Tarek Ahmed. Reservoir engineering handbook

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pressure may be selected and Steps 1 through 6 are repeated. Oth-

erwise, assume another value of N

and repeat Steps 2 through 6.

Step 8. In order to simplify this iterative process, three values of N

can

be assumed, which yield three different solutions of cumulative

gas production for each of the equations (i.e., MBE and GOR

equation).When the computed values of G

are plotted versus the

assumed values of N

, the resulting two curves (one representing

results of Step 3 and the one representing Step 5) will intersect.

This intersection indicates the cumulative oil and gas production

that will satisfy both equations.

It should be pointed out that it may be more convenient to assume val-

ues of N

as a fraction of the initial oil in place N. For instance, N

could

be assumed as 0.01 N, rather than as 10,000 STB. In this method, a true

value of N is not required. Results of the calculations would be, there-

fore, in terms of STB of oil produced per STB of oil initially in place and

scf of gas produced per STB of oil initially in place.

To illustrate the application of Tarner’s method, Cole (1969) presented

the following example:

Example 12-6

A saturated-oil reservoir has a bubble-point pressure of 2100 psi at

175°F. The initial reservoir pressure is 2925 psi. The following data sum-

marizes the rock and fluid properties of the field:

Original oil in place = 10 MMSTB

Connate-water saturation = 15%

Porosity = 12 %

= 3.6 × 10

−6

psi

−1

= 4.9 × 10

−6

psi

−1

Basic PVT Data

p, psi B

, bbl/STB B

, bbl/STB R

, scf/STB B

, bbl/scf µ

/µ

2925 1.429 1.429 1340 — —

2100 1.480 1.480 1340 0.001283 34.1

1800 1.468 1.559 1280 0.001518 38.3

1500 1.440 1.792 1150 0.001853 42.4

818 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 818

Relative Permeability Ratio

, % k

81 0.018

76 0.063

60 0.85

50 3.35

40 10.2

Predict cumulative oil and gas production at 2100, 1800, and 1500 psi.

Solution

The required calculations will be performed under the following two

different driving mechanisms:

• During the reservoir pressure declines from the initial reservoir pressure

of 2925 to the bubble-point pressure of 2100 psi, the reservoir is con-

sidered undersaturated and, therefore, the MBE can be used directly to

cumulative production without restoring to the iterative technique.

• For reservoir pressures below the bubble-point pressure, the reservoir is

treated as a saturated-oil reservoir and Tarner’s method may be applied.

Phase 1: Oil recovery prediction above the bubble-point pressure

Step 1. Arrange the MBE (Equation 11-32) and solve for the cumulative

oil as:

where

= B

− B

cS c

fw oi

ww f

()=

−













−

NE E

ofw

+[]

(12 - 57)

Predicting Oil Reservoir Performance 819

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 819

Step 2. Calculate the two expansion factors E

and E

f,w

for the pressure

declines from 2925 to 2100 psi:

= 1.480 − 1.429 = 0.051

Step 3. Calculate cumulative oil and gas production when the reservoir

pressure declines from 2925 to 2100 psi by applying Equation

12-57, to give:

At or above the bubble-point pressure, the producing gas-oil ratio

is equal to the gas solubility at the bubble point and, therefore, the

cumulative gas production is given by:

= N

= (344,656) (1340) =462 MMscf

Step 4. Determine remaining oil in place at 2100 psi.

