Pressure Drop Across an HPLC / UHPLC Column

Many of you prefer tables of data over equations that you must work out. So, instead of providing you with another equation, I have done some basic measurements for you to provide a general overview of how particle size (porous) effects System backpressure.

For simplicity, let us start with a few parameters. Pore Volume = 0.70; Linear Velocity = 1.44 mm/sec; Solvent Viscosity = 0.89 cP at 25C (Water). 

Pore Volume and Flow Resistivity will vary by column type. Obviously the back pressure will be higher with more viscous solvents (e.g. EtOH is 1.20 cP) and lower with less viscous solvents (e.g. ACN is 0.34cP). A Table of HPLC Solvent Viscosity values can be found here [ http://www.hplctools.com/lcsolvent.htm ]. Linear flow rates have been used for all column I.D.'s to better illustrate the relationship between column dimensions and flow rate. If you double the flow rate, then the pressure will approximately double as well. 

Note that when run at traditional linear velocities, most 2.5u particles are within the maximum pressure limits of most HPLC systems (under 400 bars). Only the newer sub 2.0 micron particles used in long columns exceed the 400 bar limit. The higher maximum pressure limits of many UHPLC systems allow the use of higher flow rates with these particles. Naturally, you should optimize both column efficiency and system dwell volume when developing any UHPLC method. Failure to optimize the dwell volume (and minimize all volumes) may result in very poor chromatography separations. Meeting any/all backpressure requirements to run a method does not translate to success in sample analysis. Successful ultra-fast separations require ultra-low system dwell volumes, higher sampling rates and usually smaller flow cell volumes.

HPLC Column I.D. (mm)	Particle Size (u)	Column Length (mm)	Flow Rate (mL/min)	Observed System Back Pressure (Bars)
4.6	5	250	1.000	89
4.6	5	150	1.000	54
4.6	5	100	1.000	36
4.6	5	50	1.000	18
4.6	3.5	250	1.000	182
4.6	3.5	150	1.000	109
4.6	3.5	100	1.000	73
4.6	3.5	50	1.000	36
4.6	2.5	250	1.000	357
4.6	2.5	150	1.000	214
4.6	2.5	100	1.000	143
4.6	2.5	50	1.000	71
4.6	1.9	250	1.000	618
4.6	1.9	150	1.000	371
4.6	1.9	100	1.000	247
4.6	1.9	50	1.000	124
3.0	5	250	0.430	90
3.0	5	150	0.430	54
3.0	5	100	0.430	36
3.0	5	50	0.430	18
3.0	3.5	250	0.430	184
3.0	3.5	150	0.430	110
3.0	3.5	100	0.430	74
3.0	3.5	50	0.430	37
3.0	2.5	250	0.430	361
3.0	2.5	150	0.430	217
3.0	2.5	100	0.430	144
3.0	2.5	50	0.430	72
3.0	1.9	250	0.430	625
3.0	1.9	150	0.430	375
3.0	1.9	100	0.430	250
3.0	1.9	50	0.430	125
2.1	5	250	0.210	90
2.1	5	150	0.210	54
2.1	5	100	0.210	36
2.1	5	50	0.210	18
2.1	3.5	250	0.210	184
2.1	3.5	150	0.210	110
2.1	3.5	100	0.210	73
2.1	3.5	50	0.210	37
2.1	2.5	250	0.210	360
2.1	2.5	150	0.210	216
2.1	2.5	100	0.210	144
2.1	2.5	50	0.210	72
2.1	1.9	250	0.210	623
2.1	1.9	150	0.210	374
2.1	1.9	100	0.210	249
2.1	1.9	50	0.210	125

* The results obtained in this table from are from one of our HPLC systems and reflects the total system backpressure (what the pressure gauge reads), with the column inline. Your results may vary due to differences in HPLC system used, flow path, tubing ID, column choice and mobile phase selected.

Conversion Factors microgram, nanogram, ppm, ppb and percent:

Many years ago I made up this handy sample concentration conversion table. Be sure and take into account the density of the compounds first. I find that it is still useful when reporting results to clients.

