Wednesday, July 26, 2023

TS-CHEM Solution Library - AT123D-AT

The TS-CHEM program provides an easy-to-use software environment in which to analyze contaminant plume transport, and includes a comprehensive library of more than 30 different analytical solutions to the advection-dispersion equation. Each solution incorporates different capabilities, including how it represents the contaminant source and how the plume interacts with the aquifer. For this post in the Solution Library series, we will be focusing on the AT123D-AT family of models published by Dan Burnell in 2012 which represents an updated version of the original AT123D model suite developed by G.T. Yeh at the Oak Ridge National Laboratory.

What is AT123D?

The original AT123D was a suite of analytical model solutions that are used to simulate one-, two- and three-dimensional transport in groundwater. The program is complex, and allows for many different source configurations, including

  • patch sources
  • line sources
  • point sources
  • volume sources

In contrast to many analytical plume models that represent the source using a first-type specified concentration, AT123D represents the source as a second-type specified mass flux boundary condition. This means, for example, if you know the nitrogen load from a residential dwelling to a septic system (i.e. number of residents times average daily nitrogen load per person) you can represent that source in AT123D as milligrams of nitrogen per day instead of trying to estimate a septic source concentration value. The primary difference between AT123D and AT123D-AT is in how the solver arrives at a solution to the advection-dispersion equation. AT123D-AT incorporates a Romberg numerical integration scheme that works to prevent oscillations, speed convergence, and improve accuracy for a wide range of input parameter combinations.

A conceptualization of the many possible specified mass flux source geometries available in AT123D-AT is shown in Figure 1 below, and can also be found in the Model Selection Tool in TS-CHEM:

Figure 1 - AT123D-AT Source Geometries

TS-CHEM was developed with usability in mind, so the numerous AT123D-AT solutions available to the user (differing aquifer geometries, source geometries, and source types) have been broken up into six “versions” (see table below). These pre-configured versions allow the user to select the type of AT123D-AT model that will best represent their site (aquifer and source), and to specify the desired parameter input values to represent site-specific properties, using model types that closely match conditions simulated by other analytical ADE solutions included in ­TS-CHEM’s Solution Library. This last consideration makes it easier to compare different plume transport solutions (e.g. a first-type source vs a second-type source) by selecting similar type models (e.g. with aquifer boundaries or without aquifer boundaries) from the TS-CHEM Solution Library.

The following nomenclature is used between each version to help the user quickly determine which version they are looking for: Infinite boundary (I), Finite boundary (F), Constant mass release rate (C), Instantaneous release source (I), Time-variable (transient) mass flux (T):

Model Version

Aquifer Boundary

Source Type

Analagous TS-CHEM models


Infinite unbounded

Constant mass flux

3DADE-3 or 3DADE-4 (patch source)


Infinite unbounded

Initial mass instantaneous release

3DADE-5 or 3DADE-6 (volume source)


Infinite unbounded

Constant specified concentration

ATRANS4 (with concentration stepping)


Finite bounded

Constant mass flux



Finite bounded

Initial mass instantaneous release

3DADE-5 or 3DADE-6 (volume source)


Finite bounded

Constant specified concentration

ATRANS4 (with concentration stepping)

What are the differences between the AT123D-AT models?

The two defining factors that highlight the differences between the different AT123D-AT models are 1) whether the aquifer extent is assumed to be infinite (as is the case for many analytical transport solutions) or finite (bounded horizontally or vertically), and 2) how the source concentration or flux is applied at the model boundary over time (continuous, instantaneous pulse release, or time-varying). The three different types of source concentration fluxes are conceptualized in Figure 2 below:

Figure 2 - AT123D-AT Model Source Types

As you can see in Figure 2, there are three distinct source types. The source type that is most appropriate to use in a particular application is dependent on the known conditions at a site, and/or the known or assumed conditions of the source.

What applications are the AT123D models best suited for?

As discussed in previous blog posts, TS-CHEM can assist environmental professionals with the development of conceptual site models (CSMs) that characterize the extent and behavior of groundwater contaminant plumes. The AT123D-AT models are highly flexible, able to provide users with the ability to evaluate solute fate and transport in one-, two- or three-dimensions. In its fundamental form, AT123D-AT is solving the 3D ADE equation in a 1D (X-direction only) aquifer flow field, but 2D plume transport and even 1D “column” transport can be set up using the bounded aquifer settings. i.e. the AT123D-AT “F” models (FC, FI, and FT) can be used to represent sites where the aquifer thickness and/or width is known or is believed to be bounded (finite aquifer boundary). This type of AT123D-AT model is similar to the ATRANS family of models which include an upper (water table) and lower (aquifer base) no-mass-flux boundary.

