Simulating Time-Variable Pipe Properties

The central concept of the Laplace transform A method for solving certain types of differential equations that involves transforming the equations into an algebraic form that can be readily solved, and then using an inverse transform to retrieve the solutions of the original problem. solution technique used by GoldSim to simulate transport through Pipes is that the discharge history is a linear (and time invariant) function of the input history (for details on the Laplace transform solution, see Appendix B of the Contaminant Transport Module User’s Guide).

Because the Laplace transform approach requires that the transport equations be linear and unchanging in time, if any of the properties of a Pipe (e.g., 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. for solid 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., area, perimeter, storage zone properties) change during a realization A single model run within a Monte Carlo simulation. It represents one possible path the system could follow through time., GoldSim must use an approximation to represent this change.

In particular, when a change in the properties of a Pipe occurs, the change has no effect on mass that was already in the pathway prior to the change. Mass which is already in the pathway continues to be transported based on the properties at the time it entered the pathway. Only mass that enters the pathway subsequent to the change is affected and utilizes the updated properties.

Hence, if you are simulating a Pipe which is long (i.e., has long travel times for some 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).) and has properties that vary significantly over time, this approximation can result in errors. In such a case, the way to minimize these errors is to discretize long pathways into a series of shorter pathways (such that travel time through each Pipe pathway A transport pathway element that is intended to represent a feature that essentially behaves as a fluid conduit, such as a fracture. Pipes are primarily used for simualting matrix diffusion in fractured groundwater pathways. is relatively rapid).

Note: If you do discretize a long pathway into a series of shorter Pipes, the dispersivity (which is typically defined as a fraction of the length of a pathway) should be defined in terms of the total length (not the length of each individual Pipe).