Geostatistical analysis of interwell transmissivity in heterogeneous aquifers

Abstract

Steady state flow between an injection well and a pumping well in a heterogeneous confined aquifer is investigated using a combined numerical‐empirical approach. Transmis sivity at the measurement or point support scale is modeled as an isotropic, stationary, multivariate lognormal spatial random function. In a recent study (Desbarats, 1992) it was found that the effective transmissivity of a single‐well radial flow system was very well estimated by a spatial geometric average of point transmissivities weighted by their inverse squared distance from the well bore axis. This result provides an approximate solution for steady state drawdown in a heterogeneous medium which can be used with the principle of superposition to derive an expression for the interwell head difference in a dipole well configuration. The interwell transmissivity corresponding to this head difference is shown to be the harmonic mean of transmissivities averaged over circular regions centered at each well. This deterministic averaging law and the geostatistical model for point transmissivities are combined in order to derive expressions for the ensemble mean and variance of interwell transmissivity. Expressions are also obtained for the conditional moments of interwell transmissivity when values at the two wells are available from core measurements. Multiple realizations of the heterogeneous transmissivity field, discretized on a nodal grid, are generated using the turning bands method. Interwell transmissivities obtained by spatial averaging over the grid are compared with corresponding true effective values obtained numerically using a finite difference model of steady state interwell flow. Empirical and numerical values are found to be in excellent agreement for variances of log transmissivity as high as 5. Further numerical experiments show that results of this study are relatively insensitive to moderate departures from the multivariate lognormal transmissivity model.