## A convex programming framework for optimal and bounded suboptimal well field management

Publication: Research - peer-review › Journal article – Annual report year: 2012

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**A convex programming framework for optimal and bounded suboptimal well field management.** / Dorini, Gianluca Fabio ; Thordarson, Fannar Ørn; Bauer-Gottwein, Peter; Madsen, H.; Rosbjerg, Dan; Madsen, Henrik.

Publication: Research - peer-review › Journal article – Annual report year: 2012

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*Water Resources Research*, vol 48, pp. W06525., 10.1029/2011WR010987

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*Water Resources Research*,

*48*, W06525. 10.1029/2011WR010987

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*Water Resources Research*. 2012, 48. W06525. Available: 10.1029/2011WR010987

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TY - JOUR

T1 - A convex programming framework for optimal and bounded suboptimal well field management

A1 - Dorini,Gianluca Fabio

A1 - Thordarson,Fannar Ørn

A1 - Bauer-Gottwein,Peter

A1 - Madsen,H.

A1 - Rosbjerg,Dan

A1 - Madsen,Henrik

AU - Dorini,Gianluca Fabio

AU - Thordarson,Fannar Ørn

AU - Bauer-Gottwein,Peter

AU - Madsen,H.

AU - Rosbjerg,Dan

AU - Madsen,Henrik

PB - American Geophysical Union

PY - 2012

Y1 - 2012

N2 - This paper presents a groundwater management model, considering the interaction between a confined aquifer and an unlooped Water Distribution Network (WDN), conveying the groundwater into the Water Works distribution mains. The pumps are controlled by regulating the characteristic curves. The objective of the management is to minimize the total cost of pump operations over a multistep time horizon, while fulfilling a set of time-varying management constraints. Optimization in groundwater management and pressurized WDNs have been widely investigated in the literature. Problem formulations are often convex, hence global optimality can be attained by a wealth of algorithms. Among these, the Interior Point methods are extensively employed for practical applications, as they are capable of efficiently solving large-scale problems. Despite this, management models explicitly embedding both systems without simplifications are rare, and they usually involve heuristic techniques. The main limitation with heuristics is that neither optimality nor suboptimality bounds can be guarantee. This paper extends the proof of convexity to mixed management models, enabling the use of Interior Point techniques to compute globally optimal management solutions. If convexity is not achieved, it is shown how suboptimal solutions can be computed, and how to bind their deviation from the optimality. Experimental results obtained by testing the methodology in a well field located nearby Copenhagen (DK), show that management solutions can consistently perform within the 99.9% of the true optimum. Furthermore it is shown how not considering the Water Distribution Network in optimization is likely to result in unfeasible management solutions.

AB - This paper presents a groundwater management model, considering the interaction between a confined aquifer and an unlooped Water Distribution Network (WDN), conveying the groundwater into the Water Works distribution mains. The pumps are controlled by regulating the characteristic curves. The objective of the management is to minimize the total cost of pump operations over a multistep time horizon, while fulfilling a set of time-varying management constraints. Optimization in groundwater management and pressurized WDNs have been widely investigated in the literature. Problem formulations are often convex, hence global optimality can be attained by a wealth of algorithms. Among these, the Interior Point methods are extensively employed for practical applications, as they are capable of efficiently solving large-scale problems. Despite this, management models explicitly embedding both systems without simplifications are rare, and they usually involve heuristic techniques. The main limitation with heuristics is that neither optimality nor suboptimality bounds can be guarantee. This paper extends the proof of convexity to mixed management models, enabling the use of Interior Point techniques to compute globally optimal management solutions. If convexity is not achieved, it is shown how suboptimal solutions can be computed, and how to bind their deviation from the optimality. Experimental results obtained by testing the methodology in a well field located nearby Copenhagen (DK), show that management solutions can consistently perform within the 99.9% of the true optimum. Furthermore it is shown how not considering the Water Distribution Network in optimization is likely to result in unfeasible management solutions.

U2 - 10.1029/2011WR010987

DO - 10.1029/2011WR010987

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

VL - 48

SP - W06525

ER -