Cell Pathway Example #1: Partitioning and Decay

This simple example provides an introduction to the kinds of problems that can be solved using Cells. This particular example file, Cell1_PartitioningDecay.gsm, can be found in the Contaminant Transport Examples folder in your GoldSim directory (accessed by selecting File | Open Example... from the main menu). This example illustrates how GoldSim simulates partitioning, decay and ingrowth.

Suppose that 10 g of chemicals A and B are released into a small pond. The pond contains two media Materials (such as water, sand, clay, air) that constitute (are contained within) transport pathways. GoldSim provides two types of elements for defining media: Fluids and Solids.: Water and Sediments. Chemical A degrades according to a first order reaction, with a half-life of 0.5 years. Both A and B sorb onto the Sediments. This sorption can be quantified by specifying partition coefficients The ratio of the species’ concentration in a medium to its concentration in the Reference Fluid at equilibrium. Partition coefficients are inputs to Solid and Fluid elements. (equal to 4 m³/kg for A and 2 m³/kg for B). Because the pond is shallow, it is assumed that it is well-mixed, and the Water and Sediments are instantaneously at equilibrium with respect to partitioning of the species The chemical (or non-chemical, such as bacterial or viral) constituents that are stored and transported through an environmental system in a contaminant transport model. In GoldSim, the Species element defines all of the contaminant species being simulated (and their properties).. You wish to predict the concentration of the two species in the Water and Sediments in the pond as a function of time.

To simulate this system in GoldSim, you would do the following:

1. Define two species (A and B) and specify their decay properties;
2. Define two media (Water and Sediments) and specify their properties (e.g., the partition coefficients);
3. Define a single Cell pathway A transport pathway element that is mathematically equivalent to a finite difference node. Cells are commonly applied to simulate discrete compartments in an environmental system (such as ponds, lakes, shallow soil compartments, or the atmosphere). to represent the pond;
4. Specify the quantities of Water and Sediment present in the pond Cell;
5. Specify an initial mass of species in the pond Cell; and
6. Specify the simulation settings (i.e., duration and timesteps), and run the model.

The output of this simulation, in the form of time histories of the concentrations of species A and B in the Water and Sediments in the pond, is shown below:

Note that because A decays (and B does not), the concentration of A (in Water and Sediments) decreases, while the concentration of B is constant. Because both species partition onto the Sediments, they are present in both media. The system is assumed to be well-mixed, such that equilibrium is reached immediately. As a result, the ratio of the concentration of A and in Water to that in Sediments is constant (and equal to 4 m³/kg for A and 2 m³/kg for B).

A slightly different version of this example (that includes ingrowth, such that A decays to B), Cell1_PartitioningDecayIngrowth.gsm, can be found in the Contaminant Transport Examples folder in your GoldSim directory (accessed by selecting File | Open Example... from the main menu).

Note: Because this example includes ingrowth, it requires the RT Module. If you are using the CT Module, you will not be able to open the file.

In Cell1_PartitioningDecayIngrowth.gsm, the model is defined slightly differently than the example with no ingrowth: 1) No B is initially present in the pond; 2) A decays to B; and 3) B does not partitions onto Sediments (although A still does).

The output of this simulation, in the form of time histories of the concentrations of species A and B in the Water and Sediments in the pond, is shown below:

Note that because A decays to B, the concentration of A (in Water and Sediments) decreases, while the concentration of B increases. Because A partitions onto the Sediments, it is present in both media (B is not present in Sediments). The system is assumed to be well-mixed, such that equilibrium is reached immediately. As a result, the ratio of the concentration of A and in Water to that in Sediments is constant (and equal to 4 m³/kg for A).

Note that in these simple examples, the system is closed (i.e., mass does not enter or leave the pond). Subsequent examples consider mass flux links to and from Cells.