Preview
Unable to display preview. Download preview PDF.
References
Bakr, A.A., Gelhar, L.W., Gutjahr, A.L., and Macmillan, J.R.: Stochastic analysis of spatial variability in subsurfaces flows, I. Comparison of one-and three-dimensional flows, Water Resour. Res. 14(2) (1978), pp. 263–271.
Banks, H.T.: A survey of some problems and recent results for paramater estimation and optimal control in delay and distributed parameter systems, ICASE Report No. 81–26 (1981).
Beck, J.V., and Arnold, K.J.: Parameter Estimation in Engineering and Science, John Wiley, New York, 1977.
Breit, V.S., Bishop, K.A., Green D.W., and Trompeter, E.E.: A technique for assessing and improving the quality of reservoir parameter estimates used in numerical simulators, SPE 4546 presented at the 48th Annual Meeting, Las Vegas, September 30–October 3, 1973.
Cannon, J.R., and Dogru, A.H.: Estimation of permeability and porosity from well test data, J. Pet. Tech. Forum (1980), pp. 1323–1324.
Cannon, J.R., and Du Chateau, P.D.: Determination of unknown physical properties in heat conduction problems, Int. J. Eng. Sci. 11 (1973), pp.783–794.
Cannon, J.R., and Du Chateau, P.D.: Determining unknown coefficients in a nonlinear heat conduction problem, SIAM J. Appl. Math. 24 (1973), pp. 298–314.
Cannon, J.R., and Du Chateau, P.D.: An inverse problem for a nonlinear diffusion equation, SIAM J. Appl. Math. 39 (1980), pp. 272–289.
Carter, R.D., Kemp, L.F., and Williams, D.: Performance matching with con-straints, Soc. Pet. Eng. J. (April 1974), pp. 187–196.
Chang, S., and Yeh, W.: A proposed algorithm for the solution of the large-scale inverse problem in groundwater, Water Resour. Res. 12 (1976), pp. 365–374.
Chavent, G., Dupuy, M., and Lemonnier, P.: History matching by use of optimal control theory, Soc. Pet. Eng. J. (February 1975), pp. 74–86; Trans. AIME, Vol. 259.
Chavent, G.: A new formulation of diphasic imcompressible flows in porous media, Lecture Notes in Mathematics No. 503, Springer-Verlag 1976.
Chavent, G., Cohen G., and Espy, M.: Determination of relative permeabilities and capillary pressures by an automatic adjustment method, SPE 9237 presented at 55th Annual Fall Tech. Conf. and Exhib. of SPE of AIME, Dallas, September 21–24, 1980.
Chen, W.H., Gavalas, G.R., Seinfeld, J.H., and Wassermann, M.L.: A new algorithm for automatic history matching, Soc. Pet. Eng. J. (December 1974), pp. 593–608; Trans., AIME, Vol. 257.
Chen, W.H., and Seinfeld, J.H.: Estimation of spatially varying parameters in partial differential equations, Int. J. Control 15 (1972), pp. 487–495.
Coats, K.H., Dempsey, J.R., and Henderson, J.H.: A new technique for determining reservoir description from field performance data, Soc. Pet. Eng. J. (March 1970), pp. 66–74; Trans., AIME, Vol. 249.
Cooley, R.L.: Incorporation of prior information on parameters into nonlinear regression groundwater flow models, I. Theory, Water Resour. Res. 18(4) (1982), pp. 965–976.
Dagan, G.: Stochastic modeling of groundwater flow by unconditional and conditional probabilities, I. Conditional simulation and the direct problem, Water Resour. Res. 18(4) (1982), pp. 813–833.
Darlow, B.L., Ewing R.E., and Wheeler, M.F.: Mixed finite element methods for miscible displacement problems in porous media, Proc. Sixth Symp. on Reservoir Simulation, New Orleans, 1982, pp. 137–146.
Delhomme, J.P.: A variability and uncertainty in groundwater flow parameters: a geostatistical approach, Water Resour. Res. 15(4) (1979), pp. 269–280.
