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Multi-objective optimization model for water resource management: a case study for Riyadh, Saudi Arabia

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Abstract

A multi-objective goal programming model was developed for water distribution from multiple sources to multiple users. The model was applied in Riyadh, Saudi Arabia, for the period of 2015–2050. In Riyadh, water sources are groundwater (GW), desalinated water (DW) and treated wastewater (TWW), while the users are domestic, agricultural and industrial sectors. The model was applied to: (1) satisfy water demands and quality; (2) maximize TWW reuse and GW conservation; and (3) minimize overproduction of DW and overall cost. In 2015, the required allocations of GW, DW and TWW are 3286, 662 and 609 MCM, respectively, which are projected to be 4345, 1554 and 1305 MCM in 2050, respectively. GW source is likely to satisfy the predicted withdrawal of GW till 2035, while probabilities of non-satisfaction of full demands of GW in 2040, 2045 and 2050 were 0.04, 0.23 and 0.51, respectively. Supply of DW and reuse of TWW are needed to be increased to satisfy the predicted quantities during 2015–2050.

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Abbreviations

R i :

The ith priority

W i :

Assigned weight of the ith priority

Q GW :

Current extraction of GW (MCM/year)

Q DW :

Current supply of DW (MCM/year)

Q TWW :

Generation of domestic wastewater (MCM/year)

Q D :

Domestic water demand (MCM/year)

Q A :

Agricultural water demand (MCM/year)

Q I :

Industrial water demand (MCM/year)

TDSGW :

TDS of GW (ppm)

TDSDW :

TDS of DW (ppm)

TDSTWW :

TDS of TWW (ppm)

TDSD :

Required TDS of domestic water (ppm)

TDSA :

Required TDS of agricultural water (ppm)

TDSI :

Required TDS of industrial water (ppm)

C GW :

Unit cost of GW (US $/m3)

C DW :

Unit cost of DW (US $/m3)

C TWW :

Unit cost of TWW (US $/m3)

q GWD :

GW supplied to domestic sector (MCM/year)

q GWA :

GW supplied to agricultural sector (MCM/year)

q GWI :

GW supplied to industrial sector (MCM/year)

q DWD :

DW supplied to domestic sector (MCM/year)

q TWWA :

TWW reused in agricultural sector (MCM/year)

P GW :

Positive deviation above extraction of GW (MCM/year)

N GW :

Negative deviation below extraction of GW (MCM/year)

P DW :

Positive deviation above current supply of DW (MCM/year)

N DW :

Negative deviation below current supply of DW (MCM/year)

P TWW :

Positive deviation above domestic wastewater (MCM/year)

N TWW :

Negative deviation below domestic wastewater (MCM/year)

P D :

Positive deviation above domestic water demand (MCM/year)

N D :

Negative deviation below domestic water demand (MCM/year)

P A :

Positive deviation above agricultural water demand (MCM/year)

N A :

Negative deviation below agricultural water demand (MCM/year)

P I :

Positive deviation above industrial water demand (MCM/year)

N I :

Negative deviation below industrial water demand (MCM/year)

\( P_{\text{D(blend)}}^{\text{TDS}} \) :

Positive deviation of blended water quality above domestic water quality (ppm)

\( N_{\text{D(blend)}}^{\text{TDS}} \) :

Negative deviation of blended water quality below domestic water quality (ppm)

\( P_{\text{A(GW)}}^{\text{TDS}} \) :

Positive deviation of GW quality above the quality of agricultural water (ppm)

\( {\text{N}}_{\text{A (GW)}}^{\text{TDS}} \) :

Negative deviation of GW quality below the quality of agricultural water (ppm)

\( P_{\text{A (TWW)}}^{\text{TDS}} \) :

Positive deviation of TWW quality above the quality of agricultural water (ppm)

\( N_{\text{A (TWW)}}^{\text{TDS}} \) :

Negative deviation of TWW quality below quality of agricultural water (ppm)

\( P_{\text{I (GW)}}^{\text{TDS}} \) :

Positive deviation of GW quality above the quality of industrial water (ppm)

\( N_{\text{I (GW)}}^{\text{TDS}} \) :

Negative deviation of GW quality below the industrial water (ppm)

P CGW :

Positive deviation above the cost of GW (million US $/year)

N CGW :

Negative deviation below the cost of GW (million US $/year)

P CDW :

Positive deviation above cost of current supply of DW (million US $/year)

N CDW :

Negative deviation below the cost of current supply of DW (million US $/year)

P CTWW :

Positive deviation above cost of reusing TWW (million US $/year)

N CTWW :

Negative deviation below cost of reusing TWW (million US $/year)

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Acknowledgments

The authors would like to thank the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals (KFUPM) for financial support of this work through project No. RG 1110-1 and RG 1110-2.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Water Research Group, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Muhammad Al-Zahrani, Ammar Musa & Shakhawat Chowdhury

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  1. Muhammad Al-Zahrani
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  2. Ammar Musa
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  3. Shakhawat Chowdhury
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Correspondence to Shakhawat Chowdhury.

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Al-Zahrani, M., Musa, A. & Chowdhury, S. Multi-objective optimization model for water resource management: a case study for Riyadh, Saudi Arabia. Environ Dev Sustain 18, 777–798 (2016). https://doi.org/10.1007/s10668-015-9677-3

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