Remaining oil in place = 10,000,000 − 344,656 = 9,655,344 STB

This remaining oil in place is considered as the initial oil in place

during the reservoir performance below the saturation pressure,

i.e.:

N = 9,655,344 STB

= 0.0 STB

= 0.0 scf

= 1340 scf/STB

= 1.489 bbl/STB

= 0.001283 bbl/scf

N STB

×+×

−

10 10 0 051 9 1456 10

148

344 656

[. . ]

fw,

( . )( . ) ( . )

×+×

−













=×

−−

−

1 429

36 10 015 49 10

1015

9 1456 10

820 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 820

Phase 2: Oil recovery prediction above the bubble-point pressure

First prediction period at 1800 psi:

1. Assume N

= 0.01 N and apply Equation 12-54 to solve for G

2. Calculate the oil saturation, to give:

3. Determine the relative permeability ratio k

from the available data

to give:

= 0.0100

4. Calculate the instantaneous GOR at 1800 psi by appying Equation 12-55

to give:

5. Solve again for the cumulative gas production by using the average

GOR and applying Equation 12-56 to yield:

6. Since the cumulative gas production as calculated by the two indepen-

dent methods (Step 1 and Step 5) do not agree, the calculations must

be repeated by assuming a different value for N

and plotting results of

the calculation. The final results as summarized below show the cumu-

lative gas and oil production as the pressure declines from the bubble-

point pressure. It should be pointed out that the cumulative production

above the bubble-point pressure must be included when reporting the

total cumulative oil and gas production.

GNN

−=0

1340 1650

0 01 0 14 95(. ) .

GOR scf STB=+









=1280 0 0100 38 3

1 468

0 001518

1650.(.)

owi

=− −













=− −









=() (.)

.1 1 1 0 15 1

0 01 1 468

1 480

0 835

−− −×

( . . ) ( . )( . . )

1 559 1 480 0 01 1 559 1340 0 001518

0 001518

55 17

Predicting Oil Reservoir Performance 821

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 821

Pressure N

Actual N

, STB G

Actual G

, MMscf

1800 0.0393 N 379,455 64.34 N 621.225

1500 0.0889 N 858,360 136.6 N 1318.92

PHASE 2. RELATING RESERVOIR

PERFORMANCE TO TIME

All reservoir performance techniques show the relationship of cumula-

tive oil production and the instantaneous GOR as a function of average

reservoir pressure. These techniques, however, do not relate the cumula-

tive oil production N

and cumulative gas production G

with time. Fig-

ure 12-9 shows a schematic illustration of the predicted cumulative oil

production with reservoir pressure.

The time required for production can be calculated by applying the

concept of the inflow performance relation (IPR) in conjunction with the

822 Reservoir Engineering Handbook

Figure 12-9. Cumulative production as a function of average reservoir pressure.

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 822

MBE predictions. Vogel (1969) expressed the well’s inflow performance

relationship by Equation 7-9, or:

The following methodology can be employed to correlate the predict-

ed cumulative field production with time t.

Step 1. Plot the predicted cumulative oil production N

as a function of

average reservoir pressure p as shown in Figure 12-9.

Step 2. Construct the IPR curve for each well in field at the initial aver-

age reservoir pressure p*. Calculate the oil flow rate for the entire

field by taking the summation of the flow rates. Plot the flow

rates as shown schematically in Figure 12-10 for two hypothetical

wells and establish the IPR for the field.

=−













−

























() . .

max

102 08

Predicting Oil Reservoir Performance 823

Figure 12-10. Overall field IPR at current pressure.

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 823

Step 3. Using the minimum bottom-hole flowing pressure (p

)

min

, deter-

mine the total field flow rate (Q

)

Step 4. Select a future average reservoir pressure p and determine the

future IPR for each well in field. Construct the field IPR curve as

shown in Figure 12-11.

Step 5. Using the minimum p

, determine the field total oil flow rate

)

Step 6. Calculate the average field production rate (Q

–

)

Step 7. Calculate the time ∆t required for the incremental oil production

∆N

during the first pressure drop interval, i.e., from p* to p, by:

∆

()

() ()

oT oT

824 Reservoir Engineering Handbook

Figure 12-11. Future field IPR.

