Page 216 - Fundamentals of Reservoir Engineering

OILWELL TESTING 154

-1 1 2 55 10
10 10
8 8
6 6
4 4
ei (x)
ei (x) 2 2
ei (x)
ei (x)
-In γ x
10 -2 -In x ∝ 1
8 8
6 6
4 4
x→0
ei (x) ~ (-In γ x) - × -0.5772
2 2

10 -3 10 -1
10 -3 2 5 5 10 -2 2 5 10 -1 2 5 1
x

Fig. 7.3 Graph of the ei-function for 0.001 ≤ × ×× × ≤ 5.0

Sometimes pressure tests are conducted in order to determine the degree of
communication between wells, for example, pulse testing. In such cases pressure
transients caused in one well are recorded in a distant well and, under these
circumstances, r is large and the approximation of equ. (7.9) is no longer valid.
Equation (7.6) must then be used in its full form, i.e.

2
qµ φ µ cr
p r,t = p − 4kh ei 4k t (7.11)
i
π
in which the values of the exponential integral can be obtained from fig. 7.3.

EXERCISE 7.1 ei-FUNCTION: LOGARITHMIC APPROXIMATION

A well is initially producing at a rate of 400 stb/d from a reservoir which has the
following rock and fluid properties

k = 50 mD

h = 30 ft
= 6 inches
r w
φ = 0.3

µ = 3 cp
-6
c = 10 × 10 / psi
= 1.25 rb/stb
B o
1) After what value of the flowing time is the approximation

ei(x) = − ln(γx) valid for this system?