Abstract
This paper discusses optimization of natural gas production using waterflooding of a gas reservoir. The functions governing the rate of gas withdrawal and the rate of water injection control the operation of the reservoir. These, together with volume and mass balance and the ideal gas law, give a simple system of ordinary differential equations modelling the reservoir. We use several physical and economic definitions of an optimal production rate. Under each definition, we establish the optimal controls. The relation between prices of water and natural gas and the optimal controls is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. J. Bell and D. H. Jacobson,Singular optimal control problems. Academic Press, New York, 1975.
M. E. Johnson, E. A. Monash, and M. S. Waterman, Modeling and optimizing a gas-water reservoir: enhanced recovery with waterflooding.J. of the International Assn. for Mathematical Geology, 11, 63–74 (1979).
W. Fleming,Personal Communication, 1977.
J. W. McFarland, T. E. Springer, E. A. Monash, and J. Lohrenz, MER (maximum efficient rate) definitions and calculations using a gas-water reservoir model,Los Alamos Scientific Laboratory Report, LA-6533-MS, 1976.
J. W. McFarland, T. E. Springer, E. A. Monash, and J. Lohrenz, A simulation study of MER for gas-water reservoirs,Los Alamos Scientific Laboratory, LA-6866-MS, 1978.
E. A. Monash, A basic reservoir per se mathematical model for enhanced recovery of a gas-water system by waterflooding,Systems Analysis and Development Section Report No. 77-2, Geological Survey, Conservation Division, U. S. Dept. of the Interior, July 5, 1976.
I. B. Russack, On general problems with bounded state variables,J. of Optimization Theory and Applications, 6, 424–452 (1970).
United States Energy Research and Development Administration, A national plan for energy research, development, and demonstration: creating energy choices for the future, ERDA 76-1, Vol. 1, Washington, D.C., 1976.
Author information
Authors and Affiliations
Additional information
Communicated by W. Fleming
Work performed under the auspices of the Energy Research and Development Administration.
Rights and permissions
About this article
Cite this article
Mantini, L.A., Beyer, W.A. Optimization of natural gas production by waterflooding. Appl Math Optim 5, 101–116 (1979). https://doi.org/10.1007/BF01442548
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01442548