Numerical solution analysis of water flow in porous medium under phase changes due to evaporation

Evaporation is a dynamic and nonlinear process that incorporates various internal transport mechanisms which is important in the unsaturated zone in arid regions under low soil moisture conditions [1, 2]. The governing equations are formed out of the coupled Richards equation with the heat transport equation, where the boundary conditions originate from the surface energy balance. The purpose of this contribution is to present a numerical model simulating coupled water and heat flow in a porous medium with phase changes due to evaporation. The nonlinear nature of this problem, which originates both from the nonlinear Richards equation and latent heat exchange, which in turn governs the heat gradient, requires a proper temporal discretization in order to maintain numerical solution of sufficient qualities. The net evaporation rate is temperature and water content dependent, where the heat transferred downward by thermal conduction into the soil when the soil surface is warming by solar radiation or conducted back to the surface when the temperature of the top of the soil cools. Evaporation rates from terrestrial surfaces are very common to quantify in terms of energy flow leaving the evaporating surface as latent heat of vaporization of the water vapor. In this contribution, it is presented a numerical implementation of this coupled dynamic process and describes the computational difficulties which arise from this nonlinear process, including a numerical comparison between the common approach for evaluating evaporation in soils by using the Penman-Monteith [3] equation and the coupled water and heat flow modeling approach.

References

[1] Hirotaka Saito, Jiri Simunek, and Binayak P Mohanty. Numerical analysis of coupled water, vapor, and heat transport in the vadose zone. Vadose Zone Journal, 5(2):784–800, 2006.

[2]  Masaru Sakai, Scott B Jones, and Markus Tuller. Numerical evaluation of subsurface soil water evaporation derived from sensible heat balance. Water Resources Research, 47(2), 2011.

[3]  Richard G Allen, Luis S Pereira, Dirk Raes, Martin Smith, et al. Crop evapotranspiration-guidelines for computing crop water requirements-fao irrigation and drainage paper 56. Fao, Rome, 300(9):D05109, 1998.