Which Column Should Be Used for Chromatography Scale-Up?

[staceybiomed]

Homework Statement

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.

Homework Equations

(Q₁/V₁)d_p1 = (Q₂/V₂)d_p2 (Q = inlet flow rate, V = column volume, d_p = particle diameter).

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
d_p1 and d_p2 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!

 

[KataKoniK]

Thank you for posting your question. As a fellow scientist, I am happy to assist you with finding the correct solution to this problem.

Firstly, your attempt at the solution is on the right track. However, there are a few things that need to be clarified in order to solve this problem correctly.

1. The equation you have used, (Q1/V1)dp1 = (Q2/V2)dp2, is known as the Darcy's Law. This equation is used to relate the flow rate (Q) and particle diameter (dp) to the superficial velocity (V). However, in this case, we are not given the flow rate or the superficial velocity. We are given the inlet flow rate (Q1) and the superficial velocity at lab scale (30 cm/hr). Therefore, we need to use a different approach to solve this problem.

2. In order to keep the resolution constant, we need to keep the linear velocity constant. This is because the resolution is directly proportional to the linear velocity. Therefore, we need to keep the linear velocity at lab scale (30 cm/hr) the same at plant scale.

3. You are correct in assuming that the bed height does not need to be kept constant. This is because the scale-up factor of 150 only applies to the throughput, not the bed height.

Now, let's look at how we can solve this problem.

1. First, we need to calculate the linear velocity at lab scale. This can be done by dividing the superficial velocity (30 cm/hr) by the void fraction (0.33). This gives us a linear velocity of 90.91 cm/hr.

2. Next, we need to calculate the column volume at lab scale. This can be done by multiplying the cross-sectional area (Pi * r2) by the bed height (20 cm). This gives us a column volume of 31.4 cm3.

3. Now, we can use the scale-up factor of 150 to calculate the column volume at plant scale. This gives us a column volume of 4710 cm3.

4. We can then use this column volume to calculate the cross-sectional area of the plant scale columns. This can be done by dividing the column volume by the bed height (50 cm). This gives us a cross-sectional area of 94.2 cm2 for the 14 cm (ID) column and 117.8 cm2 for the