Optimization Models for the Control of Saltwater Intrusion

Authors

  • Robert Willis Department of Environmental Resources Engineering Humboldt State University

DOI:

https://doi.org/10.5614/j.math.fund.sci.2013.45.2.3

Keywords:

coastal aquifer, optimal control, salt water intrusion, simulation and optimization, water quality.

Abstract

A general optimal control model was developed for the control of saltwater intrusion in coastal aquifer systems. The underlying sharp-interface and density-dependent hydraulic and water quality response equations are presented. Different solution algorithms are described for the control problem, including the imbedding method, Box’s algorithms, and the linked simulation-optimization methodology (LSO). Several field applications are presented. The optimization approach, despite requiring significant computation resources, is superior to conventional simulation methods. Optimization produces not only locally optimal planning, design, and operational policies, but also tradeoffs associated with environmental and hydraulic objectives.

References

Finney, B.A., Samsuhadi, & Willis, R., A Quasi-Three Dimensional Optimization Model of Jakarta Basin, J. Water Resour. Plann. and Manag., ASCE, 118(1), pp. 18-31, 1992.

Barlow, P.M. & Wild, E.C., Bibliography on the Occurrence and Intrusion of Saltwater in Aquifers along the Atlantic Coast of the United States, U.S. Geological Survey Open File Report 02-235, Reston, Virginia. 2002.

Izbicki, J.A., Seawater Intrusion in a Coastal Aquifer, U. S. Geological Survey Fact Sheet 125-96, Reston, Virginia, 1996.

Bear, J., Dynamics of Fluids in Porous Media, Elsevier, New York.1972.

Bear, J., Hydraulics of Groundwater, Elsevier, New York. 1979.

Essaid, H.I., A Multilayered Sharp Interface Model of Coupled Freshwater and Saltwater in Coastal Systems: Model Development and Application, Water Resour. Res., 27, pp. 1431-1454, 1990.

Kipp, K.L., HST3D: A Computer Code for Simulation of Heat and Solute Transport in Three-Dimensional Groundwater Flow Systems, U. S. G. S. Water Resources Investigations Report 97-4157, Denver, Colorado, 2010.

Liu, P.L.F., Cheng, A.H.D., Liggett, J.A. & Lee, J.H., Boundary Integral Equation Solutions of Moving Interface between Two Fluids in Porous Media, Water Resources Research, 17(5), pp. 1445-1452, 1981.

Taigbenu, A.E., Liggett, J.A. & Cheng, A.H-D., Boundary Integral Solution to Seawater Intrusion into Coastal Aquifers, Water Resour. Res., 20(8), pp. 1150-1158, 1984.

Huyakorn, P.S., Andersen, P.F., Mercer, J.W. & White, Jr., H.O., Saltwater Intrusion in Aquifers: Development and testing of a Three-Dimensional Finite Element Model, Water Resour. Res., 23(2), pp. 293-312, 1987.

Voss, C.I. & Souza, W.R., Variable Density Flow and Solute Transport Simulation of Regional Aquifers Containing a Narrow Freshwater--Saltwater Transition Zone, Water Resour. Res., 23(10), pp. 1851-1866, 1987.

Pinder, G.F. & Gray, W.G., Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, New York, 1977.

Hayler, C., Three Dimensional Finite Element Simulation of the Elk River Aquifer, Thesis Presented in Partial Fulfillment of Master's Degree, Depart.of Environ. Resour. Eng., HSU, Arcata, California, 2000.

Mercer, J.W., Larson, S.P. & Faust, C.R., Finite Difference Model to Simulate the Areal Flow of Saltwater and Freshwater Separated by an Interface, U. S. G. S. Open File Report 80-407, Reston, Virginia, 1980.

Pinder, G.F. & Cooper, Jr., H.H., A Numerical Technique for Calculating the Transient Position of the Saltwater Front, Water Resour. Res., 10(6), pp. 875-880, 1970.

Sage, A. & Sage, C.C., Optimum Systems Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1977.

Tabak, D. & Kuo, B.C., Optimal Control by Mathematical Programming, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.

Willis, R. & Yeh, W.W-G., Groundwater Systems Planning and Management. Prentice-Hall, Englewood Cliffs, New Jersey, 1987.

Willis, R. & Liu, P. L-F., Optimization Model for Groundwater Planning, J. Water Resour. Plann. and Manag., ASCE, 110(3), pp. 333-347, 1984.

Willis, R., Optimal Groundwater Quality Management: Well Injection of Waste Water, Water Resour. Res., 12(1), pp. 47-53, 1976.

