G11RE Reservoir Engineering
Institute of GeoEnergy Engineering
G11RE
RESERVOIR ENGINEERING
 Attempt ALL questions. Total 100 marks.
 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.
 For calculation questions clearly state any assumptions and include all intermediate steps.
 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)
Figure 2.1 – Oil and water pressure distributions.
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
 Using a sketch of the relevant pressuretemperature 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.
 Using a sketch of the corresponding changes in the pressuretemperature phase diagram discuss how socalled gas cycling may improve recovery from a gas condensate reservoir.
 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 waterwet 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 k_{2} of the middle layer is about three times larger than the horizontal permeabilities k_{1} and k_{3} 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.
Figure 5.1 – Vertical crosssection 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.
 For the base case scenario.
 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
 Discuss how rock compression affects oil and gas recovery and how it is incorporated in the material balance equation.
 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 mudlog 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.
Figure 7.1 – Reservoir crosssection (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 oilwater 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, B_{o } 
1.45 
rb/stb 
Water formation volume factor, B_{w } 
1.02 
rb/stb 
Solution gasoil ratio, R_{s} 
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/ft^{3} 
i) Identify the gasoil 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 stm^{3}/day. Figure 8.1 shows the bottomhole flowing pressures for the first 140 hours of production.
 Using the average reservoir pressure of 263.6 bar at time t = 80 hours, calculate the skin factor.
 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, B_{o} 
1.2 
rm^{3}/stm^{3} 
Oil viscosity, 
1.2 x 10^{3} 
Pa s 
Permeability, k 
85.8 
mD 
Porosity, 
0.21  
Compressibility, c 
3.0 x 10^{9} 
Pa1 
Net formation thickness, h 
20 
m 
Wellbore radius, r_{w} 
0.15 
m 
External radius, r_{e} 
325 
m 
Initial reservoir pressure, P_{i} 
289.2 
bar 
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 oilwater 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 
 Calculate the crosssectional area A between the aquifer and the reservoir.
 Briefly discuss an alternative calculation to confirm that the answer to i) is approximately correct. You do not have to carry out the calculation.
 Calculate the cumulative water influx at the end of years 2 and 4.
(14 marks)
Figure 9.1 – Sketch of reservoiraquifer geometry.
Question 9(b)
Discuss the stepbystep 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)
Figure 9.2 – Graph of material balance equation.
Unit Conversion Tables
1. ALPHABETICAL LIST OF UNITS  
To convert from 
To 
Multiply by 
acre 
meter^{2}(m^{2}) 
4.046873E+03 
atm 
MPa 
1.013250E01 
atmosphere 
pascal (Pa) 
1.013250E+05 
bar 
pascal (Pa) 
1.000000E+05 
bar 
MPa 
1.000000E01 
barrel 
meter^{3} 
1.589873E01 
