Residence time as the controlling factor for dynamic (binding) capacity for protein A affinity chromatography has been reported,
and an increased capacity was found.5,6 This can be explained by the increased number of plates gained by increasing residence time (improved mass transfer and
thus a steeper break through curve).
SCALEUP ON A VOLUME BASIS
For a chromatographic process the retention volume (V
R
) is a critical parameter. It is crucial to control the retention volume during scaleup, and for this to be achieved it will
be necessary to adjust for the difference in extra column effects (dead volume and delay volume) for the involved systems.
Our approach for a flexible and practical method for scaleup uses the principle of scaling on a volume basis while taking
extra column effects into account. This makes scaleup a two-step operation:
- Scale up the column process on a volume basis
- Correct for extra column effects created by instrumentation and auxiliaries.7
Scaling Equations
Scaling up is based on Equation (1), the van Deemter equation:
H = A + B/v + Cv.......... (1)
In gas systems the B term can be important due to significant molecular diffusion, but in liquid systems B is for all practical purposes negligible.8 Thus simplify Equation (1) to Equation (2).
H = A + Cv.......... (2)
The total number of theoretical plates of a column is given by Equation (3):
N = L/H.......... (3)
The efficiency of the column (an increase with decreasing H) is only a function of linear velocity, and that the separation, which depends on the total number of plates, is conserved
when maintaining the L/H ratio. The traditional approach has been to conserve H by keeping linear velocity constant, and as a consequence L must be constant.1 The two equations indicate that for a given N, one could vary L and H arbitrarily as long as the ratio is maintained.
This is, however, not necessarily the case. Introduce a new parameter Q, flow in CV/h, defined in Equation (4).
Q = v/L.......... (4)
Equation (3)may be rewritten. Plug Equation (2) into Equation (3). Then eliminate v with Equation (4) to arrive at Equation (5).
It is informative when N is expressed as a function of bed height and flowrate (in column volumes/time). Figure 1 is a plot
of plate numbers as a function of bed height at different flowrates. We immediately see that increased bed height will always
result in an increased plate number and thus better or equal separation. As the bed height increases further, an asymtotic
plate number is reached (N approaches 1/CQ).
According to Equation (4) an increase in L must be accompanied by an increase in v in order to maintain constant Q. Therefore, when scaling up on a volume basis, v cannot be constant.
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