Development of a Multi-Objective History Matching Model to Predict Individual Well Performance

Abstract

This study presents a new multi-objective history matching model using Pareto-optimality on the well basis for probabilistic reserve estimation. Previous works related to single-objective history matching have shown that some of individual well performance could not be predicted accurately since one linear-averaged objective function is minimized. The efficiency of multi-objective history matching depends on the number of production variables as the probability of trade-off solutions in the non-optimal objective space increases in proportion to the objectives. The author developed both dynamic goal programming and successive linear objective reduction, and integrated them with a standard multi-objective genetic algorithm. Dynamic goal programming induces convergence of the multi-objective approach by setting goals and constraints for production variables. Successive linear objective reduction enhances the optimization efficiency by excluding redundant production variables at the fitness evaluation in the genetic algorithm. Checking its validity on a multi-objective test problem, the model provides well-converged solutions with a uniform distribution along Pareto-optimum front comparing with conventional single- and multi-objective optimization approaches. The applicability of the model is verified for history matching of a synthetic light oil reservoir under waterflooding and a heavy oil reservoir under primary depletion in Canada, respectively. The model stably reduces the objectives that could overcome the scale-dependency in single-objective optimization as well as the divergence problem in multi-objective optimization. This calibration process predicts the future performance more reliably than typical optimization schemes from the equiprobable geomodels preserving the diversity of the feasible solutions, thereby unbiasedly assessing uncertainties in production forecast not only of the field but also of the wells.