Analysis of models for dichloramine removal by activated carbon in batch and packed-bed reactors using quasilinearization and orthogonal collocation methods

Selective adsorption of organic homologues onto activated carbon from dilute aqueous solutions. Solvophobic interaction approach and correlations of molar adsorptivity with physicochemical parameters

“…Weber and co-workers (13, 14) have also emphasized the synergistic benefits of controlled biological growth and adsorption on activated carbon. Detailed predictive models for the design of batch and fixed bed activated carbon reactors have also recently been used to describe the removal of single components (15,16).…”

Approximate semianalytical solution for nonlinear surface diffusion in a batch reactor

“…The homogeneous surface diffusion model (HSDM) has been widely applied to simulate the dynamics of the adsorption process for wastewater. It has been developed and analyzed by several researchers (1)(2)(3)(4)(5) to describe the process of adsorption on granular activated carbon. The partial differential equation describing the process of adsorption on carbon in spherical coordinates is linear, but the boundary equation from the isotherm equilibrium condition is nonlinear.…”

“…The partial differential equation describing the process of adsorption on carbon in spherical coordinates is linear, but the boundary equation from the isotherm equilibrium condition is nonlinear. Therefore, several researchers (4)(5)(6) have used numerical evaluation and iterative calculation to solve the HSDM. Rosen (7) obtained an expression for the adsorbed-phase adsorbate concentration q(r,t) in terms of the surface concentration, qa(t), by applying Duhamel's theorem to the solution of the partial differential equation developed by Carslaw and Jaeger (8).…”

Simplified calculation procedure for carbon adsorption model

“…The method proposed in this paper is applicable for all types of batch adsorption experimental data and is not restricted to those where film transfer resistance is insignificant as proposed by Hand et al (1983). The proposed method uses orthogonal collocation method to convert partial differential equations to ordinary differential equations as was done by previous researchers (Villadsen and Stewart, 1967;Kim et al, 1978), but then differs from the past method in solving ordinary differential equations. This paper presents the analytical solution of ordinary differential equations obtained using Laplace transforms.…”

“…Homogeneous surface diffusion model. The dimensionless homogeneous surface diffusion model developed by several researchers (Mathews and Weber, 1975;Crittenden and Weber, 1978;Hand et al, 1983;Kim et al, 1978;and Traegner and Suidan, 1989) can be stated as:…”