Distefano, N., and Rath, A.: An identification approach to subsurface hydrological systems, Water Resour. Res. 11 (1975), pp. 1005–1012.
Dixon, T.N., Seinfeld, J.H., Startzman, R.A., and Chen, W.H.: Reliability of reservoir parameters from history matched drillstem tests, SPE 4282 presented at SPE-AIME Third Symp. on Numer. Simulation of Reservoir Performance, Houston, January 10–12, 1973.
Douglas, Jim, Jr.: Finite difference methods for two-phase, incompressible flow in porous media, SIAM J. Numer. Anal., to appear.
Dogru, A.H.: Confidence limits on the parameters and predictions of one-dimensional, slightly compressible, single-phase reservoirs, Ph.D. Thesis, University of Texas, Austin (May 1984).
Dogru, A.H., Dixon, T.N., and Edgar, T.F.: Confidence limits on the parameters and predictions of slightly compressible, single-phase reservoirs, SPE 4983 presented at SPE-AIME 49th Annual Fall Meeting, Houston, October 6–9, 1974.
Dogru, A.H., and Knapp, R.M.: The reliability of the predicted performance of natural gas reservoirs using reservoir parameters from well test data containing errors, Proc. Rocky Mountain Regional SPE Meeting, Denver, April 7–9, 1975.
Dogru, A.H., and Seinfeld, J.H.: Design of well tests to determine the properties of stratified reservoirs, Proc. Fifth SPE Symp. on Reservoir Simulation, Denver, February 1–2, 1979.
Dogru, A.H., and Seinfeld, J.H.: Comparison of sensitivity coefficient calculation methods in automatic history matching, Soc. Pet. Eng. J. (October 1981), pp. 551–557.
Draper, N.R., and Van Nostrand, R.C.: Ridge regression and James-Stein estimation: review and comments, Technometrics 21 (4), pp. 451–466.
Du Chateau, P.D.: Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation, SIAM J. Appl. Math. 41 (1981), pp. 310–323.
Emsellem, Y., and de Marsily, G.: An automatic solution for the inverse problem, Water Resour. Res. 7 (1971), pp. 1264–1283.
Ewing, R.E.: Determination of coefficients in reservoir simulation, in Numerical Treatment of Inverse Problems for Differential and Integral Equations, P. Deuflhardt and E. Hairer, eds., Birkhäuser, Berlin 1982, pp. 206–226.
Ewing, R.E., Falk, R.S., Bolzan, J.F., and Whillans, I.M.: Techniques for thermal conductivity measurements in Antarctica, Ann. Glaciology 3 (1982), pp. 96–102.
Ewing, R.E., and Russell, T.F.: Efficient time-stepping methods for miscible displacement problems in porous media, SIAM J. Numer. Anal. 19 (1982), pp. 1–6.
Ewing, R.E., and Wheeler, M.F.: Galerkin methods for miscible displacement problems in porous media, SIAM J. Numer. Anal. 17 (1980), pp. 351–365.
Ewing, R.E., and Wheeler, M.F.: Galerkin methods for miscible displacement problems with point sources and sinks — unit mobility ratio case, Proc. Special Year in Numerical Analysis, University of Maryland, College Park, 1981, pp. 151–174.
Ewing, R.E., and Wheeler, M.F.: Computational aspects of mixed finite element methods, Numerical Methods for Scientific Computing, R.S. Stepleman, ed., North Holland Publ. Co., to appear.
Eykhoff, P.: System Identification, John Wiley, New York, 1974.
Falk, R.S.: Error estimates for the numerical identification of a variable coefficient, to appear.
Frick, T.C.: Petroleum Production Handbook, Vol. II, Mc-Graw-Hill, New York 1962.
Frind, E.O., and Pinder, G.F.: Galerkin solution of the inverse problem for aquifer transmissivity, Water Resour. Res. 9 (1973), pp. 1397–1410.
