PE04025_QA

MINISTRY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION

Sample Questions & Worked Out Examples For

PE-04025 RES RESERVOI RVOI R ENGI ENGI NEE NEERI NG ( I )

B.Tech(Second Year)

Petroleum Engineering

30

Ministry of Science and Technology Department of Technical and Vocational Education Petroleum Engineering Sample Questions for PE 04025 RESERVOIR ENGINEERING I Chapter 1

1.*** The following experimental data were taken in determining the gas constant. An evacuated glass flask weighs 50g. Filled with pure nitrogen at 14.40 psia and 60 °F, it weighs 51.16g. Filled with distilled water at 60 ° F, it weights 1050g. Calculate the gas constant from these data. (5 marks) 2.* Calculate the volume of one pound mole of ideal gas will occupy at (a) 14.7 psia and 60 °, (b) 14.7 psia and 32°F, (c) 14.7 psia plus 10 oz and 80 °,and (d) 15.025 psia and 60 °F. (10 marks) 3.* A 1000 cubic-foot tank is filled with air to a pressure of 25 psia at 140 °F. Calculate and  place in tabular form for comparison, the molecular weight, specific gravity, pound moles in the tank, pound in the tank, molecules in the tank, SCF at 14.7 psia and 60 °F, SCF at 14.7 psia and 32°, SCF at 14.7 psia +10oz and 80 °F, and SCF at 15.025 psia and 60 °F, for air, carbon dioxide, methane, and propane. (10 marks ) 4.** A 500 cubic-foot tank contains 10 lb of ethane at 90 °F. (a) How many moles are in the tank? (b) What is the pressure of tank in psia ? (c) What is the molecular weight of mixture. (d) What is the specific gravity of mixture. (10 marks) 5.*** Calculate the molecular weight of air if it contains 78.06 per cent nitrogen, 21.0 per cent oxygen, and 0.94 per cent argon by volume. ( 5 marks ) 6.*** What are the molecular weight and specific gravity of a gas which contains one third each of methane, ethane, and propane by volume. (5 marks) 7.** A ten-pound block of Dry Ice (solid CO 2) is placed in a 50 cubic-foot tank which contains air at atmospheric pressure 14.7 psia and 75 °F. What will be the final pressure of the sealed tank  when all the Dry Ice has evaporated and cooled the gas to 45 °F? (5 marks ) 8.* (a) A 55,000 bbl (nominal) pipe line tank has a diameter of 110 ft and a height of 35 ft. It contains 25 ft of oil at the time suction is taken on the oil with pumps which handle 20,000 bbl per  day. The breather and safety valves have become clogged so that a vacuum is drawn on the tank. If the roof is rated to withstand ¾ oz per sq in. pressure ,how long will it be before the roof  collapses? Barometric pressure is 29.1 inches. Neglect the fact that the roof is peaked and that there may be some leak. (b) Calculate the total force on the roof at the time of collapse. (c) If the tank had contained more oil, would the collapse time have been greater or less? Explain. (20 marks) 9.* What is the molecular weight of a gas which contains 50 per cent C 1, 30 per cent C 2, and 20 per cent C3 by weight? (5 marks ) 10.* What volume will 100 lb of a gas of 0.75 specific gravity ( air = 1.0 ) at 100 psia and 100°F ? (5 marks ) 11.* A 10 cubic-foot tank contains ethane at 25 psia surrounding a balloon 2 ft in diameter  filled with methane at 35 psia. Neglecting the volume of the rubber in the balloon and assuming isothermal conditions, calculate the final pressure when the balloon is burst. (10 marks )

