An Initial Guess for the Levenberg–Marquardt Algorithm for Conditioning a Stochastic Channel to Pressure Data
Tóm tắt
A standard procedure for conditioning a stochastic channel to well-test pressure data requires the minimization of an objective function. The Levenberg–Marquardt algorithm is a natural choice for minimization, but may suffer from slow convergence or converge to a local minimum which gives an unacceptable match of observed pressure data if a poor initial guess is used. In this work, we present a procedure to generate a good initial guess when the Levenberg–Marquardt algorithm is used to condition a stochastic channel to pressure data and well observations of channel facies, channel thickness, and channel top depth. This technique yields improved computational efficiency when the Levenberg–Marquardt method is used as the optimization procedure for generating realizations of the model by the randomized maximum likelihood method.
Tài liệu tham khảo
Bi, Z., 1999, Conditioning 3D stochastic channels to well-test pressure data: Doctoral Dissertation, University of Tulsa, OK, 150p.
Bi, Z., Oliver, D. S., and Reynolds, A. C. 1999, Conditioning 3D stochastic channels to pressure data (SPE-56682), in 1999 SPE Annual Technical Conference and Exhibition, p. 443-458.
Bonet-Cunha, L., Oliver, D. S., Rednar, R. A., and Reynolds, A. C., 1998, A hybrid Markov chain Monte Carlo method for generating permeability fields conditioned to multiwell pressure data and prior information: SPE J, v.3, no.3, p. 261-271.
Georgsen, F., and Omre, H., 1993, Combining fibre processes and Gaussian random functions for modelling fluvial reservoirs, in Soares A., ed., Proceedings: Geostatistics Tróia'92, Kluwer Academic, Dordrecht: p. 425-439.
Holden, L., Hauge, R., Skarem, ø., and Skorstad, A. 1998, Modeling of fluvial reservoirs with object models: Math. Geol., v.30, no.5, p. 473-496.
Kitanidis, P. K., 1995, Quasi-linear geostatiscal theory for inversing: Water Resour. Res., v.31, no.10, p. 2411-2419.
Landa, J. L., 1997, Reservoir parameter estimation constrained to pressure transients, performance history and distributed saturation data: Doctoral Dissertation, Stanford University, Stanford, CA, 251p.
Landa, J. L., and Horne R. N., 1997, A procedure to integrate well test data, reservoir performance history and 4-D seismic information into a reservoir description (SPE-38653), in 1997 SPE Annual Technical Conference and Exhibition, p. 99-114.
Li, R., Reynolds, A. C., and Oliver, D. S., 2001, History matching of three-phase flow production data (SPE 66351), in Proceedings of the 2001 SPE Reservoir Simulation Symposium, 16p.
Oliver, D. S., 1996, On conditional simulation to inaccurate data: Math. Geol., v.28, no.6, p. 811-817.
Oliver, D. S., He, N., and Reynolds, A. C. 1996, Conditioning permeability fields to pressure data, in European Conference for the Mathematics of Oil Recovery, V, p. 1-11.
Peaceman, D. W., 1983, Interpretation of well-block pressures in numerical reservoir simulation with non-square grid blocks and anisotropic permeability, Soc. Petrol. Eng. J., v.23, no.6, p. 531-543.
Rahon, D., Edoa, P. F., and Masmoudi, M., 1997, Inversion of geological shapes in reservoir engineering using well-tests and history matching of production data (SPE 38656), in 1997 SPE Annual Technical Conference and Exhibition, p. 141-150.
Reynolds, A. C., He, N., and Oliver, D. S., 1999, Reducing uncertainty in geostatistical description with well testing pressure data, in (edited by Schatzinger, R. A. and Jordan J. F.) eds., Reservoir Characterization—Recent Advances, American Association of Petroleum Geologists, p. 149-162.
Shmaryan, L. E., and Deutsch, C. V., 1999, Object-based modeling of fluvial/deepwater reservoirs with fast data conditioning: Methodology and case studies (SPE 56821), in Proceedings of the 1999 SPE Annual Technical Conference and Exhibition, p. 977-886.
Tarantola, A., 1987, Inverse problem theory: Methods for data fitting and model parameter estimation: Elsevier, Amsterdam, 613 p.
Zhang, F., Reynolds, A. C., and Oliver, D. S 2002, Evaluation of the reduction in uncertainly obtained by conditioning a 3d stochastic channel to multiwell pressure data: Math. Geol., v.34, no.6, p. 715-742.