Combination Drive

COMBINATION DRIVE RESERVOIRS Prof. T. Kumar Dept. of of Petr Petr oleum E ngg.

When a reservoir is being produced by the combination of two or more drive mechanisms, it is known as combination drive reservoir. Two combinations of driving forces are commonly found, namely, (a) depletion and a week water drive, and (b) depletion drive with a gas cap and a week water drive. Gravity segregation can play an important role in any of the other drives. The effects of gravity drainage are often difficult to evaluate and predict in most reservoir engineering studies, because, the main important equation for such studies, MB Equation can not be readily utilized to study gravity drainage effects. However, where this effect is to be accounted, its effects are incorporated in performance data like relative permeability curve. A field relative  permeability curve can be used which accounts for this effect.

Characteristics:

1. Relatively rapid pressure decline. Water encroachment and/or external gas cap expansion are insufficient to maintain ma intain reservoir pressures. 2. Water encroaching slowly into the lower part of the reservoir. Structurally low  producing wells will exhibit slowly increasing water producing rates. rates. 3. If a small gas cap is present the structurally high wells will exhibit continually increasing gas-oil ratios, provided the gas cap is expanding. It is possible that the gas cap will shrink due to production of excess free gas, in which case, the structurally high wells will exhibit a decreasing gas-oil ratio. This condition should  be avoided whenever possible, as large volumes of oil can be lost as a result of a shrinking gas cap. 4. As a substantial percentage of the total oil recovery may be due to the depletion drive mechanism, the gas-oil ratio of structurally low wells will also continue to increase due to evolution of gas from solution from oil throughout the reservoir as  pressure is reduced.

Figure below shows production history of a typical combination drive reservoir with a weak water drive and no initial free gas cap. Note that the producing gas-oil ratio remains relatively constant for a period of time. This indicates that the reservoir  pressure is above the saturation pressure. When the gas oil ratio begins to increase it is  probably due to the fact that the reservoir pressure has been reduced below the saturation pressure and the increasing gas-oil ratio is the result of evolution of dissolved gas from the oil.

E R U S R S E R

O

P

W

Pressure r o RI R O V

O

R

G

GOR E S E R

WOR

CUMULATIVE OIL PRODUCTION

FIG. 1 PRODUCTION HISTORY - COMBINATION DRIVE R ESERVOIR 

Ultimate recovery form combination drive reservoirs is usually greater than that from depletion drive reservoirs but less than that from water drive or gas cap drive reservoirs. Actual recovery will depend upon the degree to which it is possible to reduce the magnitude of recovery by depletion drive. In most combination drive reservoirs it will be economically feasible to institute some type of pressure maintenance operation, either gas injection, water injection, or both gas and water injection, depending upon the availability of the fluids.

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Indexes of Drives:

The efficiency of operation by various drive mechanisms in the combination drive is possible to be evaluated by rearranging the Material Balance equation. The generalized MBE is written as:

 N p [ Bo + ( R  p - R s ) Bg ] = N [mBoi (Bg/Bgi - 1) + (Bo - Boi ) + (R si - R s) Bg ] + (We -W p )

(1)

or N p Bo  = N (Bt - Bti) + m N Boi ( Bg/Bgi - 1) + (We - W p ) - N p (R  p - R s) Bg 

(2)

Bt = Bo + (R si - R s ) Bg 

(3)

 N(Bt - Bti ) = N[ (R si - R s) Bg + (Bo - Boi ) ]

(4)

and

LHS is the expansion of the original reservoir oil volume with all of its original dissolved gas. After reservoir pressure declines below saturation pressure, some of the original dissolved gas will be evolved from solution and will occupy space as free gas in the reservoir. Some of the free gas so evolved from the reservoir oil may be  produced.

The term N p (R  p - R s) Bg is the free gas produced which can be divided into two  parts gas cap gas production and free dissolved gas production.

