Integration of geostatistical realizations in data assimilation and reduction of uncertainty process using genetic algorithm combined with multi-start simulated annealing

This paper introduces a new methodology, combining a Genetic Algorithm (GA) with multi-start simulated annealing to integrate Geostatistical Realizations (GR) in data assimilation and uncertainty reduction process. The proposed approach, named Genetic Algorithm with Multi-Start Simulated Annealing (GAMSSA), comprises two parts. The first part consists of running a GA several times, starting with certain number of geostatistical realizations, and the second part consists of running the Multi-Start Simulated Annealing with Geostatistical Realizations (MSSAGR). After each execution of GA, the best individuals of each generation are selected and used as starting point to the MSSAGR. To preserve the diversity of the geostatistical realizations, a rule is imposed to guarantee that a given realization is not repeated among the selected individuals from the GA. This ensures that each Simulated Annealing (SA) process starts from a different GR. Each SA process is responsible for local improvement of the best individuals by performing local perturbation in other reservoir properties such as relative permeability, water-oil contact, etc. The proposed methodology was applied to a complex benchmark case (UNISIM-I-H) based on the Namorado Field, located in the Campos Basin, Brazil, with 500 geostatistical realizations and other 22 attributes comprising relative permeability, oil-water contact, and rock compressibility. Comparisons with a conventional GA algorithm are also shown. The proposed method was able to find multiple solutions while preserving the diversity of the geostatistical realizations and the variability of the other attributes. The matched models found by the GAMSSA method provided more reliable forecasts when compared with the matched models found by the GA.