Analytic Solution for Irreversible Equilibrium One Adsorbable Component

Analytic Solution for Irreversible Equilibrium (One Adsorbable Component) 

When mass transfer resistance is important the dynamic behavior of an adsorption column can generally be predicted only by numerical solution of the coupled differential heat and mass balance equations which describe the system. However, in the extreme case of an irreversible isotherm with independent of temperature, the differential mass balance and mass transfer 

Subject to the assumptions of plug flow, thermal equilibrium between fluid and solid and constant linear fluid velocity, the differential mass and heat balance equations for an adiabatic column are given by Eqs. (9.32) and (9.33), while for an irreversible system, the equilibrium isotherm is given by 

The assumption of an irreversible equilibrium relationship means that the concentration profile is not affected by temperature and is therefore the same as for an isothermal system. The simplest kinetic model is the linear rate expression for which the solution for the concentration profile has been given by Cooper (see Section 8.6)  

For saturation of an initially clean bed the appropriate initial and boundary conditions are 

---