Transport Modeling in Groundwater

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Presentation transcript:

Transport Modeling in Groundwater

Components of a Mathematical Model Governing Equation Boundary Conditions Initial conditions (for transient problems) In full solute transport problems, we have two mathematical models: one for flow and one for transport. The governing equation for solute transport problems is the advection-dispersion equation.

Conceptual Model A descriptive representation of a groundwater system that incorporates an interpretation of the geological, hydrological, and geochemical conditions, including information about the boundaries of the problem domain.

Problem with contaminant source Homogeneous, isotropic aquifer Groundwater divide Groundwater divide Impermeable Rock 2D, steady state

Processes to model Groundwater flow Transport Particle tracking: requires velocities and a particle tracking code. calculate path lines (b) Full solute transport: requires velocites and a solute transport model. calculate concentrations

Processes we need to model Groundwater flow calculate both heads and flows (q) Solute transport – requires information on flow (velocities) calculate concentrations v = q/n = K I / n Requires a flow model and a solute transport model.

Groundwater flow is described by Darcy’s law. This type of flow is known as advection. Linear flow paths assumed in Darcy’s law True flow paths The deviation of flow paths from the linear Darcy paths is known as dispersion. Figures from Hornberger et al. (1998)

In addition to advection, we need to consider two other processes in transport problems. Dispersion Chemical reactions Advection-dispersion equation with chemical reaction terms.

Allows for multiple chemical species Dispersion Chemical Reactions Advection Source/sink term Change in concentration with time is porosity; D is dispersion coefficient; v is velocity.

advection-dispersion equation groundwater flow equation

advection-dispersion equation groundwater flow equation

Flow Equation: 1D, transient flow; homogeneous, isotropic, confined aquifer; no sink/source term Transport Equation: Uniform 1D flow; longitudinal dispersion; No sink/source term; retardation

Flow Equation: 1D, transient flow; homogeneous, isotropic, confined aquifer; no sink/source term Transport Equation: Uniform 1D flow; longitudinal dispersion; No sink/source term; retardation

Models Parameters Initial Concentration: Page 224 Dispersion: Page 227/228