Aflexible model to characterize soil con tamination: adaptation of the normal distribu tion of hydrodynamic dispersion to different cases of hydric miscible displacement

Abstract

The analytical model of normal equitable distribution of micro velocities (compared to the velocity of the plane, p=1, of piston flow) for hydrodynamic dispersion has been adapted to also handle cases of biased distribution in solute transport in one dimensional soil moisture flow. The selected version of the equation includes two constants dimensionless: P_e the Peclet number, and R, the solution-soil interaction factor. The effluent break through curve for a continuous pulse of solution with concentration c₀, which displaces a soil column saturated with distilled water, is expressed as follows: p is the number of pore volumes displaced, with the volume defined by the plane of sampling of the effluent, whose concentration is c; z is the number of standard deviations. The equitable distribution model has been explained by using data from an experimental case. The equation contains the standard integral of the normal curve, which is found in the Microsoft Excel list of functions and this facilitates a rapid spreadsheet calculation (pro gram included) and visual inspection to deter mine Pe from experimental data. R is the value of p when c/c₀=0.5. The reference plane, p=1, of pis ton flow is conserved. Therefore, when R<1 or >1, a biased distribution occurs. R=1, when there is no solution-soil interaction and the distribution is equi table. The degree of association r² (program includ ed), was tested between the calculated (fitted) and experimental values of c/c0 for selected values of p for a variety of soils: a Ben Lomond sand with P_e=203.4, R=1, and r²=0.99; an Aiken clay loam (red soil,1-2 mm aggregates), P_e=9, R=0.92, and r²=0.99, both soils from California, EE.UU.; a clayey Oxic Dystropept, La Selva, Costa Rica, very aggregated, P_e=0.4 (shows preferential flows), R=0.11, and r2=0.88; a Hapludult with 48% clay and 32% silt, P_e=9, R=2 and r²=0.99, Guadalupe, Perez Zeledón, Costa Rica, and a dark red Latosol, Petrolina, Brazil, P_e=15, R=2.9 and r²=0.99.