Proposing mathematical model for seawater intrusion phenomena in the coastal aquifer

Seawater intrusion is one of groundwater quality problem which in this problem, the mixing between freshwater and saltwater in the coastal aquifer occurs. Mathematical modelling can be formulated to describe the mechanism of this phenomena. The main objective of this research is to develop the mathematical model of groundwater flow and solute transport that applicable to seawater intrusion mechanism. This mechanism is arranged as a differential equation and distinguished into 3 equations. The first equation is groundwater flow equation in dependent-density. It means that the density of groundwater (ρ) changes in spatial and temporal domain due freshwater and seawater are mixed in the coastal aquifer. The second equation is solute transport. Like as groundwater flow equation, in solute transport equation there is a change of solute concentration (С) in the spatial and temporal domain. The last equation is the relationship between groundwater density (ρ) and solute concentration (С). Special case for the third equation, in which this equation is adopted from USGS Seawat model. The first equation and second equation are governed by Eulerian mass conservation law. The main theoretical consideration of governing groundwater flow equation is such as fluid and porous matrix compressibility theory, Darcy's law for groundwater in motion theory and some properties of soil. In other hands, solute transport is involving advection transport and hydrodynamic dispersion transport. Hydrodynamic dispersion is arranged by diffusion Fick's law and dispersion in porous media theory and it depends on transversal and longitudinal dispersivity. Using Jacob Bear's theory which states that fluid density as temperature, concentration and pressure function, authors obtain three primary variables in this model. Those variables follow fluid density (ρ), total head (h) and concentration (С). In this model, isotropic and isobar condition is considered, hence fluid density (ρ) is a function of concentration (С) only. Finally, from this research, authors wish this mathematical model is applicable to modelling, describing and predicting seawater intrusion phenomena theoretically.

Download Full-text

A possible modification of groundwater flow equation using coordinate transformations

Water Science & Technology Water Supply ◽

10.2166/ws.2014.110 ◽

2014 ◽

Vol 15 (2) ◽

pp. 278-287 ◽

Cited By ~ 1

Author(s):

Abdon Atangana ◽

Ernestine Alabaraoye

Keyword(s):

Groundwater Flow ◽

Prolate Spheroid ◽

Flow Equation ◽

Time Space ◽

Adomian Decomposition ◽

Iteration Methods ◽

Groundwater Flow Equation ◽

Factor Α ◽

Modified Equation ◽

Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

Download Full-text

Application of the Lanczos Algorithm to the solution of the groundwater flow equation

Water Resources Research ◽

10.1029/wr025i003p00551 ◽

1989 ◽

Vol 25 (3) ◽

pp. 551-558 ◽

Cited By ~ 20

Author(s):

W. Scott Dunbar ◽

Allan D. Woodbury

Keyword(s):

Groundwater Flow ◽

Flow Equation ◽

Lanczos Algorithm ◽

Groundwater Flow Equation

Download Full-text

Numerical Simulation of Different Schemes’ Influence on Coastal Areas for Groundwater-Source Heat Pump Engineering

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.588-589.1278 ◽

2012 ◽

Vol 588-589 ◽

pp. 1278-1281

Author(s):

Jun Pan ◽

Shi Xiao Li ◽

Chang Liu ◽

Yang Li

Keyword(s):

Numerical Simulation ◽

Numerical Model ◽

Groundwater Flow ◽

Solute Transport ◽

Heat Pump ◽

Seawater Intrusion ◽

Underground Water ◽

Coastal Areas ◽

Simulation Results ◽

Groundwater Source

More and more people have take more attention on the problem like Seawater intrusion, The same floor recharge and "heat transfixion". This article has established the groundwater flow and solute transport and temperature coupling numerical model,to simulate the underground water temperature’s change by changing the wells’ spacing manner. Simulation results show that the two kinds of disposing Wells solutions are not cause seawater invasion, the second disposing Wells scheme help to prevent the occurrence of seawater invasion.

Download Full-text

Groundwater flow and solute transport in a laboratory-scale analogue of a decommissioned in-pit tailings management facility

Canadian Geotechnical Journal ◽

10.1139/t02-108 ◽

2003 ◽

Vol 40 (2) ◽

pp. 326-341 ◽

Cited By ~ 1

Author(s):

Anthony CF West ◽

Paul J Van Geel ◽

Kenneth G Raven ◽

Thanh Son Nguyen ◽

Mahrez Ben Belfadhel ◽

...

Keyword(s):

Groundwater Flow ◽

Early Time ◽

Solute Concentration ◽

Laboratory Scale ◽

Hydrodynamic Dispersion ◽

Concentration Data ◽

Advection Dispersion ◽

Steady Rate ◽

Tailings Management ◽

Rate Controlled

A laboratory-scale analogue of an in-pit tailings management facility (TMF) was constructed using mortar sand, fluorescent-dye-containing ground silica, and filter gravel to represent fractured host rock, tailings, and a pervious surround, respectively. In a series of experiments, the performance of the analogue was observed through collection of hydraulic head, groundwater discharge, and solute concentration data. These data were found to be sufficient to validate numerical simulations of the experiments carried out using FRAC3DVS. The validation exercise indicated that adequate discretization of the tailings' periphery was critical to accurate simulation of early time solute release from the ground silica, while accurate simulation of groundwater flow and hydrodynamic dispersion adjacent to the ground silica was critical to accurate simulation of the down-gradient solute plumes. The validated model was used to predict how the analogue would have performed over its entire "contaminating lifespan." The results of the experiments and subsequent numerical modelling were used to support the argument that, assuming no dissolution of tailings solids, solute mass flux out of a decommissioned in-pit TMF would decrease asymptotically with time from a rate controlled by diffusion at the tailings' periphery towards a steady rate controlled by advection through their core.Key words: tailings, groundwater contamination, in-pit disposal, physical model, numerical model, advection-dispersion.

Download Full-text

Groundwater flow equation, overview, derivation, and solution

E3S Web of Conferences ◽

10.1051/e3sconf/202131404007 ◽

2021 ◽

Vol 314 ◽

pp. 04007

Author(s):

Lhoussaine El Mezouary ◽

Bouabid El Mansouri

Keyword(s):

Heat Transfer ◽

Differential Equation ◽

Groundwater Flow ◽

Numerical Solutions ◽

Flow Equation ◽

Heat Transfer Equation ◽

Flow Equations ◽

Basic Law ◽

Flow Through ◽

Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

Download Full-text