Model of adsorption waste treatment including a chemical reaction

The article poses and solves the general problem of the dynamics of adsorption from a liquid in a fixed layer of adsorbent, taking into account a first-order chemical reaction and a linear adsorption isotherm. The adsorption model is based on the mass balance equations of the target component for an infinitesimal layer element and adsorption kinetics, written as a system of linear first-order partial differential equations with corresponding boundary conditions. The problem is solved by the Laplace transform method. This made it possible to reduce the joint solution of a system of equations in the originals to an independent solution in images of the Cauchy problem for an ordinary differential equation and an algebraic equation. As a result, expressions were obtained for the concentrations of the target component in the adsorbent layer and in the flow at any time and in any section of the layer. This made it possible to simulate a practical problem of the adsorption of chloroform by zeolites for the treatment of wastewater from a real swimming pool and obtain interesting graphic materials based on the solution and the developed algorithm. The results of the solution can be translated into numbers by programming in any available high-level algorithmic language. It is shown that the shape of the curves of changes in the concentrations of the target component in the adsorbent and adsorbent over the thickness of the adsorbent layer and over time does not change, although the numerical values of these parameters change in a fairly wide range. It is also noted that in the range of concentration changes considered in the article, the concentration of the adsorbent initially decreases sharply, and then smoothly along the entire length of the fixed adsorbent layer decreases slightly. It has been revealed that the use of methods, techniques and theorems of the Laplace transform method in relation to the problem of adsorption dynamics makes it possible to deeply penetrate the mechanism of the problem being solved, which is not possible with other solution methods. This allows, with a known set of initial data, to find the change in the concentrations of the target component in both phases and select the required thickness of the adsorbent layer.