Abstract: | We consider a generalized averaged model of the filtration of a weakly compressible liquid in a highly inhomogeneous medium. We construct an approximate analytical solution of the problem that describes the change in the pressure field around a well in a circular bed. We investigate the effect of the parameters of a highly inhomogeneous bed on the form of the well pressure stabilization curve.Notation
c
Euler constant
-
D
diameter of a weakly permeable block
- Ei
symbol of the integral exponential function
-
h
bed thickness
-
K(t), K
*
(t)
kernels of integral operators
-
K
0
symbol of the Macdonald function
-
k
permeability
-
P
pressure
-
Q
constant discharge of the well
-
r
radius
-
s
complex variable
-
t
time
-
t
*
time of the relaxation of a weakly permeable block
-
U(r, t)
reduced pressure
- U(t)
function taking into account the internal flow of the fluid from one medium to the other
-
fraction of the volume of the bed per block
- *
reduced coefficient of compressibility
-
characteristic scale of inhomogeneity
-
ratio of piezoconductivities of a block and a crack
-
Laplace operator
-
piezoconductivity
-
ratio of elastic amounts of weakly permeable blocks and systems of cracks
-
viscosity of the fluid
-
dimensionless time
-
integration variable. Indices: 1, weakly permeable blocks
- 2
system of cracks
- 0
initial value
- w
value in the well
-
e
effective value
- overbar
Laplace transform
Institute for the Problems of Oil and Gas of the Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 444–450, May–June, 1995. |