Calculation of space–time concentration profiles of contaminants in a fixed sorbent bed from experimental data on dynamic water purification

A formula for a mathematical description of the relationship between the breakthrough curve C ( t )/ C 0 for the dynamic sorption purification of water and the space–time concentration profile of contaminant q ( x , t ) in the fixed sorbent bed is derived. The derivation is based on the simplifying assumption that the dependence of the adsorbate concentration profile q ( x , t ) on the longitudinal coordinate x of the bed is described by the logistic function q ( x , t ) = a /{1 + exp{– k ( t )[ x – b ( t )]}}, in which a is a constant and the time-dependent parameters k ( t ) and b ( t ) are expanded into the power series k ( t ) = k 0 + k 1 t + k 2 t 2 and b ( t ) = b 0 + b 1 t + b 2 t 2 + b 3 t 3 + b 4 t 4 with the expansion coefficients b 0 , b 1 , b 2 , b 3 , b 4 , k 0 , k 1 , and k 2 , so that C ( t )/ C 0 = 1–( S /( C 0 v )) F ( t , b 0 , b 1 , b 2 , b 3 , b 4 , k 0 , k 1 , k 2 ), where C ( t ) is the breakthrough concentration of contaminant in the water effluent from at the fixed bed, C 0 is the concentration of the contaminant in the water influent into the fixed bed, S is the cross-sectional area of the bed, v is the water flow rate, and F is a definite analytic function dependent on the profile q ( x , t ). The coefficients b 0 , b 1 , b 2 , b 3 , b 4 , k 0 , k 1 , and k 2 are determined by fitting the theoretical breakthrough curve to the experimental one. With the help of this approach, space–time profiles for dynamic water purification from lead, nitrate, and perchlorate ions are calculated. It is shown that the adsorbed contaminant ions are redistributed between different parts of the fixed bed in the course of the adsorption process.