Development and validation of a pneumatic calculator for the reversed-flow differential flow modulator for comprehensive GC GC

Transcription

1 Development and validation of a pneumatic calculator for the reversed-flow differential flow modulator for comprehensive GC GC Matthew Giardina James D. McCurry May 31,

2 Is a Flow Pressure Calculator Needed? Reversed-flow modulator incorporates a vent restrictor. Calculation of vent restrictor dimensions to prevent premodulator eluent splitting. Estimation of modulator channel fill-time to prevent overfilling and ensure comprehensive analysis. Eliminate need for second detector (cost effective). Extend calculations to include configurations for splitting to MSD/FID. 2

3 Differential Flow Modulation First Generation: Forward-Fill/Forward-Inject Modulator* Loading Injection Simple design easy to use but susceptible to break-through if modulator channel is overfilled. * J.V. Seeley, F. Kamp, C.J. Hicks, Anal. Chem, 72 (2000),

4 Differential Flow Modulation Second Generation: Forward-Fill/Reverse-Inject Modulator* Loading Injection More complex design but cannot break-through is not possible due to overfilling. * J.F. Griffith, W. L. Winniford, K. Sun, R. Edam, J.C. Luong, J. Chromatogr. A, 1226 (2012), 4

5 Pre-Modulator Channel Flow Splitting Optimized System Monitor FID (or Vent) Vent Restrictor Collection Channel Inlet Column 1 Analytical FID Column 2 Flow Modulator 5

6 Pre-Modulator Channel Flow Splitting Optimized System Monitor FID (or Vent) Vent Restrictor Collection Channel Inlet Column 1 Analytical FID Column 2 Flow Modulator 6

7 Pre-Modulator Channel Flow Splitting Unoptimized System Too restrictive Monitor FID (or Vent) Vent Restrictor Collection Channel Inlet Column 1 Analytical FID Column 2 Flow Modulator 7

8 Pre-Modulator Channel Flow Splitting Unoptimized System Too restrictive Monitor FID (or Vent) Vent Restrictor Collection Channel Inlet Column 1 Analytical FID Column 2 Flow Modulator Flow through vent restrictor > Flow through column 2 during collection 8

9 Modeling the System Based upon Hagen-Poiseuille flow equation for compressible fluids. Modular fluid-circuit composed of subsystems (modular). Solution of simultaneous equations to determine unknowns. Validate models with Agilent flow pressure calculator and experimental data. 9

10 Fluid Circuit R C V 1 I V 2 P 1 F P 2 Resistance/ Conductance Potential Current CC = ππrr4 16ηηηηηη PP = PP 1 2 PP 2 2 FF Column Constant Differential Pressure Flow Rate Ohm s Law Equivalent FF = CC PP Kirchhoff s Law Equivalent FF oooooo = FF 1_iiii + FF 2_iiii 10

11 GCxGC-FID/FID System Model Collect Cycle GCxGC System Fluid Circuit 11

12 Define Variables What do we know and what do we need to know Knowns: Column 1&2 dimensions Modulator channel dimensions Column flow rates Column temperature Unknowns: Pressures to achieve desired flows (column 1 and column 2) Restrictor dimensions Modulator holdup time Carrier gas type Detector outlet pressures Flow through the vent restrictor (greater than column 1 flow) 12

13 Define Variables Outlet Flow Equations FF 1 = CC 1 PP PP 2 FF 2 = CC 2 PP PP 3 FF 3 = CC 3 PP PP 4 FF 4 = CC 4 PP PP 5 Knowns FF 1, FF 2 FF 3 = 1.1FF 1 FF 4 = FF 3 CC 1, CC 2, CC 3, PP 3, PP 4 Unknowns PP 1, PP 2, PP 4 CC 4 13

14 Explicit Solutions Step 1: find PCM pressure: PP 2 = FF 2 2 CC 2 + PP 3 Step 2: find inlet pressure PP 1 = FF 1 2 CC 1 + PP 2 Step 3: find restrictor constant: CC 4 = 1.1FF 1 PP 2 2 PP FF 1 CC 3 Step 4: find modulator outlet pressure: PP 4 = 1.1FF 1 2 CC 4 + PP 5 14

15 Average Velocities and Holdup Times Column 1 Column 2 Modulator Restrictor αα 1 = PP 1 PP 2 jj 1 = 3 2 αα αα αα 2 = PP 2 PP 3 jj 2 = 3 2 αα 2 1 αα αα 3 = PP 2 PP 4 jj 3 = 3 2 αα αα αα 4 = PP 4 PP 5 jj 4 = 3 2 αα αα vv 1 = FF 1 LL 1 VV 1 jj 1 tt 1 = LL 1 vv 1 vv 2 = FF 2 LL 2 VV 2 jj 2 tt 2 = LL 2 vv 2 vv 3 = FF 3 LL 3 VV 3 jj 3 tt 3 = LL 3 vv 3 vv 4 = FF 4 LL 4 VV 4 jj 4 tt 4 = LL 4 vv 4 15