But the AT123D-AT models are not all limited to bounded aquifer conditions. The AT123D-AT “I” models (FI, II, and IT) can be used to represent sites where there is no limitation on aquifer thickness or width (infinite aquifer boundary). This type of AT123D-AT model is similar to the 3DADE family of models, which do not impose any finite boundaries on the aquifer.

Further, the investigator can use a variety of patch source geometries to best represent the conditions at their site. For example, if an investigator has information on source mass flux at the downgradient edge of a source area, they may use a patch source. Or, if a large regional scale model is being considered, the user may want to utilize a point source to track the general plume behavior over time.

When choosing between source types, a user may choose to use a constant mass release source AT123D-AT model If only a single source concentration is known, and/or the investigator wished to perform a conservative analysis in which the source does not deplete through time. If the user wanted to investigate the plume behavior in a case where a slug of solute is introduced into the groundwater, they can use an instantaneous release source type. If information is available on the changing history (both increases and decreases) of source flux over time, the transient source type can be used.

Similar to the ATRANS1 model, the AT123D-AT FC model is useful for simulating scenarios that have aquifers of a finite extent that can be represented by a continuous mass flux. This type of analysis may be useful for evaluating a conservative maximum plume extent, or when the plume becomes stable (Figure 3):

Figure 3 - AT123D-AT FC solution showing maximum plume extent for a stable benzene plume with a constant source flux of 0.001 ld/d at 200ft, 600ft and 1000ft from the source.

The AT123D-AT FI model is useful for simulating scenarios where a slug of contaminant is assumed to have rapidly entered the groundwater. This type of model is sometimes used in an emergency spill response analysis if an investigator wants to simulate a conservative condition where a “slug” of contaminant enters the groundwater instantaneously and then is allowed to flush away from the spill area toward a possible receptor location (Figure 4):

Figure 4 - AT123D-AT FI solution showing plume concentrations up to 4000 days after an instantaneous mass input of 22.05 lbs of benzene introduced to groundwater. Concentrations are shown at 200ft, 600ft and 1000ft from the source. 

Similar to the ATRANS4 model, the AT123D-AT FT model allows the user to define transient source behavior. Unlike ATRANS4, the AT123D-AT FT model uses a second-type boundary condition and is therefore defined by time-flux pairs (instead of time-concentration pairs). The transient source condition allows the user great flexibility in how they define the time series of their source and can enable investigators to simulate complex scenarios where there may be intermittent single sources, multiple sources that overlap at different times, or even source termination that would result from remedial actions.

An example of a time-variable source flux is shown in Figure 5 below for a hypothetical release from an underground storage tank (UST). The benzene source progressively decreases until it eventually reaches zero after 2000 days. This might be indicative of a UST that leaks over time, or it could be indicative of a UST removal at around 500 days with a small amount of product remaining after removal. In either case, the benzene concentration is reduced over time through degradation/natural attenuation and flushing.

Figure 5 - AT123D-AT FT solution showing benzene plume concentrations entering groundwater from a hypothetical underground storage tank at 200ft, 600ft and 1000ft from the source.

To summarize: the AT123D-AT family of models available in the TS-CHEM Solution Library allow for a very flexible representation of the source over space and through time and can be used for a variety of environmental scenarios and conditions. The feature that sets the AT123D-AT models apart is that they are the only models in the TS-CHEM solution library that utilize a second-type (specified mass flux) source boundary condition, allowing for users to directly input an estimate of source mass flux for their site. AT123D-AT also differs from AT123D in that it incorporates enhanced solver capabilities that reduce solve times and increase solution accuracy. The six AT123D-AT model types included in TS-CHEM allow a user to easily identify which model is best for their site or application. These models can assume either a finite or infinite aquifer boundary and a multitude of source geometries and source release types.

To learn more about TS-CHEM, or to download a FREE DEMO VERSION of the software, visit the TS-CHEM Website today!

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