INTRODUCTION

Heterogeneity of porous media has been a troublesome topic from the very beginning of groundwater hydrology as a quantitative science. Darcy (1856) recognized the necessity to quantify flow through porous media using a macroscopic, rather than a microscopic, viewpoint; he defined a flux based on an average linear flow path through a representative volume of porous media. Meinzer (1932) called heterogeneity the ‘most formidable difficulty’ in quantifying aquifer parameters. Shortly after this, Theis (1935) offered a solution to the heterogeneity problem by developing a way of calculating effective aquifer parameters. He demonstrated that by measuring the drawdown of water levels in response to pumping, it is possible to use an analytical solution to calculate effective aquifer parameters for average transmission and storage characteristics. Theis' method in essence replaces the heterogeneous aquifer with an equivalent homogeneous porous medium.

Theis' technique for dealing with heterogeneity allowed groundwater hydrologists to ignore geological heterogeneity for approximately 40 years. Then, Freeze (1975) called attention to the effect of uncertainty in hydraulic conductivity on the head distribution computed using groundwater models. About the same time, researchers were beginning to attempt to use the advection–dispersion equation to describe the transport of contaminant plumes in groundwater (Bredehoeft & Pinder, 1973; Pinder, 1973), and they were confronted with the problem of quantifying the dispersion coefficient. Slichter (1905) had earlier recognized that the spreading he observed in tracer experiments could not be due solely to the effects of molecular diffusion.