Page 345 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 280

t +∆ t
m(p ) versus log 1
ws
t ∆
for the recorded pressure data will be linear for small ∆t and the extrapolated trend can
theoretically be matched by equ. (8.53). The attractive feature of the Horner buildup is
that the analysis to determine k and S does not involve the specific evaluation of
m D ( t ) in equ. (8.53) but merely requires that the early linear buildup trend be
D
1
identified. The slope of this line is
1637Q T
m = 1 (8.54)
kh

from which kh and k can be calculated, and the total skin factor, corresponding to rate
Q 1, can be determined as

(m(p ws(LIN)1 hr ) m(p )) k
−
wf
+
S′ = S DQ = 1.151 − − log 2 + 3.23 (8.55)
1
1
( c)r
m φµ iw
in which m(p ws(LIN)1-hr) is the pseudo pressure read from the extrapolated straight line at
∆t = 1 hour. The derivation of equ. (8.55) follows the same argument leading to
equ. (7.52) and therefore the calculated value of S′is independent of the value of
1
m D ( t ).
D
1
The early, transient pressure response of both flow periods can be analysed to
determine values of k, S′ and S′ (= S + DQ 2). The equation describing the transient
2
1
pseudo pressure drop at the wellbore at any time t during the first flow period is
kh 4t
−
(m(p ) m(p )) = 1 2 ln D + S′
1422Q T i wf γ 1
1
which can be expressed as

1637Q T k
+
+
−
m(p ) m(p ) = 1 log t log − 3.23 0.87S′ 1 (8.56)
i
wf
kh φµ iw 2
( c) r
Thus a plot of m(p wf) versus log t will be linear during the transient flow period with
slope
1637Q T
m = 1 (8.54)
kh
again giving the value of k, while the skin factor can be calculated by evaluating
equ. (8.56), for the specific value of m(p wf ) at t = 1 hr, as

(m(p ) m(p ) ) k
−
−
S′ = S DQ = 1.151 i wf 1 hr − log 2 + 3.23 (8.57)
+
1
1
( c)r
m φµ iw
Only the values of m(p wf) which plot as a linear function of log t are used, which
ensures that the application of transient analysis is valid.