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

The wellbore storage coefficient is calculated from a rearrangement of Eq (A-4):
0.000295 kht
C=
fltD/CD
(A-1 1)
Finally, if estimates of porosity and total-system compressibility are available, the skin factor can be calculated
from the value of the CDe2s curve selected and Eq (A-3):
s = 0.5 Pn
C De2s
0.8936C/tbc, hr,2
1
(A-12)
A.1.2
Double-Porosity Log-Log Analysis
Double-porosity media have two porosity sets that differ in terms of storage volume and permeability.
Typically, the two porosity sets are (1) a fracture network with higher permeability and lower storage, and (2)
the primary porosity of the rock matrix with lower permeability and higher storage (Gringarten, 1984). During a
hydraulic test, these two porosity sets respond differently. With high-quality test data, the hydraulic parameters
of both porosity sets can be quantified.
During a hydraulic test in a double-porosity medium, the fracture system responds first. Initially, most of the
water pumped comes from the fractures, and the pressure in the fractures drops accordingly. With time, the
matrix begins to supply water to the fractures, causing the fracture pressure to stabilize and the matrix pressure
to decrease. As the pressures in the fractures and matrix equalize, both systems produce water to the well. The
total-system response is then observed for the balance of the test.
The initial fracture response and the final total-system response both follow the single-porosity type curves
described above. By simultaneously fitting the fracture response and the total-system response to two
different CDe2scurves, fracture-system and total-system properties can be derived. Information on the matrix,
and additional information on the fracture system, can be obtained by interpretation of the data from the
transition period when the matrix begins to produce to the fractures. Two different sets of type curves can be
used to try to fit the transition-period data.
Transition-period data are affected by the nature, or degree, of interconnection between the matrix and the
fractures. Warren and Root (1963) published the first line-source solution for well tests in double-porosity
systems. They assumed that flow from the matrix to the fractures (interporosity flow) occurred under
pseudosteady-state conditions; that is. that the flow between the matrix and the fractures was directly
proportional to the average head difference between those two systems. Other authors, such as Kazemi (1969)
and de Swaan (1976). derived solutions using the diffusivity equation to govern interporosity flow. These are
known as transient interporosity flow solutions. Mavor and Cinco-Ley (1979) added wellbore storage and skin
to the double-porosity solution, but still used pseudosteady-state interporosity flow. Bourdet and Gringarten
(1980) modified Mavor and Cinco-Ley’s (1979) theory to include transient interporosity flow, and generated
type curves for double-porosity systems with both pseudosteady-state and transient interporosity flow.
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