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Cost-based model for optimal waste-load allocation and pollution loading losses in river system: simulation–optimization approach

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Abstract

The development of agricultural, industrial, and urban activities creates an increase in pollution loading in rivers that may violate water quality standards which in its turn results in damages to the river systems. An efficient model of waste-load allocation plays a significant role in improving the water quality of the rivers. In this paper, a cost-based waste-load allocation model (C-WLA) is applied to guarantee the optimal management of both costs and river water quality. To determine the optimal loading pattern and threshold limits, the trade-off between treatment cost and pollution loss from the river is considered. In this regard, the MIKE11 model is coupled with the Particle Swarm Optimization (PSO) algorithm and applied to the Karoon River in Iran to demonstrate its practicality and efficiency. The sum of water treatment cost and pollution loading loss is minimized and the monthly optimal treatment percentages and threshold limit were determined. Then, different strategies under various operations of the river system are given with insights into the impacts of the trade-off policy between costs and losses for the discharger’s TDS removal. The results demonstrated that the C-WLA model can achieve optimal management of pollution load in various operating of the river system. In addition, it is also shown that the proposed method is expected to offer better decision support to reasonable waste-load allocation where it can encourage dischargers to improve loading performance.

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Abbreviations

A :

Flow area (m2)

C :

Pollutant concentration (mg/l)

D :

Dispersion coefficient (m2/s)

H :

Flow depth (m)

K :

Linear decay coefficient (1/s)

R :

Hydraulic radius (m)

Q :

River discharge (m3/s)

U :

Flow velocity (m/s)

S :

Energy slope (m)

g :

Gravitational acceleration (m/s2)

q :

Lateral inflow (m3/s)

n :

Manning’s roughness coefficient (-)

c:

Chezi roughness coefficient (-)

u* :

Shear velocity (m/s)

S 1,  S 2,  S 3 …,  S i :

Pollutant point sources (-)

P 1,  P 2,  P 3 …,  P m :

Withdrawal points (-)

R 1,  R 2,  R 3 …,  R j :

Checkpoints (-)

N :

Number of point sources (-)

T :

Number of months (-)

M :

Number of withdrawal points (-)

J :

Number of checkpoints (-)

NC :

Number of crops (-)

i :

Index of the point pollutant source (-)

t :

Index of month (-)

j :

Index of checkpoint (-)

m :

Index of withdrawal point (-)

k :

Index of crop (-)

Z :

Objective function ($)

x (x 1 , x 2, x 3 …, x i):

Vector of treatment percentage (%)

x max :

Maximum removal rate (%)

w*:

Optimal pollution pattern (kg/s)

\(C_{s}^{*}\) :

Optimal pollution concentration (mg/l)

y :

Optimal threshold concentration limit (mg/l)

w s :

Waste load of dischargers (kg/s)

x s :

Removal percentage (%)

c s :

Treatment cost function ($/month)

d m :

Loss function ($/month)

d D :

Loss of drinking water ($/month)

d A :

Loss of agricultural production ($/month)

d E :

Loss of environmental degradation ($/month)

w s :

Waste load (kg/s)

Q s :

Discharge of point source (m3/s)

C s :

Concentration of point source (mg/l)

Q w :

Withdrawal flow (m3/s)

C 0 :

River initial concentration (mg/l)

C min :

Minimum concentration (mg/l)

C max :

Maximum concentration (mg/l)

C std :

Standard concentration (mg/l)

C jt :

Simulated concentration (mg/l)

T 1 :

Cost of water treatment plant ($/month)

T 2 :

Cost of household water purifier ($/month)

T 3 :

Cost of mineral water packaging ($/month)

T 4 :

Cost of mobile water tankers ($/month)

a, b, c, and  d :

Weighted coefficients (-)

P,  A  and  E :

Environmental conversion coefficient (-)

α, β  and  γ :

Coefficients (-)

A r :

Agricultural crop area (ha)

B e :

Crop benefit ($/kg)

Y :

Maximum crop yield (kg/ha)

Y ′ :

Crop yield under salinity stress (kg/ha)

A :

Yield reduction coefficient (%)

B :

Crop bearing salinity threshold (dS/m)

\(\overline{S}\) :

Average soil salinity (dS/m)

IR :

Irrigation depth (mm/10 days)

DP :

Deep water percolation (mm/10 days)

R :

Depth of crop root (mm/10 days)

SM :

Soil moisture (cm3/cm3)

S w :

Irrigation water salinity (dS/m)

x i :

Position of particle i (-)

v i :

The velocity of particle i (-)

r 1  and r 2 :

Uniformly distributed random numbers (-)

c 1  and c 2 :

Tuning parameters (-)

\(\omega\) :

Inertia weight (-)

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Acknowledgements

The authors were grateful for the support of the Iran National Science Foundation (Grant No. 97014928) and Tarbiat Modares University (TMU) for this research.

Funding

The authors have no financial or proprietary interests in any material discussed in this article. The authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Department of Water Engineering and Management, Tarbiat Modares University, Tehran, Iran

    B. Fakouri, J. Mohamad Vali Samani & M. Mazaheri

  2. Department of Civil Engineering, Shahid Chamran University, Ahvaz, Iran

    H. Mohamad Vali Samani

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  1. B. Fakouri
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  3. H. Mohamad Vali Samani
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Correspondence to J. Mohamad Vali Samani.

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Editorial responsibility: Babatunde Femi Bakare.

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Fakouri, B., Mohamad Vali Samani, J., Mohamad Vali Samani, H. et al. Cost-based model for optimal waste-load allocation and pollution loading losses in river system: simulation–optimization approach. Int. J. Environ. Sci. Technol. 19, 12103–12118 (2022). https://doi.org/10.1007/s13762-022-04422-2

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