Fractional Dimension Analysis of Constant-Pressure Well Tests

Abstract

ABSTRACT This paper presents a discussion of spatial dimension and applies a generalized dimension approach to interpreting constant-pressure well tests. The spatial dimension of a well test is determined by the power by which either the surface area or reservoir properties change with distance from the source. The dimension equals the power of variation plus one. Fractional dimensions arise when the power of variation is not an integer. Fractional dimension behavior may indicate either fractal reservoir geometries or non-fractal geometries which are not space-filling. The dimension of a well test is distinctive in logarithmic plots of flow rate versus time. For dimensions between 1 and 2, the flow rate declines along a straight line with a slope equal to n/2-1 where n is the dimension. Determination of reservoir properties is complicated by uncertainties in the space-filling proportion of the reservoir, conducting surface areas of the reservoir, and the effective radius of the well.