| Summary: | We analyze the movement of DNAPL in a three-dimensional randomly heterogeneous porous medium, saturated with water, that is initially pooled above a water table or flows at a constant flux. We consider the front to form a sharp boundary at which the capillary pressure head, assumed equal to the entry pressure head of DNAPL, is prescribed either deterministically or randomly, treat log conductivity as a statistically homogeneous random field with given mean, variance and covariance; cast the corresponding boundary-value problem in the form of an integro-differential equation, in which the parameters and domain of integration are random; expand this equation in a Taylor series about the mean position of the front; and take ensemble mean. To quantify the predictive uncertainty associated with this mean solution, we develop a set of integro-differential equations for the corresponding second ensemble moments. We solve the resulting moment equations analytically and numerically in one and two dimensions to second order in the standard deviation of log conductivity. A comparison of our one-dimensional solutions with the results of Monte Carlo simulations verifies its accuracy. We also show that a probabilistic analysis of wetting front instability due to Chen and Neuman (1996) applies to a DNAPL front.
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