Page 124 - A Practical Companion to Reservoir Stimulation

DIVERSION AND TREATMENT EVALUATION

EXAMPLE H-4
Then Eq. 15-5 becomes
Diverter Pseudoskin Factor and Diverter Quantity
2nkh
Assuming that there is a linear relationship between cake
resistance and the diverter pseudoskin factor and that there is
a linear relationship between resistance and mass of diverter which then is equated with Eq. H-9. Thus,
per unit area, develop a relationship between injection rate per
A dP* -
layer and this pseudoskin factor as a function of time. __ 2nkh
-
211th (H-12)
cdiv dt p[ln(G/rw,) +s+ --r (KIpA)]
Solution (Ref. Section 15-5)
(With special thanks to DK L. Prouvost) which defines an ordinary differential equation.
The injection rate in each layer is given by Eq. 15-5, and the Simple solution results in
relationship for the Scukr is given by Eq. 15-3. From Eq. 15-4, 2nkhAp 1
the injection rate can be given in terms of mass of divertercake &= (H-13)
deposited per unit area and the diverter concentration in the p [In ( r, 1 + SI y:r+K2t '
acid:
where

(H-9) 8 n2 kh)2 K, Ap C,,,.
(
K2 = A2p [In ( r, /rw ) + sI2' (H-14)
If a linear relationship is assumed between R, the cake
resistance, and the pA, the mass of diverter, then from K, is the experimentally determined slope between mass of
Eq. 15-3, diverter per unit area and the resistance of the diverter cake.
2zkh
sc<ike = - (H-10)
(Kl PA),
A
where K, is a constant.

H-3