The Averaging Process in Permeability Estimation From Well-Test Data

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Abstract
Summary: Permeability estimates from the pressure derivative or the slope of the semilog plot usually are considered to be averages of some large ill-defined reservoir volume. This paper presents results of a study of the averaging process, including identification of the region of the reservoir that influences permeability estimates, and a specification of the relative contribution of the permeability of various regions to the estimate of average permeability. The diffusion equation for the pressure response of a well situated in an infinite reservoir where permeability is an arbitrary function of position was solved for the case of small variations from a mean value. Permeability estimates from the slope of the plot of pressure vs. the logarithm of drawdown time are shown to be weighted averages of the permeabilities within an inner and outer radius of investigation. The estimate is shown to be influenced most strongly by permeabilities at a distance r=0.015(k¯t/ϕμct)½[5.6×10−5]. Fully 50% of the contribution to the permeability estimate is from the reservoir volume in the range from r=0.011(k¯t/ϕμct)½[4.1×10−5] to r=0.022(k¯t/ϕμct)½[8.1×10−5]. An analytic expression for the weighting function is derived in this paper.

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