Numerical evaluation of volumetric weighted mean transmissivity estimates in laterally heterogeneous aquifers

SummaryMost previous investigations to evaluate the “effective” or average transmissivity in heterogeneous environments have used calculations based on areas to weight the effects of each heterogeneity. Analysis of spatial volumetric variations within the cone of depression expressed at the potentiometric surface offers a more general solution to evaluate the meaning of transmissivity (T) and storativity (S) values derived from aquifer tests in these environments. The [Cooper Jr., H.H., Jacob, C.E. 1946. A generalized graphical method for evaluating formation constants and summarizing well-field history. Eos Trans. AGU, 27(4), 526–534] method is used to demonstrate that T variations reflected in slope changes in plots of the pumping well drawdown data correspond to changes in the volumetric weighted mean transmissivity (VWMT) over time.Lognormal distributions of transmissivity are represented by block heterogeneities within two simulated aquifers, for both spatially random and spatially correlated data sets. By analyzing the volumetric evolution of the cone of depression observed in the potentiometric surface, the nature of T averaging within the cone of depression as a function of time is illustrated. Volumetric analysis shows that the average aquifer T varies with time as the cone of depression progressively envelops different heterogeneities. The initial trend is controlled primarily by the heterogeneities directly surrounding the pumping center. If steady-shape conditions are not achieved, late-time VWMT values do not approach an asymptotic limit.