# Lesson 1 - Unit 9 Overview

Experience shows that as flow takes place [through a porous medium] the tracer gradually spreads and occupies an ever increasing portion of the domain, beyond the region it is expected to occupy according to the average flow alone. This spreading phenomenon is called hydrodynamic dispersion…

Jacob Bear

In the previous Units, we introduced the concept that there were two different ways we might represent parts of an environmental system.  In Units 5, 6 and 7 we described how we could represent some components using one or more well-mixed compartments. These kinds of systems can be represented mathematically using a set of ordinary differential equations. This would be appropriate, for example, when dealing with a system of well-mixed tanks, ponds, or perhaps a stratified lake.

In some parts of a system, however, the concentration varies continuously spatially over the component, and the governing equation includes a concentration gradient. These kinds of systems must be represented using partial differential equations, in that concentration is a function of both time and space. In Unit 8, we discussed one such equation, the diffusion equation (Fick’s Second Law). We pointed out, however, that diffusion is a relatively slow process (in water), and in many systems is of limited importance.  This is because in most systems transport is advectively-dominated.

The compartment models we discussed in earlier Units (e.g., with well-mixed tanks) transported mass via advection. But in this Unit, we consider a different kind of advectively-dominated system: one in which like diffusively-dominated systems, the governing equation includes a concentration gradient and the system must be represented using a partial differential equation. In particular, we consider systems described by the advection-dispersion equation (which we discussed briefly in Unit 3).

The advection-dispersion equation can be used to describe transport in surface water bodies such as rivers, ponds, lakes and the ocean. However, for various reasons (e.g., the types of problems you are likely to use GoldSim for, the multi-dimensional complexity of surface water transport) we will focus on using the equation to describe contaminant transport through porous media (e.g., groundwater systems).

We begin by first discussing the advection-dispersion equation in general terms and how GoldSim solves this equation.  We then introduce one of the two pathways used to solve this equation, the Aquifer pathway. As this is one of the most widely used pathway elements in GoldSim, we spend several Lessons describing its use.  We then introduce the second of the two pathways used to solve this equation, the Pipe pathway, and compare and contrast it to the Aquifer pathway.  Note that both of these pathways solve the one-dimensional (1D) form of the advection-dispersion equation.

We close the Unit by discussing some more advanced topics (simulating suspended solids in Aquifers and Pipes, dealing with looping networks of pathways and computing concentrations at specific locations).

This Unit has three Exercises, and numerous Examples that we will walk through together. It has a total of 14 Lessons (including this overview and a summary at the end).