Page 253 - Introduction to Petroleum Engineering

240 TRANSIENT WELL TESTING
for r ≤ r where r is the radius of investigation (ft), r is the drainage radius (ft), k
e
inv
e
inv
is the permeability (md), Δt is the shut‐in time (hr), ϕ is the porosity (fraction), μ is
the gas viscosity (cp), and c is the total compressibility (1/psia). The radius
T
of investigation for gas wells has the same functional dependence as the radius of
investigation for oil wells, but the coefficient is larger for a gas well than an oil well.
Example 12.5 Gas Well Radius of Investigation
Calculate radius of investigation of a pressure buildup (PBU) test in a shale gas
well when the elapsed time (t) is 1, 7, 30, and 365 days. Use the following data:
permeability k = 0.0001 md, porosity ϕ = 0.05, initial gas viscosity μ = 0.02 cp,
and initial total compressibility c = 1×10 per psia.
−4
T
Answer
Radius of investigation at 1 day = 24 hr:
.
kt 0 0001 md 24 hr
.
.
r 0 0325 0 0325 5ft
inv 4 4
.
c 0050 02 cp 10 10 /psia
.
.
t
Radius of investigation at 7 days = 168 hr is 13 ft.
Radius of investigation at 30 days = 720 hr is 28 ft.
Radius of investigation at 365 days = 8760 hr is 96 ft.
Notice that radius investigated in shale by a PBU test is relatively short even
after a relatively long elapsed time.
12.3.4 Pressure Drawdown Test and the Reservoir Limit Test
A procedure that is analogous to the PBU test analysis is used to analyze pressure
drawdown tests in gas wells. The drawdown test measures pressure response to a
gas flow rate q for a gas well that was shut in long enough to achieve a static pressure,
that is, a pressure that does not change. The change in real gas pseudopressure is

mp mp mp
i wf
qT kt
.
1637 log 3230 869 S (12.28)
.
kh cr 2
Tw
S S Dq
where t is the time the well is flowing at rate q. Results of the drawdown test are ana-
lyzed by first plotting Δm(p) versus log t. Flow capacity
qT
kh 1637 (12.29)
m
is estimated from the slope m.