Page 272 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Material Balance and Volumetric Analysis 241

state compressible flow should be used, and that water encroachment generally
follows the constant pressure solution to the radial diffusivity equation. Solutions
to the radial diffusivity equation have been provided by van Everdingen and
Hurst [253] in terms of dimensionless time, t,, and a dimensionless fluid flow
function, Qm, which is determined at t,:

6.323 x loJ kt
t, = (5-166)
@w2

where k is permeability in md, t is time in days, is the fractional porosity, c
is the compressibility in psi-l, and r is the reservoir radius in ft. Values of Q,
are given in tabular form as a function of t,in the paper by van Everdingen
and Hurst [253] and have been reproduced in several texts [17,197]. Because
of the length of the tables, they will not be reproduced in this section. The
water encroachment, We in barrels, can be estimated from:

(5-167)
where dp is the pressure drop is psi, and the constant B is:

8
B = 1.12@h~'- (5-168)
360
where h is the reservoir thickness in ft, 0 is the angle subtended by the reservoir
circumference (e is 360" for a circular reservoir and 8 is 180" for a semicircular
reservoir against a fault), and the other terms are as defined above [17]. From
the slope of cumulative water influx at various times versus the summation term
at those times, the aquifer constant, B, can be obtained, and the cumulative
water influx for any pressure history can be estimated from Equation 5-167. Plots
of Qco versus t, for various dimensionless reservoir sizes are also available
[17,253] and extensions of these data are available as well 11971.

Volumetric Calculations for Recovery of Gas and Oil

The volumetric equations for original oil and gas in place were given earlier.
In this section, volumetric equations will be given for the recovery of gas and
oil reservoirs under several common instances.

Recovery of Gas
The volume of gas recovered, GP in scf, from a dry-gas reservoir is:

(5-169)

where 7,758 is the number of barrels per acre-ft, A is the areal extent in acres,
h is the reservoir thickness in ft, @ is the fractional porosity, Sw is the fractional
water saturation, B, is the initial gas formation volume factor in reservoir barrels
per scf, and BB is the gas formation volume factor in RB/scf at the abandonment