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

with subscripts:
i = individual flow period
j = individual flow period
n = number of flow periods considered.
In general, the fewer the number of points used in calculating the derivative, the more accurate it will be.
Three-point derivatives, calculated using only the nearest neighbor on either side of a point, usually provide
enough resolution to distinguish most important features. However, excessive noise in the data sometimes
makes it necessary to use five- or seven-point derivatives, or various "windowing" procedures, to obtain a
smooth curve. Unfortunately, these procedures may also smooth out some of the features of the curve needed
for interpretation.
The type curves published by both Gringarten et al. (1979) and Bourdet et al. (1984) were derived for
flow-period (drawdown) analysis. In general, the curves can also be used for buildup-period analysis, so long
as it is recognized that, at late time, buildup data will fall below the drawdown type curves because of
superposition effects.
If the test analysis is to be performed manually, the drawdown or buildup data are plotted as pressure change
since drawdown or buildup began (Ap) versus elapsed time since drawdown or buildup began (t) on log-log
paper of the same scale as the type curves. The derivative of the pressure change is also plotted using the same
vertical axis as the Ap data. The data plot is then laid over the type curves and moved both laterally and
vertically, so long as the axes remain parallel, until a match is achieved between the data and pressure and
pressure-derivative curves with the same CDe2s value. When the data fit the curves, an arbitrary match point is
selected, and the coordinates of that point on both the data plot, t and Ap, and on the type-curve plot, pD and
t&D, are noted. The permeability-thickness product is then calculated from a rearrangement of Eq (A-1):
PD
kh = 141.2qBp -
AP
(A-8)
The groundwater-hydrology parameter transmissivity, T, is related to the permeability-thickness product by
the following relationship, modified from Freeze and Cherry (1979):
where:
T = k hpg/p
p = fluid density, M/L3
g = gravitational acceleration, L/T~
p = fluid viscosity, M/LT
(A-9)
When T is given in ft2/day, kh is given in millidarcy-feet,p is given in g/cm3, g is set equal to980.665crn/s2, andp
is given in centipoises, Eq (A-9) becomes:
T = 2.7435 x khplp (A-10)
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