Let ‘f’ be defined as the fraction of produced free gas which comes from the gas cap, then the free gas production can be separated as follows: Gas cap gas production = f N p (R  p - R s) Bg 

(5)

Free Dissolved Gas production = (1 - f) N p (R  p - R s) Bg 

(6)

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The term m N Boi (Bg/Bgi - 1) is the expansion of the original free gas cap. Some of the gas cap may be produced, given in the equation (5) will have to be subtracted to get gas cap expansion. Similarly N (Bt - Bti ) represents the expansion of the original reservoir oil with its dissolved gas, so free dissolved gas production given in the equation (6) will have to be subtracted from N (B t - Bti ) to get the net expansion of the original reservoir oil with all of its original reservoir dissolved gas. We - W p is the next water influx term. Rearranging the equation (2) as previously discussed yields:  N p Bo = [ N(Bt - Bti ) - (1 - f) N p (R  p - R s) Bg ] + [mNBoi (Bg/Bgi - 1) - f N p (R  p - R s) Bg ] + (We - W p )

(7)

The first bracket term in the equation (7) is the net expansion of the reservoir oil with its dissolved gas and the second bracketed term is the net gas cap expansion. Thus equation (7) shows that the reservoir oil produced is a result of the combined effect of (1) net expansion of the reservoir oil with its original dissolved gas, plus (2) the net gas cap expansion and, plus (3) net water encroachment. Dividing equation (7) by N p Bo :

1 =

+

+

[ N (Bt - Bti ) - (1 -f) N p (R  p - R s ) Bg ] ---------------------------------------------- N p Bo [ mNBoi (Bg/Bgi - 1 ) - f N p (R  p - R s) Bg ] ------------------------------------------------------ N p Bo

(We - W p ) ----------------- N p Bo

(8)

The three terms on RHS are the Depletion Drive, Gas cap Drive, and the Water Drive Index respectively.

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Determining the fraction of the produced gas which comes from the gas cap may be difficult at times, although usually enough production and reservoir engineering data will be available to satisfactorily determine this number. The usual method of determining f is to determine the change in gas-oil contact from producing wells, after which, with a knowledge of the reservoir size the amount of gas cap gas production can  be calculated.

The sum of the drive indexes will be equal to 1. Thus to increase one of them, the other(s) would have to be decreased. The approach should be to utilize the most efficient drive i.e. water drive and minimize depletion drive index. Where water drive is weak, then energy provided by gas cap expansion should be used. While utilizing the gas cap expansion energy, the conservation of gas cap must be considered for its effective utilization. This can be done by avoiding gas production from gas cap.

Water drive index can be increased by shutting in wells producing very large quantity of water. Reducing the oil production rate could result in an increased water drive index and correspondingly decreased depletion drive index containing a weak water drive.

The recovery by gas cap drive in general is not rate sensitive, as the gas is readily expansible. However, where the vertical permeability is low, the expansion of gas cap could be limited, hence, gas cap drive index could be rate sensitive.

Ideally, for more efficient reservoir operation, if the depletion drive index can  be reduced to zero, relatively good recovery can be expected from the reservoir. This is difficult, because, it requires complete maintenance of reservoir pressure. The drive indexes should be evaluated at regular intervals in order to understand the type of drives operative in the reservoir at various time intervals and also to take decisions to change them to get advantage of the drive mechanism which will have maximum efficiency.

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Predicting Reservoir Performance:

The method of predicting the future reservoir performance of the combination drive reservoir is same as of depletion drive reservoir given by Tarner. However, the MB equation and oil saturation equation have to be rewritten for combination drive reservoir.

1.

MBE which includes both an original free gas cap and water encroachment is:

 N p R  p = 1/Bg [ N(Bt - Bti ) + mN Boi ( Bg/Bgi - 1) + (We - W p) + N p R s Bg - N p Bo ]

2.

