Partially Separated Meta-Models with Evolution Strategies for Well Placement Optimization

Abstract

Finding the optimal location of non-conventional wells increases significantly the project's Net Present Value (NPV). This problem is nowadays one of the most challenging problems in oil and gas fields development. When dealing with complex reservoir geology and high reservoir heterogeneities, stochastic optimization methods are the most suitable approaches for optimal well placement. However, these methods require in general a considerable computational effort (in terms of number of reservoir simulations, which are CPU time demanding). This paper presents the use of the CMA-ES (Covariance Matrix Adaptation -Evolution Strategy) optimizer, which is recognized as one of the most powerful derivative free optimizers, to optimize well locations and trajectories. A local regression based meta-model is incorporated into the optimization process in order to reduce the computational cost. The objective function (e.g., the NPV) can usually be split into local components referring to each of the wells: it depends in general on a smaller number of principal parameters, and thus can be modeled as a partially separable function. In this paper, we propose to exploit the partial separability of the objective function into CMA-ES coupled with meta-models, by building partially separated meta-models. Thus, different meta-models are built for each well or set of wells, which results in a more accurate modeling.An example is presented. Results show that taking advantage of the partial separability of the objective function leads to a significant decrease in the number of reservoir simulations needed to find the "optimal" well configuration, given a restricted budget of reservoir simulations. This approach is practical and promising when dealing with a large number of wells to be located. IntroductionNowadays, the environment and the conditions in which oil and gas fields are discovered are more and more complex and challenging. Both existing fields and new discoveries need an optimal production scheme to be economically viable. One of the most important issues that must be addressed by reservoir engineers to maximize a given project's asset value is to optimally decide where to drill wells. Hence, the well placement optimization problem is nowadays a major focus in the petroleum industry. Many studies already investigated the well placement using different optimization methods: stochastic methods such as genetic algorithms (e.g., Bukhamsin et al., 2010, Emerick et al., 2009, Guyaguler and Horne, 2000, Montes et al., 2001, Morales et al., 2010, Yeten et al., 2003) and deterministic methods in particular adjoint methods (e.g., Sarma & Chen, 2008, Forouzanfar et al., 2010, Zandvliet et al., 2008, Vlemmix et al., 2009).Stochastic optimization methods were shown to be an appropriate approach for the well placement problem given the multiple local optima and the non-smoothness of the objective function. A promising method is the Covariance Matrix AdaptationEvolution Strategy (CMA-ES), a state of the art stochastic optimizer first...

Local-meta-model CMA-ES for partially separable functions

“…In the following we will also assume not only that the function is partially separable but also that one has access to the function value of each element function. As argued above this assumption is reasonable as it models the case for the well placement problem [4]. History matching is another problem in petroleum engineering in which this assumption is reasonable.…”

“…A suitable way to model the objective function is to suppose that the profit corresponding to a given well depends only on its location and on the distances of this well to the others. Using the distances between the wells as an element variable implies using a nonlinear combination of the parameters of the problem [4].…”

Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models

“…We believe, however, that performance over CMA-ES could be more significantly improved by exploiting, within the algorithm, knowledge, and relevant information about the optimization problem at hand, such as the problem structure. Some first steps in that direction have been conduced in [10,11] where the fact that the objective function can be split into local components referring to each of the wells where each depends on a smaller number of parameters (i.e., partial separability of the objective function) is exploited. Another approach could be to exploit some a priori information such as well allocation factors and connectivity using the work developed in [15].…”

Review of Field Development Optimization of Waterflooding, EOR, and Well Placement Focusing on History Matching and Optimization Algorithms

“…The method applied by Emerick et al [98] does not utilize a proxy model and in some cases involves more than 100 decision variables and thousands of reservoir simulation runs, possibly limiting the utility of the method. Bouzarkouna et al [99] propose optimal well location can be found through the use of a covariance matrix adaptation evolution strategy that uses adaptive penalization with rejection to deal with constraints. This method is used in conjunction with a meta-model that utilizes an approximate stochastic ranking procedure to rank the fitness of individual wells.…”