Multi-objective Optimization of Different Management Scenarios to Control Seawater Intrusion in Coastal Aquifers

Abstract

Seawater intrusion (SWI) is a widespread environmental problem, particularly in arid and semi-arid coastal areas. Therefore, appropriate management strategies should be implemented in coastal aquifers to control SWI with acceptable limits of economic and environmental costs. This paper presents the results of an investigation on the efficiencies of different management scenarios for controlling saltwater intrusion using a simulation-optimization approach. A new methodology is proposed to control SWI in coastal aquifers. The proposed method is based on a combination of abstraction of saline water near shoreline, desalination of the abstracted water for domestic consumption and recharge of the aquifer by deep injection of the treated wastewater to ensure the sustainability of the aquifer. The efficiency of the proposed method is investigated in terms of water quality and capital and maintenance costs in comparison with other scenarios of groundwater management. A multi-objective genetic algorithm based evolutionary optimization model is integrated with the numerical simulation model to search for optimal solution of each scenario of SWI control. The main objective is to minimize both the total cost of management process and the total salinity in aquifer. The results indicate that the proposed method is efficient in controlling SWI as it offers the least cost and least salinity in the aquifer.

Appendix: Governing equations

The SUTRA employs hybrid finite-element and integrated-finite-difference method to approximate the governing equations that describe the variable-density ground-water flow and solute transport processes in aquifer system within saturated-unsaturated conditions. Consequently, conservation of mass of fluid and conservation of mass of solute are the main equations that responsible for these processes respectively (Voss and Provost 2010). The general forms of these equations summarized below:

Fluid mass balance equation:

$$ \left({S}_w\rho {S}_{op}+\varepsilon \rho \frac{\partial {S}_w}{\partial p}\right)\frac{\partial }{\partial }+\left(\varepsilon {S}_w\frac{\partial p}{\partial C}\right)\frac{\partial C}{\partial t}-\underset{\bar{\mkern6mu}}{\nabla}\left[\left(\frac{\underset{\bar{\mkern6mu}}{\underset{\bar{\mkern6mu}}{k}}{k}_r\rho }{\mu}\right).\left(\underset{\bar{\mkern6mu}}{\nabla }p-\rho \underset{\bar{\mkern6mu}}{g}\right)\right]={Q}_P $$

Solute mass balance equation:

$$ \begin{array}{l}\frac{\partial \left(\varepsilon {S}_w\rho C\right)}{\partial t}+\frac{\partial \left[\left(1-\varepsilon \right){\rho}_s{c}_s\right]}{\partial t}=\\ {}-\underset{\bar{\mkern6mu}}{\nabla }.\left(\varepsilon {S}_w\rho \underset{\bar{\mkern6mu}}{v}C\right)+\underset{\bar{\mkern6mu}}{\nabla }.\left[\varepsilon {S}_w\rho \left({D}_m\underset{\bar{\mkern6mu}}{\underset{\bar{\mkern6mu}}{I}}+\underset{\bar{\mkern6mu}}{\underset{\bar{\mkern6mu}}{D}}\right)\right].\underset{\bar{\mkern6mu}}{\nabla }C\Big]+\varepsilon {S}_w\rho {\varGamma}_w+\left(1-\varepsilon \right){\rho}_s{\varGamma}_s+{Q}_pC*\end{array} $$

where:

S_w :

water saturation [dimensionless]

ρ:

fluid density [M/L³]

ε:

porosity [dimensionless]

ρ_s :

density of solid grains in solid matrix[M/L³]

P:

fluid pressure [M/(L.T²)]

t:

time [T]

C:

solute mass fraction in fluid [M_s/M]

C*:

solute concentration of fluid sources [M_s/M]

C_s :

specific concentration of adsorbate on solid grains [M_s/M_G]

∇ :

divergence of vector

k :

solid matrix permeability [L²]

k_r :

relative permeability to fluid flow [dimensionless]

μ:

fluid viscosity [M/(L.T)]

g:

gravity vector [L/T²]

Q_p :

fluid mass source [M/(L³.T)]

I :

identity tensor [dimensionless]

D :

dispersion tensor [L²/T]

ν :

vector with components in i, j, and k directions [L/T]

г_w :

solute mass source in fluid due to production reactions [M_s/(M_G.T)]

г_s :

adsorbate mass source due to production reactions within adsorbed material itself [M_s/(M.T)]

D_m :

apparent molecular diffusivity of solute in solution in a porous medium including tortuosity effects [L²/T]

S_op :

specific pressure storativity [M_f/(L.T²)]⁻¹; S_op = [(1-ε)α + εβ] α and β are porous matrix and fluid compressibility respectively [M/(L.T²)]⁻¹