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

Abstract

Simulating 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.