Scalable Risk-Averse Well-Placement Optimization Using Quadratic Knapsack Problem and Randomized Singular Value Decomposition

Summary Unconventional shale developments require decisions about where to drill among thousands of possible well sites. Each site has an uncertain net present value (NPV) and is geologically correlated with its neighbors. We present a practical framework that helps a risk-averse operator select wells under this spatial uncertainty. The framework uses a geostatistical model to estimate each candidate’s NPV and the statistical relationships between wells, and it assumes that the decision-maker’s preferences are represented by a constant-absolute-risk-aversion (CARA) utility. Under these assumptions, the total profit of a set of wells can be approximated by a normal distribution, so maximizing expected utility becomes a binary quadratic optimization that balances expected profit against risk. Directly solving this optimization is computationally demanding because of the large covariance matrix, so we compress the matrix using a randomized singular-value decomposition and reduce the cost of each solver iteration by orders of magnitude. On synthetic field-scale examples with thousands of candidates, the low-rank surrogate yields speedups ranging from 10X to 1,851 while producing certainty-equivalent (CE) errors between 0.1% and 1% (and ≤0.3% at r = 100 across tested kernels). We derive bounds linking the approximation error to the spectrum of the covariance matrix and the decision maker’s risk parameter λ, providing guidance on rank selection for practical implementations.