PARALLEL WELL LOCATION OPTIMIZATION USING STOCHASTIC ALGORITHMS ON THE GRID COMPUTATIONAL FRAMEWORK

The determination of optimal well locations is a challenging problem in oil production since it depends on geological and fluid properties as well as on economic parameters. This work addresses the efficient solution of this problem by using advanced techniques for coupling three important components of autonomic optimization: the Integrated Parallel Accurate Reservoir Simulator (IPARS) for production prediction, new optimization algorithms, in particular the Simultaneous Perturbation Stochastic Approximation (SPSA) approach, and the Grid infrastructure to access computational resources on the network in a seamless way. We illustrate the methodology using numerical results based on real data. Optimizing how and where wells are drilled in an oil reservoir is a problem with both high economic impact and high complexity. Traditionally, this task is carried out by analyzing a few scenarios with a numerical reservoir simulator. However, this may potentially result into misleading decisions with large consequences. Optimization algorithms promise to perform a systematic exploration of a broader set of scenarios and aim at finding the optimum under some given conditions. Together with the experience of specialists, they also allow for a better assessment of uncertainty and reduction of risk in decision-making. The main constraint for their use is the cost of repeatedly evaluating different exploitation scenarios via numerical solution of a complex set of coupled nonlinear partial differential equations on up to millions of gridblocks. In this study, we present a computational framework for this problem, including Grid enabled technologies [4] to automatically discover and use available computational resources in a distributed environment, efficient optimization algorithms, and an efficient reservoir simulator. Using this framework, we have generated a complete dataset for a small but realistic test case in which only the two horizontal co-ordinates of a vertical well are subject to optimization. This large dataset is at the outer reaches of what is presently feasible with today's computational facilities. The test case shows a number of pathologies that also need to be expected in more realistic problems, including a large number of local optima. In this paper, we use it to test and explore how two different optimization algorithms perform. The optimization algorithms we present in this paper are a version of the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm [8] that was modified to handle the fact that the optimization domain is a bounded integer lattice, and a version of a Finite Difference Gradient algorithm adapted to the same constraints. As will be shown, both algorithms need about as many function evaluations, but SPSA is significantly less prone to get caught in local maxima, and is thus a more reliable tool for optimization of problems with many local extrema. The software used for these computations builds on the DISCOVER toolkit which allows agents running on geographically distributed machines to communicate with each other, to detect avail