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Genetic algorithm for estimating multiphase flow functions from unsteady-state displacement experiments

Akın, Serhat
Demiral, Birol
Relative permeability and capillary pressure are the primary flow parameters required to model multiphase flow in porous media. Frequently, these properties are estimated on the basis of unsteady state laboratory displacement experiments. Interpretation of the flood process to obtain relative permeability data is performed by one of two means: application of frontal advance theory or direct computer simulation. Application of frontal advance theory requires a number of experimental restrictions such that the pressure drop across the core is sufficiently large that capillary effects, particularly at the outlet end of the core, are negligible. A parameter estimation technique overcomes significant limitations of the classic calculation procedure. In this approach, functional representations or point values are chosen for the relative permeability curves. Adjustable parameters are then picked to minimize a least squares objective function. Previous applications of this approach have used Gauss-Newton's method with or without Marquardt's modification. More recently, a simulated annealing method was also utilized. In this study we propose an interpretation method using recently developed genetic algorithms. The advantage and convenience of a genetic algorithm is that the method converges in all situations to a global optimum unlike Gauss-Newton methods, and it is as fast as the simulated annealing method. The performance of the algorithm is demonstrated with data from hypothetical and laboratory coreflood-displacement experiments where a computerized tomography scanner is utilized. It has been determined that the performance.of the algorithm depends on the probabilities of crossover and mutation, and the proper usage of the fitness function.