Adjusting the HPLC Gradient Time For Changes in Column Diameter and/or Length (same particle size)

Changes to the column diameter (to scale the method up or down) can be calculated. For an established HPLC method using the same support type (same exact material and particle size) where the column dimensions and flow rate are known. Note: If only the diameter changes and the lengths remain the same (proper linear flow rates used in both cases), then the resulting gradient times will also be similar. If the column lengths change, then the gradient time will change.

Changes to the Gradient Time (Tg2) used for a second column which has a different diameter, "Dc2" and/or length, "Lc2" can be calculated if you know: 

• Tg1 [Time, of initial Gradient on Column #1];
• Tg2 [Time of second Gradient on Column #2];
  
• Fc1 [Flow Rate of Column 1] ;
• Fc2 [Flow Rate of Column 2];
• Dc1 [Diameter of Column 1]
• Dc2 [Diameter of Column 2];
• Lc1 [Length of Column 1];
• Lc2 [Length of Column 2].

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

 

Example: Initial Method utilizes a 4.6 x 150 mm, 5u column run at 1.00 mL/min with a 10 minute gradient program and we wish to transfer this gradient method over to a column with a 2.1 mm diameter (ID) x 100 mm column run at 200 ul/min.

   Tg2 = 10 x (1 / 0.2) x (2.1² / 4.6²) x (100 /150)

   Tg2 = 10 x (5) x (4.41/21.16) x (0.67) 

   Tg2 =  50 x 0.208 x 0.67

   Tg2 =  6.97 minutes.

The gradient time used on the 2.1 x 100 mm column run at 0.200 mL/min would be ~ 7 minutes (vs 10 minutes on the 4.6 x 150 mm column at 1 mL/min).

 

NOTE: A note about optimized flow rates. If the Column PARTICLE SIZE changes, esp from greater than 3.5 u to less than 3.5 u, then the optimized flow rate may also change too. Please refer to my article; 

• "Speed Up HPLC Analysis Time Using Higher than "Normal" Flow Rates with SMALLER Particles" for more information.

HPLC Column Cross-Sectional Area and Scaling

Here is a simple formula to use when scaling up or down Internal Column Diameter to maintain retention values (under constant linear velocity). Flow rate must be adjusted to account for any changes made to the column's cross-sectional area. We usually refer to these types of changes as the "Scaling Factor". To determine the scaling factor, we need to know the internal column diameters of the two columns we are scaling from (actually, we need to know the radius, but once we have the diameter, we simply divide the diameter by 2 to obtain the radius). *In this discussion, changes in cross-sectional area are the only parameters we are concerned with as column length does not affect scaling.

• Scaling Factor = (S);
• Column #1 Radius =  (R1);
• Column #2 Radius =  (R2).

     S = R2² / R1²

Example #1: 250 x 4.60 mm column scaled down to a 250 x 2.10 mm column. 

          Answer = 0.208. 

• If the original flow rate was 1.000 mL/min, the the scaled down flow rate would be 0.208 of the original or 0.208 mL/min for the 2.10 mm ID column. *For practical use and application, we often use either 200 ul/min or 210 ul/min to simplify the value.

Example #2: 250 x 4.60 mm column scaled up to a 250 x 10.00 mm ID semi-prep column.

          Answer  = 4.726. 

• If the original flow rate used was 1.000 mL/min with the 4.60 mm ID column, then we would increase the flow rate to 4.726 mL/min on the 10.00 mm ID column to maintain the same relative velocity (and relative retention). *For practical use and application, we often use 5 mL/min to simplify (round off) the value. 

Notes:

1. Flow rate optimization should always be carried out by running a standard at different flow rates and plotting the plate height (N) vs the flow rate. Test flow rates that are slightly below the predicted linear velocity and up to 2 times higher than that rate to find and optimize the flow rate for your sample (it must be determined through experimentation for your specific method). 
    
2. HPLC Columns packed with sub 2 micron supports may have optimum flow rates 2 to 5 times more than the predicted std linear flow rate so actual testing is critical to determining the most efficient flow rate. I recommend optimizing the flow rate used with analysis methods which use any particles which are 2.5 microns or smaller in diameter.