Langmuir-Hinshelwood model of soil phosphorus kinetics
1999
Overman, A.R. | Scholtz, R.V.
A mathematical model is needed to relate the dynamics of soil phosphorus (P) chemistry in a batch reactor to the soil/solution ratio and to initial P in the reactor. The Langmuir-Hinshelwood model appears to describe this system quite well. According to this model reversible adsorption of P from solution to the colloidal surface (Langmuir component) is followed by an irreversible reaction of the surface species (Hinshelwood component). The system is an example of heterogeneous catalysis. Adsorption follow 2nd order kinetics related to solution P concentration and concentration of available surface sites for adsorption. Desorption and reaction are assumed to follow 1st order kinetics. This system described by three simultaneous equations, two of which are 1st order nonlinear ordinary differential equations. Numerical intergration is by the Euler finite difference method. Data from the literature are used to calibrate the model and to demonstrate its characteristics for a sandy soil. Rapid drop in solution P concentration is followed by a gradual decline. The first step in calibration is to assume quasi-equilibrium in the early phase (analogous to that in enzyme kinetics), which leads to values for the total concentration of adsorption sites, So, and the Langmuir coefficient, potassium (K). The second step then estimates the adsorption coefficient, ka, and the reaction coefficient, kr. Full simulation of the transient process over time requires great care in size of time step, t, to maintain stability and accuracy in the procedure. Analysis shows a linear correlation between total surface sites, So, and soil/solution ratio, M, as expected.
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