Page 174 - Well Logging and Formation Evaluation

164 Well Logging and Formation Evaluation

approximation originates from the fact that 1atm is in fact 1.01325 *
5
5
10 Pa, and not 10 Pa.
In oilfield units, and incorporating the conversion from downhole to
surface conditions via B o, the equation becomes:
-3
Q =-1 127 10 * k ( m )* D P ( * B o * L)
*
.
2
where Q is in stb/day, k is in md, A is in ft , m is in cp, P is in psi, and L
is in ft.
For radial flow into a borehole, incorporating the porosity and effect of
fluid/pore compressibility, Darcy’s equation becomes:

( 1 r) ∂∂ ( r r ∂ p ∂ r) =∂ p t * * C k m (11.4.3)
*
*
*
f
∂
where r = radial distance from the center of the borehole (in m), f= poros-
ity, and C = composite compressibility, in 1/Pa. The composite
compressibility is given by:
)
C = C o * (1 - S w + C w * S w + C f (11.4.4)

where compressibility is expressed as C o for oil, C w for water, and C f for
porespace.
A system is said to be in a steady state when pressure does not vary as
a function of time, i.e., ∂p/∂t is zero. A system is said to be in a semi-
steady state when ∂p/∂t is a constant.
Every closed finite system that is produced at a constant rate will
asymptotically approach a semi-steady state. An infinitely extended
system will never approach a semi-steady state.
Equation 11.4.3 has solutions depending on the boundary conditions
that are applied. For a situation in which the boundary of the area being
drained is maintained at a constant pressure, a steady state will eventually
develop for which:

e (
PP w = ( *m ( * p*2 k h)) ( * ln r r w ) -1 2 ) (11.4.5)
*
Q
-
where:
P = mean pressure in the drainage area, in Pa
P w = bottomhole flowing pressure, in Pa
3
Q = flow rate in reservoir, m /sec
h = thickness of reservoir, in m