Inferring spatial distribution of the radially integrated transmissivity from pumping tests in heterogeneous confined aquifers

Abstract

Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single estimates of representative flow parameters. However, natural subsurface formations are intrinsically heterogeneous, and hence, the flow parameters influencing the drawdown vary as the cone of depression expands in time. In this paper a novel procedure for the analysis of pumping tests in heterogeneous confined aquifers is developed. We assume that a given heterogeneous aquifer can be represented by a homogeneous system whose flow parameters evolve in time as the pumping test progresses. At any point in time, the interpreted flow parameters are estimated using the ratio of the drawdown and its derivative observed at that particular time. The procedure is repeated for all times, yielding time‐dependent estimates of transmissivity $T_{i}(t)$ and storativity, $S_{i}(t)$. Based on the analysis of the sensitivity of drawdown to inhomogeneities in the $T$ field, the time‐dependent interpreted transmissivity values are found to be a good estimate of $T_{g}(r)$, the geometric mean of the transmissivity values encompassed within a progressively increasing radius $r$ from the well. The procedure is illustrated for Gaussian heterogeneous fields with ln($T$) variances up to a value of 2. The impact of the separation distance between the pumping well and observation point on data interpretation is discussed. The results show that information about the spatial variability of the transmissivity field can be inferred from time‐drawdown data collected at a single observation point

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