A Simulated Annealing Approach to Constrained Nonlinear Optimization of Formation Parameters in Quantitative Log Evaluation

Abstract

Abstract Quantitative log evaluation is essentially a model-based inversion of well logs, which is a constrained nonlinear global optimization problem when a prior information is sparse, where how to obtain global optimal solutions is the key problem. While many previous papers either avoid the nonlinearity by transformation methods, or simplify the nonlinearity in log analysis by linear approximation, or even use "steepest descent", or conjugate gradient techniques which are inapplicable for finding a global optimal solution in log analysis, based on an analogy between the model-algorithm system and a statistical mechanical system, this paper investigates the use of an efficient, global, stochastic optimization method, that of simulated annealing, for determining the optimal estimates of formation parameters in log analysis in such a case of constrained nonlinear optimization which is based on a well log interpretive model. This paper presents the algorithm of simulated annealing global optimization of log analysis. The methods are given to determine the key parameters in such a simulated annealing. And finally both the advantages and limitations of this approach are pointed out. A field example presented from China demonstrates the usefulness of this new approach and its comparison with the results processed by another log analysis software widely used in China indicates that this approach can efficiently overcome local minimum problem and provides more accurate estimates of formation parameters.