Identification of spatially discontinuous parameters in second-order parabolic systems by piecewise regularization

A novel piecewise regularization approach has been developed for the identification of spatially discontinuous parameters in second-order parabolic systems. First, the identification approach is rigorously formulated in a functional analytic framework. Then, the theoretical results are applied to the history-matching of one-dimensional fractured reservoirs. The performance of the proposed algorithm is evaluated by numerical experiments.

[1]  P. C. Shah,et al.  Reservoir History Matching by Bayesian Estimation , 1976 .

[2]  D. F. Shanno,et al.  Matrix conditioning and nonlinear optimization , 1978, Math. Program..

[3]  S. Nakagiri,et al.  Identifiability of Spatially-Varying and Constant Parameters in Distributed Systems of Parabolic Type , 1977 .

[4]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[5]  J. Aubin.  Approximation of Elliptic Boundary-Value Problems , 1980 .

[6]  C. Kravaris,et al.  Identification of spatially varying parameters in distributed parameter systems by discrete regularization , 1986 .

[7]  A. Tarantola.  Inversion of seismic reflection data in the acoustic approximation , 1984 .

[8]  Costas Kravaris,et al.  History matching by spline approximation and regularization in single-phase areal reservoirs , 1986 .

[9]  C. Kravaris,et al.  Identification of parameters in distributed parameter systems by regularization , 1983, The 22nd IEEE Conference on Decision and Control.

[10]  Patricia K. Lamm,et al.  Estimation of discontinuous coefficients in parabolic systems: applications to reservoir simulation , 1987 .

[11]  W. Yeh.  Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[12]  George Finlay Simmons,et al.  Introduction to Topology and Modern Analysis , 1963 .

[13]  C. Kravaris,et al.  Identifiability of spatially-varying conductivity from point observation as an inverse Sturm-Liouville problem , 1986 .