1
Midterm: Reservoir Engineering Show your work! 18 Feb 2016
1. (10) Estimate the volume (stb) of oil in place per square mile in a 75-foot-thick formation with 18%
porosity, water saturation of 22%, and Bo of 1.68 rb/stb. The reservoir pressure is above bubble-point
pressure.
2. (5) A well produces 800 stb of water per day. Estimate the reservoir equivalent withdrawal rate of this
water.
3. (30) Derive an expression for Bg starting with the real gas equation: PV=znRT. Then, use that equation to
estimate Bg in rb/Mscf for a 0.75 gravity gas at 180°F and 2300 psia. Use the dashed line for condensates in the
attached Fig 1.7 for critical properties from Dake. Dake’s z chart is also attached.
4. (10) At bubble-point pressure of 2800 psia for a reservoir, Bo is 1.600 rb/stb. The average oil
compressibility above Pbp is 16×10-6 psi-1
. What is the Bo at 3400 psi?
5. (30) A reservoir with PVT properties in Table 1 on p 3 operates at an average pressure of 2770 psi. The
production rate of oil is 650 stb/day and the gas rate is 1.30 MMscf/day. What is the volumetric withdrawal
rate including gas and oil at reservoir conditions?
6. (10) Neglecting water encroachment, simplify the complete material balance for an oil reservoir operating
above the bubble-point pressure.
?! ?! + ?! – ?! ?! + ?!?!
= ? ?! – ?!” + ? ?!” – ?! ?! + ???!”
?!
?!”
– 1 + 1 + ? ??!”
?!?!” + ?!
1 – ?!”
??
+ ?!?!
7. (10) Use Hawkins formula to estimate skin given the following: well diameter is 10 inches; the damaged
zone beyond the diameter of the well is one inch wide; permeability of the reservoir is 30 md; permeability of
the damaged zone is 1 md.
8. (15) Find flow rate (stb/day) of oil to a well (8 inch diameter) that penetrates a 35-ft-thick formation with
permeability of 65 md. Average reservoir pressure is 1500 psi and well-bore pressure is 1000 psi. Oil viscosity
is 2.5 cp. The formation volume factor is 1.35 rb/stb. Drainage radius for the well is 850 feet. Skin is 8.
9. (20) While sitting on a beach, you wonder about permeability of the sand. You guess the porosity is about
36%. You estimate the average diameter of sand grains: 0.03 inches. Use the following consistent-unit
equation to estimate permeability: ? = !!!!
!”# !!! !. Give your final answer in Darcies.
Potentially Useful Equations
? – ?! = 141.2???!
?h ln
?
?!
+ ?
? – ?! = ??
2??h ln
?
?!
? = – ????
??
? = ?
?!
– 1 ln
?!
?!
?!”# – ?! = 141.2???!
?h ln
?
?!
– 1
2 + ?
?!
rb
mcf = 5.02
??
?
2
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 17
3.0
2.8 2 6. 2.4 2 2.
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1 1.
1.1
1.45
1.35
1.25
1.05
1.2
1.3
1.1
1.0
0.9
0.8
0.7
0.6
Z -factor
Pseudo reduced pressure
0.5
Pseudo reduced temperature
0.4
0.3
0.2
0.1
0
012345678
1 1. 5
1 0. 5
Fig. 1.6 The Z-factor correlation chart of Standing and Katz11 (Reproduced by courtesy
of the SPE of the AIME)
If the gas composition is not available, the Standing-Katz correlation can still be used
provided the gas gravity, based on the scale air = 1, at atmospheric pressure and at
60°F, is known (refer sec. 1.6). In this case fig. 1.7, is used to obtain the pseudo critical
pressure and temperature; then equs. (1.18) and (1.19) can be applied to calculate the
pseudo reduced parameters required to obtain the Z-factor from fig. 1.6.