31

12.** (a) What per cent methane by weight does a gas of 0.65 specific gravity contain which composed only of methane and ethane? What per cent by volume. (b) Explain why the per cent by volume is greater than the per cent by weight? ( 5 marks ) 13.* (a) A 1500 cubic-foot tank contains methane at 30 psia and 80 °F. To it are added: 1.80 moles of ethane at 14.4 psia and 60 °F, 25 lb of butane at 75°F, 4.65× 1026 molecules of propane at 30°F, and 500 SCF(14.7 psia and 60 °F) of nitrogen. If the final temperature of the mixture is 60°F, what is the final pressure of the tank? (b) Of what significance are the temperature given in the part (a), with the mole of ethane, the pound of butane, and the molecules of propane? Explain. (20 marks) 14.* A 50 cubic-foot of tank contains gas at 50 psia and 50°F. It is connected to another tank  which contains gas at 25 psia and 50 °F. When the valve between the two is opened, the pressure is equalizes at 35 psia at 50 °F. What is the volume of other tank ? (5 marks ) 15.** A high-pressure cell has a volume of 0.330 cu ft and contains gas at 2500 psia and 130 °F, at which conditions its deviation factor is 0.75. When 43.6 SCF measured at 14.7 psia and 60 °F are bled from the cell through the wet test meter, the pressure dropped to 1000 psia , the temperature remaining at 130 °F. What is the gas deviation factor at 1000 psia and 130 °F? (10 marks) 16.* (a) Calculate the bulk volume of the gas cap of a reservoir whose aerial extent is 940 acres, i.e., the area enclosed by the zero thickness contour. The areas enclosed by the 4,8,12,16,and 20-ft isopach lines are 752 ,526,316,142, and 57 acres, respectively. The greatest thickness within the 20-ft isopach line is 23 ft . (b) Show that when the ratio of the area enclosed  by two successive contours is 0.50, the error introduced by using the trapezoidal formulae is 2 per  cent greater than the pyramidal formula. (c) What error is introduced by using the trapezoidal formula instead of the pyramidal formula when the ratio of the areas is 0.333? (20 marks) 17.** A volumetric gas field has an initial pressure of 4200 psia, a porosity of 17.2 per cent , and connate water of 23 per cent. The gas volume factor at 4200 psia is 292 SCF/cu ft and at 750 psia is 54 SCF/cu ft. (a) Calculate the initial in place gas in standard cubic feet on a unit basis. (b) Calculate the initial gas reserve in standard cubic feet on a unit basis, assuming an abandonment  pressure of 750 psia . ( 10 marks ) 18.* A volumetric gas field has an initial pressure of 4350 psia, a porosity of 16.75 per cent , and connate water of 20 per cent. The gas volume factor at 4350 psia is 285 SCF/cu ft and at 755  psia is 57.5 SCF/cu ft. (a) Calculate the initial reserve of a 640-acre unit whose average net  productive formation thickness is 34 ft, assuming an abandonment pressure of 755 psia. (b) Calculate the recovery factor based on abandonment pressure of 755 psia. (10 marks) 19.* The “M” Sand is a small gas reservoir with an initial bottom-hole pressure of 3200 psia and bottom-hole temperature of 220 °F. It is desired to inventory the gas in placed at three  production intervals. The pressure production history and gas volume factor in cu ft/SCF at standard condition of 14.7 psia and 60 °F are as follows; Pressure Cumulative gas Production Gas volume factor   psia MM CF cu ft / SCF 3200 0 0.0052622 2925 79 0.0057004 2525 221 0.0065311 2125 452 0.0077360 (c) Calculate the initial gas in place using production data at the end of each of the  production intervals, assuming volumetric behavior. (b) Explain why the calculations of the part (a) indicate a water drive. (10 marks)

