Kinetic mass transfer adsorption model for treating dairy wastewater with stone cutting solid waste

- A closed form solution is obtained for a presented kinetic adsorption mass transfer model.
- The effects of the various parameters on the theoretical kinetic curves are presented and discussed.
- The model is used to fit experimental curves for treating dairy wastewater with stone cutting waste.

This paper presents a mass transfer model for the kinetics of the batch adsorption process, with a closed form solution. The model is applied to the adsorption of organic pollutants from the industrial wastewater onto mineral particles obtained from stone cutting waste. Theoretical adsorption curves are plotted as dimensionless concentration in the wastewater, and on the particle surface, as functions of the dimensionless time. They are obtained from the mathematical solution of a system of ordinary differential equations, derived from the differential mass balance and the rate equation. The effects of the dimensionless equilibrium parameter, the particle dosage and the mass transfer coefficient on the fractional removal of the pollutants are presented. Experimental adsorption data for treating dairy wastewater with stone cutting solid waste are fitted well with the model. A simplified fitting methodology is illustrated. The obtained fitting parameters, including the equilibrium and the mass transfer coefficients, are summarized.

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