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CSMoS Comments on the Potential Limitations of the Domenico-based Fate and Transport Models
Potential limitations of the Domenico-based fate and transport models have been identified in recently published articles (Guyonnet and Neville, 2004; Srinivasan et al., 2007; and West et al., 2007). CSMoS distributes four software packages (BIOSCREEN, BIOCHLOR, FOOTPRINT, and REMChlor) that use Domenico-based models. BIOSCREEN and REMChlor use the original Domenico model (1987), while BIOCHLOR and FOOTPRINT use the modified version of the model (Martin-Hayden and Robbins, 1997). CSMoS acknowledges that the Domenico-based models are approximate analytical solutions of the advective-dispersive solute transport equation; therefore, they could generate an error for a given set of input parameters when compared with the exact solutions. The error is largely sensitive to high values of longitudinal dispersivity (Srinivasan et al., 2007 and West et al., 2007). However, CSMoS noticed that the error is insignificant when longitudinal dispersion is reasonably low (see Figures 2b and 5b of Srinivasan et al., 2007). Furthermore, longitudinal dispersivity is a calibration parameter, not a parameter that is measured in the field, in real-world modeling applications. Therefore, CSMoS believes that the Domenico-based models in their current forms are reasonable for screening level tools, such as BIOCHLOR, BIOSCREEN, FOOTPRINT, and REMChlor. However, the users should be aware of selecting a reasonably low longitudinal dispersivity in order to minimize the potential error.
There are three different approaches outlined in West et al. (2007) for estimating longitudinal dispersivity (αx). These are:
- αx = 10% of plume length;
- αx = 10% of L, where L is the longitudinal distance to the reference point (i.e., the x distance at any observation point) according to Pickens and Grisak (1981); and
- αx = 0.83(log10 L)2.414 according to Xu and Eckstein (1995).
In the first method, αx is constant throughout the model domain, while for the second and third methods, it increases proportionally with L (i.e., x distance at any observation point). Although the above stated methods would give a reasonable first estimation of αx, in reality, the calibrated value could be even smaller than those estimated from the three methods, and hence, would minimize the error resulting from the approximation in the Domenico-based models.
Guyonnet and Neville (2004) found from dimensionless analysis that the original Domenico model (1987) shows minimal error when the Peclet Number, Pe, is greater than 6, which represents a relatively permeable aquifer. By definition, Pe is equal to VL/Dx, where V is the seepage or ground water velocity, L is the longitudinal distance to the reference point, and Dx is longitudinal dispersion. Therefore, higher Pe means advection dominated transport, while lower Pe means both mechanical dispersion and molecular diffusion can significantly influence the transport. CSMoS found from West et al. (2007) that the difference between the Domenico model (1987) and the exact solution by Wexler (1992) is relatively small for Pe = 10 (i.e., when αx ≈ 0.1L) (see Figure 1 of West et al., 2007). To this end, CSMoS recommends to safely use BIOCHLOR, BIOSCREEN, FOOTPRINT, and REMChlor for advection-dominated transport conditions (i.e., when Pe≥10) and be cautious when the transport processes are highly influenced by dispersion (i.e., when the aquifer is relatively impermeable).
References
Domenico, P.A. (1987). An analytical model for multidimensional transport of a decaying contaminant species. Journal of Hydrology, 91, 49–58.
Domenico, P.A. and G.A. Robbins. (1985). A new method of contaminant plume analysis. Ground Water, 23 (4), 476–485.
Guyonnet, D. and C. Neville. (2004). Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater. Journal of Contaminant Hydrology, 75, 141–153.
Martin-Hayden, J. and G.A. Robbins. (1997). Plume distortion and apparent attenuation due to concentration averaging in monitoring wells. Ground Water, 35 (2), 339–346.
Pickens, J. and G. Grisak. (1981). Scale-dependent dispersion in a stratified granular aquifer. Water Resources Research, 17(4), 1191–1211.
Srinivasan, V., T.P. Clement, and K.K. Lee. (2007). Domenico solution—is it valid? Ground Water, 45(2), 136–146.
West, M.R., B.H. Kueper, and M.J. Ungs. (2007). On the use and error of approximation in the Domenico (1987) solution. Ground Water, 45(2), 126–135.
Wexler, E. (1992). Analytical solutions for one-, two-, and three-dimensional solute transport in groundwater systems with uniform flow. Techniques of Water Resources Investigations of the United States Geological Survey, Chapter B-7, Book 3, Applications of Hydraulics, 79 pp.
Xu, M. and Y. Eckstein. (1995). Use of weighted least-squares method in evaluation of the relationship between dispersivity and field scale. Ground Water, 33(6), 905–908.