(9)

MBE which includes a weak water drive without an original free gas cap. A. Equation for pressures above the saturation pressure:

 N p/N

= (Bo -

Boi)/Bo + (We - W p)/NBo 

(10)

B. Equation for pressures below the saturation pressure:

 N(Bt-Bti ) + (We - W p) + N p R s Bg - N p Bo  N pR  p =

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

(11)

Bg

3. Oil Saturation Equation: Let

A1 = Average cross-sectional area of the gas-invaded position of the reservoir, acres. A2 = Average cross-sectional area of the water-invaded portion of the reservoir acres. h1 = Thickness of the gas-invaded zone in the reservoir, ft. h2 = Thickness of the water-invaded zone in the reservoir, ft.

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

= Porosity of the reservoir, fraction

Sorg = Residual oil saturation in the gas-invaded portion of the reservoir, fraction. Sorw  = Residual oil saturation in the water-invaded portion of the reservoir, fraction. So (at any time) Remaining oil in the Remaining oil zone =

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

(12)

Remaining oil zone size.

Remaining oil in the remaining oil zone = Total remaining oil zone -Oil volume in the  bypassed zone.

= (N - Np) Bo - [ 7758 A1h1  Sorg + 7758 A2 h2  Sorw ]

(13)

Also :

Remaining oil zone size = Original Oil zone size - Size of the bypassed zones

 NBoi =

---------- [ 7758 A1h1   + 7758 A2h2  )

(14)

1-Swi

Sq + Sorg + Swi = 1

(15)

or Sg, the increase in the gas saturation in the gas invaded zone over Swi

= 1 - Swi - Sorg 

(16)

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mN Boi (Bg/Bgi - 1 ) 7758 A1h1



=

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

(17)

1-Swi - Sorg

Similarly,

Sw + Swi + Sorw = 1

(18)

Sw’ Increase in water saturation in the water-invaded zone of the reservoir, above Swi

= 1 - Swi - Sorw 

(19)

We - W p 7758 A2h2



= -------------------

(20)

1-Swi - Sorw

Combining the equations (10), (13), (14), (17) and (20) results in

mNBoi(Bg / Bgi - 1 ) Sorg ( We - W p) Sorw (N-N p) Bo [ ----------------------------------- + ------------------1 - Swi - Sorg 1 - Swi - Sorw So = ----------------------------------------------------------------------------- NBoi mNBoi (Bg/Bgi - 1) We - W p -------- - ---------------------------- + --------------------1-Swi 1 - Swi - Sorg 1-Swi - Sorw

(21)

If the amount of gas cap gas which is produced is either known or can be assumed, then equation (21) can be modified to take this into consideration.

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(1-f)mNBoi(Bg/ Bgi - 1 ) Sorg ( We - W p) Sorw (N-N p) Bo - [ ----------------------------------- + ------------------- ] 1 - Swi - Sorg 1 - Swi - Sorw So = ----------------------------------------------------------------------------- NBoi  (1-f)mNBoi (Bg/Bgi - 1) (We - W p) -------- - [ ---------------------------- + --------------------- ] 1-Swi 1 - Swi - Sorg 1-Swi - Sorw

(22)

where

f = fraction of gas cap expanded volume which is produced. Where all of the expanded gas cap gas is produced equation (22) reduces to:

So =

(We - W p) Sorw (N-N p) Bo - -------------------1 - Swi - Sorw ----------------------------------------------- NBoi (We - W p) -----------------------------1- Swi 1-Swi - Sorw

(23)

It is very important to select the proper oil saturation equation, as the relative  permeability relationships are critical functions of oil saturation. Therefore, determination of correct oil saturation equation is an important step in a reliable  predication of reservoir performance.

4.

Instantaneous Gas-Oil Ratio equation which is used for prediction is given as:

R = K g/K o . o/g

.

Bo/Bg

+ R s 

(24)

As given earlier, the prediction will involve the calculation of gas produced by MBE and GOR eqn. independently for an assumed value of N p. If the values of gas  produced by both the equations are same, then the assumption of N p  is taken as the

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correct value, otherwise the calculation repeated with new assumed N p value till the correct value is obtained. This process is continued till the N p  value is reached corresponding to the abandonment pressure. Finally, Pressure vs N p  and GOR vs. N p are plotted as the performance curves.

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