Modelling of type I fracture network: Objective function formulation by fuzzy sensitivity analysis. (English) Zbl 1165.74347

Summary: 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.


74R10 Brittle fracture
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI


[1] Mauldon, A.D., An inverse technique for developing models for fluid-flow in fracture systems using simulated annealing, Water resources research, 29, 11, 3775-3789, (1993)
[2] Deutsch, C.V.; Cockerham, P.W., Practical considerations in the application of simulated annealing to stochastic simulation, Mathematical geology, 26, 1, 67-82, (1994)
[3] Day-Lewis, F.D.; Hsieh, P.A.; Gorelick, S.M., Identifying fracture-zone geometry using simulated annealing and hydraulic-connection data, Water resources research, 36, 7, 1707-1721, (2000)
[4] Nakao, S.; Najita, J.; Karasaki, K., Hydraulic well testing inversion for modeling fluid flow in fractured rocks using simulated annealing: A case study at raymond field site, California, Journal of applied geophysics, 45, 3, 203-223, (2000)
[5] Gauthier, B.D.M.; Garcia, M.; Daniel, J.M., Integrated fractured reservoir characterization: A case study in a north africa field, Spe reservoir evaluation & engineering, 5, 4, 284-294, (2002)
[6] Tran, N.H.; Chen, Z.; Rahman, S.S., Integrated conditional global optimisation for discrete fracture network modelling, Computers & geosciences, 32, 1, 17-27, (2006)
[7] Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulated annealing, Science, 220, 4598, 671-680, (1983) · Zbl 1225.90162
[8] Sen, M.K.; Stoffa, P.L., Global optimization methods in geophysical inversion, (), 281, xi · Zbl 0871.90107
[9] Kosko, B., Neural networks and fuzzy systems : A dynamical systems approach to machine intelligence, (1991), Prentice Hall Englewood Cliffs, NJ, xxvii, p. 449
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.