Scale effects in transmissivity

Abstract

Heterogeneity accounts for several paradoxes in groundwater flow and solute transport. One of the most striking observations is the emergence of scale effects in transmissivity, that is, the increase in effective transmissivity (or hydraulic conductivity, for that matter) with increasing scale of observation. Traditional stochastic approaches, where transmissivity is treated as a multilog-normal random function, lead to a large-scale effective transmissivity equal to the geometric average of local measurements.

We present several field cases in which large-scale transmissivities are indeed larger than the geometric average of local tests. This suggests that the assumption of multilog-normality may not be valid in many cases, even if point T values display a log-normal distribution. We conjecture that scale dependence of T may, in part, be a consequence of high T zones being better connected than average or low T zones, a feature which may occur in many geological environments, but which is not consistent with multinormal log-T fields. We go on to generate a suite of log-T fields with a normal distribution for point values but non-multinormal spatial correlation. In all our fields, high T zones show longer correlations than average of low T zones. By simulating flow through these synthetic fields under simple boundary conditions, and estimating their effective transmissivity values, we conclude that these types of departures from the multilog-normality assumption lead consistently to scale effects.

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