Combination of fuzzy ranking and simulated annealing to improve discrete fracture inversion

Mathematical and computational modelling of discrete fracture networks is critical for the exploration and development of natural resource reservoirs. Utilizing the concept of fuzzy memberships, this paper advances the fundamental understanding in fracture network inversion and presents a systematic procedure to solve the most important problem in global optimization (simulated annealing): objective function formulation. First, a comprehensive field study identifies all potential components of an objective function. The components are statistical, geostatistical, mathematical and spatial measurements of fracture properties (location, orientation and size). The characteristic measurements can be input in parametric or non-parametric, discrete or continuum forms. Next, sensitivity analysis and fuzzy logic are combined to rank the candidate components based on their effects on the final objective function value and optimization convergence. The process negates guess works in objective function formulation by automatic selection of highly ranked components and their corresponding weighting factors. A case study is applied to a surface DFN in New York. The derived discrete fracture network is representative of the field data.