Theory and equations

Temperature and water-content dependence of reactions

Temperature dependence

The transport and reaction parameters (diffusion coefficients, sorption coefficients, Henry's constant, decay and production rates, mass-transfer coefficients) can depend on the temperature after the Arrhenius equation Stumm and Morgan (1981):

a_T = a_r exp[ E_a (T^A − T_r^A) / (R_u T^A T_r^A) ]

with the parameter value a_r at the reference absolute temperature T_r^A = 293.15 K (20 °C), the absolute temperature T^A [K], the universal gas constant R_u = 8.314 J/mol/K and the activation energy E_a [J/mol] of the parameter. The temperature comes from the heat transport, or is the constant initial temperature of each node.

Water-content dependence

Degradation is often slower in dry soil. Following Walker (1974), the reaction rates can be reduced below a reference water content:

a(θ) = a_r (θ/θ_ref)^B for θ < θ_ref; a(θ) = a_r otherwise

with the exponent B (≈ 0.7) and the reference water content θ_ref = θ(h_ref) at the reference pressure head h_ref, defined separately for each rate.

Alternatively, a trapezoidal function per reaction (file MoistDep.in) multiplies the rate: ReacMin0 below θ₀, a linear rise to 1 at θ₁, 1 up to θ₂, and a linear decrease to ReacMin1 at θ₃ (oxygen limitation in wet soil). HYDRUS-1D writes the file but does not use it; Rusteau does.

Literature cited in this topic

Stumm, W., and J. J. Morgan (1981). Aquatic Chemistry. 2nd ed., John Wiley & Sons, New York, 780 pp.
Walker, A. (1974). A simulation model for prediction of herbicide persistence. Journal of Environmental Quality 3(4): 396–401. doi:10.2134/jeq1974.00472425000300040021x

All sources: References.