Defining Initial/Boundary Conditions for an Aquifer

In this section, we discuss defining an initial and/or boundary condition for an Aquifer.

An initial condition/boundary condition for an Aquifer is specified using the drop-list directly below the Discrete Changes field within the Aquifer dialog. This drop-list provides three options:

In all three of these cases, if the Source Zone Length is zero (the default), the mass is applied at the beginning of the Aquifer (the first Cell). If the Source Zone Length is greater than zero, the mass is distributed uniformly over the specified length.

• Initial Inventory. This is the default, and represents the initial inventory of each species in the pathway. This field only accepts vectors by species with dimensions of mass. Moreover, this input cannot be specified as a function of time (if it is, GoldSim will display a fatal error when you try to run the model).

• Cumulative Input. This option provides a mechanism for simultaneously specifying an initial condition and a rate of mass addition (that may change with time). This field only accepts vectors by species with dimensions of mass. It represents the cumulative amount of mass of each species added to the Aquifer at a given time. Hence, if it is constant, it represents an initial condition. If it increases with time, its rate of change represents a specified rate of addition. Correct use of the "Cumulative Input" is summarized in the table below:

Warning: The Cumulative Input must stay constant or increase with elapsed time. That is, you cannot remove mass from an Aquifer using the Cumulative Input field. If the value ever begins to decrease with time, a fatal error occurs.

• Input Rate. The third option is used to specify a rate of mass addition (that may change with time). This field only accepts vectors by species with dimensions of mass/time. It represents the rate at which mass of each species is added to the Aquifer over the next timestep.

Note: One way to easily enter a vector of data into an input field without having to create a separate element is to use GoldSim’s vector constructor function. For example, entering “vector(1g)” into the Cumulative Input field results in an initial condition of 1 g of each species being present in the Aquifer.

Although the Input Rate and Cumulative Input options provide a quick and convenient way to enter mass input rates, if mass input rates into an Aquifer are changing with time (e.g., because the inflow concentration is changing), a slightly more accurate way (both numerically and conceptually) to specify such a boundary condition is to create a “Source Cell” that is defined using a Defined Concentration.

As an example, consider a case in which you have a boundary condition with a constant inflow rate (Flow_Rate) and a time-varying Inflow_Concentration. The Aquifer has a constant outflow rate (equal to the inflow rate). You could model this in two ways:

• In the second approach, you define a “Source_Cell” that looks like this:

The volume is set to an arbitrarily small number (it is not used to compute concentrations since the concentration is fixed). A Defined Concentration is specified for this Source_Cell that will flow into Aquifer. That is, the Source_Cell has an outflow to the Aquifer:

If we run this model (for 100 days with a 5 day timestep) and compare the results for these two different approaches to representing the boundary condition (in terms of the concentration leaving the Aquifer), they look like this:

What we see is that the mass that is input “externally” (using the Input Rate) lags by one timestep. This is because in this, due to the way the external boundary condition must be applied when solving the pathway equations, a one timestep lag is introduced. Hence, the second approach is a more accurate representation (although for a small timestep, the differences would likely be insignificant). Conceptually, however, this is a bit more accurate way to represent the boundary condition (since the boundary condition is actually treated as part of the pathway network).

In addition to specifying the input boundary condition for an Aquifer, you can also control the output boundary condition. In particular, the checkbox Enable dispersive and diffusive outfluxes to downstream pathway(s) changes the outflux boundary condition.

If this box is cleared (the default), only advective transport out of the pathway is allowed. If the box is checked, a zero concentration in the receiving pathway is assumed, and dispersive and diffusive transport into downstream pathways is allowed.

These two boundary condition options represent two possible extremes for the behavior of the system. The actual behavior of most real-world systems would be somewhere between these two extremes (although in most real-world systems, it will be very close to either one or the other). The default boundary condition (no dispersive and diffusive fluxes) is most appropriate if the downstream concentration is similar to the concentration leaving the pathway. In this case, the concentration gradient is small (and hence the dispersive and diffusive fluxes would be small). If the box is checked, dispersive and diffusive transport into downstream pathways is allowed (assuming a zero concentration in those pathways). This might be appropriate, for example, if the downstream pathway represents a rapidly-flowing, “clean” pathway.

The impact of this boundary condition can be evaluated by comparing the behavior of an Aquifer to the behavior of the same system simulated using a different solution technique and boundary condition (the Pipe pathway, which uses a Laplace transform solution).

To specify this:	Enter the following into the "Cumulative Input" field:
An initial condition (at the beginning of the Aquifer)	A constant vector with dimensions of mass
An initial condition and a constant rate of addition (at the beginning of the Aquifer)	An expression such as: Initial + Rate Etime*, where Initial is a constant vector (with dimensions of mass) and Rate is a constant vector (with dimensions of mass/time).
An initial condition and a time-variable rate of addition (at the beginning of the Aquifer)	The output of a Pool, Reservoir or Integrator element (with output dimensions of mass) with a specified Initial Value and (time-variable) Rate of Change.