SPE 142043 Using Multiscale Regularization to Obtain Realistic Optimal Control Strategies

Smart well technology is attracting increasing attention because it promises to add operation flexibility and potentially increases oil recovery. However, it remains difficult to find the best strategy for production optimization. One challenge is to find a good optimization algorithm, as some optimization algorithms require prohibitive work to compute the gradients of the objective function with respect to the well controls. These methods also require access to the simulator code, which makes them difficult to use with commercial software. Another challenge is to find a reasonable frequency for well control adjustment: adjusting well controls too frequently imposes unrealistic control burdens on operations, increasing well management cost. Moreover, high–frequency control adjustment increases the risk of optimization algorithms being trapped at local optima as the problem is more under–determined. On the other hand, excessively low–frequency control adjustment may not truly optimize oil recovery. To address these issues, two simulator-independent optimization algorithms were investigated: ensemble-based optimization (EnOpt) and bound optimization by quadratic approximation (BOBYQA). Multiscale regularization was applied to both to find appropriate frequencies for well control adjustment. In a synthetic case study, if multiscale regularization was not used, then EnOpt converged to a higher net value of production than BOBYQA —even though BOBYQA uses second order Hessian information (EnOpt uses first order gradients). BOBYQA performed comparably only if multiscale regularization was used. After multiscale regularization, both methods obtained net value of production (NVP) that equalled or exceeded unregularized optimization, with simpler well control strategies and convergence in fewer iterations. Introduction Since the first smart well was installed at Saga’s Snorre Tension Leg Platform in North Sea in 1997, more than 300 smart well systems have been installed worldwide (Gao, Rajeswaran, and Nakagawa 2007). The benefits of smart wells have been demonstrated in theoretical studies and practical applications (Brouwer et al. 2001; Jansen et al. 2002; Ramakrishnan 2007; van Essen et al. 2009; Meshioye et al. 2010; van Essen et al. 2010). These benefits can summarized as two types: (1) for highly heterogeneous reservoirs, smart wells can help avoid early water or gas breakthrough from high permeability zones, and (2) for multilateral wells (or monobore wells with multiple segments), smart wells provide flexibility to control each branch (or segment) of the well independently. Smart wells can do this because, unlike conventional wells, smart wells have permanent downhole sensors and controls. Those sensors provide realtime rates, pressures and temperatures; the control valves allow control of flow in each reservoir interval. The data feedback and inflow control valves (ICVs) are the key components of smart well systems. Based on the feedback, the downhole control valves are adjusted to suppress unwanted fluid production and increase oil recovery. There are two approaches for using smart well technology, reactive control and proactive control (Aitokhuehi 2004; Yeten, Durlofsky, and Aziz 2002; Addiego-Guevara, Jackson, and Giddins 2008). With reactive control, the ICVs are adjusted either by continuously reducing the interval rate or closing the interval entirely to control excessive water or gas production. Proactive control is also called defensive control. With this strategy, the valve settings are optimized a priori using a predictive reservoir model. Optimization algorithms can be used to find the optimum valve settings. These methods can be categorized into two classes, gradient–free methods and gradient methods. Gradient–free methods do not rely on gradient information to guide the optimization search. Their primary benefits are their potential to find the global optimum and the ability to handle discrete design variables. Because they are capable of discrete parameter optimization, gradient–free methods are also used in well placement optimization (Onwunalu and Durlofsky 2010). A considerable disadvantage of gradient–free methods is that they