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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

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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