32

20.** The gas cap of the “ S.J ”oil field had a bulk volume of 17000 ac-ft when the reservoir   pressure had declined to the 634 psig. Core analysis shows an average porosity of 18 per cent, and average interstitial water of 24 per cent. It is desired to increase the recovery of oil from the field  by repressuring the gas cap to 1100 psig. Assuming that no additional gas dissolves in the oil during repressuring, calculate the SCF (14.7psia and 60 °F) required. The deviation factor for both the reservoir gas and the injected gas are 0.86 at 634 psig and 0.78 at 1100 psig, both at 130 °F. (10 marks) 21.** (a)A well drilled in to a gas cap for recycling purposes is found to be in an isolated fault  block. After injecting 50MM SCF (14.7psia and 60°F), the pressure increased from 2500 to 3500psia. Deviation factors for the gas are 0.90 at 3500 and 0.80 at 2500 psia and the bottom hole temperature is160°F. What the cubic feet of gas storage space in the fault block? (b) If the average  porosity is 16 per cent, average connate water is 24 per cent, and average sand thickness is 12 ft, what is the aerial extent of the fault block? (10 marks) 22.* A gas reservoir under partial water drive produced 12.0MMM SCF (14.7psia and 60 • F) when the average reservoir pressure had dropped from 3000psia to 2200psia. During the same interval an estimated 5.20MM bbl of water entered the reservoir based on the volume of the invaded area. If the gas deviation factor at 3000psia and bottom-hole temperature of  170• F is 0.88 and at 2200psia is 0.78, what is the initial volume of gas in place measured at 14.7psia and 60 • F? ( 10 marks ) 23.** A gas-producing formation has a uniform thickness of 32 ft, a porosity of 19 per cent, and connate water saturation of 26 percent. The gas deviation factor is 0.83 at the initial reservoir   pressure of 4450psia and reservoir temperature of  175• F. (S.C. 14.7psia and 60 • F) (a) Calculate the initial in-place gas per acre-foot of bulk reservoir rock. (b) How many years will it take a well to deplete by 50 percent a 640-acre unit at the rate of 3MM SCF/day? (10 marks ) 24.** Calculate the daily gas production including the condensate and water gas equivalents for  a reservoir with the following daily production. Separator gas production = 6MM SCF Condensate production = 100 STB Stock tank gas production = 21M SCF Fresh water production =10bbl Initial reservoir pressure = 6000psia Current reservoir pressure = 2000psia Reservoir temperature = 225• F Water vapor content at 6000psia and 225• F = 0.86 bbl/MM SCF Condensate gravity = 50ο API (10 marks ) 25.* A gas condensate reservoir initially contains 1300 MSCF of residue ( dry or sale gas ) per  ac-ft and 115 bbl of condensate. Gas recovery is calculated to be 85 per cent and condensate recovery 58 per cent by depletion performance. Calculate the value of initial gas and condensate reserves per ac-ft if the condensate sells for $ 2.50/bbl and the gas sells for 20 cent / MSCF. (10 marks) 26.** A well produces 45.3 bbl of condensate and 742 MSCF of sales gas daily. The condensate has a molecular weight of 121.2 and gravity of 52.0 ° API at 60F. (a) What is the gas oil ratio on dry gas basis? (b) What is the liquid content expressed in bbl/MMSCF on a dry gas basis? (c) What is the liquid content expressed in GPM on a dry gas basis? (10 marks) 27.* The initial daily production from a gas-condensate reservoir is 186 bbl of condensate, 3750 MSCF of high pressure gas, and 95 MSCF 0f stock tank gas. The tank oil has a gravity of  51.2° API at 60° F. The specific gravity of the separator is 0.712 and of the stock tank gas, 1.30.

33

The initial reservoir pressure is 3480 psia and reservoir temperature is 220 °F. Average hydrocarbon porosity is 17.2 per cent . Assume standard condition of 14.7 psia and 60 °F. (a) What is the average gravity of the produced gases? (b) What is the initial gas oil ratio? (c) Estimate the molecular weight of the condensate? (10 marks) 28.** In a  PVT  study of a gas-condensate fluid 17.5 cu cm of wet gas (vapor) measured at cell  pressure of 2500 psia and temperature of 195 °F was displaced into an evacuated low-pressure receiver of 5000 cu cm volume which was maintained at 250 °F to insure that on liquid phase developed in the expansion. If the pressure of the receiver rose to 620mm Hg, what is the deviation factor of the gas in the cell at 2500 psia and 195 °F, assuming the gas in the receiver   behaved ideally? (10 marks ) 29.** Calculate the contents of a tank of ethane in moles, pounds, molecules, and SCF. Data are as a 500 cu ft tank of ethane at 100 psia and 100 °F. (5 marks ) 30.* Calculate the gas deviation factor of the Bell Field gas from its specific gravity. Use the Fig.1.2 and Fig.1.3 of textbook. The required data are as follows: Specific gravity = 0,665 (air =1.0) , CO 2 content = 0.10 mole per cent  N2 content = 2.07 mole per cent, Reservoir temperature = 213 °F Reservoir pressure = 3250 psia (10 marks ) 31.** Calculate the net volume of an idealized reservoir from the isopachous map data (planimetered areas): Area (acres)

