Cleopatra’s Nose and the Diagrammatic Approach to Flow Modelling in Random Porous Media

Abstract

“Cleopatra’s nose: if it had been shorter, the face of the whole world would have been changed.” Mentioning B. Pascal’s famous passage here aims at emphasizing the power of an image and the important consequences that it may have in real world situations. Mutatis mutandis, the idea behind the use of diagrammatic representations in groundwater flow modelling is based on the concept that the qualitative grasp of form, shape and geometric order may go deeper than the quantitative grasp of abstract mathematical symbol and number. In this spirit, the proposed approach uses topological diagrams which reduce the original stochastic groundwater flow problem to a closed set of equations for the statistical moments. Random integral forms of flow are considered in the light of porous media description operators and graphic Green’s functions. Graphic visualizations of the underlying flow processes allow previously undetected features to be seen and can yield more general and accurate results than traditional methods. Depending upon the choice of a porous medium description operator, the diagrammatic approach can handle both cases of small and large fluctuations and can work at long as well as short range correlation scales.