# Chromatography Scale-up

1. May 1, 2010

### staceybiomed

1. The problem statement, all variables and given/known data
The problem requires the scale up of a linear gradient ion exchange chromatography column by a factor of 150 (throughput). The lab scale column is 1 cm (ID) x 20 cm (bed height) with 20 micron particle size and 30 cm/hr superficial velocity. Resolution must be kept constant in the plant scale column. The scale up uses a 40 micron particle size and we
have a choice of 2 columns: 14 cm (ID) x 50 cm (length) and 18 cm (ID) x 50 cm
(length). Add'l info: viscosity of mobile phase = 1.0 cp, void fraction for resin in plant scale = 0.33
Determine which column to use, resin bed height, and superficial velocity.

2. Relevant equations
(Q1/V1)dp1 = (Q2/V2)dp2 (Q = inlet flow rate, V = column volume, dp = particle diameter).

3. The attempt at a solution
Q1 = A * u = Pi * r2 * 30 cm/hr = 3.14 * 0.52 * 30 = 23.6 cm3/hr
V1 = Pi * r2 * l = 3.14 * 0.52 * 20 = 15.7 cm3
dp1 and dp2 are known. Therefore V2 and Q2 are unknown.

I have come up with answers in a few different ways to solve the whole problem but I just don't know which one is right! In order to keep resolution constant, I should keep superficial velocity constant, right? I believe that since the particle size is changing, I don't need to keep bed height constant. The 150 scale-up factor should be for both the V2 and Q2 but none of my solutions have both of them at 150x. Can anyone help me solve this problem? Thanks!!

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