An inverse method to estimate adsorption kinetics of light hydrocarbons on activated carbon

• Inverse adsorption kinetics estimation inside a porous particle is presented.
• The effective and surface diffusivities are estimated using the inverse method.
• The Knudsen diffusion, surface diffusion, slip and viscous flows is considered.
• The conjugate gradient is utilized for optimization procedure of the inverse method.
• The incremental differential quadrature is used for solving the governing equations.

An inverse algorithm to estimate the adsorption kinetics inside the spherical particles in a constant molar flow (CMF) gas adsorber reservoir by measuring the bulk pressure is developed. The formulation includes Knudsen diffusion, surface diffusion, slip and viscous flows. To obtain an efficient algorithm, the conjugate gradient method (CGM) for optimization procedure and the incremental differential quadrature method (IDQM) for solving the governing equations are adopted. The results show that the Knudsen diffusion, surface diffusion, slip and viscous flows effects depend on the type of adsorbate and adsorbent gases. It is shown that the effective diffusivity is not constant and goes through a minimum at an intermediate pressure. Also, it is found that the Knudsen diffusion and the viscous flow are the dominant parts of the mass transfer process at low and high pressure, respectively, and despite the viscous flow, the Knudsen diffusion is highly sensitive to temperature change.