Modeling of solute transport in a heterogeneous porous medium with a random source using stochastic finite element method

Abstract

Most of the probabilistic studies in solute transport literature are focused on predicting the concentration uncertainty due to the heterogeneity of the governing flow and transport parameters. The randomness in the source condition can also be a major source of uncertainty in the concentration field. Some of the studies have also looked into this aspect and analysed the effect of random source condition while considering the system to be deterministic. For a deterministic system the analysis of probabilistic behavior of concentration due to source uncertainty is performed using a response/impulse function, which is obtained analytically or numerically for a unit pulse source condition. However, a more general form of the problem formulation is to consider both random source condition and system parameters. Under this condition, the response function becomes a random function and depends on the random system parameters. In the present study an attempt is made to include the system uncertainty and to assess the relative effects of system uncertainty and source uncertainty on the probabilistic behavior of concentration. Here the random source is modeled as a Poisson process, which results in concentration being a filtered Poisson process. The probabilistic behavior of the random response function is obtained by using a perturbation based stochastic finite element method. In this method the parameters of each element are treated as random variables. The mean and covariance matrix are obtained from the specified mean and covariance function of the parameters. The proposed method is applied for analyzing the solute transport problem in one dimensions considering flow and transport parameters as a random fields and treating the amount and timing of the mass released from the source as random.