Parts per million (ppm)	Percent (%)
1	0.0001
10	0.001
100	0.01
1,000	0.1
10,000	1.0
100,000	10.0
1,000,000	100.0

ppm = ug/ml

1,000 ug/ml	=	0.1 %	=	1,000 ppm
100 ug/ml	=	0.01 %	=	100 ppm
10 ug/ml	=	0.001 %	=	10 ppm
1 ug/ml	=	0.0001 %	=	1 ppm
100 ng/ml	=	0.00001 %	=	100 ppb
10 ng/ml	=	0.000001 %	=	10 ppb
1 ng/ml	=	0.0000001 %	=	1 ppb

ESI Charge State Calculator Application

Here is a neat program, created by Robert Winkler, which allows you to calculate the Mw of proteins using data from your electrospray ionization (ESI) mass spec source.

ESIprot 1.0    [http://www.bioprocess.org/esiprot/]

Reference this journal article:  Winkler R. "A universal tool for charge state determination and molecular weight calculation of proteins from electrospray ionization mass spectrometry data." Rapid Commun Mass Spectrom, 24(3),  285-294, 2010.

HPLC to UHPLC Conversion Notes (Column Dimensions, Flow Rate, Injection Volume & System Dispersion)

The use of ultra-high performance liquid chromatography (UHPLC) columns to reduce analysis times and sometimes improve detection limits is a hot topic. UHPLC presents a number of new issues. The incorporation of smaller 1.9 to 3.0 micron particles and smaller frits will raise backpressures and increase system wear and tear. Smaller diameter lines are often used (I.D. of 0.12mm or less) which can increase blockages and clogs if you do not filter your mobile phase and samples through a 0.45 or 0.2 micron filters. Piston seals and valve rotors can wear out early due to the very high pressures, heating and stress imposed on them. You should monitor your HPLC system carefully over time and consider increasing the frequency of preventative maintenance and inspection services as well. However, the smaller particle sizes can provide better resolution in some applications so they are well worth evaluating.

I must answer twenty or so questions each week in the area of UHPLC. The most common questions deal with selection of an UHPLC column and making adjustments to a method for the changes which effect: (1) Column Dimensions; (2) Flow Rate; (3) Injection Volume and (4) System Dispersion. The good news is that some of these questions can be answered with some basic math while others just require a basic understanding of how the system works.

(1) COLUMN DIMENSIONS: Let's start by making things as simple and brief as possible (this is supposed to be a "hint & tip", not a thirty page article). When initially converting from a convention HPLC column (e.g. with 5 micron particles) to an UHPLC column (e.g. with 1.9 to 3 micron particles), initially select a column with the same I.D. and length for the calculation. This way only the particle size changes. *I like to change one variable at a time. If you would like to change the column length to take advantage of some of the increased efficiency (and decrease the pressure!) which results from smaller particles, then please refer to the following equation.

     EQUATION A:  'Lc2' = ('Lc1' * 'p2') / 'p1'

[ 'Lc1' = Length of Column #1 in mm; 'Lc2' = Length of Column #2 in mm; 'p1' = particle size of Column #1 in microns; 'p2' = particle size of Column #2 in microns].
                    
   Example: Column # 1 is a standard HPLC column;  4.6 mm x 250 mm (5u) Column. You want to find out the length of an equivalent column which uses 1.9 micron particles instead of the 5 micron particles.

   'Lc2' = (250 * 1.9) / 5 ; Answer is: 'Lc2' = 95 mm. *So a 10 cm long column would be a good choice here.


(2) FLOW RATE: Flow rate is directly proportional to column diameter and as we saw above in Equation A, the particle size can also affect it too. If you keep the column length and internal diameter the same, then the linear flow will be unchanged with the same particle size. A change to the particle size alone will change the flow rate as follows: 'Fc2' = 'Fc1' x ('p1'/'p2').

A change to a smaller diameter column to compensate for the improved efficiency will require a change to the original flow rate to preserve the linear velocity. Please refer to the following equation.