A0 450 -

A1 375 5

A2 303 5

A3 231 5

A4 154 5

A5 74 5

A6 0 Interval (ft) 4 ( 5 marks ) 32.* Calculate the initial gas reserve of a 160 acre unit of the Bell Gas Field by volumetric depletion and under partial and complete water drive. The required data are given as follows: Average porosity = 22 %, Connate water = 23 % , Areas = 160 acres ,  Net productive thickness = 40 ft, Bgi =188.0 SCF/ cu ft at pi =3250 psia Bg =150.0 SCF/ cu ft at 2500 psia and 27. 6 SCF/ cu ft at 500 psia, Residual gas saturation after water displacement = 34 % (10 marks ) 33.* Calculate the initial gas in place and the initial reserve of a gas reservoir from pressure  production data for a volumetric reservoir. Required data are as follows: Initial pr. = 3250 psia , Reservoir temp. = 213 °F , Standard pr. =15.025 psia , Standard temp. = 60 °F , 9 Cumulative production = 1.0 × 10 SCF, Avg. res. pr. = 2864 psia , Gas deviation factor at 3250 psia =0.910 , Gas deviation factor at 2864 psia =0.888 , Gas deviation factor at 500 psia = 0.951 . (10 marks) 34.** Calculate the water influx and residual gas saturation in water drive reservoir. Required data are as follows: Average porosity = 0.172 , Average connate water = 0.25 , Initial pressure = 3200 psia, Final pressure = 2925 psia, Bw = 1.03 bbl/STB , G p = 935.4 MMSCF at 14.7 psia and 60°F , Bgi = 0.005262 cu ft/SCF,14.7 psia and 60 °F , Bgf  = 0.005700 cu ft/SCF, 14.7 psia and 60 °F, Cumulative water production = 15200 bbl (surface) , Bulk volume invaded by water at 2925 psia = 13.04 MMCF.

34

Bulk reservoir volume, initial = 415.3 MMCF,

(10 marks)

35.* Calculate the total daily gas production including the gas equivalents of water and condensate. Required data are as follows: Initial reservoir pressure = 4000 psia , Reservoir temperature = 220°F , Current reservoir pressure = 1500 psia, Condensate gravity = 55 °API (0.759 sp. gr) Daily gas saperator production = 3.25 MMSCF, Daily stock tank gas =10 MSCF , Daily stock tank condensate = 53.2 STB , Daily fresh water production = 5.5 bbl (10 marks) 36.** The “M” Sand is a small gas reservoir with an initial bottom-hole pressure of 3200 psia and bottom-hole temperature of 220 °F. It is desired to inventory the gas in placed at three  production intervals. The pressure production history and gas volume factor in cu ft/SCF at standard condition of 14.7 psia and 60 °F are as follows; Pressure Cumulative gas Production Gas volume factor   psia MM CF cu ft / SCF 3200 0 0.0052622 2925 79 0.0057004 2525 221 0.0065311 2125 452 0.0077360 (a) Show that a water drive exists by plotting the cumulative production versus p/z. (b) Based on electric log and core data , volumetric calculations on the “ M “ Sand showed that initial volume of gas in place is 1018 MMSCF . If the sand is under the partial water drive, what is the volume of  water encroached at the end of each of the periods? There was no appreciable water production. ( 20 marks ) 37.** The gas cap of the “ S.J ”oil field had a bulk volume of 17000 ac-ft when the reservoir   pressure had declined to the 634 psig. Core analysis shows an average porosity of 18 per cent, and average interstitial water of 24 per cent. It is desired to increase the recovery of oil from the field  by repressuring the gas cap to 1100 psig. Assuming that no additional gas dissolves in the oil during repressuring, calculate the SCF (14.7psia and 60 °F) required. The deviation factor for both the reservoir gas and the injected gas are 0.86 at 634 psig and 0.78 at 1100 psig, both at 130 °F. If  injected gas has a deviation factor 0.94 at 634 psig and 0.88 at 1100 psig, and the reservoir gas deviation factors are as above, recalculate the injected gas required. (20 marks) 38.** The initial daily production from a gas-condensate reservoir is 200 bbl of condensate, 3700 MSCF of high pressure gas, and 100 MSCF 0f stock tank gas. The tank oil has a gravity of  51.2° API at 60° F. The specific gravity of the separator is 0.712 and of the stock tank gas, 1.30. The initial reservoir pressure is 3475 psia and reservoir temperature is 223 °F. Average hydrocarbon porosity is 17.5 per cent . Assume standard condition of 14.7 psia and 60 °F. (a)Calculate the specific gravity (air = 1.0) of the total well production. (b)Calculate the gas deviation factor of the initial reservoir fluid at initial reservoir pressure. (c)Calculate the initial moles in place per ac-ft. (10 marks ) 39.** Calculate the initial gas reserve of a 225 acre unit of the “ X “ gas field by volumetric depletion and under partial and complete water drive. The required data are given as follows: Average porosity = 18.75 %, Connate water = 22.35 % , Areas = 225 acres ,  Net productive thickness = 30 ft, Bgi =188.0 SCF/ cu ft at pi =3250 psia Bg =150.0 SCF/ cu ft at 2500 psia and 27. 6 SCF/ cu ft at 500 psia, Residual gas saturation after water displacement = 27.5 % (10 marks ) 40.* Calculate the initial oil and gas in place per acre-foot for a gas condensate reservoir.

