Minimizing the Risk in the robust life-cycle production optimization using stochastic simplex approximate gradient

We develop a framework based on the lexicographic method and the newly developed Stochastic-Simplex-Approximate-Gradient (StoSAG) algorithm to maximize the expected net-present-value (NPV) and minimize the associated risk or uncertainty in robust life-cycle production optimization. With the lexicographic method, we first maximize the expectation of the life-cycle NPV value, then we minimize the risk using the resulting optimal value of expected NPV as a constraint. This constrained optimization problem is solved with the augmented Lagrangian method. The measures of risk considered include the standard deviation, the worst-case scenario (minimum NPV over the set of realizations) and conditional-value-at-risk (CVaR). Results obtained with different risk measures are benchmarked using two reservoir examples, namely, a channelized reservoir model and the well-known Brugge reservoir model in order to determine the effect of the choice of the risk measure. In addition, the performance of the one-step (unconstrained) CVaR is compared with that of the two-step CVaR (lexicographic-based CVaR).