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 18
MISCELLANEOUS GASES
CONDENSATE WELL FLUID
PSEUDO CRITICAL PRESSURE, psia PERATURE, degrees Rankine M PSEUDO CRITICAL TE
GAS GRAVITY (Air = 1)
700
650
600
550
500
450
400
350
300
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Fig. 1.7 Pseudo critical properties of miscellaneous natural gases and condensate
well fluids19
c) Direct calculation of Z-factors
The Standing-Katz correlation is very reliable and has been used with confidence by
the industry for the past thirty-five years. With the advent of computers, however, there
arose the need to find some convenient technique for calculating Z-factors, for use in
gas reservoir engineering programs, rather than feeding in the entire correlation chart
from which Z-factors could be retrieved by table look-up. Takacs14 has compared eight
different methods for calculating Z-factors which have been developed over the years.
These fall into two main categories: those which attempt to analytically curve-fit the
Standing-Katz isotherms and those which compute Z-factors using an equation of
state. Of the latter, the method of Hall-Yarborough15 is worthy of mention because it is
3
Table 1. Estimated PVT parameters
Pressure, psia Bo, rb/stb Rs, scf/stb Bg, rb/mcf
4530 1.674 1240
4130 1.686 1240
3730 (Pbp) 1.699 1240 0.766
3420 1.626 1120 0.815
3100 1.555 990 0.888
2770 1.486 870 0.980
2430 1.418 740 1.111
Conversion Factors
Force
1 dyne = 1 g cm/s2
1 N = 1 kg m/ s2 = 105 dyne = 0.2248 lbf
1 lbf (pound-force) = 32.17 lbm ft/ s2 = 4.448 N
Length
1 mi (mile) = 5280 ft
1 ft (foot) = 12 in = 30.48 cm
1 in (inch) = 2.54 cm
0.001 in = 25.4 um (micrometers)
1 m (meter) = 100 cm = 106 um
Permeability
1 d (darcy) = 1000 md (millidarcy) = 0.9869 x 10-8 cm2
Pressure
1 Pa (Pascal) = 1 N/m2
1 psi = 1 lbf/in2
1 bar = 14.504 psi = 0.9869 atm = 106 dyne/cm2
1 atm = 14.696 psi = 1.0133 x 106 dyne/cm2 = 1.0133 x 105 Pa
1000 psi = 6.89 MPa = 6,890 kPa
Time
1 day = 86,400 s
Viscosity
1 poise = 100 cp = 1 g/cm/s
1 cp = 0.01 g/cm/s
1 Pa-s (Pascal-second) = 10 poise
1 mPa-s (milliPascal-second) = 1 cp
Volume
1 Bbl = 5.615 ft3
1 ft3 = 28,317 cm3

1
Midterm: Reservoir Engineering Show your work! 18 Feb 2016
1. (10) Estimate the volume (stb) of oil in place per square mile in a 75-foot-thick formation with 18%
porosity, water saturation of 22%, and Bo of 1.68 rb/stb. The reservoir pressure is above bubble-point
pressure.
2. (5) A well produces 800 stb of water per day. Estimate the reservoir equivalent withdrawal rate of this
water.
3. (30) Derive an expression for Bg starting with the real gas equation: PV=znRT. Then, use that equation to
estimate Bg in rb/Mscf for a 0.75 gravity gas at 180°F and 2300 psia. Use the dashed line for condensates in the
attached Fig 1.7 for critical properties from Dake. Dake’s z chart is also attached.
4. (10) At bubble-point pressure of 2800 psia for a reservoir, Bo is 1.600 rb/stb. The average oil
compressibility above Pbp is 16×10-6 psi-1
. What is the Bo at 3400 psi?
5. (30) A reservoir with PVT properties in Table 1 on p 3 operates at an average pressure of 2770 psi. The
production rate of oil is 650 stb/day and the gas rate is 1.30 MMscf/day. What is the volumetric withdrawal
rate including gas and oil at reservoir conditions?
6. (10) Neglecting water encroachment, simplify the complete material balance for an oil reservoir operating
above the bubble-point pressure.