35

Given: Initial pressure 2740 psia Reservoir temperature 215°F Average porosity 25% Average connate water 30% Daily tank oil 242bbl Oil gravity , 60°F 48°API Daily separator gas 3100MCF Separator gas gravity 0.650 Daily tank gas 120MCF Tank gas gravity 1.20 (10 marks ) 41.* The initial daily production from a gas-condensate reservoir is 200 bbl of condensate, 3700 MSCF of high pressure gas, and 100 MSCF 0f stock tank gas. The tank oil has a gravity of  51.2° API at 60° F. The specific gravity of the separator is 0.712 and of the stock tank gas, 1.30. The initial reservoir pressure is 3475 psia and reservoir temperature is 223 °F. Average hydrocarbon porosity is 17.5 per cent . Assume standard condition of 14.7 psia and 60 °F.(a) Calculate the more fraction which is gas in the initial reservoir fluid. (b) Calculate the initial (sales) gas and condensate in place per acre-foot. (10 marks ) 42.*** Gas was contracted at 5.5 cents per MCF at contract conditions of 14.4 psia and 80 °F. What is the equivalent price at a legal temperature of 60 °F and pressure of 15.025 psia? (5 marks ) 43.** A gas producing formation has a uniform thickness of 32 ft, a porosity of 19%, and connate water saturation of 26%. The gas deviation factor is 0.83 at the initial reservoir pressure of 4450 psia and reservoir temperature of 175 °F.(S.C.14.7 psia and 60°F ). (a) If the reservoir is under an active water drive so that the decline in reservoir pressure is negligible, and during the  production of 50.4MMM SCF of gas, measured at 14.7psia and 60 • F, water invades 1280 acres, what is the per cent recovery by water drive? (b) What is the gas saturation as per cent of total  pore space in the water invaded portion of the reservoir? (10 marks ) 44.* The initial volume of gas in place in the ' P' sand reservoir of the Holden Field is calculated from electric log and core data to be 200MMMSCF (14.7 psia and 60 °F) underlying 2250 productive acres, at the initial pressure of 3500 psia and 140 °F. The pressure-production history is Pressure, psia Production ( MMMSCF ) Gas deviation factor at 140°F 3500 ( initial ) 0.0 0.85 2500 75.0 0.82 (a) What is the initial volume of gas in place as calculated from the pressure-production history assuming no water influx? (b) Assuming uniform sand thickness, porosity, and connate water, if  the volume of gas in place from pressure-production data is believed to be correct, how many acres of extension to the present limits of the " P " Sand are predicted? (c) If, on the other hand, the gas in place calculated from the log and core data is believed to be correct, how much water  influx must have occurred during the 75MMMSCF of production to make the two figures agree? (20 marks) 45.** Calculate the contents of a tank of ethane in moles, pounds, molecules, and SCF. Given a 1500 cu-ft tank of ethane at 325 psia and 120 °F. (10 marks ) 46.** Calculate the gas deviation factor of the Bell Field gas from its specific gravity. Given data are the following. Specific gravity 0.75, CO 2 content is 0.15 moles per cent, N 2 content is 2.2 moles per cent, reservoir temperature 200 °F, reservoir pressure 3500 psia. Used the Fig.1.2 and Fig.1.3. (10 marks ) 47.* Calculate the gas deviation factor for the gas-condensate fluid whose composition at 5280  psia and 265°F is given as follows: Component C1 C2 C3 C4 C5 C6 C+7 Gas condensate 87.07 4.39 2.29 1.74 0.83 0.60 3.80 + Mol. wt C 7 225 181 112 157 … GOR, SCF/bbl 625 2000 18200 105000 Inf.

36

Tank gravity, API

34.3

50.1

60.8

54.7

(10 marks)

48.* Calculate the gas deviation factor for the " Z " Field gas from its composition given below. Used the Fig.1.2 and 1.3. Component Comp: Mole Fraction Mol: wt Pc Tc Methane 0.8612 16.04 673 343 Ethane 0.0591 30.07 708 550 Propane 0.0358 44.09 617 666 Butane 0.0172 58.12 550 766 Pentane 0.0050 72.15 490 846 CO2 0.0010 44.01 1070 548  N2 0.0207 28.02 492 227 (20 marks ) 49.** Calculate the initial oil and gas in place per acre-foot for a gas condensate reservoir. Given data are as follows: Initial pressure ………………………………………2740psia Reservoir temperature ……………………………… 215 ο F Average porosity……………………………………..25 per cent Average connate water……………………………….30 per cent Daily tank oil…………………………………………242 bbl Oil gravity, 60 ο F  …………………………………… 48.0 ο API Daily separator gas……………………………………3100 MCF Separator gas gravity………………………………….0.650 Daily tank gas …………………………………………120 MCF Tank gas gravity……………………………………….1.20 Use the Fig.1.2 and 1.3. (10 marks) 50.*

