Courses: The GoldSim Contaminant Transport Module:

Unit 11 - Using Features of the RT Module: Modeling Complex Source Terms

Lesson 2 – What is a Source Element and When Should You Use It?

Before describing how a Source element is defined, it is useful to first describe conceptually what a Source element actually models.  Doing so will provide insight into whether or not you need to use it (or instead can use a simpler approach of directly specifying a release rate).

First, it is important to understand that the definition of what is meant by a “source” is completely determined by the user. A “source” may represent an entire landfill (e.g., with a liner), a single buried drum, a group of buried drums or tanks, a concrete vault, or a large number of high integrity waste packages disposed in an engineered underground facility. Moreover, in a given system, multiple sources may exist.

Whatever it physically represents, the Source element produces as an output a vector of contaminant mass release rates (for each species) which then serves as input to the pathway network (which subsequently transports mass throughout some environmental system), as shown below:

In effect, a Source can be viewed as a “black box” whose outputs are release rates for each species in the system to a transport pathway that exists “outside” of the Source. In the example above, the Source element “Buried_Drums” provides mass input to the Cell pathway called "Soil".

Every Source has one or more inventories. This is the amount of mass that is present for each species at the beginning of the simulation (as we shall see, there may be multiple inventories, as the mass can exist at different locations within the Source). Note that prior to this mass being released from the Source (via the mechanisms discussed below) the mass can decay and ingrow, and this can be extremely important to take into account.

A Source explicitly represents two processes which control release of mass:

  • exposure of the contaminant mass within a Source; and
  • transport of exposed contaminant mass through and away from the Source.

The term exposure, as applied to a Source, has a specific meaning within GoldSim. In particular, species mass in a Source is considered to be exposed if it is available for mass transfer within and away from the Source. Within a Source, exposure is controlled by two processes:

  • Loss of containment. The mass in a Source is specified to be present in the Source in discrete packages (e.g., 100 separate drums or perhaps a single concrete vault). For each individual package, zero, one or two layers of containment (barriers) can be explicitly considered to exist (e.g., no effective barrier, a drum, or a drum and a liner within the drum). Mass cannot be released until the barriers, if they exist, fail. Different mass inventories can then be specified to exist in various places within the barrier system inside a package (e.g., between the outer and inner barriers, inside both barriers). Barrier failure rates are described in terms of probability density functions of failure frequency (i.e., failure rates).
  • Degradation of waste matrix. All or portions of the species mass within the Source can be specified to exist within one or more waste matrix materials, such as cement, grout, solidified glass, or metal. Species that are bound in such a matrix are not released until the matrix itself degrades (e.g., dissolves, corrodes or alters) in some manner. Release of species mass from the matrix is then assumed to be congruent with the degradation of the matrix.

These two processes together determine the rate of exposure of contaminant mass within a Source. If a contaminant is present inside an intact barrier, or bound within intact matrix material of some sort (e.g., grout, metal, glass), it is not available for mass transport, and hence is considered to be unexposed. The mass cannot be transported until it is physically liberated from barriers and/or matrix material present in the Source.

Once mass is exposed within a Source, it is available for transport within and away from the Source. GoldSim allows both advective and diffusive transport mechanisms to be explicitly represented. Mass transport within and away from a Source is controlled by the following:

  • Partitioning. The Source can contain multiple fluid and solid transport and storage media (e.g., water, oil, rust, soil, air), with partition coefficients between the various media. Exposed contaminant mass will be partitioned between the various media within the Source based on the partition coefficients and the masses or volumes of the media. This in turn, will affect transport rates.
  • Solubility constraints. Solubility limits for the contaminants can be specified within the Source. Precipitated mass (which may be present as a solid or liquid phase) cannot be transported in water (but could be transported via advection of particulates onto which it has precipitated).
  • Mass transfer. Media flow rates through the Source, geometric considerations, and contaminant properties (e.g., diffusivities) control the advective and diffusive mechanisms by which exposed mass can be transported.

As we shall see, the transport of mass through and away from a Source is actually implemented within GoldSim by associating (i.e., linking) one or more Cell pathways with each Source. Cells that are associated with Sources in this way take on some special properties.

Mass exposure and mass transport can be viewed as competing processes with regard to controlling the rate of release of a species from a Source. Often, one of these processes dominates for a given species in a Source.  For example, consider a Source consisting of a species that was stored  in a large number of drums that gradually failed over time. Depending on the solubility and the container failure rate, the release rate for this species could be controlled by mass transport considerations (the mass is exposed due to drum failure faster than it can be transported away), or by the exposure rate (the mass is transported away faster than it is exposed).

So given this description of what a Source models, when should you use it? The rule for whether or not you need to use a Source element in your model is relatively straightforward: If you cannot represent the introduction of mass into your model (i.e., the source term) in an accurate manner using a simple equation, you should probably use a Source element.

That is, if you can't describe the introduction of mass into your system by using an initial or boundary condition in a pathway, you should use a Source element. This will often be the case if 1) your source term involves barriers that fail over time; 2) your source term includes one or more matrix materials that release species mass as they degrade; and/or 3) the source term is modified by reactions (e.g., decay and ingrowth) prior to and during release. If any of these processes are active, describing the source term using simple algebraic equations becomes difficult, if not impossible (since in these situations, representing the source term accurately involves the solution of integrals and/or coupled systems of equations). These processes, however, can be explicitly represented using a Source element.