Algorithm-aided decision-making in reservoir management

Sound reservoir management involves making decisions in the presence of uncertainty and complexity. Because projects handled in the oil and gas industry are often highly risky and uncertain, the decision-making methods the geoscientists employ must be self-consistent, systematic, and defensible. This dissertation addressed three example problems commonly encountered in reservoir management: water injection allocation optimization, horizontal well refrac scheduling, and infill drilling scheduling. Solutions to each problem employ different algorithms and data analytic techniques that allow a coherent integration of uncertainty and decisions. The specific algorithms and statistical tools used for each problem are provided below. The solution to water injection allocation draws from simple models as well as appropriate statistical methods. The capacitance-resistance model (CRM) is used to model interactions between injectors and producers to help predict the reservoir’s fluid production response. The CRM is paired with Koval’s K-Factor method to decouple oil and water from total fluid production. The models are fitted using a bootstrapped dataset to generate a diverse distribution of history matched solutions. Next, the best injection scheme corresponding to each history matched model is determined using ensemble optimization (EnOpt). Finally, a sampling algorithm called Thompson sampling is called upon to determine the optimal injection scheme while reducing the number of less promising simulations. This way, one can select the best injection scheme that is robust to uncertainties in history matching while simultaneously minimizing the number of simulation runs where it is unnecessary. Validation against a reservoir simulation model is provided at the end to confirm that the injection scheme selected is indeed optimal. The refrac scheduling problem examines a horizontal gas well that is a candidate to refracturing. The analysis employs a real options approach to find the current and future conditions in which refracing is the best decision, as well as to provide an accurate valuation that reflects the managerial flexibility of the project. An algorithm called least-squares Monte Carlo (LSM) will be used to achieve the two goals. In parallel, the Ornstein-Uhlenbeck model is calibrated using the ensemble Kalman filter (EnKF) to account for the gas price changes through time stochastically. The results of the valuations are compared against a myopic Monte Carlo/discounted cash flow (MC-DCF) method to demonstrate that the latter provides an underestimate of the true value. The underestimation results from that the MC-DCF approach neglects the alternatives available in managing the project. The difference between the two estimates of project value is calculated to determine the value of flexibility. Finally, the optimal policies determined is examined to confirm that the recommended response to the realization of uncertainties is intuitively consistent. Finally, a Monte Carlo tree search (MCTS) algorithm is paired with a reservoir simulator to optimize the infill drilling schedule in a reservoir undergoing waterflooding. Because of the permutative nature of sequence-dependent actions, the problem suffers from the curse of dimensionality. MCTS allows the user to find an approximate solution to the scheduling problem that is otherwise intractable. The final optimized schedule specifies 1) whether an infill well should be drilled at candidate locations, 2) whether an injector or producer should be drilled, and 3) when the well should be drilled. A provisional validation is provided at the end by comparing the cumulative oil production and the NPV of the MCTS-optimized schedule against those resulting from randomly generated schedules. Overall, the goal of this dissertation is to demonstrate that different algorithms can be tailored to optimize decisions or policies. The proposed solutions systematically integrate the relevant uncertainties in the analysis as they search for the most preferred action. Such rational approach where uncertainty plays an active role in decision-making provides the geoscientists with the confidence that the final optimized decision is the best action to take. Workflows designed and recommended in this dissertation are strongly preferred over the alternatives where uncertainty and sensitivity analyses are conducted after decisions have already been made using deterministic methods