Lesson 12 - Unit 7 Summary

In this Unit we continued to consider systems in which mass is being transported between well-mixed compartments represented by Cell pathways.

We began by pointing out that in the real world, we would expect the volumes and flows associated with environmental compartments to dynamically change during a simulation (e.g., responding to seasons, or simply daily fluctuations). We then spent several Lessons discussing how this can be represented in GoldSim. As part of this, we discussed the numerical problems that can arise when volumes are changing very rapidly and/or Cells go completely empty and how to address these.

Next we pointed out that in some cases at some locations in the system you are simulating, the dissolved chemicals may be present at high enough concentrations such that they precipitate out of solution (i.e., exist in both a dissolved state as well as a solid or liquid state). In these situations, the solute is still present in water, but its concentration is fixed at its solubility limit. This process can obviously have an enormous impact on mass transport, as it has the impact of limiting the dissolved concentration (and hence the advective flux) of contaminants through a system. While for some applications, it may be necessary to model the various geochemical processes in great detail, in many cases such an approach may not be necessary or appropriate at all. We described a simpler approach that can be readily implemented in GoldSim, in which you specify a solubility value for each species that you are modelling.

Advection is the transport of material (e.g., contaminants or other chemicals) via the bulk movement of the medium with which those materials are associated.  Typically, the medium of interest is water, and the materials that are advected are solutes that are dissolved in that water. However, advection does not need to involve only fluids such as water.  Conceptually, chemicals can also be advected with solids.  The chemicals must first become associated with the solid in some way.  Most commonly, they will be sorbed (partitioned) onto the solid, but they may also be precipitated out of solution (due to solubility constraints) onto the solid. Once they are associated with the solid, the mass can be advected in two different ways: 1) the solid itself can move (e.g., soil erosion); or 2) the solid can be suspended in a water and be transported with the water.  We spent several Lessons discussing these kinds of processes.

For most systems that you will simulate, advection will typically be the dominant transport process that you will model. As we will discuss in later Units, for many systems, the processes of diffusion and dispersion can also be important. However, there may be some types of processes that transport and/or modify the mass in your system that cannot be easily described using just advection or diffusion. This is typically because they are relatively complex processes (e.g., animal burrowing, plant uptake, chemical treatment) that would be very difficult to fully describe and represent accurately using the actual physical and chemical processes controlling them, but can be readily approximated using a simplified approach.  We described two of the specialized features in GoldSim for representing these kinds of processes.

So far in this Course, we have been representing systems using one or more well-mixed compartments and the mass transport from one location to the other has been a function of only the mass (or concentration) in the “upstream” compartment. This will certainly be appropriate for many parts of the systems you will simulate. However, in other parts of the system (e.g., mass transport through an aquifer), this would not be an appropriate way to represent mass transport.  That is, in many cases, concentrations will vary continuously such that the governing equation is defined in terms of a concentration gradient. This requires a different approach to solving the mass transport equations. We will start to discuss these kinds of systems in the next Unit.