Abstract
Uncertainty in future reservoir performance is usually evaluated from the simulated performance of a small number of reservoir realizations. Unfortunately, most of the practical methods for generating realizations conditional to production data are only approximately correct. It is not known whether or not the recently developed method of Gradual Deformation is an approximate method or if it actually generates realizations that are distributed correctly. In this paper, we evaluate the ability of the Gradual Deformation method to correctly assess the uncertainty in reservoir predictions by comparing the distribution of conditional realizations for a small test problem with the standard distribution from a Markov Chain Monte Carlo (MCMC) method, which is known to be correct, and with distributions from several approximate methods. Although the Gradual Deformation algorithm samples inefficiently for this test problem and is clearly not an exact method, it gives similar uncertainty estimates to those obtained by MCMC method based on a relatively small number of realizations.
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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.1, p. 261-271.
Hegstad, B. K., and Omre, H., 1997, Uncertainty assessment in history matching and forecasting, in Baafi, E. F., and Schofield, N. A., eds., Geostatistics Wollongong' 96, v.1: Kluwer Academic, p. 585-596.
Hegstad, B. K., and Omre, H., 2001, Uncertainty in production forecasts based on well observations, seismic data and production history: SPE J. v.6, no.4, p. 409-424.
Holden, L., Skare, Ø., Omre, H., and Tjelmeland, H., 2001, Sampling algorithms for Bayesian history matching, Tech. Rep. No. SAND/04/01: Norwegian Computing Center, Oslo, Norway.
Hu, L. Y., 2000, Gradual deformation and iterative calibration of gaussian-related stochastic models, Math. Geol., v.32, no.1, 87-108.
Hu, L. Y., Ravalec, M. L., and Blanc, G., 2001, Gradual deformation and iterative calibration of truncated Gaussian simulations: Petrol. Geosci., v.7, p. 25-30.
Hu, L. Y., Ravalec, M. L., Blanc, G., Roggero, F., Nœtinger, B., Haas, A., and Corre, B., 1999, Reducing uncertainties in production forecasts by constraining geological modeling to dynmaic data, SPE paper no. 56703, p. 1-8.
Le Ravalec, M., Hu, L. Y., and Nœtinger, B., 1999, Stochastic reservoir modeling constrained to dynamic data: Local calibration and inference of the structural parameters, SPE paper no. 56556, p. 1-9.
Le Ravalec, M., Hu, L. Y., and Nœtinger, B., 2000, Sampling the conditional realization space using the gradual deformation method: Geostatistics (Cape Town), v.1, p. 176-186.
Le Ravalec, M., and Nœtinger, B., 2002, Optimization with the gradual deformation method: Math. Geol., v.34 no.2, p. 125-142.
Liu, N., and Oliver, D. S., 2003, Evaluation of Monte Carlo methods for assessing uncertainty: SPE J., v.8, no.2, p. 1-15.
Oliver, D. S., Cunha, L. B., and Reynolds, A. C., 1997, Markov chain Monte Carlo methods for conditioning a permeability field to pressure data: Math. Geol., v.29, no.1, p. 61-91.
Oliver, D. S., He, N., and Reynolds, A. C., 1996, Conditioning permeability fields to pressure data, in Proc. Eur. Conf. Math. Oil Recov., V (ECMOR V), Leoben, Austria, p. 1-11.
Omre, H., 2001, Stochastic reservoir models conditioned to non-linear production history observations, Tech. Rep. Statistics No. 3/2001: Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway.
Roggero, F., and Hu, L. Y., 1998, Gradual deformation of continuous geostatistical models for history matching, SPE paper no. 49004.
Skjervheim, J. A., 2002, Gradual deformation: Unpublished class project, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway.
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Liu, N., Oliver, D.S. Experimental Assessment of Gradual Deformation Method. Mathematical Geology 36, 65–77 (2004). https://doi.org/10.1023/B:MATG.0000016230.52968.6e
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DOI: https://doi.org/10.1023/B:MATG.0000016230.52968.6e