (4°C)

pascal (Pa)

9.806380E+01

centipoise

pascal second (Pas)

1.000000E-03

centistokes

meter2 per second

(m2/s)

1.000000E-06

cp

Pas

1.000000E-03

cSt

mm2/s

1.000000E+00

cu in

meter3(m3)

1.638706E-05

cubic yard

meter3(m3)

7.645549E-01

darcy

m2

9.869233E-13

degree (angle)

radian (rad)

1.745329E-02

degree API

g/cm3

141.5/(131.5+˚API)

degree Celsius

kelvin (K)

Tk = Tc + 273.15

degree Fahrenheit

degree Celsius

Tc = (TF -32)/1.8

degree Fahrenheit

kelvin (K)

Tk = (TF + 459.67)/1.8

degree Rankine

kelvin (K)

Tk = TR /1.8

dyne

newton (N)

1.000000E-05

dyne cm

newton meter (Nm)

1.000000E-07

dyne/cm2

pascal (Pa)

1.000000E-01

foot

in (inch)

1.200000E+01

foot

meter

3.048000E-01

foot of water (39.2°F)

pascal (Pa)

2.988980E+03

ft lbf

joule (J)

1.355818E+00

ft lbf/hr

watt(W)

3.766161E-04

ft lbf/min

watt(W)

2.259697E-02

ft lbf/s

watt(W)

1.355818E+00

ft/hr

meter per second (m/s)

8.466667E-05

ft/min

meter per second (m/s)

5.080000E-03

ft/s

meter per second (m/s)

3.048000E-01

ft/s2

meter per second2

(m/s2)

3.048000E-01

ft2

meter2(m2)

9.290304E-02

ft3

meter3(m3)

2.831685E-02

g/cm3

kilogram per meter3

(kg/m3)

1.000000E+03

gallon (U.K.Liquid)

meter3 (m3)

4.546092E-03

gallon (U.S.Liquid)

meter3 (m3)

3.785412E-03

hour

second

3.600000E+03

hydraulic horsepower hhp

kW

7.460430E-01

inch

meter

2.540000E-02

inch

meter (m)

2.540000E-02

inch of mercury (32°F)

pascal (Pa)

3.386380E+03

inch of mercury (60°F)

pascal (Pa)

3.376850E+03

inch of water (39.2°F)

pascal (Pa)

2.490820E+02

inch of water (60°F)

pascal (Pa)

2.488400E+02

kelvin

degree Celsius

Tc = Tk - 273.15

kgf m

newton meter (Nm)

9.806650E+00

kgf s2/m (mass)

kilogram (kg)

9.806650E+00

kgf/cm2

pascal (Pa)

9.806650E+04

kgf/m2

pascal (Pa)

9.806650E+00

kgf/mm2

pascal (Pa)

9.806650E+06

kilogram force (kgf)

newton (N)

9.806650E+00

kilogram mass (kgm)

lbm

4.420751E-02

kilowatthour (kW hr)

joule(J)

3.600000E+06

km/hr

meter per second (m/s)

2.777778E-01

lbf

N

4.448222E+00

lbf/in2

GPa

6.894757E-06

lbm

kilogram (kg)

4.535924E-01

lbm

kg

4.535924E-01

lbm/ft3

kg/m3

1.601846E+01

litre

meter3(m3)

1.000000E-03

micron

meter (m)

1.000000E-06

mile

meter (m)

1.609300E+03

millibar

pascal (Pa)

1.000000E+02

millidarcy

m2

9.869233E-16

s/ft

s/m

3.280840E+00

ohm centimeter

ohm meter (m)

1.000000E-02

pascal (Pa)

psi

1.451000E-04

poise

pascal second (Pas)

1.000000E-01

pound force (lbf)

newton (N)

4.448222E+00

ppg

psi/ft

5.200000E-02

psi

MPa

6.894757E-03

psi/ft

kPa/m

2.262059E+01

psi-1

Pa-1

1.450377E-04

scf/bbl

standard m3/m3

1.801175E-01

sq in

meter2(m2)

6.451600E-04

stokes

meter2 per second

(m2/s)

1.000000E-04

tonne

kilogram (kg)

1.000000E+03

ton (UK)

kilogram (kg)

1.016047E+03

watt

Js-1

1.000000E+00

yard

foot

3.000000E+00

SI UNIT PREFIXES

multiplication factor

SI prefix

Symbol

1018

exa

E

1015

peta

P

1012

tera

T

109

giga

G

106

mega

M

103

kilo

k

102

hecto

h

10

deka

da

10-1

deci

d

10-2

centi

c

10-3

milli

m

10-6

micro

10-9

nano

n

10-12

pico

p

10-15

femto

f

10-18

atto

a

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