Gavalas, G.R, Shah, P.C., and Seinfeld, J.H.: Reservoir history matching by Bayesian estimation, Soc. Pet. Eng. J. 16 (December 1976), pp. 337–350; Trans., AIME, Vol. 261.
Gelhar, L.W., and Axness, C.L.: Three-dimensional stochastic analysis of macro-dispersion in aquifers, Water Resour. Res. 19(1) (1983), pp. 161–180.
Golub, G.H., Heath, M., and Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21(2) (1979), pp. 215–223.
Gorelick, S.M., Voss, C.I., Gill, P., Murray, M., Saunders, M., and Wright, M.: Aquifer reclamation design: the use of contaminant transport simulation combined with nonlinear programming, Water Resour. Res. 20(4) (1984), pp. 415–427.
Gorelick, S.M.: A review of distributed parameter groundwater management modeling methods, Water Resour. Res. 19(2) (1983), pp. 305–319.
Hirasaki, G.J.: Estimation of reservoir parameters by history matching oil displacement by water or gas, SPE 4283 presented at Third Symp. on Numer. Simulation of Res. Performance, Houston, January 10–12, 1973.
Hornung, U., and Messing W.: Identification of soil parameters for an infiltration problem, Finite Elements in Water Resources, Proc. Fourth Int. Conf., Hannover, 1982, Springer-Verlag, Berlin.
Jacquard, P.: Theory de l'interpretation des mesures de pression, Revue de L'Institut France du Petrole (March 1984).
Jacquard, P., and Jain C.: Permeability distribution from field pressure data, Soc. Pet. Eng. J. (December 1965), pp. 281–294; Trans., AIME, Vol. 234.
Jahns, H.O.: A rapid method for obtaining a two-dimensional reservoir description for well response data, Soc. Pet. Eng. J. (December 1966), pp. 315–327; Trans., AIME, Vol. 237.
Keelan, D.K.: A critical review of core analysis techniques, J. Can. Pet. Tech. (April 1972), pp. 1–14.
Kitanidis, P.K, and Vomvoris, E.G.: A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations, Water Resour. Res., 19(3) (1983), pp. 667–690.
Kubrusky, C.: Distributed parameter system identification: a survey, Int. J. Control 26 (1977), p. 509–535.
Matthews, C.S., and Russell, D.G.: Pressure Buildup and Flow Tests in Wells, Monograph Vol. 1, Henry L. Doherty Series, SPE of AIME, 1967.
Nelson, R.N.: In-place determination of permeability distribution for heterogeneous porous media through analysis of energy dissipation, Soc. Pet. Eng. J. 8 (1968), pp. 33–42.
Neuman, S.P.: A statistical approach to the inverse problem of aquifer hydrology, III. Improved solution method and added perspective, Water Resour. Res. 16(2) (1980), pp. 331–346.
Neuman, S.P., Fogg, A., and Jacobson, E.: A statistical approach to the inverse problem of aquifer hydrology, II. Case study, Water Resour. Res. 16 (1980), pp. 33–58.
Neuman, S.P., and Yakowitz, S.: A statistical approach to the inverse problem of aquifer hydrology, I. Theory, Water Resour. Res. 15(4) (1979), pp. 845–860.
Odeh, A.S.: Steady-state flow capacity of wells with limited entry to flow, Trans., AIME, Vol. 243 (1968), p. 43.
Peaceman, D.W.: Fundamentals of Reservoir Simulation, Developments in Petroleum Science 6, Elsevier Publishing Co., Amsterdam, 1977.
Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir simulation, Soc. Pet. Eng. J. (June 1978), pp. 183–194.
Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir with nonsquare grid blocks and anisotropic permeability, Proc. Sixth SPE Symp. on Reservoir Simulation, New Orleans, February 1–3, 1982.
Polis, M.P.: The distributed system parameter identification problem: a survey of recent results, Control and Distributed Parameter System Systems, J.J. Barbay and L. Letty, eds., IFAC, 1982, pp. 45–58.
