USP Guideline Note: HPLC Column Diameter Changes to Maintain Flow Rate Linear Velocity

USP Allowed Variations in HPLC Column Diameter (*USP 32, Second Supplement, Dec 1, 2009). In the previous USP version, a change of up to 50% of the flow rate was allowed. This has been changed in the more recent version. A wide range of column diameter changes are now allowed, provided that the linear velocity is kept constant. *We addressed the effect of changing column diameter on flow rate in a previous blog post, but this time I have also expanded on the calculation by including the extra variable for column length (L1 and L2) as well.

*Adjusting the Column Flow Rate for Changes in the HPLC Column Diameter.

Linear Velocity Formula:

   New Linear Flow Rate₂ = Flow Rate₁ x (L2 x D2²) / (L1 x D1²)

Flow Rates are in ml/min.

L1 = Column Length (original) in mm.

L2 = Column Length (proposed) in mm.

D1 = Column Diameter (original) in mm.

D2 = Column Diameter (proposed) in mm.

Example #1:

Original column is a 150mm x 4.6mm (L x ID) used at 1.000 ml min. We would like to determine what the equivalent flow rate (F₂) would be for a column which is 150mm x 2.1mm (L x ID) to maintain the same linear velocity. This is a proposed change in column diameter of > 50% so it would not have been allowed under the old guidelines. The newer guidelines take into account that with the same particle size, changing the column diameter will not change the chromatography if the linear velocity is maintained as before. Let’s calculate the new flow rate using the formula above.

1.000 x (150 x 2.1²) / (150 x 4.6²) = F₂

                    1 x (661.50 / 3,174) = F₂

                              0.208 ml/min = F₂

Common HPLC Calculations:

Capacity Factor / Retention Factor / Capacity Ratio:  k1 (K Prime)

k1 = T(R) - T(0) / T(0)
where T(R) equals the retention time of the peak in minutes and T(0) is
the retention time of an unretained peak. *For chromatography to take place, K Prime must be > 1.00 and for most modes of chromatography, should be greater than 1.5 or 2.0 for all samples !


Tailing Factor: USP: 't'

t = W(5.0)/tw/2

where tw equals the distance between peak front and T(R) at 5% of peak height units. W(5.0) equals peak width at 5% height, in minutes.


Theoretical Plates: USP and ASTM, 'N'

N = 5.54 x (T(R)/W(50))2          

Assumes width at peak half height (50)
* More info can be found at this link.


Resolution: USP, ASTM, 'R'

R = (T(R)(b)-T(R)(a)) x 2.35/(W(50)(b) + W(50)(a))/2

Assumes width at half height (50%) with peaks (a) and (b).

*Notes: Visually, "Baseline" resolution is R = 1.5. Your goal should be R = or > 2.0. ** R of 1.5 provides 99.8% separation which means you cannot accurately quantify a 0.1% impurity so develop the method to have a resolution value of at least 2.0.


Note: The appropriate formula(s) for use with your samples may depend on which of the many pharmaceutical guidelines and regulations apply in your country. Always consult the appropriate guidelines.