IDENTIFIABILITY VERSUS HETEROGENEITY IN GROUNDWATER MODELING SYSTEMS
الكلمات المفتاحية:
groundwater modeling، inverse problem، identification، optimisation، heterogeneityالملخص
Review of history matching of reservoirs parameters in groundwater flow raises the problem of identifiability of aquifer systems. Lack of identifiability means that there exists parameters to which the heads are insensitive. From the guidelines of the study of the homogeneous case, we inspect the identifiability of the distributed transmissivity field of heterogeneous groundwater aquifers. These are derived from multiple realizations of a random function Y = log T whose probability distribution function is normal.
We follow the identifiability of the autocorrelated block transmissivities through the measure of the sensitivity of the local derivatives DTh = (∂hi ∕ ∂Tj) computed for each sample of a population N (0; σY, αY). Results obtained from an analysis of Monte Carlo type suggest that the more a system is heterogeneous, the less it is identifiable.
التنزيلات
المراجع
- Kitamura S. and Nagakiri S., "Identifiability of spatially varying and constant parameters in Distributed Systems of Parabolic type", SIAM J. Contr. Optimiz., 15 (5), (1977).
- Chaven G., Dupuy M. and Lemmonier P., "History matching by use of optimal theory", Soc of Petrol. Eng. Journal, (1975), pp. 74-86.
- Carrera J.C., Neuman S.P., "Estimation of aquifers parameters under transient and steady state conditions", Water res. research, (1989).
- Hill M.C., "Methods and guidelines for effective model calibration with application to Ucode and Modflowp", US Geological Water Survey, Water Resources Investigations, report 98-4005, Denver-Colorado, (1998), p. 90.
- Doherty J., Brebber L. and White L., "PEST a model independent parameter estimation", Watermark computing, (1994), p. 146.
- Angel E. and Bellman R., "Dynamic programming and partial differential equation", Vol.88, in Mathematics in Science and Engineering, Academic press, New York, (1972), p. 202.
- Tarantola A., "Inverse problem theory Methods for data fitting and model parameter estimation", Elsevier, New
York, (1987), p. 613.
- Kubrusly C.S., "Distributed parameter system : a survey", International Journal of Control, 26 (4), (1977), pp. 509-535.
- Yakowitz S. and Duckstein L., "Instability in aquifer parameter identification : Theory and case studies", Water Res. Research, 16 (6), (1980), pp. 1045-1064.
- Mantoglu A. and Wilson J.L., "Simulation of random fields with the turning bands method", report n° 264, Ralph M. Parsons Lab., dept of civil eng., MIT, (1981).
- McElwee C.D., "Sensitivity analysis and the groundwater inverse problems", Groundwater 20 (6), (1982), pp. 723-735.
- Benali A.M., "Correlation links between the diagonal elements of the flow matrix : Preliminary results", MNEM’95, Vème Colloque Maghrébin sur les Méthodes Numériques de l’Ingénieur, Rabat 21-23 nov., (1995).
- Shah P.C, Gavalas G.R. and Seinfeld J.H., 'Errors analysis in history matching. The optimum level of parametrization", Soc of Pet. Eng. Jour., (1978), pp. 219-228.