16 GCxGC-FID/FID System Model Inject Cycle GCxGC System Fluid Circuit 16

17 In Silico Validation Compare MathCAD Calculations to Agilent Pressure Flow Calculator Conditions Length (m) Diameter (um) Column Column Restrictor TBD 100 Modulator Temperature = 140 C Gas = H 2 Flow (ml/min) Column Column 2 20 Restrictor 0.55 Results Flow Pressure Calculator GCxGC Calculator Difference PCM Pressure (Column 2) psi psi psi Inlet Pressure (Column 1) psi psi psi Modulator Outlet pressure NA psi NA Restrictor Length 5.13 m* m m Flow Pressure Calculator (min) GCxGC Calculator (min) Difference Column 1 holdup time Column 2 holdup time Restrictor holdup time 0.10* Modulator holdup time NA NA * Estimated from PCM pressure 17

18 Approach to Experimental Validation 1. Calibrate columns to determine actual length. 2. Model system to determine restrictor size and predict holdup times. 3. Measure holdup times in fully plumbed system. 4. Measure modulator holdup time. 5. Compare to calculations. 18

19 Experimental Validation Restrictor Holdup Time SSL Uncoated m x mm FID Conditions Temperature 140 C Pressure psi Marker Methane Carrier Gas Hydrogen Split Flow 600 ml/min Measured to the nearest mm! Calculated Holdup Time Nominal min (100 µm ID) Maximum min (97 µm ID) Minimum min (103 µm ID) Measured Holdup Time t o = min Calculated Length Nominal m (100 µm ID) Minimum m (97 µm ID) Maximum m (103 µm ID) 19

20 Experimental Validation Restrictor Holdup Time Problem: minor contributions to holdup time can be significant for small volumes t o_measured = t o_inject + t o_syringe + t o_inlet + t o_column + t o_detector + t o_das + t o_other 20

21 Experimental Validation System Delay Time Reduce complexity t o_measured = t o_system + t o_inlet + t o_column t o_system = (t o_inject + t o_syringe + t o_detector + t o_das + t o_other ) 21

22 Experimental Validation System Holdup Time Measurement Calculated Measure holdup time with restrictor of known dimensions Subtract holdup time contribution from inlet Subtract holdup time contribution from restrictor Measured or Calculated System holdup time 22

23 Experimental Validation Liner Contribution - Zero Liner Volume Calibration Method t inlet = liner volume / split flow Holdup Time (min) 0,0842 0,0840 0,0838 0,0836 0,0834 0,0832 0,0830 0,0828 0,0826 0,0824 0, Inlet Liner Volume (µl) y = (1.6352x10-6 min/µl) x min Extrapolate holdup time at zero liner volume: min = t o_system + t o_column 23

24 Experimental Validation Liner Contribution Liner Contribution Subtraction Method t o_inlet = liner volume/split flow Liner Diameter (mm) Liner Volume (µl) Split Flow (ml/min) Calculated Inlet Residence Time (min) Measured Holdup (min) System + Column (min) Average Subtract calculated inlet residence time from measured holdup: min 24

25 Experimental Validation System Delay Time Based upon calibration with restrictor with known dimensions. Restrictor Length (m) Diameter (µm) ± ± 3 Conditions Temperature 140 C Pressure psi Calculated Holdup Time Marker Carrier Gas Split Flow Methane Hydrogen 600 ml/min Nominal min (100 µm ID) min (97 µm ID) min (103 µm ID) t o_system = (t o_measured - t o_inlet ) - t o_column = ( min) min = min 25

26 Experimental Validation In Situ Calibration Method Eliminate Inlet Effects pa Time FID B Vent Restrictor Methane PCM (Hydrogen) pa Time FID A Column 2 Collection Cycle 26

27 Experimental Validation In Situ Calibration Method Eliminate Inlet Effects pa Time FID B Vent Restrictor Methane PCM (Hydrogen) pa Time FID A Column 2 Injection Cycle 27

28 Experimental Validation Prediction Accuracy Injection of methane into fully plumbed system with modulator either on (inject cycle flow through column 2) or off (collect cycle flow through restrictor) Difference in Holdup Time (min) (Predicted - Measured) 0,12 0,08 0,04 0,00-0,04-0,08 Nominal Length Holdup Time Measured Length Corrected Holdup Collect Cycle Inject Cycle In Situ Holdup Percent Error Nominal Length Holdup Time Measured Length Corrected Holdup Collect Cycle Inject Cycle In Situ Holdup -0,

29 Experimental Validation Prediction Accuracy Adjust pulse timing to modulate 50% of the first dimension peak. This is a measure of the average holdup time at the distal end of the modulator channel. 1,00 Normalized Peak Area 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 Modulated Peak y = -10,986x + 26,653 R² = 0,9973 0,00 2,20 2,30 2,40 2,50 2,60 Modulation Time (min) Measured Holdup Time = min Calculated Holdup Time = min Difference = min Error = 0.23 % 29

