Modeling and Numerical Simulation of Non-isothermal Water and Organic Solute Transport in Soil Vadose Zone
by
Josep M Gasto1, Jordi Grifoll1 and Yoram Cohen2
1Universitat Rovira i VirgiliAvinguda dels Països Catalans, 26
Tarragona, Catalunya 43007
Spain / 2University of California-Los Angeles
Department of Chemical Engineering
5531 Boelter Hall
Los Angeles, CA 90095
Presented at AIChE 2002 Annual Meeting, November 3 - 8, Indianapolis, Indiana.
ABSTRACT
A non-isothermal transport model for the unsaturated soil zone that considers the transport of organics has been developed. The model consists of five coupled PDEs that include mass transport for liquid water, vapor water, gaseous phase as a whole, the organic compound as well as an energy balance. Liquid water movement is modeled by means of Richards' equation subject to dynamic surface boundary conditions that consider either evapotranspiration or rain infiltration. Water vapor movement is modeled considering the temperature-dependence of vapor pressure and the decrease of vapor pressure with capillary pressure for liquid water. Movement of the gaseous phase as a whole is due mainly to liquid water displacement and change of gas density with temperature. In addition to the classical mechanisms and processes that govern chemical transport (convection, dispersion, diffusion, sorption to the organic matter and partition between liquid and gas phases), the model includes chemical surface adsorption and its dependence on water vapor pressure and temperature. The energy balance equation considers local thermal equilibrium, conduction in all phases, and convective and dispersive transport in the fluid phases. The top boundary condition for the energy equation takes into account downward and upward radiative fluxes and convective heat flow to the atmosphere at the soil surface. The radiation processes includes, for the short waves, the dependence with respect to the sun declination, local latitude, hour angle of the sun, the actual earth-sun distance, atmospheric transmission, soil reflection as well as incoming and outgoing long wave radiation.
The five coupled-partial differential model equations, for a series of one-dimensional studies, were discretized following the finite volume formulation for the balance equations, central difference scheme for the fluxes and fully implicit time integration to ensure numerical stability. The grid spacing and the time step were non- uniform to provide sufficient numerical description of the space-temporal variations of the different dependent variables with monitoring of the local compliance of the standard restrictions (Courant and Peclet number limits). All simulations were tested for grid-spacing independence of the simulation result.
Simulation results agreed well with experimental results with respect to water movement measured by different authors for natural bare soil conditions. After soil irrigation and in a drying period, both experimental and simulation results showed a volumetric water content (hereafter VWC) daily oscillation cycle with decreasing amplitude with soil depth. Soil drying was described remarkably well without the need for adjustable parameters. In addition to water movement, the model was capable of matching experimental data, to a reasonable level of accuracy, for the organic compound transport and volatilization fluxes under natural soil conditions, including conditions that lead to diurnal variations for the volatilization flux.
Several test cases were simulated to demonstrate the coupling between water movement and organic compound transport during soil drying episodes. These simulations were used to explore the relative role and importance of the different phases and transport mechanisms in the migration of the organic compound near the soil surface. Three organic compounds of different volatility were selected (ethanol, 1,3-dichlorbenzene and lindane) to cover a reasonable range of physicochemical parameters that spans three orders of magnitude for the Henry's law constant. The above simulations were accomplished for two different soil scenarios. The first was a wet soil scenario, corresponding to the initial stage of a soil drying process (i.e., when the VWC of the soil is still high) while the second was a dry scenario that corresponded to the later stage in the drying process (i.e., when the VWC near the surface is very low). Simulation results for the water evaporation flux and organic compound volatilization rates obtained under natural conditions exhibit markedly diurnal variations cycles controlled by the soil temperature with maximum and minimum values located when the soil temperature is at its highest and lowest value, respectively. The results suggest that large diurnal variations in volatilization rates are higher for slightly volatile organic, being these variations greater when the soil is dryer.
Results obtained for the organic compounds and selected soil scenarios suggest that the influence of water liquid dynamics on chemical migration and volatilization is stronger for compounds with a relatively low Henry's law constant (e.g., ethanol and lindane). On the other hand, results for the 1,3-dichlorbenzene showed that, for this specific compound, transport in the vadose zone occurs mostly in the gas phase. The liquid and gas phase contribution to the organic compound transport from the soil subsurface to the atmosphere can all be significant, to varying degrees, during different hours of the day. In the case of organic compounds like ethanol, with a high water solubility and relatively low Henry's law constant, dispersion mechanism dominates the transport in the soil-liquid phase, while for organic compounds with a stronger tendency to volatilize, like 1,3-dichlorbenzene, diffusion and dispersion (in the soil) dominate the transport in the gas phase. Finally, the simulation results also demonstrate the impact on the dynamics of contaminant transport due to variations in adsorption affinity, caused by daily temperature and soil dryness.