Well testing in fractured media: flow dimensions and diagnostic plots

Abstract

Hydraulic tests in heterogeneous media, particularly fractured media, are difficult to analyze because of the absence of radial flow. The theory of flow dimensions introduced by Barker in 1988 (Water Resour. Res. 24(10). 1988. 1796) provided a method of analyzing pumping (constant-rate) tests in non-radial systems, and this approach was later extended to constant-pressure tests. However, little use seems to be made of the flow-dimension approach to well-test analysis, perhaps because no easily applied method has been presented for determining, at the initial stage of an analysis, if such an approach would be productive. Depending on the distribution of heterogeneities within an aquifer, flow to a well may have almost any dimension (not limited to linear, radial, or spherical), or no constant dimension at all. Any well-test analytical solution requires that hydraulic properties be stable on some scale before those properties can be uniquely quantified. For each type of hydraulic test (constant-rate, constant-pressure, or slug/pulse), we suggest that a diagnostic plot of the scaled first or second derivative of the pressure or flow-rate response be created to determine, first, if a stable flow dimension was reached during the test and. second, what the value of that flow dimension is. If a stable flow dimension was reached, the scaled derivative will exhibit a constant value (scaled to be equal to the flow dimension). If the scaled derivative does not stabilize at a constant value, then no flow dimension can be specilied and no unique hydraulic properties can be inferred analytically from the test. In all cases, the scale of testing must be appropriate to the scale of underlying interest.