Pore volume and surface diffusion model to characterize batch adsorption of Cu(II) over chemically modified Cucurbita moschata biosorbent: simulation using gPROMS

This work describes the successful application of the pore volume and surface diffusion (PVSD) model characterizing the batch adsorption of Cu(II) on a chemically modified Cucurbita moschata biosorbent. The PVSD model captures the convective transport of Cu(II) from the bulk solution to the biosorbent surface, followed by its surface and pore diffusion inside the biosorbent. The adsorption of Cu(II) is mimicked using the Langmuir isotherm. The algebraic, ordinary, and partial differential equations, involved in the PVSD model, are solved using the general process modeling system (gPROMS). The model simulation results, depicted by the Cu(II) concentration decay curve, show an excellent match with experimental data. The external mass transfer coefficient (≈10−3 m/s) indicated no restriction on approaching Cu(II) toward the biosorbent surface. Within the biosorbent, surface diffusion was dominant over pore volume diffusion. The statistical analysis of the PVSD model results has been done by calculating R2, Chi-square value, normalized standard deviation, p-value, and root-mean-square error. The PVSD model approach presented in this work could be beneficial to other heavy metal–biosorbent systems.