30 GC GC-FID/FID Calculator Example Flow Splitting If vent restrictor too restrictive compared to column 2, flow splitting can occur 1,20 1, ml/min Split Fraction 0,80 0,60 0, ml/min Calculated Flow Ratio - Restrictor Calculated Flow Ratio - Column 2 Measured Peak Area Ratio - Restrictor Measured Peak Area Ratio - Column 2 0, ml/min 0.17 ml/min 0,00 0,35 0,4 0,45 0,5 0,55 0,6 0,65 Restrictor Length (m) 30

31 GCxGC-FID/FID Calculator Implementation Translated MathCAD to Excel Spreadsheet Reverse Inject GCxGC Modulator Calculator - PROTOTYPE PLEASE DO NOT DISTRIBUTE Step 1 - Configure Columns Note: changed pressures to gc pressures, add calculation for actual C2 flow, modify viscosity calcuation, add modulator channel flush volumes Diameter (mm) Length (m) Radius (mm) Column 1 (first dimension) Unit Conversion Column 2 (second dimension) ml/min = E-08 m 3 /s Modulator Channel psia = Pa Restrictor Step 2 - Select Conditions: Column Temperature, Reference Temperatures and Pressures, and Gas Viscosity Column temperature Reference temperature Reference pressure 50 C 25 C psi Viscosity Table (From Temperature-Program Gas Chrom Viscosity at standard temperature (ηst) 8.362E-06 Pa*s (select from table ) Gas He H 2 N2 Gas-dependent exponent (ξ) (select from table ) ηst (µpa*s) Viscosity E-06 Pa*s ξ Step 3 - Pick Flows Column 1 (first dimension) 0.5 ml/min Column 2 (second dimension) 22 ml/min Restrictor flow increase 10 % (a minimum flow increase of 10% is recommended ) Desired restrictor flow 0.55 ml/min Step 4 - Pick Pressures Column 2 outlet Restrictor oulet psia psia Calculated Column Constants Column 1 (first dimension) 6.032E-19 m 5 s 3 /kg 2 Column 2 (second dimension) 7.983E-18 m 5 s 3 /kg 2 Modulator Channel 4.967E-15 m 5 s 3 /kg 2 Restrictor 1.981E-19 m 5 s 3 /kg 2 Calculated Pressures Head pressure for column 2 (PCM) psia psig Head pressure for column psia psig Modulator outlet pressure psia psig Calculated Restrictor Length Restrictor length calculated 6.00 m (a minimum restrictor length of 0.5 m is recommended ) Restrictor length used 6.00 m Calculated Modulator and Restrictor Flows Actual restrictor column constant E-19 m 5 s 3 /kg 2 31

32 GCxGC-FID/MSD Calculator Same approach to modeling add purged splitter 32

33 GCxGC-FID/MSD Calculator Implementation Translated MathCAD to Excel Spreadsheet Reverse Inject GCxGC Modulator Calculator for MSD - PROTOTYPE PLEASE DO NOT DISTRIBUTE Step 1 - Configure Columns Diameter (mm) Length (m) Radius (mm) Unit Conversion Column 1 (first dimension) ml/min = E-08 m 3 /s Column 2 (second dimension) psia = Pa Modulator Channel Monitor Restrictor Split Restrictor MSD Restrictor Step 2 - Select Conditions: Column Temperature, Reference Temperatures and Pressures, and Gas Viscosity Column temperature 60 C Reference temperature 25 C Viscosity Table (From Temperature-Program Gas Chromatography, Reference pressure psi Gas He H 2 N 2 Ar ηst (µpa*s) Viscosity at standard temperature (η st) 1.87E-05 Pa*s (select from table ) ξ Gas-dependent exponent (ξ) (select from table ) Viscosity 2.14E-05 Pa*s Step 3 - Pick Flows Column 1 (first dimension) Column 2 (second dimension) MSD 0.5 ml/min 22 ml/min 2 ml/min Step 4 - Pick Pressures Monitor Detector (FID) Analytical Detector (FID) Analytical Detector (MSD) psia psia 2.707E-07 psia Step 5 - Pick AuxEPC Pressure and Percent Flow Increase AuxEPC Pressure 2.5 psig Percent flow increase 10 % (a minimum flow increase of 10% is recommended ) Split channel outlet flow 22.2 ml/min Calculated Column Constants Column 1 (first dimension) 2.515E-19 m 5 s 3 /kg 2 Column 2 (second dimension) 5.533E-18 m 5 s 3 /kg 2 Modulator Channel 1.482E-15 m 5 s 3 /kg 2 Monitor Restrictor 1.265E-19 m 5 s 3 /kg 2 Actual Split Restrictor E-17 m 5 s 3 /kg E-17 m 5 s 3 /kg 2 MSD Restrictor E-18 m 5 s 3 /kg E-18 m 5 s 3 /kg 2 Calculated Pressures 33

34 Conclusions Flow model allows the calculation of restrictor sizing for forward fill/reverse inject modulator. - Prevents flow splitting between modulator channel to second dimension column - