Partial Infeasibility Method for Chance‐Constrained Aquifer Management
Publication: Journal of Water Resources Planning and Management
Volume 120, Issue 1
Abstract
A pump‐and‐treat system of extraction wells is modeled to create a hydraulic capture zone to immobilize a plume of contaminants in a confined aquifer with uncertain hydraulic transmissivity. The stochastic approach is used to model the transmissivity as a random field and to generate random realizations of the field. The linear‐response‐matrix method is used to address a joint chance‐constrained optimization problem in which constraints on velocities must be simultaneously satisfied with high probability. In the literature, the multiple‐realization approach provides a robust solution but does not allow for prespecification of a desired reliability. We develop a partial‐infeasibility method, in which the pumping strategy is obtained through heuristic methods that require the designed reliability level to be satisfied for a training set consisting of multiple realizations of the uncertain transmissivity. Empirical Monte Carlo testing shows that as the size of the training set increases, the actual reliability approaches the design criterion. Thus, the method combines the intuitive appeal of the multiple‐realization method with the ability to prescribe a desired reliability level.
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References
1.
Andricevic, R., and Kitanidis, P. K. (1990). “Optimization of the pumping schedule in aquifer remediation under uncertainty.” Water Resour. Res., 26(5), 875–885.
2.
Chan, N. Y. (1992). “Optimal hydraulic aquifer management with reliability constraints,” PhD dissertation, Dept. of Operations Research, Stanford Univ., Stanford, Calif.
3.
Charnes, A., and Cooper, W. W. (1959). “Chance‐constrained programming.” Mgmt. Sci., 6, 73–79.
4.
Colarullo, S. J., Heidari, M., and Maddock III, T. (1984). “Identification of an optimal ground‐water management strategy in a contaminated aquifer.” Water Resour. Bull., 20(5), 747–760.
5.
Deninger, R. A. (1970). “Systems analysis of water supply systems.” Water Resour. Bull., 6(4), 573–579.
6.
Dongarra, J. J. (1979). LINPACK user's guide. Society for Industrial and Applied Mathematics, Philadelphia, Pa.
7.
Dupacova, J., and Wets, R. (1988). “Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems.” Annals of Stat., 16(4), 1517–1549.
8.
Ellis, J. H. (1990). “Integrating multiple long‐range transport models into optimization methodologies for acid rain policy analysis.” European Journal of Operational Research, 43(6), 313–321.
9.
Ellis, J. H., McBean, E. A., and Farquhar, G. J. (1985). “Chance‐constrained/stochastic linear programming model for acid rain abatement—I. complete colinearity and noncolinearity.” Atmos. Environ., 19(6), 925–937.
10.
Ellis, J. H., McBean, E. A., and Farquhar, G. J. (1986). “Chance‐constrained/stochastic linear programming model for acid rain abatement—II. limited colinearity.” Atmos. Environ., 20(3), 501–511.
11.
Gill, P. E., Hammarling, S. J., Murray, W., Saunders, M. A., and Wright, M. H. (1986). “User's guide for LSSOL (version 1.0): a Fortran package for constrained linear least‐squares and convex quadratic programming,” Tech. Rep. 86‐1, Systems Optimization Laboratory, Department of Operations Research, Stanford Univ., Stanford, Calif.
12.
Gorelick, S. M. (1980). “Numerical management models of groundwater pollution,” PhD dissertation, Stanford Univ., Stanford, Calif.
13.
Gorelick, S. M. (1983). “A review of distributed parameter groundwater management modeling methods.” Water Resour. Res., 19(2), 305–319.
14.
Gorelick, S. M. (1987). “Sensitivity analysis of optimal ground water contaminant capture curves: Spatial variability and robust solutions.” Proc., NWWA Conf. Solving Ground Water Problems with Models. National Water Well Association, Dublin, Ohio, 133–146.
15.
Gorelick, S. M. (1990). “Large scale nonlinear deterministic and stochastic optimization: formulations involving simulation of subsurface contamination.” Math. Prog., 48, 19–39.
16.
Hoeksema, R. J., and Kitanidis, P. K. (1985). “Analysis of spatial structure of properties of selected aquifers.” Water Resour. Res., 21(4), 563–572.
17.
Kankova, V. (1989). “Estimates in stochastic programming—chance constrained case.” Prob. of Control and Inform. Theory, 18(4), 251–260.
18.
Kitanidis, P. K. (1986). “Parameter uncertainty in estimation of spatial functions: Bayesian analysis.” Water Resour. Res., 22(4), 499–507.
19.
Kitanidis, P. K., and Lane, R. W. (1985). “Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss‐Newton Method.” J. Hydrol., 79, 59–71.
20.
Lee, S. I., and Kitanidis, P. K. (1991). “Optimal estimation and scheduling in aquifer remediation with incomplete information.” Water Resour. Res., 27(9), 2203–2217.
21.
Maddock III, T. (1972). “Algebraic technological function from a simulation model.” Water Resour. Res., 8(1), 129–134.
22.
Molz, F. J., and Bell, L. C. (1977). “Head gradient control in aquifers used for fluid storage.” Water Resour. Res., 13(4), 795–798.
23.
Remson, I., and Gorelick, S. M. (1980). “Management models incorporating ground‐water variables.” Operations research in agriculture and water resources. D. Yaron and C. S. Tapiero, eds., North‐Holland, Amsterdam, The Netherlands.
24.
Tung, Y. K. (1986). “Groundwater management by chance‐constrained model.” J. Water Resour. Plng. Mgmt., ASCE, 112(1), 1–19.
25.
Voss, C. I. (1984). “SUTRA: a finite element simulation model for saturated‐unsaturated fluid density dependent groundwater flow with energy transport or chemically reactive single species solute transport,” U.S. Geological Survey Water Resources Investigations Rep. 84‐4369. U.S. Geological Survey, Washington, D.C.
26.
Wagner, B. J., and Gorelick, S. M. (1987). “Optimal groundwater quality management under parameter uncertainty.” Water Resour. Res., 23(7), 1162–1174.
27.
Wagner, B. J., and Gorelick, S. M. (1989). “Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: from data to design.” Water Resour. Res., 25(10), 2211–2225.
28.
Yeh, W. W‐G. (1992). “Systems analysis in ground‐water planning and management.” J. Water Resour. Plng. Mgmt., ASCE, 118(3), 224–237.
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Copyright © 1994 American Society of Civil Engineers.
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Received: Aug 3, 1992
Published online: Jan 1, 1994
Published in print: Jan 1994
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