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.