A 725 cubic-foot tank contains 12.5-lb of methane and 21.5-lb of ethane at 95 °F. (c) How many moles are in the tank? (d) What is the pressure of the tank in psia ? psig ? (e) What is the molecular weight of the mixture? (f) What is the specific gravity of the mixture? (10 marks)

* = Must know, ** = Should know, *** = Could know

37

Ministry of Science and Technology Department of Technical and Vocational Education Petroleum Engineering Worked Out Examples for PE 04025 RESERVOIR ENGINEERING I

1. Calculate the contents of a tank of ethane in moles, pounds, molecules, and SCF. Data are as a 500 cu ft tank of ethane at 100 psia and 100 °F. Solution:

Assuming ideal gas behavior, Moles Pounds Molecules

=

100 × 500

= 8.324

10.732 × 559.7

= 8.324 × 30.07 = 250.3

= 8.324 × 2.733 × 1026 = 2.275 × 1027

At 14.7 psia and 60°F, SCF = 8.324 ×379.4 = 3158 SCF =

SCF =

(or)

100 × 500 × 519.7 = 3158 (or) 559.7 × 14.7 nRT 

=

8.324 × 10.73 × 519.7

= 3157

14.7

 p

2. Calculate the gas deviation factor of the Bell Field gas from its specific gravity. Use the Fig.1.2 and Fig.1.3 of text book. The required data are as follows: Specific gravity = 0,665 (air =1.0), CO 2 content = 0.10 mole per cent  N2 content = 2.07 mole per cent , Reservoir temperature = 213F Reservoir pressure = 3250 psia Solution: are

From the Fig .1.2 the critical pressure and temperature corrected for CO 2 and N2

 pc = 669 – ( 2.07 × 1.7 ) + (0.10 = 666 psia Tc = 378 – ( 2.07 = 373°R 

×

×

2.5 ) - ( 0.10

4.4 )

×

0.8 )

For 3250 psia and 213 °F, pseudoreduced pressure and pseudoreduced temperature are

38

 pr  =

 p  pc

=

3250 666

= 4.88 , Tr  =

460 + T  T c

=

460 + 213 373

= 1.80 Enter Fig.1.3 with the values of pr  = 4.88, and Tr  = 1.80 . Then we obtain the value of z = 0.90 .

3. Calculate the gas deviation factor for the " Z " Field gas from its composition given below. Used the Fig.1.2 and 1.3. Component Methane Ethane Propane Butane Pentane CO2  N2

Comp: Mole Fraction 0.8612 0.0591 0.0358 0.0172 0.0050 0.0010 0.0207

Mol: wt 16.04 30.07 44.09 58.12 72.15 44.01 28.02

Pc

Tc

673 708 617 550 490 1070 492

343 550 666 766 846 548 227

Solution :

Mole Fraction × Mol: wt Mole Fraction × Pc Mole Fraction × Tc 13.81 579.59 295.39 1.78 41084 32.51 1.58 22.08 23.84 1.00 9.46 13.18 0.36 2.45 4.23 0.04 1.07 0.55 0.58 10.18 4.70 ................ ........................ .................... 19.15 666.67 374.40 The specific gravity may be obtained from the sum 19.15 , which is the average molecular weight of the gas , 19.15

= 0.661 28.97 The sum 666.67 and 374.40 are the pseudocritical pressure and temperature, respectively. Then at 3250 psia and 213°F, the pseudocritical pressure and temperature

SG

=

39

 P r 

=

3250 666.67

=

4.87

673

= 1.80 374.4 The gas deviation factor using Fig. 1.3 is z = 0.91

T r 

=

4. Calculate the initial gas reserve of a 160-acre unit of the Bell Gas Field by volumetric depletion and under partial and complete water drive. Given Average porosity = 22  per cent Connate Water = 23 per cent Residual gas saturation after water displacement = 34 per cent Bgi = 188.0 SCF / cuft at Pi = 3250 psia Bg = 150.0 SCF / cuft at 2500 psia = 27.6 SCF / cuft at 500 psia Area = 160 acres  Net productive formation = 40 ft Solution :

