Assignment 2 MBE

7/31/2019 Assignment 2 MBE

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Reservoir Engineering II (PCB2053)

Assignment 2

MATERIAL BALANCE EQUATIONS & APPLICATIONSDue date: 19 July 2012 during class hour

1. An undersaturated reservoir containing 4,843 Mstb of OIIP is discovered at 4,300 psia.At the bubble point pressure of 2,900 psia, 100 Mstb of oil have been produced.Assuming that all of the solution gas with its compliment of oil is produced, how muchoil would the reservoir produce by the time the pressure declines to 2, 000 psia? The PVTdata are in the following table.

Pressure (psia) Bo (rvb/stb) Bg (rvb/Mscf) Rs (Mscf/stb)2,000 1.36 1.14 0.732,900 1.42 1.03 0.944,300 1.40 0.87 0.94

2. For an undersaturated reservoir above the bubble point, P b, show that the overallcompressibility of the formation ( cf ), connate water ( cw) and oil ( co) can be summarized as

o

f wcwooeffective

S

cS cS cC

++=

3. 80 Mstb of oil and 60 MMscf of gas have been produced from a reservoir discovered at apressure of 4,200 psia., and the reservoir is currently at a pressure of 3,400 psia. Twodescriptions of the reservoir have been proposed. The first description states that there are245 Mstb of oil in place with a gas cap containing 1000 MMscf. The second descriptionindicates that there are 675 Mstb of initial oil in place and 1,500 MMscf of gas in place.Which description is correct? PVT data are in the following table.

Pressure(psia)

Oil formation vol.factor, B o (rvb/stb)

Gas formation vol.factor, B g (rvb/Mscf)

Solution gas-oil ratioRs

(Mscf/stb)3,400 1.28 0.89 0.900

4,200 1.34 0.86 1.250


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4. An undersaturated reservoir, which was discovered at initial pressure of 3685 psihas the following properties. Additionally,the field production and PVT data areshown in the following table. Using the straight line MBE (Havlena & Odeh method),determine the OIIP.S wi = 24%cw = 3.62 X 10 -6 psi -1 c f = 4.95 X 10 -6 psi -1

Bw = 1.0 res bbl/stbP b = 1500 psi

Avg Pres(psi)

B o (resbbl/stb)

N p (Mstb) W p (Mstb)

3685 1.3102 0 03680 1.3104 20.481 03676 1.3104 34.750 03667 1.3105 78.557 03664 1.3105 101.846 03640 1.3109 215.681 03605 1.3116 364.613 03567 1.3122 542.985 0.1593515 1.3128 841.591 0.8053448 1.3130 1273.530 2.5793360 1.3150 1691.887 5.0083275 1.3160 2127.077 6.500

3188 1.3170 2575.330 8.000

5. The production history and the PVT data of a gas-cap drive reservoir are given inTABLE 1 below.

Table 1Avg reservoir

Pressure(psi)

N p (Mstb)

G p (Mscf)

B t (res bbl/stb)

Bg (bbl/scf)

4415 - - 1.6291 0.00431

3875 492.5 751.3 1.6839 0.004453315 1015.7 2409.6 1.7835 0.004902845 1322.5 3901.6 1.9110 0.00556

The initial gas solubility is 975 scf/stb. Determine the amount of oil and gas initially in place(OIIP & GIIP respectively). State assumptions in your calculations. Hint: plot of F/Eo vs.Eg/Eo.


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APPENDIX: General form of MBE and its Applications

( )[ ] ( ) ( )[ ]

( ) ginjinjwinjewi

t wiwoi

gi

goigssioiow pgs po

BG BW W PS

cS c Bm N

B BmNB B R R B B N BW B R R B N

+++

+

++

+

++=++

11

1

Straight-line MBE as proposed by Havlena & Odeh

injinjwinjew f go BG BW W E mE E N F +++++= , , where,

m is the ratio of initial gas-cap gas reservoir vol. to initial reservoir oil vol.,oi

gi

NB

GBm =

F is the underground withdrawal, w pgs po p BW B R R B N F ++=

E o is the expansion of oil and originally dissolved gas, ( ) ( ) gssioioo B R R B B E +=

E g is the expansion of gas-cap gas,

= 1

gi

goig B

B B E

E f,w is the expansion of connate water and rock matrix, PS

cS c Bm E wc

f wcwoiw f

+=

1)1(,

Undersaturated oil reservoir

w f o E E N F ,+= (without water encroachment)

Saturated oil reservoir

[ ]o E N F = (water and rock expansion is small in comparison with soln. gas expansion)

Gas- cap drive reservoir

go mE E N F += (without water encroachment & negligible water and rock expansion)

Water drive reservoirs

ego W mE E N F ++= (negligible water and rock expansion)

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Assignment 2 MBE