Page 366 - Fundamentals of Reservoir Engineering
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NATURAL WATER INFLUX 301
Darcy Units Field Units
kt kt
t = 2 (t-sec) t D = constant × 2 (9.9)
D
φµ cL φµ cL
constant, same as for equ. (9.7)
U = wLhφc (cc/atm) U = .1781 wLhφc (bbl/psi) (9.10)
Other characteristic features of the plots of W D(t D) versus t D depend upon whether the
aquifer is bounded or infinite in extent.
Bounded Aquifers
Irrespective of the geometry there is a value of t D for which the dimensionless water
influx reaches a constant maximum value. This value is, however, dependent upon the
geometry as follows
2
Radial W D (max = 1 2 ( eD − ) 1 (9.11)
)
r
Linear W D (max ) 1= (9.12)
Note that if W D in equ. (9.11) is used in equ. (9.4), for a full radial aquifer (f = 1), the
result is
2
2
2
0
e
W = 2πφ hcr ×∆ p× 1 2 (r − r )
0
e
r 0 2
2
2
= π (r − r )h c p
φ ∆
0
e
But this latter expression is also equivalent to the total influx occurring, assuming that
the ∆p is instantaneously transmitted throughout the aquifer. A similar result can be
obtained using equ. (9.12) for linear geometry. Therefore, once the plateau level of
W D (t D) has been reached, it means that the minimum value of t D at which this occurs
has been sufficiently large for the instantaneous pressure drop ∆p to be felt throughout
the aquifer. The plateau level of W D(t D) is then the maximum dimensionless water influx
resulting from such a pressure drop.
Infinite Aquifer
Naturally, no maximum value of W D (t D) is reached in this case since the water influx is
always governed by transient flow conditions. For radial geometry, values of W D (t D)
can be obtained from the graphs for r eD = ∞. There is no plot of W D (t D) for an infinite
linear aquifer. Instead, the cumulative water influx can be calculated directly using the
following equation
φ kct
W = 2hw ×∆ p (ccs) (9.13)
e
πµ