Mathematical Modeling of Effect of Pumping Rate on Contaminant Transport in Riverbank Filtration System

Riverbank filtration (RBF) is a natural technology that is used for river water treatment. This research seeks to investigate the effect of pumping rate on the transport of colloids in RBF. However, this work considered Dissolved Organic Matter (DOM) as a nutrient for bacteria. The mathematical model consists of groundwater flow equation and colloids concentration equations. The equations were solved analytically using parameter expanding method and Eigen function expansion techniques. The results obtained are presented graphically and discussed. It was observed that increase in pumping rate value enhance both the hydraulic head and concentration of colloids which slightly reduces the quality of pumped water from RBF. Keywords: Riverbank filtration, analytical model, colloids, hydraulic head and pumping rat

Groundwater flow equation, overview, derivation, and solution

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.

Modeling an Aquifer: Numerical Solution to the Groundwater Flow Equation

We present a model of groundwater dynamics under stationary flow and, governed by Darcy’s law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of a homogeneous and isotropic media; the more realistic case of an homogeneous anisotropic soil is also considered. Taking into account some geophysical parameters we develop a computational routine, in the Finite Difference Method, which solves the resulting elliptic partial equation, both in a homogeneous isotropic and in a homogeneous anisotropic media. After calibration of the numerical model, this routine is used to begin a study of the Ayamonte-Huelva aquifer in Spain, a modest analysis of the system is given, and we compute the average discharge vector as well as its root mean square as a first predictive approximation of the flux in this system, providing us a signal of the location of best exploitation; long term goal is to develop a complete computational tool for the analysis of groundwater dynamics.

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.