Beauheim 1987 - Waste Isolation Pilot Plant - U.S. Department of ...

The same equations are used to derive the fracture and matrix parameters, except that the matrix geometry
must now be known or assumed to obtain the interporosity flow coefficient, A, from rearrangement of Eq (A-21)
or (A-22).
A.1.3
Semilog Analysis
Two semilog plotting techniques were employed in this report to interpret pumping-test and DST-buildup data.
These techniques produce a Horner plot and a dimensionless Horner plot.
Horner Plot
Horner (1951) provided a method of obtaining permeability and static formation pressure values independent
of log-log type-curve matching, although the two methods are best used in conjunction. Horner's method
applies to the buildup (recovery) of the pressure after a constant-rate flow period in a well that fully penetrates a
homogeneous, isotropic, horizontal, infinite, confined reservoir. For a recovery after a single flow period,
Horner's solution is:
where:
p(t1 = p* - 162.6qBp kh
log 15.4
p(t) = pressure at timet, psi
p' = static formation pressure, psi
t, = duration of previous flow period, hr
dt = time elapsed since end of flow period. hr
(A-23)
and other terms areas defined above under Eq (A-4). For a recovery after multiple flow periods, the time groi
in Eq (A-23) is replaced by the superposition function given in the right-hand side of Eq (A-7).
P
The permeability-thickness product (kh) is obtained by (1) plotting p(t) versus log [(t, + dt)/dt] (or the
superposition function), (2) drawing a straight line through the data determined from the log-log pressurederivative
plot to be representative of infinite-acting radial flow, and (3) measuring the change in p(t) on this
line over one log cycle of time (m). Equation (A-23) can then be rearranged and reduced to:
kh = 162.6 qBp/m.
(A-24)
Static formation pressure is estimated by extrapolating the radial-flow straight line to the pressure axis where
log [(t, + dt)/dt] = 1, representing infinite recovery time. In the absence of reservoir boundaries, the pressure
intercept at that time should equal the static formation pressure.
Horner (1951) also suggested a modification of his method for the case where the flow rate was not held
constant. This modification was later theoretically verified for the case of constant-pressure, variable-rate
production by Ehlig-Economides (1979). The modification entails calculating a modified production time:
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