Pryor, W.A.: Reservoir inhomogeneities in some recent sand bodies, Soc. Pet. Eng. J. (June 1972), pp. 229–245; Trans. AIME; Vol. 253.
Richter, G.R.: An inverse problem for the steady-state diffusion equation, SIAM J. Appl. Math. 41 (1981), pp. 210–221.
Seinfeld, J.H., and Kravaris, C.: Distributed parameter identification in geophysics-petroleum reservoirs and aquifers, Distributed Parameter Control Systems, S.G. Tzafestas, ed., Pergamon, 1982.
Shah, P.C., Gavalas, G.R., and Seinfeld, J.H.: Error analysis in history matching: the optimum level of parameterization, Soc. Pet. Eng. J. (June 1978), pp. 219–228.
Slater, G.E., and Durrer, E.J.: Adjustment of reservoir simulation models to match field performance, Soc. Pet. Eng. J. (September 1971), pp. 295–305.
Solorzano, L.N., and Arrendondo, S.E.: Methods for automatic history matching of reservoir simulation models, SPE 4594 presented at 48th Annual Meeting, Las Vegas, September 30-October 3, 1973.
Thomas, L.K., Hellums, L.J., and Rehais, G.M.: A nonlinear automatic history matching technique for reservoir simulation models, Soc. Pet. Eng. J. (December 1972), pp. 508–514.
Varah, J.M.: Pitfalls in the numerical solution of linear ill-posed problems, SIAM J. Sci. Stat. Comput., 4(2) (1983), pp. 164–176.
Veatch, R.W., Jr., and Thomas, G.W.: A direct approach for history matching, SPE 3515 presented at SPE 46th Annual Meeting, New Orleans, October 3–6, 1971.
Wahba, G.: Practical approximation solution to linear operator equations when the data are noisy, SIAM J. Numer. Anal. 14 (1977), pp. 651–667.
Wasserman, M.L., Emanuel, A.S., and Seinfeld, J.H.: Practical applications of optimal control theory to history matching multi-phase simulator models, Soc. Pet. Eng. J. (August 1975), pp. 347–355; Trnas. AIME, Vol. 259.
Watson, A.T.: Estimation of two-phase petroleum reservoir properties, Ph.D. Thesis, California Institute of Technology, Pasadena, 1979.
Watson, A.T., Seinfeld, J.H., Gavalas, G.R., and Woo, P.T.: History matching in two-phase petroleum reservoirs, Soc. Pet. Eng. J. (December 1980), pp. 521–532.
Way, S.C., and McKee, C.R.: In-situ determination of three-dimensional aquifer permeabilities, Ground Water 20(5) (1982), pp. 594–603.
Yakowitz, S., and Duckstein, L.: Instability in aquifer identification: theory and cases, Water Resour. Res. 16(6) (1980), pp. 1045–1061.
Yanosik, J.L., and McCracken, T.A.: A nine-point difference reservoir simulator for realistic prediction of unfavorable mobility ratio displacements, SPE 5734, Proc. Fourth Symp. on Numerical Simulation of Reservoir Performance, Los Angeles, 1076.
Yeh, W., and Tauxe, A.W.: Optimal identification of aquifer diffusivity using quasi-linearization, Water Resour. Res. 7 (1971), pp. 955–962.
Yeh, W., and Yoon, Y.S.: A systematic optimization procedure for the identification of inhomogeneous aquifer parameters, in Advances in Groundwater Hydrology, American Water Resources Assoc., Minneapolis, 1976, pp. 72–82.
Yeh, W., Yoon, Y.S., and Lee, K.S.: Aquifer parameter identification with kriging and optimum parametrization, Water Resour. Res. 19(1) (1983), pp. 225–233.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Ewing, R.E., George, J.H. (1985). Identification and control for distributed parameters in porous media flow. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005650
Download citation
DOI: https://doi.org/10.1007/BFb0005650
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15872-1
Online ISBN: 978-3-540-39661-1
eBook Packages: Springer Book Archive