Pipe Pathways use a Laplace transform approach to provide analytical solutions to a broad range of advectively-dominated transport processes involving one-dimensional advection, longitudinal dispersion (and diffusion), retardation, decay and ingrowth, and exchanges with immobile storage zones (e.g., matrix diffusion).
The geometry of the pathway is defined by specifying a length, a cross-sectional area, and a perimeter. Mass enters at one end of a Pipe (or along some specified length of the pipe), advects through (and disperses and diffuses within) the mobile zone of the Pipe, and then exits at the other end. Unlike Cell pathways, Pipe pathways contain only a single fluid medium (which is always, by definition, the Reference Fluid). They can, however, contain solid media which can impact transport (e.g., by modifying the porosity of the pathway and/or acting to sorb and hence retard species).
The boundary condition for the Pipe is as follows:
Concentration goes to 0 as x goes to ∞.
Effectively, this allows dispersive/diffusive outfluxes, with a downstream concentration (immediately after the Pipe) that is actually quite close to the concentration in the Pipe (resulting in a low dispersive outflux).
Two types of simple contaminant retardation processes can be represented within a Pipe pathway:
•equilibrium partitioning between the fluid in the pathway and a user-specified infill medium; and
•equilibrium partitioning between the fluid in the pathway and a user-specified coating medium (around the perimeter of the pathway).
In addition to these linear retardation mechanisms, Pipe Pathways can also represent interchanges with two types of immobile storage zones along the length of the pathway:
•matrix diffusion zones, in which the transfer rate into and out of the zone is proportional to the concentration gradient and the diffusive properties of the zone; and
•a “stagnant” dispersive zone, in which the transfer rate into and out of the zone is proportional to the concentration difference and the flow rate in the pathway.
Finally, suspended Solids can be specified to be present in the Pipe. These Solids are assumed to be advected and dispersed along the Pipe, but are not subject to retardation processes or interactions with storage zones. Species which partition onto the suspended Solids are transported with them as they move through the Pipe.
Warning: Solubility
constraints are not applied within Pipes. (They are only applied within
Cells and Aquifers). Hence, if the concentration of a species entering a
Pipe (e.g., via a boundary condition) exceeds the solubility limit, the
concentration leaving a Pipe could exceed the limit.
The mathematical and computational details of how Pipe pathways are implemented within GoldSim are provided in Appendix B of the Contaminant Transport User’s Guide.