Pore Volume = 43560 × 0.22 × 160 × 40 = 61.33 × 106 cu ft Initial gas in place ; G1 = 61.33 × 106 × ( 1- 0.23 ) × 188.0 = 8878 MMSCF Gas in place after volumetric depletion to 2500 psia ; G2 = 61.33 × 106 × ( 1- 0.23 ) × 150.0 = 7084 MMSCF Gas in place after volumetric depletion to 500 psia ; G3 = 61.33 × 106 × ( 1- 0.23 ) × 27.6 = 1303 MMSCF Gas in place after water invasion at 3250 psia; G4 = 61.33 × 106 × 0.34 × 188.0 = 3920 MMSCF Gas in place after water invasion at 2500 psia; G5 = 61.33 × 106 × 0.34 × 150 = 3128 MMSCF Initial reserve by depletion to 500 psia ; G1 – G3 = ( 8878 – 1303 ) × 106 = 7575 MMSCF Initial reserve by water drive at 3250 psia ; G1 – G4 = ( 8878 – 3920 ) × 106 = 4958 MMSCF Initial reserve by water drive at 2500 psia ; ( G1 – G2 ) + ( G 2 – G5 ) = ( G1 – G5 ) = ( 8878 – 3128 ) × 106 = 5750 MMSCF If there is one updip well, the initial reserve by water drive at 3250 psia is

40

1 2

1

(G–G)=

( 8878 – 3920 )

×

2 = 2479 MMSCF

106

5. Calculate the initial gas in place and the initial reserve of a gas reservoir form pressure production data for a volumetric reservoir. Given; Initial Pressure = 3250 psia Reservoir temperature = 213°F Standard temperature = 60° F Standard pressure = 15.025 psia Cumulative production = 1.00 × 109 SCF Average reservoir pressure = 2864 psia Gas deviation factor at 3250 psia = 0.910 Gas deviation factor at 2864 psia = 0.888 Gas deviation factor at 500 psia = 0.951 Solution;

The reservoir gas pore volume V i 15.025 × 1.00 × 10 9 520

3250 × V i

=

0.910 × 673

−

2864V i 0.888 × 673

Vi = 56.17 MM cu ft The initial gas in place is G

=

 P iV i

×

 z i T 

T  sc

=

3250 × 56.17 × 10 6 × 520 0.910 × 673 × 15.025

 p sc

= 10.32 MMSCF 

The gas remaining at 500 psia abandonment pressure is Ga

=

 P aV i  z aT 

×

T  sc  p sc

=

500 × 56.17 × 10 6 × 520 0.951 × 673 × 15.025

= 1.52 MMSCF 

The initial gas reserve based on a 500 psia abandonment pressure is the difference  between the initial gas in place and remaining at 500 psia or  Gr  = G - Ga = (10.32 – 1.52 ) × 109 = 8.80 MMSCF 6. Calculate the water influx and residual gas saturation in water drive reservoir. Required data are as follows: Average porosity = 0.172 , Average connate water = 0.25 , Initial pressure = 3200 psia, Final pressure = 2925 psia, G p = 935.4 MMSCF at 14.7 psia and 60°F , Bgi = 0.005262 cu ft/SCF, 14.7 psia and 60 °F ,

41

Bgf  = 0.005700 cu ft/SCF, 14.7 psia and 60 °F, Bw = 1.03 bbl/STB , Cumulative water production = 15200 bbl (surface) , Bulk volume invaded by water at 2925 psia = 13.04 MMCF. Bulk reservoir volume, initial = 415.3 MMCF, Solution:

Initial gas in place = G =

415.3 × 10 6 × 0.172 × (1 − 0.25)

0.005262 = 10180 MMSCF at 14.7 psia and 60° F

We = 935.4 × 106 × 0.005700 - 10,108 × 106 = ( 0.005700 – 0.005262 ) + 15200 × 1.03 ×5.615 = 960400 cu ft This much water has invaded 13.04 MM cu ft of bulk rock, which initially contained 25  per cent connate water. Then the final water saturation of the flooded portion of the reservoir is S w

=

Connatewat er  + Water inf lux  Porespace

=

(13.04 × 10 6 × 0.172 × 0.25) + 960400 13.04 × 10 6 × 0.172

= 0.68 or 68 percent Then the residual gas saturation S gr is 32 per cent. ------------------------------------7. Calculate the initial oil and gas in place per acre-foot for a gas condensate reservoir. Given data are as follows: Initial pressure ………………………………………2740psia Reservoir temperature ……………………………… 215ο F Average porosity……………………………………..25 per cent Average connate water……………………………….30 per cent Daily tank oil…………………………………………242 bbl Oil gravity, 60 ο F  …………………………………… 48.0 ο API Daily separator gas……………………………………3100 MCF Separator gas gravity………………………………….0.650 Daily tank gas …………………………………………120 MCF Tank gas gravity……………………………………….1.20 Use the Fig.1.2 and 1.3. Solution:

