Scale-up Calculations

1. Power Costs

There are several ways to determine how to scale up a fermentation process. Two methods are:

For Equal Mixing Times

Keeping equal mixing times is important for some processes. The relationship between smaller and larger scale processes for this constraint is:

(Smaller Mixing Speed)^4*(Large Impeller Diameter) = (Larger Mixing Speed)^4*(Smaller Impeller Diameter)

Since you're scaling the fermentor up proportionally to the lab fermentor, you can determine the size of the larger impeller from the volume you have chosen. In this equation, you need to solve for the larger impeller speed.

With the larger impeller speed, you can calculate the power cost of the larger fermentor.

For Equal Power-to-Volume Ratios

Keeping the Power-to-Volume ratio of the original fermentor is a more practical way to scale up fermentation processes. The relationship between the smaller and larger fermentors is:

(Smaller Power Number)*(Smaller Impeller Speed)^3*(Smaller Impeller Diameter)^5*(Larger Volume) =

(Larger Power Number)*(Larger Impeller Speed)^3*(Larger Impeller Diameter)^5*(Smaller Volume)

Again, you need to solve for the larger impeller speed.

When you've calculated the Larger Impeller Speed, you can use that value to calculate the Power cost of the larger fermentor as explained in Step 3. We suggest that you calculate the scaled-up power costs using both methods described above. After you have calculated both power costs, you can determine which method will yield a more practical result. Use the more practical method for the iterative calculations explained in the Step 3 Homepage.

2. Capital Cost

The Capital Cost is the amount of money that is spent yearly on paying for the equipment that was constructed to run the fermentor. In our case, the Capital Cost will be the yearly payment to the bank for the fermentor itself.

To find the formulas for the Capital Charge of the fermentor (the amount the fermentor costs when constructed), check a Perry's Chemical Engineer's Handbook or any process design text.

The Yearly Capital Cost of the fermentor will be given by:

Capital Cost = (Capital Charge)*(Over-estimate factor)/(3 years)

The Over-estimate factor is a number usually equal to 4. It is a number that varies from company to company. It is a number that incorporates interest rate, depreciation, architects' fees, etc. The 3 years in the above formula is the pay-back period to the bank for allowing us to borrow the money for this plant.

To return to Step 4, click here.
Homepage by Charles Armesto, MIT Chem Eng '97
Graphics by CyclopsX, Inc.