?! ?! + ?! – ?! ?! + ?!?!
= ? ?! – ?!” + ? ?!” – ?! ?! + ???!”
?!
?!”
– 1 + 1 + ? ??!”
?!?!” + ?!
1 – ?!”
??
+ ?!?!
7. (10) Use Hawkins formula to estimate skin given the following: well diameter is 10 inches; the damaged
zone beyond the diameter of the well is one inch wide; permeability of the reservoir is 30 md; permeability of
the damaged zone is 1 md.
8. (15) Find flow rate (stb/day) of oil to a well (8 inch diameter) that penetrates a 35-ft-thick formation with
permeability of 65 md. Average reservoir pressure is 1500 psi and well-bore pressure is 1000 psi. Oil viscosity
is 2.5 cp. The formation volume factor is 1.35 rb/stb. Drainage radius for the well is 850 feet. Skin is 8.
9. (20) While sitting on a beach, you wonder about permeability of the sand. You guess the porosity is about
36%. You estimate the average diameter of sand grains: 0.03 inches. Use the following consistent-unit
equation to estimate permeability: ? = !!!!
!”# !!! !. Give your final answer in Darcies.
Potentially Useful Equations
? – ?! = 141.2???!
?h ln
?
?!
+ ?
? – ?! = ??
2??h ln
?
?!
? = – ????
??
? = ?
?!
– 1 ln
?!
?!
?!”# – ?! = 141.2???!
?h ln
?
?!
– 1
2 + ?
?!
rb
mcf = 5.02
??
?
2
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 17
3.0
2.8 2 6. 2.4 2 2.
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1 1.
1.1
1.45
1.35
1.25
1.05
1.2
1.3
1.1
1.0
0.9
0.8
0.7
0.6
Z -factor
Pseudo reduced pressure
0.5
Pseudo reduced temperature
0.4
0.3
0.2
0.1
0
012345678
1 1. 5
1 0. 5
Fig. 1.6 The Z-factor correlation chart of Standing and Katz11 (Reproduced by courtesy
of the SPE of the AIME)
If the gas composition is not available, the Standing-Katz correlation can still be used
provided the gas gravity, based on the scale air = 1, at atmospheric pressure and at
60°F, is known (refer sec. 1.6). In this case fig. 1.7, is used to obtain the pseudo critical
pressure and temperature; then equs. (1.18) and (1.19) can be applied to calculate the
pseudo reduced parameters required to obtain the Z-factor from fig. 1.6.
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 18
MISCELLANEOUS GASES
CONDENSATE WELL FLUID
PSEUDO CRITICAL PRESSURE, psia PERATURE, degrees Rankine M PSEUDO CRITICAL TE
GAS GRAVITY (Air = 1)
700
650
600
550
500
450
400
350
300
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Fig. 1.7 Pseudo critical properties of miscellaneous natural gases and condensate
well fluids19
c) Direct calculation of Z-factors
The Standing-Katz correlation is very reliable and has been used with confidence by
the industry for the past thirty-five years. With the advent of computers, however, there
arose the need to find some convenient technique for calculating Z-factors, for use in
gas reservoir engineering programs, rather than feeding in the entire correlation chart
from which Z-factors could be retrieved by table look-up. Takacs14 has compared eight
different methods for calculating Z-factors which have been developed over the years.