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 824

Step 8. Repeat the above steps and calculate the total time t to reach an

average reservoir pressure p by:

t =Σ∆t

PROBLEMS

1. Determine the fractional oil recovery, during depletion down to bub-

ble-point pressure, for the reservoir whose PVT parameters are listed

in Table 3-7 and for which:

= 3.5 × 10

−6

psi

−1

= 3.5 × 10

−6

psi

−1

= 0.20

2. The Big Butte field is a depletion drive reservoir that contains 25

MMSTB of oil initially in place. Tables 3-4 through 3-7 show the

experimental PVT data of the crude oil system. The initial reservoir

pressure is recorded as 1936 psi at 247°F. The relative permeability

ratio k

is given by:

= 0.007 e

11.513 Sg

Given

= 35% S

= 3% S

= 25%

Using a pressure drop increment of 200 psi, predict the reservoir

future performance in terms of:

• Cumulative oil production N

• Cumulative gas production G

• Oil saturation S

• Gas saturation S

• Instantaneous GOR

• Cumulative producing gas-oil ratio R

Plot results of the calculations to an abandonment pressure of 500

psi. Use the following three methods:

1. Tracy’s method

2. Muskat’s method

3. Tarner’s method

Predicting Oil Reservoir Performance 825

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 825

REFERENCES

1. Cole, F., Reservoir Engineering Manual. Houston: Gulf Publishing Compa-

ny, 1969.

2. Craft, B. C., and Hawkins, M. (revised by Terry, R. E.), Applied Petroleum

Reservoir Engineering, 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1991.

3. Dake, L. P., Fundamentals of Reservoir Engineering. Amsterdam, Elsevier,

1978.

4. Economides, M., Hill, A., and Economides, C., Petroleum Production Sys-

tems. Englewood Cliffs, NJ: Prentice Hall, 1994.

5. Havlena, D., and Odeh, A. S., “The Material Balance as an Equation of a

Straight Line,” JPT, August 1963, pp. 896–900.

6. Havlena, D., and Odeh, A. S., “The Material Balance as an Equation of a

Straight Line. Part II—Field Cases,” JPT, July 1964, pp. 815–822.

7. Hawkins, M., “Material Balances in Expansion Type Reservoirs Above Bub-

ble-Point,” SPE Transactions Reprint Series No. 3, 1955, pp. 36–40.

8. Muskat, M., “The Production Histories of Oil Producing Gas-Drive Reser-

voirs,” Journal of Applied Physics, 1945, Vol. 16, p. 167.

9. Tarner, J., “How Different Size Gas Caps and Pressure Maintenance Programs

Affect Amount of Recoverable Oil,” Oil Weekly, June 12, 1944, Vol. 144.

10. Tracy, G., Simplified Form of the MBE,” Trans. AIME, 1955, Vol. 204, pp.

243–246.

11. Vogel, J. V., “Inflow Performance Performance Relationships for Three-

Phase Flow,” SPE Paper 25458 presented at the SPE Production Operations

Symposium, Oklahoma City, March 21–23, 1993.

826 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 12 2001-10-25 16:04 Page 826

Reservoirs containing only free gas are termed gas reservoirs. Such a

reservoir contains a mixture of hydrocarbons, which exists wholly in the

gaseous state. The mixture may be a dry, wet, or condensate gas, depend-

ing on the composition of the gas, along with the pressure and tempera-

ture at which the accumulation exists.

Gas reservoirs may have water influx from a contiguous water-bearing

portion of the formation or may be volumetric (i.e., have no water

influx).

Most gas engineering calculations involve the use of gas formation

volume factor B

and gas expansion factor E

. Both factors are defined in

Chapter 2 by Equations 2-52 through 2-56. Those equations are summa-

rized below for convenience:

• Gas formation volume factor B

is defined is defined as the actual vol-

ume occupied by n moles of gas at a specified pressure and tempera-

ture, divided by the volume occupied by the same amount of gas at

standard conditions. Applying the real gas equation-of-state to both

conditions gives:

• The gas expansion factor is simply the reciprocal of B

, or:

==35 37. (13 - 2)

==0 02827. (13 -1)

827

CHAPTER 13

GAS RESERVOIRS

Reservoir Eng Hndbk Ch 13 2001-10-24 15:13 Page 827