Page 236 - Principles of Applied Reservoir Simulation 2E

Part HI: Case Study 22!

For an isotropic reservoir in which horizontal permeability does not depend on
direction, that is, K x = K y, we estimate the equivalent radius of a well in the
center of a gridblock as
2 2 !/2
« 0.14(A* + Ay )
r o
The shut in time Af, at which the PBU pressure should be obtained is calculated
from the following physical parameters:
3x lO^psia" 1
c r
13 x lO^psia 1
C 0
1
3 x lO^psia
c w
0.7
S 0
0.3
S w
0.71 cp
^0
d> 0.20
K 75 md

~ 0.14 (200 2
The equivalent radius of the well block is estimated to be r 0
2 /2
+ 200 )' = 39.6 ft, while the total compressibility is given by C T = c r + S 0 c 0 +
6
6
6
1
6
S wc w = 3 x 10' + 0.7 (13 x 10' ) + 0.3 (3 x ]0' ) * 13 x 10' psia' . The PBU shut
in time corresponding to these values is
2
Af - 1688 (0-20) (0.71) (13 x IQ-«) (39.6)
75
= 0.065 hr. « 4 minutes
This early time part of the PBU curve could be masked by wellbore storage
effects. Since the shut in pressure P ws of the actual well equals the simulator well
block pressure P 0 at a shut in time A^, the shut in pressure P ws may have to be
obtained by extrapolation of the radial flow curve.

Throughput Estimate
Model timestep size is estimated by calculating pore volume throughput
from well flow rates. In our case, pore volume throughput is given by