A new approach to nonlinear groundwater management methodology is presented which optimizes aquifer remediation with the aid of artificial neural networks (ANNs). The methodology allows solute transport simulations, usually the main computational component of management models, to be run in parallel. The ANN technology, inspired by neurobiological theories of massive interconnection and parallelism, has been successfully applied to a variety of optimization problems. In this new approach, optimal management solutions are found by (1) first training an ANN to predict the outcome of the flow and transport code, and (2) then using the trained ANN to search through many pumping realizations to find an optimal one for successful remediation. The behavior of complex groundwater scenarios with spatially variable transport parameters and multiple contaminant plumes is simulated with a two‐dimensional hybrid finite‐difference/finite‐element flow and transport code. The flow and transport code develops the set of examples upon which the network is trained. The input of the ANN characterizes the different realizations of pumping, with each input indicating the pumping level of a well. The output is capable of characterizing the objectives and constraints of the optimization, such as attainment of regulatory goals, value of cost functions and cleanup time, and mass of contaminant removal. The supervised learning algorithm of back propagation was used to train the network. The conjugate gradient method and weight elimination procedures are used to speed convergence and improve performance, respectively. Once trained, the ANN begins a search through various realizations of pumping patterns to determine whether or not they will be successful. The search is directed by a simple genetic algorithm. The resulting management solutions are consistent with those resulting from a more conventional optimization technique, which combines solute transport modeling and nonlinear programming with a quasi‐Newton search. The results suggest that the ANN approach has the following advantages over the conventional technique for the test remediations: more independence of the flow and transport code from the optimization, greater influence of hydrogeologic insight, and less computational burden due to the potential for parallel processing of the flow and transport simulations and the ability to “recycle” these simulations. The ANN performance was observed upon variation of the problem formulation, network architecture, and learning algorithm.

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Determination of the location of new wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, and economic criteria. Various approaches have been proposed for this problem. Among those, direct optimization using the simulator as the evaluation function, although accurate, is in most cases infeasible due to the number of simulations required. In this study a hybrid optimization technique based on the genetic algorithm (GA), polytope algorithm, kriging algorithm and neural networks is proposed. Hybridization of the GA with these helper methods introduces hill-climbing into the stochastic search and also makes use of proxies created on the fly. Performance of the technique was investigated on a set of exhaustive simulations for the single well placement problem and it was observed that the number of simulations required was reduced significantly. This reduction in the number of simulations reduced the computation time, enabling the use of full-scale simulation for optimization even for this full-scale field problem. It was also seen that the optimization technique was able to avoid convergence to local maxima due to its stochastic nature. Optimal placement of up to four water injection wells was studied for Pompano, an offshore field in the Gulf of Mexico. Injection rate was also optimized. The net present value of the waterflooding project was used as the objective function. Profits and costs during the time period of the project were taken into consideration.

Determination of the location of new wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, and economic criteria. Various approaches have been proposed for this problem. Among those, direct optimization using the simulator as the evaluation function, although accurate, is in most cases infeasible due to the number of simulations required. In this study a hybrid optimization technique based on the genetic algorithm (GA), polytope algorithm, kriging algorithm and neural networks is proposed. Hybridization of the GA with these helper methods introduces hill-climbing into the stochastic search and also makes use of proxies created on the fly. Performance of the technique was investigated on a set of exhaustive simulations for the single well placement problem and it was observed that the number of simulations required was reduced significantly. This reduction in the number of simulations reduced the computation time, enabling the use of full-scale simulation for optimization even for this full-scale field problem. It was also seen that the optimization technique was able to avoid convergence to local maxima due to its stochastic nature. Optimal placement of up to four water injection wells was studied for Pompano, an offshore field in the Gulf of Mexico. Injection rate was also optimized. The net present value of the waterflooding project was used as the objective function. Profits and costs during the time period of the project were taken into consideration. Introduction Numerical models are detailed and powerful predictive tools in reservoir management. While not perfect they are often the best representation of the subsurface available. Optimization methodologies run these numerical models perhaps thousands of times searching for the most profitable solution to reservoir management questions. Because of the computational time involved optimization methodologies are not used as much as they could be. Various researchers have explored speeding up optimization by either using a speedier evaluation of the objective function (i.e. simpler model or proxy for the full numerical model) or improving the efficiency of the optimization search itself. This paper uses the latter approach focussing on search improvement, yet harnesses some of the techniques often used in proxy development to allow the search to step toward optimality more skillfully. Researchers have looked into optimization of well placement and rate using numerical simulation. Beckner and Song1 formulated the problem as a traveling-salesman problem and used simulated annealing to optimize well location and drilling schedule. Bittencourt and Horne2 investigated optimization of well placement using a hybrid of genetic algorithm (GA) and polytope method. Güyagüler and Gümrah3 optimized production rates for a gas storage field using GAs. Aanonsen et al4 coupled a CPU efficient reservoir simulator with an optimization algorithm and made use of a kriging proxy to find optimum well locations. Pan and Horne5 also used kriging to decrease the necessary number of simulations required to optimize well location. Rogers and Dowla6 and Centilmen et al7 used neural networks as a substitute for numerical simulation. We have been exploring search improvements in GA8 to decrease the total number of individual simulations required for convergence of the optimization problem. The GA is popular for its strengths in avoiding suboptimal solutions, freedom from requiring derivatives, and ease of parallelization. The GA was chosen over other popular heuristic search algorithms, such as simulated annealing, because of the concept of population and the greater ease of parallelization. Parallelization obviously has the potential to speed calculations. The concept of population integrates well with the formulation of the search improvements of this work. Some of the same traits that make the GA robust and powerful also make it slow and inexact in refinement of the solution. The GA typically has rapid initial progress during the search, but has problems locating the final optimal solution.