bbl/day 
meter^{3}/day 
1.589873E01 
centimeter of mercury (0°C) 
pascal (Pa) 
1.333220E+03 
centimeter of water (4°C) 
pascal (Pa) 
9.806380E+01 
centipoise 
pascal second (Pas) 
1.000000E03 
centistokes 
meter^{2 }per second (m^{2}/s) 
1.000000E06 
cp 
Pas 
1.000000E03 
cSt 
mm^{2}/s 
1.000000E+00 
cu in 
meter^{3}(m^{3}) 
1.638706E05 
cubic yard 
meter^{3}(m^{3}) 
7.645549E01 
darcy 
m^{2} 
9.869233E13 
degree (angle) 
radian (rad) 
1.745329E02 
degree API 
g/cm^{3} 
141.5/(131.5+˚API) 
degree Celsius 
kelvin (K) 
T_{k} = T_{c} + 273.15 
degree Fahrenheit 
degree Celsius 
T_{c} = (T_{F} 32)/1.8 
degree Fahrenheit 
kelvin (K) 
T_{k} = (T_{F} + 459.67)/1.8 
degree Rankine 
kelvin (K) 
T_{k} = T_{R} /1.8 
dyne 
newton (N) 
1.000000E05 
dyne cm 
newton meter (Nm) 
1.000000E07 
dyne/cm^{2} 
pascal (Pa) 
1.000000E01 
foot 
in (inch) 
1.200000E+01 
foot 
meter 
3.048000E01 
foot of water (39.2°F) 
pascal (Pa) 
2.988980E+03 
ft lbf 
joule (J) 
1.355818E+00 
ft lbf/hr 
watt(W) 
3.766161E04 
ft lbf/min 
watt(W) 
2.259697E02 
ft lbf/s 
watt(W) 
1.355818E+00 
ft/hr 
meter per second (m/s) 
8.466667E05 
ft/min 
meter per second (m/s) 
5.080000E03 
ft/s 
meter per second (m/s) 
3.048000E01 
ft/s^{2} 
meter per second^{2} (m/s^{2}) 
3.048000E01 
ft^{2} 
meter^{2}(m^{2}) 
9.290304E02 
ft^{3} 
meter^{3}(m^{3}) 
2.831685E02 
g/cm^{3} 
kilogram per meter^{3 } (kg/m^{3}) 
1.000000E+03 
gallon (U.K.Liquid) 
meter^{3 }(m^{3}) 
4.546092E03 
gallon (U.S.Liquid) 
meter^{3} (m^{3}) 
3.785412E03 
hour 
second 
3.600000E+03 
hydraulic horsepower hhp 
kW 
7.460430E01 
inch 
meter 
2.540000E02 
inch 
meter (m) 
2.540000E02 
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 
T_{c} = T_{k}  273.15 
kgf m 
newton meter (Nm) 
9.806650E+00 
kgf s^{2}/m (mass) 
kilogram (kg) 
9.806650E+00 
kgf/cm^{2} 
pascal (Pa) 
9.806650E+04 
kgf/m^{2} 
pascal (Pa) 
9.806650E+00 
kgf/mm^{2} 
pascal (Pa) 
9.806650E+06 
kilogram force (kgf) 
newton (N) 
9.806650E+00 
kilogram mass (kgm) 
lbm 
4.420751E02 
kilowatthour (kW hr) 
joule(J) 
3.600000E+06 
km/hr 
meter per second (m/s) 
2.777778E01 
lbf 
N 
4.448222E+00 
lbf/in^{2} 
GPa 
6.894757E06 
lbm 
kilogram (kg) 
4.535924E01 
lbm 
kg 
4.535924E01 
lbm/ft^{3} 
kg/m^{3} 
1.601846E+01 
litre 
meter^{3}(m^{3}) 
1.000000E03 
micron 
meter (m) 
1.000000E06 
mile 
meter (m) 
1.609300E+03 
millibar 
pascal (Pa) 
1.000000E+02 
millidarcy 
m^{2} 
9.869233E16 
s/ft 
s/m 
3.280840E+00 
ohm centimeter 
ohm meter (m) 
1.000000E02 
pascal (Pa) 
psi 
1.451000E04 
poise 
pascal second (Pas) 
1.000000E01 
pound force (lbf) 
newton (N) 
4.448222E+00 
ppg 
psi/ft 
5.200000E02 
psi 
MPa 
6.894757E03 
psi/ft 
kPa/m 
2.262059E+01 
psi^{1} 
Pa1 
1.450377E04 
scf/bbl 
standard m^{3}/m^{3} 
1.801175E01 
sq in 
meter^{2}(m^{2}) 
6.451600E04 
stokes 
meter^{2} per second (m^{2}/s) 
1.000000E04 
tonne 
kilogram (kg) 
1.000000E+03 
ton (UK) 
kilogram (kg) 
1.016047E+03 
watt 
Js1 
1.000000E+00 
yard 
foot 
3.000000E+00 
SI UNIT PREFIXES
multiplication factor 
SI prefix 
Symbol 
10^{18} 
exa 
E 
10^{15} 
peta 
P 
10^{12} 
tera 
T 
10^{9} 
giga 
G 
10^{6} 
mega 
M 
10^{3} 
kilo 
k 
10^{2} 
hecto 
h 
10 
deka 
da 
101 
deci 
d 
102 
centi 
c 
103 
milli 
m 
106 
micro 

109 
nano 
n 
1012 
pico 
p 
1015 
femto 
f 
1018 
atto 
a 