Introduction to PDE-Constrained Optimization in the Oil and Gas Industry

This article is an expanded version of a tutorial on applications of PDE-constrained optimization in the oil and gas industry that was given at the Frontiers in PDE-Constrained Optimization workshop. (The workshop was held at the Institute for Mathematics and its Applications June 6–10, 2016.) We begin with an overview of the oil and gas supply chain that highlights the importance of PDE-constrained optimization. Next, we take an in-depth look at two key applications: full-wavefield inversion and reservoir history matching. For each application, we introduce a PDE model, derive the gradient of the objective function using the adjoint-state method, and present simple numerical results. We conclude with a discussion of key challenges.