Computationally efficient techniques for well control and well placement optimization under geological uncertainty

Abstract

Hydrocarbon field development plans outline the specific exploitation strategy with the aim of maximizing economic returns over the lifetime of the resource. These plans encompass a wide array of decision variables, including well location and trajectory, drilling schedule, well type, platform location, well control settings (injection/production rates and/or bottom-hole pressure), amongst other considerations. Given the highly nonlinear relationship between these development variables and the production volumes (and hence the economic returns), optimization techniques are applied to find the most optimal solution (i.e., field development plan). However, it is essential that any proposed technique is pragmatic and consider the computational cost of the optimization algorithms. Even with improvements in computing hardware, realistic reservoir models can still be computationally demanding. Hence, the implementation of optimization algorithms into reservoir engineering workflows may be hindered if optimization process is computationally intense. To this end, this thesis investigates the development and implementation of state-of-the-art techniques for the efficient optimization of well control settings and well location under geological uncertainty. To begin, the thesis develops and implements a novel gradient-based optimization algorithm, Adam-SPSA, for high-dimensional well control problems. The proposed algorithm combines the adaptive moment estimation framework with simultaneous perturbation stochastic approximation. The adaptive moment framework utilizes first-order gradient information to generate dimension-wise stepsizes. This allows for faster convergence to an optimum. The proposed algorithm is applied to two well control problems. The first being a two-dimensional heterogeneous reservoir model produced under water-flooding with four producers and four injectors. The second problem is a three-dimensional model produced through 20 production wells and 10 injection wells. The developed algorithm, Adam- SPSA, achieved improvements of up to 91% in convergence speeds and up to 5% improvements in objective function value when compared to the popular steepest descent framework. The promising results of Adam-SPSA when applied to well control problems encouraged the investigation of applying the algorithm to the well placement and trajectory optimization problem. This investigation was done under the premise of a stringent computational budget and the availability of a heuristic-based initial guess. This takes advantage of the algorithm’s ability to efficiently converge to local optimum from a suitable starting point. The performance of Adam-SPSA was demonstrated through the application to two experimental problems. The first problem studied the placement of four vertical wells, resulting in a low-dimensional problem of only eight decision variables. The second problem was the placement of 20 nonconventional (i.e., deviated, horizontal and/or slanted) wells, resulting in a 120-dimensional optimization problem. The proposed algorithm, Adam-SPSA, consistently outperformed the steepest descent framework and a local derivative-free algorithm (i.e., generalized pattern search). The work was then expanded further with an in-depth discussion surrounding the effect of parameterization on optimization performance as well as constraint handling techniques within gradient approximations. An alternate approach was undertaken for the efficient optimization of well placement under strict computational budgets. The study investigated the use of a surrogate-based optimization approach, utilizing manifold mapping as a two-stage treatment, for well placement optimization. Manifold mapping was coupled with multiple surrogates including analytical – kriging and quadratic approximation – and a physics-based (reduced-order model) surrogate – local grid coarsening. The methodology was applied to two experimental problems, including the placement of four production wells in the presence of two pre-existing production wells and the placement of five production wells in a more complex three-dimensional model undergoing water-flooding. The proposed approach showed a reduction of computational costs of up to 80% compared to a local derivative-free algorithm. The results also gave insights into the most applicable scenario for the use of analytical surrogates and physics-based surrogates. It was shown that analytical surrogates are sufficient for simple reservoir models undergoing primary depletion. However, as the complexity of the reservoir models increases, such as secondary recovery through water-flooding, higher fidelity physics-based surrogates are more applicable as their accuracy is sufficient enough to model the trends of the full-physics simulations. A natural progression was the joint optimization of well control settings and well placement concurrently. However, this type of problem is very computationally intensive as it requires a large number of full-physics reservoir simulations for convergence. As such, a novel technique was proposed which included the use of capacitance resistance models (CRM) to improve the efficiency of the optimization. This was implemented in a bilevel approach for the simultaneous optimization of well controls and well locations. The outer loop was the well placement optimization solved by particle swarm optimization. The inner loop was the well control optimization solved by Adam-SPSA assisted by CRMs. The proposed approach was tested against the full-physics approach on two reservoir models of varying levels of complexity. The proposed bilevel approach found solutions that were up to 22% higher in objective function value than the conventional full-physics approach and accompanied by a decrease of up to 99% in the number of required reservoir simulations. The last research gap investigated in this thesis relates to the efficient incorporation of geological uncertainty in field development optimization problems. Typically, a full set of geological realizations (in the order of 100s to 1000s) are available to do this, however; including the full ensemble into an optimization problem makes it intractable. It was argued that previous work focussed on an intermediate goal of ranking base-case scenarios, static properties or a combination of these to select a subset of realizations. A reformulation of the subset selection problem to one which aims at ensuring consistent ranking of development strategies between the full set and the selected subset of realizations was introduced. The developed technique is a more relaxed problem and is not restricted in application. An application to well placement under uncertainty resulted in a reduction of computational costs, on average, by a factor close to 9, compared to the full set optimization. This result did not compromise the quality of the solution either.