On solving Large-scale well positioning problems

We consider several mathematical aspects of technological objects positioning applied to oil and gas fields. Best results of these algorithms obtained while dealing with non-great fields of complex structure; these algorithms are suitable for non-regular well location problems, when one cannot define a strong pattern for well positions. Proposed problems are formulated in terms of Boolean programming. We present a new iterative method of solving described Boolean problems finding optimum within a reasonable time. This method is a clustering algorithm designed to deal with Boolean parameters. We introduce a Monte-Carlo-like approach forecasting the optimal value for a certain problem. Several applications of formulated algorithms applied to test field models with properties similar to real field models. We present both Boolean problems solutions. Comparing different scales, we show complexity of proposed algorithm. We also present comparisons between computational time and number of iterations for different initialization schemes. Optimal solutions of formulated problems are good as initial points for other iterative (gradient-based) algorithms of well location problems. Proposed algorithms are practical for field development cases applied to complex oil and gas fields.