Determination of Lower and Upper Bounds of Predicted Production from History-matched Models

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. This is accomplished through a hierarchical optimization procedure, which limits the solution space of a secondary optimization problem to the null-space of the primary optimization problem. We applied this procedure to a model of a channelized reservoir with a life-cycle of 6 years after 1.5 years of production. We performed a history match based on synthetic data, starting from a uniform prior, and using a gradient-based minimization procedure. For the remaining 4.5 years, minimization and maximization of net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying in the null space. I.e. we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. For the remaining 4.5 years of production, the method gives lower and upper bounds of the predicted NPV of 63 % above and below the average respectively. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem.