Modeling and Numerical Simulation of Non-isothermal Water and
Organic Solute Transport in Soil Vadose Zone
by
Josep M
1Universitat
Gasto1,
Rovira i Virgili
Jordi Grifoll1 and Yoram Cohen2
2University
of California-Los Angeles
Avinguda dels Països Catalans, 26
Department of Chemical Engineering
Tarragona, Catalunya 43007
5531 Boelter Hall
Spain
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 temperaturedependence 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 onedimensional 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 soilliquid 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.