An extended evolution strategy for the characterization of fracture conductivities from well tests

The characterization of fractured reservoirs involves: (1) the design of geological models integrating statistical and/or deterministic fracture properties; (2) the validation of flow simulation models by calibrating with dynamic field data e.g. well tests. The latter validation step is critical since it also validates the underlying geological model, it allows one to reduce some uncertainties among the fracture geometrical and distribution properties, and it is often the only mean to characterize fracture conductivities. However this is usually an ill-posed inverse problem: field data are usually not sufficient to fully characterize the fracture system. It is of interest to explore the parameters space effectively, so that multiple solutions may be characterized, and many production development scenarii may be studied. This paper presents a well tests inversion method to characterize fracture sets conductivities. The Covariance Matrix Adaptation-Evolution Strategy (CMA-ES) has been used as the optimization algorithm. It has been tested with some local optimization algorithms for comparison, and extended in order to detect several solutions simultaneously using a local proxy of the response surface. Moreover, uncertainty analyses are performed in regions of interest. Applications are presented for a fracture system with two fracture sets.