     EQUATION B:   'Fc2' = ('d2' / 'd1')^2 * 'Fc1'

['Fc1' = Flow Rate of Column #1 in ml/min; 'Fc2' = Flow Rate of Column #2 in ml/min; 'd1' = Column #1 Diameter in mm; 'd2' = Column #2 Diameter in mm].
                     
   Example: Column # 1 is a standard 4.6 mm ID Column. You want to find out what the linear flow rate should be if you use a smaller diameter column (2.1mm in this example).

   'Fc2' = (2.1/4.6)^2 * 1.000 ; Answer is: 'Fc2' = 0.208 ml/min. *A flow rate of 200 ul/min would be fine. 

However, one other factor should be considered. The optimum flow rate for sub 2.5u particles are often about double that of the "normal" linear flow rate used with conventional particles (>2.5u). Evidence for this has been shown through analysis of the van Deemter curve with the tiniest particles showing much flatter curves. Retention (K prime) can often be maintained by combining twice the normal flow rate and speeding up the gradient time by a factor of 2. So a method utilizing std sized particles with a linear flow rate of 0.200 ml/min might benefit from a faster flow rate of 0.400 ml/min and a twice as fast gradient composition change.


(3) INJECTION VOLUME: A change in the column dimension may require a change to the injection volume (note: "volume" and concentration are two different things. If the solution concentration remains the same and you inject less, the on-column sample concentration will also be less). The smaller the internal volume of the column, the smaller the injection volume. To calculate the linear change in volume, please refer to the following equation.

     EQUATION C:   'V2' = 'V1' * {('d2'^2 * 'L2') / ('d1'^2 * 'L1')}

['V1' = Injection Volume #1 in ul; 'V2' = Injection Volume #2 in ul; 'L1' = Column #1 Length in mm; 'L2' = Column #2 Length in mm; 'd1' = Column #1 Diameter in mm; 'd2' = Column #2 Diameter in mm].
                     
   Example: Current injection volume is 10 ul. Column # 1 is a standard 4.6 mm ID x 250 mm Column. You want to find out what the equivalent injection volume should be for a 2.1 mm ID x 150 mm column.

   'V2' = 10 * (2.1^2 * 150) / (4.6^2 * 250) ; Answer is: 'V2' = 1.25 ul.



(4) SYSTEM DISPERSION: When converting HPLC methods to "UHPLC" methods, few parameters effects the results obtained more than the HPLC system's System Dispersion. The volume of liquid that is contained between the injector needle and flow cell (with the column removed or by-passed) is know as the system dispersion volume. This volume is determined by how the specific HPLC is designed and plumbed. On most HPLC systems, it can be easily changed and optimized to fit the specific application desired and only requires that you have a solid understanding of how the HPLC system works. The choice of connection tubing ID and length, how the autoinjector is programmed, its loop size and the detector's flow cell volume all contribute to the system dispersion volume. In the same way that changes to the total column volume can effect the peak shape and resolution, the internal system dispersion volume also contributes to the results. 

With standard sized analytical columns (i.e. 4.6 x 250 mm), the typical HPLC's system volume is so small relative to the volume of the column (e.g. 100 ul system dispersion vs 2900 ul column volume, or 3.5%) that it does not negatively impact the chromatography. However, anytime we utilize a tiny HPLC column whose column volume is a fraction of that found in a standard column (i.e. 100 ul system dispersion vs 2.1 x 50 mm column with 120 ul volume), diffusion and band spreading can quickly become so significant that effective plate numbers are quickly reduced below values found on a standard sized column. As column volume decreases (and approaches the system volume) the total system dispersion volume must also decrease. In general, try and keep the system dispersion volume at or below 10% of the column dead volume. This is most easily accomplished by reducing the number of connections and fittings used, reducing the lengths of all tubing used, using much narrower ID tubing (e.g. 0.12 mm vs 0.17 mm ID), reducing flow cell volume and reducing the flow-through volume in the autoinjector (i.e. loop size, needle seat, etc). The injector is often the largest contributor to the system dispersion so concentrate efforts here (e.g. after injection, switch the loop out of the flow path).