Since Aquifers and Pipes are meant to represent one-dimensional conduits, the concentration reported by these two pathways represents the average concentration discharging from the pathway, and any spatial variation in the concentration (perpendicular to the flow direction) is not represented.
In many cases, however, real world concentrations will vary spatially at the end of a flow path due to dispersion in the horizontal or vertical transverse direction and/or a source term which is not uniformly distributed across the area of the conduit being simulated.
In order to allow you to address this spatial variation, GoldSim provides a special function that returns a correction factor that can be used to multiply the Aquifer’s or Pipe’s concentration output in order to compute the actual (as opposed to spatially-averaged) concentration at an observation point at some distance perpendicular to the flow path at the end of the pathway.
The Plume function (which is analogous to other GoldSim functions like sin or max) has eleven input arguments which describe the properties of the pathway to which you wish to apply the correction, the size of the source, the dispersive properties of the pathway, and the exact location of the observation point. The source is assumed to be a point, rectangle or box centered on the midpoint of the flow path (the pathway), and the observation point is located at the end of the pathway some specified distance from the centerline.
The following diagram illustrates the various input arguments required by the Plume function.
The arguments are as follows (the numbers reference lengths in the figure above):
•Pathway Length (1)
•Pathway cross-sectional Area
•Source Length (2)
•Depth (vertical distance) from the ground surface (or top of the flowing zone) to the observation point (3)
•Horizontal (transverse) distance from the source center to the observation point (4)
•Depth of the top of the source (5)
•Width of the source (6)
•Vertical thickness of the source (7)
•Total thickness of the pathway being simulated (8)
•Horizontal dispersivity
•Vertical dispersivity
Note that the Plume function appears in the function list accessible by right-clicking in an input field and selecting Functions from the context menu (it can be found in the “Contaminant Transport” category). When you insert it, to assist in specifying the large number of inputs, GoldSim puts in temporary placeholders for the arguments (that you will of course need to replace with the actual input arguments):
When specifying these inputs, the following rules should be observed to ensure that the Plume function is physically consistent with the pathway concentrations to which you are applying it:
•The first three arguments should use the same values as those assigned to the pathway itself. Note that the pathway area does not impact the result (as long as the same pathway area is used in the Pathway and the Plume function).
•The product of the width and thickness of the source should not exceed the pathway Area.
The arguments to the Plume function can be links or expressions, and the output of the Plume function is dimensionless. The arguments can also be arrays (vectors or matrices), in which case the output of the function is an array. In such a case, not all of the arguments need to be arrays (arguments defined as scalars are applied to all items of the array). However, all arguments that are defined as arrays must have the same array labels sets.
Because you can specify the length, width and thickness of the source (and any of these can be zero), there is a great degree of flexibility in defining the dimensions of the source. A source can be defined as:
•A point;
•A horizontal area on the surface of an aquifer;
•A vertical area perpendicular to the pathway; or
•A volumetric box region.
The thickness of the aquifer (or river) is required because at a certain distance downgradient from the source, the vertical spread of the plume will encounter and reflect off the bottom. Further downgradient, it will reflect back off the top, and eventually the aquifer will be fully-mixed vertically. GoldSim automatically accounts for these reflections. Horizontal dispersion is assumed to be unlimited, however.
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