# Comparison of an AT123D Model with an MT3D Model of Contaminant Transport

## By Darrel Dunn, Ph.D., PG, Hydrogeologist

## Purpose and Scope

The purpose of this webpage is to present an AT123D model of contaminant (solute) transport in a groundwater system and compare it to an analogous MT3D model. The comparison is for transport in surficial sediments on a hill slope. This webpage uses relatively non-technical language with some parenthetical technical language. The MT3D model used in this comparison is described on another webpage (MT3D MODPATH Correlation).

## AT123D (Analytical Transient One-, Two-, and Three-Dimensional)

AT123D is a computer program developed by G. T. Yeh and published by Oak Ridge National Laboratory in 1981. It has subsequently been modified by the International Ground Water Modeling Center, Colorado School of Mines. For my own use, I made some minor modifications in the input and output routines, including the generation of a file that I can use to produce maps using modern computer language (Python).

AT123D contains many options, so that one can model various contaminant source configurations and releases, various aquifer configurations, various types of contaminants, and various mechanisms affecting contaminant transport. The mechanisms affecting contaminant transport include movement with the water (advection), spreading due to movement around the grains of the aquifer (hydrodynamic dispersion), adsorption onto aquifer solids, and decay (usually radioactive decay). AT123D is a very comprehensive model. However, it can only deal with simple aquifer configurations, including uniform permeability (hydraulic conductivity), uniform porosity, uniform aquifer thickness, and uniform or infinite lateral extent. The hydraulic gradient (slope of the water table in the present case) must also be uniform.

AT123D has a small input file that can be developed and modified quickly. It uses very little computer time, so that one need not wait to see the result of running a particular input file. Consequently, it is inexpensive to use in preliminary stages of a project when expensive modeling is not warranted due to cost and lack of comprehensive data. It might be used prior to field exploration involving test holes, pumping tests, water quality sampling, and other expensive and time-consuming activities. It tends to be a reconnaissance level tool.

AT123D is an analytical model. It uses mathematical functions to calculate the contaminant concentration at a specified location and time. Consequently, the number of calculations is limited by the number of locations and times specified. This limitation means that a computer can execute the required calculations quickly. The locations can be specified as points in a grid, which allows for the representation of a groundwater contaminant plume. Calculations can be made for a sequence of times, which allows for representation of the development of a plume. The sequence of times can be made lengthy enough to reach a condition where concentrations are not changing significantly (steady-state).

## MT3D (Modular Transport, Three Dimensional)

MT3D, on the other hand, is a numerical model, which involves the discretization of space and time. An MT3D model is usually based on a parent MODFLOW model in which the aquifer is discretized into a grid of rectangular parallelepipeds (usually cube-like, called cells), and the permeability (hydraulic conductivity) may vary from cell to cell in the grid. This variation allows for a more realistic representation of the groundwater system. The parent MODFLOW model provides an output file that contains the flow rate across all of the cell faces. This file is input to the MT3D model, which uses the flow data to simulate the transport of chemical contaminants (solutes) from cell to cell through the model. In the MT3D model, this discretization results in a mathematical equation governing the concentration in each cell based on groundwater flow across the cell faces, chemical dispersion, adsorption, et cetera. Hence, there is a large system of interrelated equations governing concentration in the cells. These equations must be solved simultaneously. Computer input files may be lengthy because values of input parameters must be specified for each cell, and computer computation time can be lengthy because the solution iterates over all of the cells many times until the simultaneous solution is found. Since large input files may be required, and the iterative solution may involve long computer run times, MT3D is a more time-consuming method than AT123D. However, it provides a more realistic estimate of concentrations in a contaminant plume. There are several versions of MT3D. The version used in the present study is MT3D-USGS.

## MT3D AT123D Comparison

The MT3D model used in this comparison is described in the webpage named MT3D MODPATH Correlation. The MODFLOW parent is described in the webpage named Surficial Sediment MODFLOW Model. The AT123D model uses the same source location, source concentration, and contaminant release rate as the MT3D model. The aquifer thickness in the AT123D model is a uniform 10 feet compared to the variable saturated thickness in the MT3D model. The saturated thickness of the MT3D model is derived from the parent MODFLOW model and is shown in Figure 3 of the webpage named Surficial Sediment MODFLOW Model. The representative constant slope of the water table input to AT123D is also estimated from this figure. The constant hydraulic conductivity of the AT123D model is 77 ft/day, which is averaged (geometric mean) from 16 randomly located sites in the modeled area. The variable hydraulic conductivity in the parent MODFLOW model is shown in Figure 4 of the webpage named Surficial Sediment MODFLOW Model. The measures of chemical dispersion (longitudinal and transverse dispersivity) are the same values used in the MT3D model (300 feet and 30 feet, respectively). The contaminant is treated as completely mobile in both models (distribution coefficient = 0), and not subject to decay (not a radionuclide).

Figure 1 compares the results of the AT123D and MT3D models. The MT3D contours are black. They are the same as shown in the webpage named MT3D MODPATH Correlation. The AT123D contours are red. The contours shown for the MT3D results are 100, 10, and 1 milligrams per liter (mg/l). The contours shown for the AT123D results are 10, 1, and 0.1 mg/l. Although both models show the axis of the plume intersecting the river at the same place, the location of the southern part of the plume differs. The westward deflection of the MT3D plume appears to be caused by local deviation of the direction of slope of the water table as simulated in the parent MODFLOW model. There is no deflection of the plume in the AT123D model because the water table is planar with a constant slope. The water table produced by the MODFLOW model is shown in Figure 1 in the webpage named Groundwater Flow Path Model: MODPATH. The eastward deflection of the MT3D plume near the stream appears to be caused by increased aquifer thickness near the stream (which results in increased transmissivity). The saturated thickness of the aquifer is shown in Figure 3 of the webpage named Surficial Sediment MODFLOW Model. The difference in maximum concentration and lateral spread of the plume may be caused by local differences in saturated thickness and by the fact the the AT123D model treats the aquifer as infinite in lateral extent. Some error in the MT3D solution might also be involved.

Figure 1. Comparison of results from an AT123D model and an MT3D model of the same groundwater system. Black contours are MT3D. Red contours are AT123D. Dots are annual MODPATH points.

## Conclusions Based on Comparison of the AT123D Model with the MT3D Model

AT123D serves as a quick method for estimating the concentration of a groundwater contaminant originating at a source location in a simplified representation of a groundwater system; whereas MT3D is a more realistic method. But MT3D is more time-consuming and expensive. AT123D results may be relatively unrepresentative at some locations in the system, but AT123D provides a reconnaissance-level model of contaminant transport. It can provide a cost-effective initial estimate of the nature of a plume that includes the effects of chemical dispersion and other factors affecting the development of the plume.

Posted 9/13/2021