A non-equilibrium model for soil heating and moisture transport during extreme surface heating: the soil (heat–moisture–vapor) HMV-Model Version 1

Abstract

Abstract. Increased use of prescribed fire by land managers and the increasing likelihood of wildfires due to climate change require an improved modeling capability of extreme heating of soils during fires. This issue is addressed here by developing and testing the soil (heat-moisture-vapor) HMVmodel, a 1-D (one-dimensional) non-equilibrium (liquidvapor phase change) model of soil evaporation that simulates the coupled simultaneous transport of heat, soil moisture, and water vapor. This model is intended for use with surface forcing ranging from daily solar cycles to extreme conditions encountered during fires. It employs a linearized Crank-Nicolson scheme for the conservation equations of energy and mass and its performance is evaluated against dynamic soil temperature and moisture observations, which were obtained during laboratory experiments on soil samples exposed to surface heat fluxes ranging between 10 000 and 50 000 W m −2 . The Hertz-Knudsen equation is the basis for constructing the model's non-equilibrium evaporative source term. Some unusual aspects of the model that were found to be extremely important to the model's performance include (1) a dynamic (temperature and moisture potential dependent) condensation coefficient associated with the evaporative source term, (2) an infrared radiation component to the soil's thermal conductivity, and (3) a dynamic residual soil moisture. This last term, which is parameterized as a function of temperature and soil water potential, is incorporated into the water retention curve and hydraulic conductivity functions in order to improve the model's ability to capture the evaporative dynamics of the strongly bound soil moisture, which requires temperatures well beyond 150 • C to fully evaporate. The model also includes film flow, although this phenomenon did not contribute much to the model's overall performance. In general, the model simulates the laboratoryobserved temperature dynamics quite well, but is less precise (but still good) at capturing the moisture dynamics. The model emulates the observed increase in soil moisture ahead of the drying front and the hiatus in the soil temperature rise during the strongly evaporative stage of drying. It also captures the observed rapid evaporation of soil moisture that occurs at relatively low temperatures (50-90 • C), and can provide quite accurate predictions of the total amount of soil moisture evaporated during the laboratory experiments. The model's solution for water vapor density (and vapor pressure), which can exceed 1 standard atmosphere, cannot be experimentally verified, but they are supported by results from (earlier and very different) models developed for somewhat different purposes and for different porous media. Overall, this non-equilibrium model provides a much more physically realistic simulation over a previous equilibrium model developed for the same purpose. Current model performance strongly suggests that it is now ready for testing under field conditions.

Validity of Assuming Equilibrium Between Liquid Water and Vapor for Simulating Evaporation

“…This is because of the strong, near exponential variation of which plays a particularly important role for the Quincy sand case under surface fire conditions. This calls into question the results of Massman () who claimed that the nonequilibrium evaporation source term he used in his model, one version of which was based on Novak (), was critical to the improved performance of his simulations compared with Massman () and the original theory in Campbell et al (). The results herein suggest that the more likely source of the improvement was the inclusion of liquid flow which was neglected in both Campbell et al () and Massman ().…”

“…Yamanaka et al () used a different sand but the same loam and clay soils in their numerical evaporation simulations based on PdV57. The Quincy sand was one of the soils used in the Campbell et al () surface fire experiments and numerical calculations and the Massman (, ) surface fire numerical simulations. The dependence of h v on T shown in the figure is solely due to the dependence of D v on T , which was given by D v ( T )=2.12×10 −5 ( T /273.15) 2 m 2 s −1 (Campbell, ).…”

Utilization of Nonequilibrium Phase Change Approach to Analyze the Nonisothermal Multiphase Flow in Shallow Subsurface Soils

“…The f = 1 correction factor in Equation 8 accounts for the nonuniformity of the porous media, that is, represents smooth uniform spherical grains. Smits et al (2012) and Massman (2015) considered the film flow according to Equation 8 in their models and acknowledged the importance of considering the hydraulic conductivity due to the film flow for dry state conditions. But they found no improvement in the numerical results.…”

“…In addition, the experimental observation showed that the liquid‐gas interfacial area reaches its maximum value at a low saturation degree for sands (Costanza‐Robinson & Brusseau, 2002). Since there is limited research on predicting the interfacial area, a parabolic function proposed by Costanza‐Robinson and Brusseau (2002) and Massman (2015) is used in this study with a slight modification: α 1 = 50, α 2 = 20, α 3 = 0.22, and α 4 = 0.25 are fitting parameters. Considering Equation and the fitting parameters, the interfacial area reaches its maximum value at S l = 1%.…”

“…Nuske et al (2014) extended the model proposed by Class et al (2002) to include the effects of thermal and chemical nonequilibrium phenomena, where they concluded that considering chemical nonequilibrium (which may lead to NEPC) is of higher importance than the thermal nonequilibrium. Moreover, Massman (2015) studied the coupled mass and heat flow during wildfires considering a NEPC model. He proposed that the chemical potential of water cannot be in equilibrium with water vapor for soils closed to dry condition when almost no liquid water exists.…”