Efficient Monte Carlo With Graph‐Based Subsurface Flow and Transport Models

Abstract

AbstractSimulating flow and transport in fractured porous media frequently involves solving numerical discretizations of partial differential equations with a large number of degrees of freedom using discrete fracture network (DFN) models. Uncertainty in the properties of the fracture network that controls flow and transport requires a large number of DFN simulations to statistically describe quantities of interest. However, the computational cost of solving more than a few realizations of a large DFN can be intractable. As a means of circumventing this problem, we utilize both a high‐fidelity DFN model and a graph‐based model of flow and transport in combination with a multifidelity Monte Carlo (MC) method to reduce the number of high‐fidelity simulations that are needed to obtain an accurate estimate of the quantity of interest. We demonstrate the approach by estimating quantiles of the breakthrough time for a conservative tracer in an ensemble of fractured porous media. Our results demonstrate that a multifidelity MC estimate, whose computational cost is equal to the cost of 10 DFN simulations, can be as accurate as a standard MC estimate that utilizes 1,000 DFN simulations. Thus the combination of our graph‐based model with multifidelity MC estimates effectively reduces the computational cost of the problem by a factor of approximately 100.