Willis, R., & Finney, B.A., Optimal Control of Nonlinear Groundwater Hydraulics: Theoretical Development and Numerical Exponents, Water Resour. Res., 21(10), pp. 1476-1482, 1985.

Das, A. & Datta, B., Development of Multiobjective Management Models for Coastal Aquifers, J. Water Resour. Plann. and Manag., ASCE, 125, pp. 76-87. 1999a.

Das, A. & Datta, B., Development of Management Models for Sustainable use of Coastal Aquifers, J. Irrigation and Drainage Engr., ASCE, 125, pp. 112-121, 1999b.

Shamir, U., Bear, J. & Gamliel, A., Optimal Annual Operation of a Coastal Aquifer, Water Resources Research, 20(4), pp. 435-444, 1984.

Benhachmi, M.K., Ouazar, D., Naji, A., Cheng, A.H-D.,& El Harrouni, K. Chance Constrained Optimal Management in Saltwater Intruded Coastal Aquifers using Genetic Algorithms, Proc. of the 1st Inter. Conf. on Saltwater Intrusion and Coastal Aquifers - Monitoring, Modeling, and Management, Essaouira, Morocco. 2001a (CD-ROM).

Benhachmi, M.K., Ouazar, D., Naji, A., Cheng, A. H-D., & El Harrouni, K., Optimal Management in Saltwater-Intruded Coastal Aquifers by Simple Genetic Algorithm, Proc. of the 1st Inter. Conf. on Saltwater Intrusion and Coastal Aquifers - Monitoring, Modeling, and Management, Essaouira, Morocco. 2001b (CD-ROM).

Gordu, F., Yurtal, R., & Motz, L.H., Optimization of Groundwater Use in the Goksu Delta at Silife, Turkey, Proc. of the 1st Inter. Conf. on Saltwater Intrusion and Coastal Aquifers - Monitoring, Modeling, and Management, Essaouira, Morocco, April 2001 (CD-ROM).

Voss, C.I., SUTRA (Saturated-Unsaturated Transport): 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. G. S. National Center, Reston, Virginia, 1984.

Samsuhadi, Simulation and Optimization Models for the Jakarta Groundwater Basin, Thesis, Presented in Partial Fulfillment of Master's Degree, Depart. of Environ. Resour. Engr., HSU, Arcata, California, 1990.

Nishikawa, T., Water-Resources Optimization Model for Santa Barbara, California, J. Water Resour. Plann. and Manag., ASCE, 124(5), pp. 252-263, 1998.

Reichard, E.G., Groundwater-Surface Water Management with Stochastic Water Supplies: A Simulation-Optimization Approach, Water Resour. Res., 31(11), pp.2842-2865, 1995.

Murtagh, B.A. & Saunders, M.A., MINOS 5.3 User's Guide, Systems Optimization Laboratory, Technical Report 83-20, Depart. of Operations Research, Stanford University, Stanford, California, 2003.

Johnson, T., Reichard, E., Land, M. & Crawford, S., Monitoring, Modeling, and Managing Saltwater Intrusion, Central and West Coast Groundwater Basin, Los Angeles County, California, Proc. of the 1st Inter. Conf. on Saltwater Intrusion and Coastal Aquifers - Monitoring, Modeling, and Management, Essaouira, Morocco, April 2001 (CD-ROM).

Nishikawa, T. & Reichard, E.G., Evaluating Strategies to Manage Seawater Intrusion, Bathala, C. T. (ed.), North American Water and Environmental Congress, ASCE, Reston, Virginia, 1996.

Bhattacharjya, R.K., & Datta, B., Optimal Management of Coastal Aquifers Using Linked Simulation Optimization Approach, Water Resources Management, 19, pp. 295-320, 2005.

Bhattacharjya, R.K., Datta, B., & Satish, M.G., Artificial Neural Networks Approximation of Density Dependent Saltwater Intrusion Process in Coastal Aquifers, Jour. of Hydrologic Engr., ASCE 12(3), May 1, pp. 273-282, 2007.

Dhar, A. & Datta, B., Saltwater Intrusion Management of Coastal Aquifers. I: Linked Simulation-Optimization, Jour. of Hydrologic Engr, ASCE, 14(12), pp.1263-1272, 2009.

Box, M., A New Method of Constrained Optimization and a Comparison with Other Methods, Computer J., 8, pp. 42-52. 1965.

Haith, D. A., Environmental Systems Optimization, John Wiley and Sons, New York, 1982.

Curtis, E., & Willis, R., A Multi-Objective, Linked-Simulation-Optimization of Henry's Saltwater Intrusion Problem using HST3D and Box's Method, American Jour. of Undergraduate, 10(4), pp. 19-30, 2012.

Downloads

Published

2014-07-01

Issue

Section

Articles