Page 77 - Principles of Applied Reservoir Simulation 2E

62 Principles of Applied Reservoir Simulation

Table 7-2
Analytical Injection Rates for Selected Well Patterns
Pattern Rate

3541 khbP
Five-Spot f a ]
In — - 0.619
* \r w)

The calculation of analytical injection rates, even under a set of restrictive
assumptions, provides a methodology for designing well patterns without using
a reservoir simulator. More accurate estimates of injection rates under a less
restrictive set of assumptions are obtained using reservoir simulators. For
example, simulators have been used to correlate volumetric sweep efficiency
with mobility ratio and permeability variation in a reservoir that is being
subjected to a pattern flood [Wilhite, 1986]. One measure of permeability
variation is the Dykstra-Parsons coefficient of permeability variation.
The Dykstra-Parsons coefficient can be estimated for a log-normal
permeability distribution as

V Dp = 1- exp - jertk
*H

is the arithmetic average permeability for n samples
where k A
K
k K A --f k i
~
L
n /=!
and k H is the harmonic average permeability
JL_ ly _L
« ~
k H k t
The Dykstra-Parsons coefficient should be in the range 0 < V DP < 1. For a
perfectly homogeneous reservoir, V DP = 0 because k A = k H. An increase in
reservoir heterogeneity increases V DP. Typical values of the Dykstra-Parsons
coefficient are in the range 0.4 < V DP < 0.9.
Correlations of volumetric sweep efficiency with mobility ratio and
permeability variation show that volumetric sweep efficiency declines as