These fall into two main categories: those which attempt to analytically curve-fit the
Standing-Katz isotherms and those which compute Z-factors using an equation of
state. Of the latter, the method of Hall-Yarborough15 is worthy of mention because it is
3
Table 1. Estimated PVT parameters
Pressure, psia Bo, rb/stb Rs, scf/stb Bg, rb/mcf
4530 1.674 1240
4130 1.686 1240
3730 (Pbp) 1.699 1240 0.766
3420 1.626 1120 0.815
3100 1.555 990 0.888
2770 1.486 870 0.980
2430 1.418 740 1.111
Conversion Factors
Force
1 dyne = 1 g cm/s2
1 N = 1 kg m/ s2 = 105 dyne = 0.2248 lbf
1 lbf (pound-force) = 32.17 lbm ft/ s2 = 4.448 N
Length
1 mi (mile) = 5280 ft
1 ft (foot) = 12 in = 30.48 cm
1 in (inch) = 2.54 cm
0.001 in = 25.4 um (micrometers)
1 m (meter) = 100 cm = 106 um
Permeability
1 d (darcy) = 1000 md (millidarcy) = 0.9869 x 10-8 cm2
Pressure
1 Pa (Pascal) = 1 N/m2
1 psi = 1 lbf/in2
1 bar = 14.504 psi = 0.9869 atm = 106 dyne/cm2
1 atm = 14.696 psi = 1.0133 x 106 dyne/cm2 = 1.0133 x 105 Pa
1000 psi = 6.89 MPa = 6,890 kPa
Time
1 day = 86,400 s
Viscosity
1 poise = 100 cp = 1 g/cm/s
1 cp = 0.01 g/cm/s
1 Pa-s (Pascal-second) = 10 poise
1 mPa-s (milliPascal-second) = 1 cp
Volume
1 Bbl = 5.615 ft3
1 ft3 = 28,317 cm3

1
Midterm: Reservoir Engineering Show your work! 18 Feb 2016
1. (10) Estimate the volume (stb) of oil in place per square mile in a 75-foot-thick formation with 18%
porosity, water saturation of 22%, and Bo of 1.68 rb/stb. The reservoir pressure is above bubble-point
pressure.
2. (5) A well produces 800 stb of water per day. Estimate the reservoir equivalent withdrawal rate of this
water.
3. (30) Derive an expression for Bg starting with the real gas equation: PV=znRT. Then, use that equation to
estimate Bg in rb/Mscf for a 0.75 gravity gas at 180°F and 2300 psia. Use the dashed line for condensates in the
attached Fig 1.7 for critical properties from Dake. Dake’s z chart is also attached.
4. (10) At bubble-point pressure of 2800 psia for a reservoir, Bo is 1.600 rb/stb. The average oil
compressibility above Pbp is 16×10-6 psi-1
. What is the Bo at 3400 psi?
5. (30) A reservoir with PVT properties in Table 1 on p 3 operates at an average pressure of 2770 psi. The
production rate of oil is 650 stb/day and the gas rate is 1.30 MMscf/day. What is the volumetric withdrawal
rate including gas and oil at reservoir conditions?
6. (10) Neglecting water encroachment, simplify the complete material balance for an oil reservoir operating
above the bubble-point pressure.
?! ?! + ?! – ?! ?! + ?!?!
= ? ?! – ?!” + ? ?!” – ?! ?! + ???!”
?!
?!”
– 1 + 1 + ? ??!”
?!?!” + ?!
1 – ?!”
??
+ ?!?!
7. (10) Use Hawkins formula to estimate skin given the following: well diameter is 10 inches; the damaged
zone beyond the diameter of the well is one inch wide; permeability of the reservoir is 30 md; permeability of
the damaged zone is 1 md.
8. (15) Find flow rate (stb/day) of oil to a well (8 inch diameter) that penetrates a 35-ft-thick formation with
permeability of 65 md. Average reservoir pressure is 1500 psi and well-bore pressure is 1000 psi. Oil viscosity
is 2.5 cp. The formation volume factor is 1.35 rb/stb. Drainage radius for the well is 850 feet. Skin is 8.
9. (20) While sitting on a beach, you wonder about permeability of the sand. You guess the porosity is about
36%. You estimate the average diameter of sand grains: 0.03 inches. Use the following consistent-unit
equation to estimate permeability: ? = !!!!
!”# !!! !. Give your final answer in Darcies.
Potentially Useful Equations
? – ?! = 141.2???!
?h ln
?
?!
+ ?
? – ?! = ??
2??h ln
?
?!
? = – ????
??
? = ?
?!
– 1 ln
?!
?!
?!”# – ?! = 141.2???!
?h ln
?
?!
– 1
2 + ?
?!
rb
mcf = 5.02
??
?
2
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 17
3.0
2.8 2 6. 2.4 2 2.
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1 1.
1.1
1.45
1.35
1.25
1.05
1.2
1.3
1.1
1.0
0.9
0.8
0.7
0.6
Z -factor
Pseudo reduced pressure
0.5
Pseudo reduced temperature
0.4
0.3
0.2
0.1
0
012345678
1 1. 5
1 0. 5
Fig. 1.6 The Z-factor correlation chart of Standing and Katz11 (Reproduced by courtesy
of the SPE of the AIME)
If the gas composition is not available, the Standing-Katz correlation can still be used
provided the gas gravity, based on the scale air = 1, at atmospheric pressure and at
60°F, is known (refer sec. 1.6). In this case fig. 1.7, is used to obtain the pseudo critical
pressure and temperature; then equs. (1.18) and (1.19) can be applied to calculate the
pseudo reduced parameters required to obtain the Z-factor from fig. 1.6.
SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 18
MISCELLANEOUS GASES
CONDENSATE WELL FLUID
PSEUDO CRITICAL PRESSURE, psia PERATURE, degrees Rankine M PSEUDO CRITICAL TE
GAS GRAVITY (Air = 1)
700
650
600
550
500
450
400
350
300
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Fig. 1.7 Pseudo critical properties of miscellaneous natural gases and condensate
well fluids19
c) Direct calculation of Z-factors
The Standing-Katz correlation is very reliable and has been used with confidence by
the industry for the past thirty-five years. With the advent of computers, however, there
arose the need to find some convenient technique for calculating Z-factors, for use in
gas reservoir engineering programs, rather than feeding in the entire correlation chart
from which Z-factors could be retrieved by table look-up. Takacs14 has compared eight
different methods for calculating Z-factors which have been developed over the years.
These fall into two main categories: those which attempt to analytically curve-fit the
Standing-Katz isotherms and those which compute Z-factors using an equation of
state. Of the latter, the method of Hall-Yarborough15 is worthy of mention because it is
3
Table 1. Estimated PVT parameters
Pressure, psia Bo, rb/stb Rs, scf/stb Bg, rb/mcf
4530 1.674 1240
4130 1.686 1240
3730 (Pbp) 1.699 1240 0.766
3420 1.626 1120 0.815
3100 1.555 990 0.888
2770 1.486 870 0.980
2430 1.418 740 1.111
Conversion Factors
Force
1 dyne = 1 g cm/s2
1 N = 1 kg m/ s2 = 105 dyne = 0.2248 lbf
1 lbf (pound-force) = 32.17 lbm ft/ s2 = 4.448 N
Length
1 mi (mile) = 5280 ft
1 ft (foot) = 12 in = 30.48 cm
1 in (inch) = 2.54 cm
0.001 in = 25.4 um (micrometers)
1 m (meter) = 100 cm = 106 um
Permeability
1 d (darcy) = 1000 md (millidarcy) = 0.9869 x 10-8 cm2
Pressure
1 Pa (Pascal) = 1 N/m2
1 psi = 1 lbf/in2
1 bar = 14.504 psi = 0.9869 atm = 106 dyne/cm2
1 atm = 14.696 psi = 1.0133 x 106 dyne/cm2 = 1.0133 x 105 Pa
1000 psi = 6.89 MPa = 6,890 kPa
Time
1 day = 86,400 s
Viscosity
1 poise = 100 cp = 1 g/cm/s
1 cp = 0.01 g/cm/s
1 Pa-s (Pascal-second) = 10 poise
1 mPa-s (milliPascal-second) = 1 cp
Volume
1 Bbl = 5.615 ft3
1 ft3 = 28,317 cm3