. .



 -dc/dt = K*a*(c-c*)

Where c is the concentration of solute in the bulk liquid, c* is the concentration in equilibrium with the loading on the adsorbent, k is the external liquid phase mass transfer coefficient, a  is the external surface area of the adsorbent per unit volume of liquid.

2. Continuous Mode:  In this case both liquid and solids flow continuously through a perfectly mixed vessel. The above equation is converted to an algebraic equation because, as in a perfectly mixed reaction vessel (CSTR), the concentration, c, throughout the vessel, is equal to the exit (outlet) concentration, cout. Thus in terms of the residence time in the vessel, tres:

( Cf -Cout )/Tres = K*a*( C - C* )


or Rearranging


Cout  = ( Cf +k *a* T res *C)/(1+K*a*Tres)


3. Semi continuous Mode:  In this case the adsorbent is retained in the vessel, but the feed liquid enters and exits the vessel at a fixed, continuous flow rate. Both concentration, c, and loading , q, vary with time. With perfect mixing, the outlet concentration is given by the above equation and c* is related to q in the suspension by an appropriate isotherm (c* = (q/k)n). Combining all the above equations we get :


S (d q /d t) = K * a * ( Cout - C*) * Tres *Q

 Where S is the batch mass adsorbent in the suspension and Q is the steady, volumetric liquid flow rate.

 The above diagram is a schematic of the semi continuous adsorption process. The simulation is based on this particular mode.

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