(adsbygoogle = window.adsbygoogle || []).push({}); 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

(Q_{1}/V_{1})d_{p1}= (Q_{2}/V_{2})d_{p2}(Q = inlet flow rate, V = column volume, d_{p}= particle diameter).

3. The attempt at a solution

Q_{1}= A * u = Pi * r^{2}* 30 cm/hr = 3.14 * 0.5^{2}* 30 = 23.6 cm^{3}/hr

V_{1}= Pi * r^{2}* l = 3.14 * 0.5^{2}* 20 = 15.7 cm^{3}

d_{p1}and d_{p2}are known. Therefore V_{2}and Q_{2}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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# Homework Help: Chromatography Scale-up

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