# Lesson 14 - Unit 9 Summary

In the previous Units, we introduced the concept that there are two different ways we might represent parts of an environmental system.  In particular, 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, or perhaps a stratified lake.

In some parts of a system, however, the concentration varies 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 will be of limited importance.  This is because in most systems transport will be 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 considered 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 considered systems described by the advection-dispersion equation.

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) in this Course we focus on using the equation to describe contaminant transport through porous media (e.g., groundwater systems). GoldSim provides two different pathway elements for representing the advection-dispersion equation. Note that both of these pathways solve the one-dimensional (1D) form of this equation.

We began the Unit by first discussing the advection-dispersion equation in general terms and how GoldSim solves this equation.  We then introduced the first of two pathways used to solve this equation, the Aquifer pathway. As this is one of the most widely used pathway elements in GoldSim, we spent a number of Lessons describing its use.

We then introduced the second of the two pathways used to solve this equation, the Pipe pathway, and compared and contrasted it to the Aquifer pathway. The Pipe pathway uses a different approach than the Aquifer pathway to solve the advection-dispersion equation. For many applications, the Aquifer and the Pipe could be used interchangeably. Nevertheless, due to some important limitations associated with Pipes, for most applications, an Aquifer pathway should be used instead of a Pipe pathway. However, there is one set of systems that cannot be simulated using Aquifers, but can be simulated using Pipes: those involving transport through fractures. In particular, contaminant transport through fractures is typically impacted by the process of matrix diffusion, and this can be readily represented using Pipes. We spent a Lesson exploring this process and how it can be simulated using Pipes.

We closed 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).

We have now covered all of the primary pathway elements in GoldSim (there are two others that we will mention in Unit 12, but will not discuss in detail). By combining the use of Cell, Aquifer and Pipe pathways, you can represent nearly any kind of environmental system.