PERCOLATION THEORY AND THE FUTURE OF HYDROGEOLOGY

Two difficulties provide the chief constraints to hydrogeological modeling: quantification of connectivity, and the treatment of heterogeneity. The theory of connectivity, percolation theory, has already been demonstrated to provide the framework for the most accurate calculations of effective transport (or flow) coefficients in heterogeneous media. I give the basis for comprehensive treatment of flow and transport in porous media and show the relevance of percolation theory to calculations of a representative elementary volume, hysteresis, effective hydraulic conductivity, solute diffusion, air permeability, and other properties. I show the deficiencies of other theoretical constructions, e.g., stochastic methods and capillary bundle models, such as Kozeny-Carman treatments. Thus I argue that for both successful hydrogeological modeling and theoretical understanding, percolation theory is essential. If hydrogeology is to become a predictive science, and this predictability is to arise from anything other than massive simulations, the framework for problem solution must be altered.