Adsorption

A component can be separated from a mixture if it selectively adsorbs onto a solid surface. This is the basis of the adsorption unit process. Adsorbents are usually porous solids, and adsorption occurs mainly on the pore walls "inside" particles. Examples of adsorbents include:

Ideally, one would be able to construct a continuous countercurrent system, but moving solids is tricky. Instead, most commercial applications use small particles of adsorbent in a fixed bed. Fluid passes down through the bed (down instead of up to avoid fluidization) and components adsorb onto the solid. The steps can be summarized:

  1. solute diffuses through the fluid to an area near the solid particle surface
  2. solute diffuses into the pores of the particle
  3. solute diffuses to the pore wall
  4. solute adsorbs to the pore wall surface

Ion exchange is a similar process; however, in this case ions create complexes with the solid instead of adsorbing.

When a bed nears saturation, the flow is stopped and the bed is regenerated to cause desorption. The adsorbate can thus be recovered and the adsorbent reused. Regeneration can be accomplished in several ways, and these lead to the "cycle type":

Temperature swing is usually the slowest of these (since the bed has to heat/cool before reuse).

Adsorption Equilibrium

Isotherms

Adsorption equilibrium data is typically plotted in the form of an adsorption isotherm (i.e. at constant temperature) with the mass adsorbed on the y-axis and the mass in the fluid on the x-axis. The shape of the curve is significant and factors heavily into design. "Favorable" isotherms permit higher solid loadings at lower solution concentrations. These tend to start out steep and level out. Isotherms which start out flat are "unfavorable", since they only work well at high concentrations of solute. Usually, as temperature increases the amount adsorbed decreases (permitting thermal regeneration).

Several fits have been proposed for isotherms. A linear isotherm seems to work for very dilute solutions, but not for many others. The Freundlich isotherm describes physical adsorption from liquids and can also be used for the adsorption of hydrocarbon gases on activated carbon. It is a two parameter model, of the form

Freundlich isotherm
Maybe the best known is the Langmuir isotherm, given by
Langmuir isotherm
which assumes that the number of adsorption sites is fixed and that adsorption is reversible.

Breakthrough Curves

Adsorption is a transient process. The amount of material adsorbed within a bed depends both on position and time. Consider the time dependence. As fluid enters the bed, it comes in contact with the first few layers of absorbent. Solute adsorbs, filling up some of the available sites. Soon, the adsorbent near the entrance is saturated and the fluid penetrates farther into the bed before all solute is removed. Thus the active region shifts down through the bed as time goes on.

Adsorption Profile vs. Length

The fluid emerging from the bed will have little or no solute remaining -- at least until the bulk of the bed becomes saturated. The break point occurs when the concentration of the fluid leaving the bed spikes as unadsorbed solute begins to emerge. The bed has become ineffective. Usually, a breakpoint composition is set to be the maximum amount of solute that can be acceptably lost, typically something between 1 and 5 percent.

As the concentration wave moves through the bed, most of the mass transfer is occurring in a fairly small region. This mass transfer zone moves down the bed until it "breaks through". The shape of the mass transfer zone depends on the adsorption isotherm (equilibrium expression), flow rate, and the diffusion characteristics. Usually, the shape must be determined experimentally.

Adsorption Profile vs. Time

The wave front may change shape as it moves through the bed, and the mass transfer zone may broaden or diminish. Unfavorable and linear isotherms tend to broaden. Favorable Langmuir and Freundlich isotherms may broaden at first, but quickly achieve a constant pattern front, an asymptotic shape. This means that the mass transfer zone is constant with respect to both position and time. When dealing with a constant pattern front, one can make measurements on a small scale apparatus and scale-up the results to a full-size adsorber bed.

Calculations

When scaling up an adsorber, the key design parameter is the length of the bed. The total length is split into the "required length" of an "ideal" fixed bed process and a segment of "unused bed" that is the length leftover at breakthrough. By adding these together, you obtain a bed that can achieve the needed removal, but not waste solute.

The diameter of the bed is calculated from the fluid flow rate and the desired cycle time. Usually, superficial velocities on the order of 0.15 to 0.45 m/s are targeted.

Capacity calculations are made based on plots of the composition vs. time (usually near the exit of the bed). Curves are integrated (analytically, numerically, or graphically) to obtain capacities (measured in time units, or how long a bed can run).

The time required for a bed to become totally saturated is obtained by integrating as time goes to infinity:

Capacity
In operation, you want to stop the process before solute breaks through, so integration to the breakpoint time gives the "usable" capacity:
Usable Capacity
Most of the time the breakthrough time is very close to the time elapsed at usable capacity.

The capacity times are directly related to bed length:

Used and Unused Height
The unused height can also be readily measured by experiment. The total design height of a bed is determined by adding the required usable capacity to the unused height
Height Needed
Simple ratios allow direct scaleup to a new bed size.


References:

  1. Geankoplis, Christie J., Transport Processes and Unit Operations (3rd Edition), Prentice-Hall, 1993, pp. 697-704.
  2. McCabe, W.L., J.C. Smith, and P. Harriott, Unit Operations of Chemical Engineering (6th Edition), McGraw-Hill, 2001, pp. 812-21.
  3. Seader, J.D. and E.J. Henley, Separation Process Principles, John Wiley, 1998, pp. 841.


R.M. Price
Original: 11/21/2002
Modified: 3/4/2003

Copyright 2002, 2003 by R.M. Price -- All Rights Reserved