HPLC to UHPLC Conversion Notes (Gradient Time Program Adjustment)

In an earlier article we discussed how to adjust the flow rate, injection volume and column dimensions when scaling an HPLC method UP or Down. The formula's needed to do this are fairly simple. If we adjust for changes in the column dimensions or flow rate, what types of changes are needed to adjust the gradient time? The formula to make this adjustment is also very simple. Here is the information you need.

Terms Used in Formula:

Time in minutes, Gradient (Initial): Tg1

Time in minutes, Gradient (New):   Tg2

Flow Rate in mL/min, Column (Initial): Fc1

Flow Rate in mL/min, Column (New): Fc2

Column Diameter, mm (Initial): Dc1

Column Diameter, mm (New): Dc2

Column Length, mm (Initial): Lc1

Column Length, mm (New): Lc2

• Tg2 = Tg1 x (Fc1/Fc2) x ((Dc2²) / (Dc1²)) x (Lc2 x Lc1)

Here is an example problem to solve for. 

If we start with a flow rate of 1.000 mL/min (Fc1) on a 4.6 x 250 mm column with 5 micron support (Dc1 & Lc1) and have an initial Gradient Time of 10 minutes (Tg1), then what would the new gradient time be if we switched to a sub 2 micron support in a 2.1 x 50 mm column (Dc2 & Lc2) at 0.200 mL/min (Fc2)? 

To solve the equation we will plug-in the values for each part of the equation separately, then multiply them to obtain the result.

  (Fc1/Fc2):    1.000/0.200 = 5

  (Dc2²) / (Dc1²)  4.41/21.16 = 0.21

   (Lc2 x Lc1) = 50/250 = 0.20

  Tg2 = 10 x 5 x 0.21 x 0.20 

  Tg2 = 2.10 (or 2.10 minutes)

If a 2.1 x 50 mm column was substituted for the 4.6 x 250 mm AND the flow rate was changed from 1.000 mL/min to 0.200 mL/min, then the initial programmed gradient time of 10 minutes would be changed to 2.1 minutes