Prediction of tracer plume migration in disordered porous media by the method of conditional probabilities

The purpose of this study is to develop a method for predicting the spatial moments and concentration of a tracer plume conditional to locally measured data. The author set this study in a probabilistic frame due to the inherent inability to characterize deterministically the flow domain. The starting point is the Dagan (1984) conceptual model which relates the concentration to the translocation of tagged elements of solute mass. Then, using Darcy's law and the flow equations, he describes that translation using a random function of model for the velocity. Comparison with numerical simulations shows this model to be favorable for variances of the log conductivity as large as 2.56 (Dykstra-Parsons coefficient of 0.8). It is shown how this random function model is correlated with the hydraulic head and conductivity fields, and furthermore, how it can be made conditional to measured data. It is concluded that conditioning improves predictions of the spatial moments of the tracer plume by making a more comprehensive use of available data and has a potential for a large range of applications.

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