Page 252 - Introduction to Petroleum Engineering

GAS WELL PRESSURE TRANSIENT TESTING 239
observation that dimensionless real gas pseudopressure increases linearly with
the logarithm of time during the infinite‐acting period to find the solution of the real
gas diffusivity equation as

1637 qT kt
m p m p log 3230 869 S
.
.
i
ws
kh cr w 2 (12.22)
T
S S Dq
where m(p ) is the dimensionless real gas pseudopressure evaluated at well shut‐in
ws
pressure p , m(p ) is the dimensionless real gas pseudopressure evaluated at initial
i
ws
pressure p , q is the surface flow rate of gas (MSCF/D), T is the reservoir temperature
i
(°R), k is the permeability (md), h is the formation thickness (ft), S is the skin (dimen-
sionless), and D is the non‐Darcy flow coefficient ((MSCF/D) ). The skin factor S is
−1
the skin factor S characterizing formation damage plus a factor proportional to gas
rate q that accounts for turbulent gas flow at high flow rates. Application of these
equations to the PBU case gives
qT
m p ws m p i 1637 log t H (12.23)
kh
where t is the dimensionless Horner time:
H
t t
t F (12.24)
H t
Results of the buildup test are analyzed by first plotting m(p ) versus Horner time
ws
(t + Δt)/Δt on a semilogarithmic Horner plot. Flow capacity
F
qT
kh 1637 (12.25)
m
is estimated from the slope m of the Horner plot. The slope m should not be confused
with real gas pseudopressure m(p). The skin factor S is given by

mp mp k
.
.
S 1 151 1hr wf log 2 323 (12.26)
m cr
Tw
where m(p ) is real gas pseudopressure extrapolated to a shut‐in pressure of 1 hr.
1 hr
12.3.3 Radius of Investigation

The radius of investigation r for a PBU test in a gas well is an estimate of the
inv
distance the pressure transient moves away from the well during shut‐in time Δt. It is
estimated using
kt
r inv 0 0325 (12.27)
.
c T