مدلسازیشبکه شکست نوع I : فرمولاسیون تابع هدف توسط تجزیه و تحلیل حساسیت فازی

This paper advances the fundamental understanding in mathematical and computational modelling of discrete fracture networks (Type I). It presents a systematic procedure to solve the most important problem in modelling by global optimization — objective function formulation, which negates guesswork in objective function formulation by automatic selection of highly ranked components and their corresponding weighting factors. The procedure starts from real data to identify potential components of the objective function. The components are then ranked by fuzzy sensitivity analysis, based on their effects on the final objective function value and simulation convergence. The final fracture network inversion is subsequently realized and validated. Results of the study provide an explanation why previous methods such as stochastic simulations are not sufficiently reliable, compared to global optimization methods.

Type I fracture networks refer to those where the rock matrix is non-porous and non-permeable and fractures dominate both storage and flowing capacities. Among underground natural resources, the type I fracture behaviours are most noticeable in fractured granite basement petroleum reservoirs and fractured sandstone geothermal sources. This type I performance is typically characterized by high production derivability at initial time and sudden/ rapid declines afterwards. Modelling discrete fractures in a type I fracture network is the essential first step in understanding the fluid storage and flowing mechanisms. To date, there have been a wide range of approaches that model discrete fracture networks, among which global optimization methods (mostly simulated annealing) can be ranked as the most computationally and technologically advanced. They can provide fracture network inversions with certain success [1], [2], [3], [4] and [5]. Recently, Tran et al. [6] further advance global optimization methodology by combining it with comprehensive fracture characterization, neuro-stochastic simulation, object-based and conditional modelling. The authors identify that the two determinant aspects of a successful global optimization model are: (1) an appropriate objective function, such that when minimized, the output is indeed a representation of the target; and (2) an efficient modification scheme. In the previous works, objective functions are chosen arbitrarily. Many components and measurements are not representative to a normal fracture system. Significant improvement has been made by combining the formulation of an objective function with comprehensive fracture characterization and by introducing non-parametric components [6]. However, it is realized that determining appropriate components and weighting factors for objective functions remain the major issue that limits applications of global optimization in practical geoscience modelling. This paper applies a fuzzy-logic-based sensitivity analysis to help ranking components of an objective function based on their behaviour towards solution convergence. The procedure is illustrated using a fracture outcrop of the New York area as an example (Fig. 1). Full-size image (99 K) Fig. 1. Target fracture network map (and the corresponding fracture density map m/m2. Lighter colours indicate denser fracture distribution).

This paper has presented a systematic and efficient fuzzy ranking procedure to tackle the most important aspect of global optimization: objective function formulation. The application of sensitivity analysis and fuzzy ranking negates guesswork and produces more reliable result. It furthers the advantages of global optimization: no assumptions of prior statistical distributions, flexibility in combining parameters of different characteristics, ability to honour more data and produce more reliable fracture networks than conventional geostatistical simulation techniques. Even though it takes a large number of iterations, with the current high standard of the computer’s processing capability, the whole process is efficiently fast. Two further important conclusions can be drawn from the results of this study: • It confirms the common perception that simple first-order statistics are important. • It proves that the second-order variograms and fracture density distribution do play more crucial roles. The conclusions provide an insight into why most previous models (especially stochastic simulations) are not sufficiently reliable, as they utilize only statistical distributions and do not incorporate the field distribution of fracture density nor experimental variograms.