Miscible displacement techniques were used to study the movement of picloram (4-amino-3,5,6-trichloropicolinic acid) through a water-saturated Norge loam soil. The equilibrium adsorption and desorption isotherms for picloram and Norge loam soil were not single-valued relations. Picloram mobility was reduced significantly when the average pore-water velocity was decreased from 145 to 14.2 cm/day. Observed and predicted effluent concentration distributions were compared. Predictions were made with a S/360 CSMP simulation model, using two kinetic rate equations and an equilibrium Freundlich equation. The two kinetic models and the equilibrium model each satisfactorily described the observed effluent concentration distributions at low pore-water velocities provided the nonsingle-valued character of the adsorption-desorption process was included in the calculations. At high pore-water velocities, the kinetic adsorption models were found inadequate to predict the picloram movement. An empirical model was then developed, based on the assumption that equilibrium existed during displacement and that only a fraction of the soil participated in the adsorption process. This fraction was found to be a function of the average pore-water velocity. With the empirical model, a reasonable fit between data and calculated effluent curves was obtained for all pore-water velocities. Additional Index Words: herbicide movement, adsorption, molecular diffusion, miscible displacement, computer simulation, S/360 CSMP. R ECENTLY, several mathematical models have been proposed to describe the movement of chemicals through adsorbing porous media (7, 12, 13, 14). One of the earliest solutions for equilibrium adsorption between the solution and adsorbed phases was presented by Lapidus and Amundson (10). Hashimoto et al. (7) obtained a similar solution which included the longitudinal mixing process as well as equilibrium and linear adsorption during one-dimensional flow. Their solution, including the "retardation factor," was later used by Kay and Elrick (9). Lindstrom et al. (13) and Davidson and Chang (2) used a similar solution to describe the movement of several organic chemicals through porous media. These solutions assumed instantaneous adsorption and a linear and single-valued adsorption-desorption relation. These assumptions may not be valid for all conditions that occur in a soil-water system. Kay and Elrick (9) and Davidson and Chang (2) showed considerable deviation between the mathematical model based on the assumption of equilibrium adsorption (7) and experimental data, especially at the high flow velocities. The two studies suggested that for high pore-water velocities, the use of a kinetic rate equation to describe the adsorption process may be necessary. Lapidus and Amundson (10), Oddson et al. (14) and Lindstrom et al. (12) each presented solutions that included a rate equation in a convective type transport equation to describe the displacement of a chemical in a sorbing porous medium. Oddson et al. (14) and Lapidus and Amundson (10) used a first-order rate equation, but assumed that the diffusion and dispersion processes were negligible in the transport equation in order to obtain an analytical solution. Lindstrom et al. (12) used an adsorption rate equation as well as a "sticking probability" factor. The presence of a non-single-valued (hysteretic) adsorption-desorption relation has received little attention in earlier studies. Swanson and Dutt (16), studied the movement of 2-chloro-4-ethylamino-6-isopropylamino-i'-triazme (atrazine) through different soils and encountered such a non-single-valued adsorption-desorption relationship. They found that both the adsorption and desorption isotherms were of the Freundlich form, but that the coefficients for adsorption were not equal to those for desorption. These same authors were able to predict the movement of atra30 SOIL SCI. SOC. AMER. PROC., VOL. 38, 1974 zine reasonably well with a computer model that assumed instantaneous adsorption and desorption. The purpose of this study was to use some of the available adsorption models in a transport equation to describe experimental laboratory data. A S/360 CSMP (Continuous System Modeling Program) computer program (8) was developed for three different adsorption models, based on equations presented by Lindstrom et al. (12), Oddson et al. (14), and an equilibrium Freundlich adsorption relationship, respectively. Computer results were then compared with experimentally determined picloram effluent concentration distributions from a water-saturated Norge loam soil. ADSORPTION EQUATIONS The movement of adsorbed chemicals through a porous medium under steady state soil-water conditions was assumed to obey the following differential equation: