Page 225 - Principles of Applied Reservoir Simulation 2E

210 Principles of Applied Reservoir Simulation

increase in water volume at reservoir conditions as oil is produced and reservoir
pressure decreases.

1 . Calculate the decrease in oil volume AF 0 (RB):
Let
N = original oil in place = OOIP (STB)
=
B oi oil FVF (RB/STB) at initial pressure P (
f
A , = oil produced (STB) at pressure P and time t
= oil FVF (RB/STB) at pressure P and time t
B 0
Then
= OOIP (RB) at initial reservoir pressure
NB oi P f
(N - N p) B 0 = OIP (RB) at pressure P and time t

Therefore the change in oil volume is given by

AF 0 = NB oi- (N-N p)B o

2, Calculate the increase in water volume AF W (RB):
Let
W = original water in place = OWIP (RB) at initial pressure P f
= water FVF (RB/STB) at pressure P and time t
B w
W p = water produced (STB) at pressure P and time /
= water influx (RB)
W e
Then
W B w = cumulative water produced (RB) at pressure P and time /

Therefore the change in water volume is given by
W- WB - W = W - WB

3 . The assumption that the volume of the reservoir remains constant implies A V 0
- A V w. Combining results from steps 1 and 2 above gives the material balance
equation for depletion of an incompressible, undersaturated oil reservoir with
aquifer influx: