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Lecture

Solute Transport in Porous Media

In course

ENG-400: Water quality modeling

This course builds on environmental chemistry and microbiology taken in previous courses. The emphasis is on quantification using the public domain package, PHREEQC, which is an excellent computation tool. Numerous applications are investigated during the ...

Description

This lecture covers the advection-diffusion/dispersion equation for solute transport in 1D saturated porous media, including spatially constant porosity and transport coefficients. It also discusses initial and boundary conditions, reactions as sources and sinks, and the ADR equation. The PHREEQC software for transport modeling is introduced, along with terminology for boundary conditions. The lecture delves into open and closed boundaries, entrance and exit conditions, and the impact of reactions on solute transport. It concludes with a detailed explanation of the numerical methods and options for transport modeling in PHREEQC.

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Instructor

David Andrew Barry

Research InterestsSubsurface hydrology, constructed wetlands, ecological engineering, in particular contaminant transport and remediation of soil and groundwater; more generally, models of hydrological and vadose zone processes; application of mathematical methods to hydrological processes; coastal zone sediment transport, aquifer-coastal ocean interactions; hydrodynamics and modelling of lakes.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Discrete exterior calculus

Related concepts (32)

Robin boundary condition

In mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Cauchy boundary condition

In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

Mixed boundary condition

In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.

Porosity

Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface (cf. closed-cell foam). There are many ways to test porosity in a substance or part, such as industrial CT scanning.

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