Page 244 - Introduction to Petroleum Engineering

OIL WELL PRESSURE TRANSIENT TESTING 231
of the diffusivity equation for flow of oil in a porous medium with outer boundary
at r → is
D
1 r 2
pr t D Ei D (12.5)
,
D
D
2 t 4 D
The term Ei(⋯) is the exponential integral

e u
Ei x du (12.6)
x u

Dimensionless pressure p in oil field units is
D
kh
p D p i p wf (12.7)
.
141 2 qB
where k is the permeability (md), h is the thickness (ft), q is the flow rate (STB/d), B
is the formation volume factor (RB/STB), μ is the viscosity (cp), p is the initial
i
reservoir pressure (psia), and p is the well flowing pressure (psia).
wf
Equation 12.5 is valid from the outer diameter of the well at dimensionless radius
r = 1 to the outer boundary of the reservoir at r → . If we use an approximation of
D
D
the exponential integral solution that is valid when t / r D 2 10 at r = 1 and express
D
D
variables in oil field units, we obtain
qB k
.
.
p wf p i 162 6 log t log 2 0 87 S 323. (12.8)
kh cr
Tw
Skin typically ranges from −5 < S < 50. A positive value of skin S indicates well
damage. If skin S is negative, it suggests that the well is stimulated.

Example 12.1 Dimensionless Time
Calculate dimensionless time given the following data: wellbore radius
r = 0.25 ft, permeability k = 150 md, time t = 2 hr, porosity ϕ = 0.14, initial
w
liquid viscosity μ = 0.9 cp, and initial total compressibility c = 8 × 10 psia .
−6
−1
T
Answer
kt
.
Solve t 0 000264 using the previous data:
D 2
c r
T i w
150 md 2 hr
t 0 000264 12 .6610 6
.
D 6 2
.
.
014 0.9cp 8 10 /psia 025 ft