Multivariate Production Systems Optimization


James Aubrey Carroll, III







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The objective of this research has been to investigate the effectiveness of nonlinear optimization techniques to optimize the performance of hydrocarbon producing wells.

The performance of a production well is a function of several variables. Examples of these variables are tubing size, choke size, and perforation density. Changing any of the variables will alter the performance of the well. There are several ways to optimize the function of well performance. An insensible way to optimize the function of well performance is by exhaustive iteration: optimizing a single variable by trial and error while holding all other variables constant, and repeating the procedure for different variables. This procedure is computationally expensive and slow to converge--especially if the variables are interrelated.

A prudent manner to optimize the function of well performance is by numerical optimization, particularly nonlinear optimization. Nonlinear optimization finds the combination of these variables that results in optimum well performance by approximating the function with a quadratic surface. The advantages of nonlinear optimization are many. Using nonlinear optimization techniques, there is no limit to the number of decision variables that can be optimized simultaneously. Moreover, the objective function may be defined in a wide variety of ways. Nonlinear optimization achieves quadratic convergence in determining the optimum well performance and avoids a trial and error solution. Several different optimization methods are investigated in this study: Newtonís Method, modified Newtonís Method with Cholesky factorization, and the polytope heuristic.

Significant findings of this study are: the performance of Newtonís Method can be greatly improved by including a line search procedure and a modification to ensure a direction of descent; For nonsmooth functions, the polytope heuristic provides an effective alternative to a derivative-based method; For nonsmooth functions, the finite difference approximations are greatly affected by the size of the finite difference interval. This study found a finite difference interval of one-tenth of the size of the variable to be advisable.

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Copyright 1990, James Aubrey Carroll, III: Please note that the reports and theses are copyright to their original authors. Authors have given written permission for their work to be made available here. Readers who download reports from this site should honor the copyright of the original authors and may not copy or distribute the work further without the permission of the author, James Aubrey Carroll, III.

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