Dynamic Optimization of Water Flooding with Smart Wells Using Optimal Control Theory

Abstract

Abstract We used optimal control theory to develop optimization algorithms for the valve settings in smart wells. We focussed on their use in injectors and producers for waterflooding of heterogeneous reservoirs. As a follow-up to an earlier, intuitive, optimization approach, we developed systematic algorithms and investigated the effect of well constraints on the scope for optimization. The objective was to maximize recovery or net present value over a given time period. We concluded that:For wells operating on bottom hole pressure constraints the benefit of using smart wells is mainly reduced water production rather than increased oil production.For wells operating on rate constraints, there is a very large scope for accellerating production and increasing recovery, in combination with a drastic reduction in water production. Introduction In an earlier study, we investigated the static optimization of water flooding with smart wells, using heuristic algorithms1. Static implies that the injection and production rates of the inflow control valves (ICVs) in the wells were kept constant during the displacement process, until water breakthrough at the producers occurred. Later, we addressed the same problem using an optimization technique known as optimal control theory2. In addition to being more systematic, this technique allowed for dynamic water flooding control, through varying the flow rates over time. Optimal control theory has been used before in reservoir engineering. Fathi and Ramirez used it to optimize surfactant flooding processes3,4, Mehos to optimize CO2 flooding5, Liu to optimize steam flooding6, and Zakirov et al. to optimize production from a thin oil rim7. Furthermore, the same technique has been used in history matching reservoir models with production data. Optimization of water flooding using optimal control theory has been studied before by Asheim8, Virnovski9, Sudaryanto &Yortsos10,11,12 and Dolle et al.2. The optimization objective was either to maximize water breakthrough time at given field rates, or to maximize cumulative oil production or net present value (NPV) within a given time. In all these water flood optimization cases, the flow in the reservoir was controlled with wells that operated at constant field injection and production rates, i.e. the total injection and production rates were kept constant but the distribution over the wells was changed over time. In real life, however, a production strategy with constant field rates will often not be feasible, because it would require unrealistic bottom hole pressures, e.g. too low pressures at the producers, resulting in lift die-out, or too high pressures at the injectors, exceeding maximum allowable formation or equipment pressures. In the present study we investigated the scope for dynamic optimization for the two extreme cases of well constraints. The first extreme is the completely rate-constrained case with constant field rates for injection and production, and no pressure constraints. The other extreme is the completely pressure constrained case in which the field rates cannot be controlled directly.