Optimization Workflow Using Deep Learning Based Forward Models for Waterflooded Oil Reservoirs

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Summary In specific reservoir engineering problems, such as medium-term oil production forecast in waterflooded reservoirs, data-driven models are interesting alternatives to complex numerical simulations, as they can speedup decision making without compromising accuracy. In this work, an optimization framework using deep neural networks (DNNs) as surrogate models was established to optimize the waterflooding strategy in two synthetic cases of distinct geological complexity. Although DNNs have been tested for production forecasting in literature, the novelty of this work is the application of DNNs to optimize the injection schedule of brown fields and its comparison against a commercially available solution. Three different families of optimization algorithms were considered: gradient-free, gradient-based, and ensemble-based. Their results are compared against a commercial simulator-based software that performs a streamline-based optimization with a given water availability target. The benchmark is run using the “true” geological model. The first case is a 2D reservoir, with 5 injection wells and 4 production wells. It has uniform geological properties, with two high permeability streaks connecting two injector-producer pairs. The second case is Olympus, a realistic 3D reservoir with many geological heterogeneities and non-linearity sources, with 7 injection wells and 11 production wells. For each model a DNN was trained using synthetically generated historical data. Results are compared in terms of Net Present Value (NPV) considering oil price, cost of water produced and injected, and actualization rate. In the first case, the NPV was improved similarly by the three algorithms by reducing injections along the high permeability streaks, thus promoting the drainage of unswept areas. The benchmark achieved poor performances, promoting instead the injection in the high permeability streaks. In the second case, the three algorithms and the benchmark achieved similar NPVs with slightly different injection strategies. The ensemble-based optimizer proved to be the best-performing algorithm, as opposed to the gradient-free which required a higher number of objective function evaluations, and the gradient-based which tended to get trapped in local optima. The presented framework proved to be successful in optimizing the waterflooding strategy even in a complex geological setting. Compared to simulator-based optimization, the main benefit of the proposed methodology lies in its reduced computational time, both in model calibration and objective function evaluation. The time saving is especially significant when a tuned 3D model of the reservoir is unavailable or too expensive to build.