Average gas gravity =

3100 × 0.650 + 120 × 1.20 3100 + 120

=

0.670

42 γ  o =

 M o

=

 R

=

141.5

6084 48.0 − 5.9

0.7883

= 144.5

3100 + 120 242

γ  w =

=

48.0 + 131.5

× 1000 = 13300SCF  / bbl 

13300 × 0.670 + 4584 × 0.7883

=

13300 + 132800 × 0.7883 / 144.5

0.893

From Fig. 1.2 , Tc = 425°R , Pc = 652 psia using the condensate curves. Then Tr  = 1.59 and Pr  = 4.20 , from which, using Fig. 1.3, the gas deviation factor is 0.82 at 2740 psia and 215°F. Then the total initial gas in place per ac-foot of bulk reservoir rock is G

=

379.4 pV 

=

379.4 × 2740 × 43560 × 0.25 × (1 − 0.30) 0.82 × 10.73 × 675

 zRT 

= 1334

MCF/ac ft

Since the volume fraction equals the mole fraction in the gas state, the fraction of the total which is produced on the surface as gas is  f   g 

=

n g  n g  + no

 R / 379.4

=

 R / 379.4 + 350 × 0.7883 / 144.5

=

0.9483

Then, Initial gas in place = 0.9483 × 1334 = 1265 MCF/ac ft Initial oil in place =

1265 × 10 3 13300

=

95.1bbl / acft 

8. A gas condensate reservoir initially contains 1300 MSCF of residue ( dry or sale gas ) per acft and 115 bbl of condensate. Gas recovery is calculated to be 85 per cent and condensate recovery 58 per cent by depletion performance. Calculate the value of initial gas and condensate reserves per ac-ft if the condensate sells for $ 2.50/bbl and the gas sells for 20 cent / MSCF. Solution:

The value of initial condensate reserve = 115 × 0.58 = 66.7 bbl = 66.7 × 2.5 = $ 166.75 The value of initial gas reserve = 1300 ×0.85 = 1105 MSCF = 1105 × 0.20 = $ 221

43

9. A well produces 45.3 bbl of condensate and 742 MSCF of sales gas daily. The condensate has a molecular weight of 121.2 and gravity of 52.0 ° API at 60F. (a) What is the gas oil ratio on dry gas basis? (b) What is the liquid content expressed in bbl/MMSCF on a dry gas basis? (c) What is the liquid content expressed in GPM on a dry gas basis? Gas production rate = 742MSCF Condensate production rate = 45.3 bbl 742 × 10 3 (c) Gas-Oil ratio on a dry gas basis = = 16380 SCF/bbl 45.3 Solution:

(d) Liquid content in barrel per million standard cu ft on a dry gas basis Liquid content =

1bbl 

= 61.05bbl / millionSCF  16380SCF  1bbl  42 gal  (c) Liquid content in GPM = × × 1000 = 2.56 GPM 16380SCF  1bbl 

10. The initial daily production from a gas-condensate reservoir is 186 bbl of condensate, 3750 MSCF of high pressure gas, and 95 MSCF 0f stock tank gas. The tank oil has a gravity of  51.2° API at 60° F. The specific gravity of the separator is 0.712 and of the stock tank gas, 1.30. The initial reservoir pressure is 3480 psia and reservoir temperature is 220 °F. Average hydrocarbon porosity is 17.2 per cent . Assume standard condition of 14.7 psia and 60 °F. (a) What is the average gravity of the produced gases? (b) What is the initial gas oil ratio? (c) Estimate the molecular weight of the condensate? Solution:

(c)

Initial daily production of condensate = 186 bbl Stock tank gas = 95 M SCF High pressure gas = 3750 M SCF S.G of separator gas = 0.712 S.G of tank gas = 1.3 API = 52.1°, T = 60°F, Pi = 3480 psia , Ti = 220 °F , 95.3 × 1.3 + 3750 × 0.712 95 + 3750 = 0.727

Average gas gravity =

=

(95 + 3750) × 10 3

(d)

Initial GOR

(c)

Molecular weight of condensate Mo =

=

186

6084 51.2 − 5.9

=

= 20672 SCF/bbl 6084

 API  − 5.9

134.3

--------------------------------------

Φ = 17.2%