Optimization Model for Ground‐Water Planning
Publication: Journal of Water Resources Planning and Management
Volume 110, Issue 3
Abstract
A planning model is presented for the optimal management of groundwater systems. The model, which is formulated as a bi‐objective optimization problem, allocates over a series of planning periods, groundwater to competing water (irrigation) demands in a river basin. The model is predicated on the response equations of the ground‐water system. The equations are developed for an inhomogeneous, isotropic aquifer system with the Galerkin finite element method. The matrix calculus is used to obtain a continuous solution in time relating the hydraulic head and the initial state of the system, the system's time dependent boundary conditions, and the planning or management policies. The planning model is applied to the Yun Lin groundwater basin in southwestern Taiwan. Parametric linear programming is used to generate optimal planning policies, the set of non‐inferior solutions, and the relationship between the total water deficit and: (1) The maximum pumping rate; and (2) the minimum permissible head values in the aquifer system.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aguado, E., and Remson, I., “Groundwater Hydraulics in Aquifer Management,” Journal of the Hydraulics Division, ASCE, Vol. 100, No. HY1, 1974, pp. 103–118.
2.
Aguado, E., Sitar, N., and Remson, I., “Sensitivity Analysis in Aquifer Studies,” Water Resources Research, Vol. 13, No. 4, 1977, pp. 733–737.
3.
Aronofsky, J. S., and Williams, A. C., “The Use of Linear Programming and Mathematical Models in Underground Oil Production,” Management Science, Vol. 8, No. 3, July, 1962, pp. 374–407.
4.
Bellman, R., Introduction to Matrix Analysis, McGraw‐Hill, New York, N.Y., 1960.
5.
Cohon, J., and Marks, D., “A Review and Evaluation of Multi‐Objective Programming Techniques,” Water Resources Research, Vol. 11, No. 2, 1975, pp. 208–220.
6.
Cooley, R., “Finite Element Solutions for the Equations of Groundwater Flow,” Technical Report Series H‐W, Publication No. 18, Desert Research Institute, Nev., 1974.
7.
Elango, K., and Rouve, G., “Aquifer Finite Element Linear Programming Model,” Journal of the Hydraulics Division, ASCE, Vol. 106, No. HY10, 1980, pp. 1641–1658.
8.
Futagami, T., Tamai, N., and Yatsuzuka, M., “FEM Coupled with LP for Water Pollution Control,” Journal of the Hydraulics Division, ASCE, Vol. 102, No. HY7, 1976, pp. 881–897.
9.
Haimes, Y. Y., Hierachical Analyses of Water Resources Systems, McGraw‐Hill, New York, N.Y., 1977.
10.
Haimes, Y. Y., and Dreizin, Y. C., “Management of Ground and Surface Water Systems via Decomposition,” Water Resources Research, Vol. 13, No. 1, 1977.
11.
Haji‐Djafari, S., and Wiggert, D. C., “Two‐Dimensional Analysis of Tracer Movement and Transient Flow in a Phreatic Aquifer,” presented at the Second International Symposium Finite Element Methods, Rapallo, Italy, 1976.
12.
Ko, H.‐S., Briefings Yun Lin Irrigation Association, May, 1979, Sept., 1980, and Dec., 1980, Tou Liu, Taiwan.
13.
Loucks, D. P., Stedinger, J., and Haith, D. A., Water Systems Planning and Management, Prentice‐Hall, New York, N.Y., 1980.
14.
Lee, A. S., and Aronofsky, J. S., “A Linear Programming Model for Scheduling Crude Oil Production,” Journal of Petroleum Technology, AIME, Vol. 213, July, 1958, pp. 51–54.
15.
Liu, P., and Willis, R., “Groundwater System Modeling: An Evaluation of the BIEM and Finite Element Modeling,” presented at the 3rd International Conference on Mathematical Modeling, Univ. of Southern California, Los Angeles, Calif., July, 1981.
16.
Maddock, T., “Algebraic Technological Function from a Simulation Model,” Water Resources Research, Vol. 8, No. 1, 1972, pp. 129–134.
17.
Matrix Eigensystem Routines: EISPACK, Springer‐Velag, New York, 1976.
18.
Pinder, G. F., and Frind, E., “Application of Galerkin's Procedure to Aquifer Analysis,” Water Resources Research, Vol. 8, No. 1, 1972, pp. 108–120.
19.
Rosenwald, G. W., and Green, D. W., “A Method for Determining the Optimum Location of Wells in a Reservoir Using Mixed‐Integer Programming,” Journal of Petroleum Engineering, Feb., 1974, pp. 44–54.
20.
Tsao, Y.‐S., et al., “Finite Element Modeling of the Yun Lin Groundwater Basin,” report prepared for the Provincial Water Conservancy Bureau, Tai Chung, Taiwan, 1980.
21.
Water Resources Planning Commission, Hydrologic Features of Taiwan, Republic of China, 1980.
22.
Wattenbarger, R. A., “Maximizing Seasonal Withdrawals from Gas Storage Reservoirs,” Journal of Petroleum Technology, Aug., 1970, pp. 994–998.
23.
Willis, R., and Dracup, J. A., “Optimization of the Assimilative Waste Capacity of the Unsaturated and Saturated Zones of an Unconfined Aquifer System,” UCLA Engineering Report, No. 7394, 1973.
24.
Willis, R., “Optimal Groundwater Quality Management: Well Injection of Waste Waters,” Water Resources Research, Vol. 12, No. 1, 1976, pp. 47–53.
25.
Willis, R., and Newman, B., “A Management Model for Groundwater Development,” Journal of Water Resources Planning and Management Division, ASCE, Vol. 103, No. WR1, 1977, pp. 159–171.
26.
Willis, R., “A Planning Model for the Management of Groundwater Quality,” Water Resources Research, Vol. 15, No. 6, 1979, pp. 1305–1312.
27.
Willis, R., “A Stochastic Planning Model for Conjunctive Ground and Surface Water Resources Management,” proceedings International Conference on Water Resources Development, Taipei, Taiwan, May, 1980.
28.
Zadeh, L. A., “Optimality and Non‐Scalar‐Valued Performance Criteria,” IEEE, Tran Auto Control, AC‐Vol. 8, No. 1, 1963, pp. 59–60.
Information & Authors
Information
Published In
Copyright
Copyright © 1984 ASCE.
History
Published online: Jul 1, 1984
Published in print: Jul 1984
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.