Prep scale purification is a manufacturing process with many variables. It is about finding the best combination of parameters to obtain a target compound with the highest productivity. It requires answers of some fundamental question as follows: http://chromatographyshop.com/knowledge/column-based-hplc-processes/process-scale-chromatography/ If you require confidentiality you may contact me directly
I've been using a very easy method for several years now. It is described in more detail here:
Article An overview of analytical-to-preparative liquid chromatograp...
The procedure is:
On your prep column, use a model compound to set your desired retention time with an isocratic run
Using your analytical column, run a scouting gradient with that same model compound and solvent system, and correlate the retention to your isocratic run. There is an Excel file in the supporting documents of the paper mentioned above that makes the calculation easy- you are using these two runs to determine an apparent gradient delay.
Run the compound you want to purify on your analytical column with the same scouting gradient. You may change solvents or modifiers, if needed, so long as your prep run uses the same solvents and modifiers.
Using the apparent gradient delay (the excel file I mentioned), calculate a focused gradient for your prep column.
Steps 1 and 2 only need to be run once.
The paper also lists other techniques to go from analytical to prep using a simple scouting run. The Time-on-Target algorithm is used in the Teledyne Isco ACCQPrep system. (https://www.teledyneisco.com/en-us/chromatography/accqprep ).
These techniques are fast, and account for dwell volume and column volume in the different LC systems. They are fast (once they are set up) because the methods are being calculated for you.
Keep in mind ionizable compounds may elute from the prep column at a different time than expected- see:
https://www.teledyneisco.com/en-us/liquidChromatography/Chromatography%20Documents/Application%20Notes/Focused%20Gradients,%20pH%20Control%20and%20Ionizable%20Compounds%20App%20Note.pdf .This is true of all the methods described in the paper.
The other way to do this is to make the method on your analytical column, then scale-up. This is done by converting the elution time to column volumes, and scaling up in terms of column volumes.
This resource has some of the equations:
https://gimitec.com/file/720003120en.pdf
They neglect to mention that the time for each gradient step, using the flow rate equations they describe, is proportional to the column length. If your analytical column is 50 mm long, and the prep column is 150 mm long, then each gradient step is 3 times that on the analytical column.
Here are some on-line tools, too:
https://www.phenomenex.com/Tools/preplc-scaleup
Supelco HPLC Calculator for Isocratic or Gradient Method Transfer | Sigma-Aldrich
These techniques generally don't account for dwell volume in the different LC systems.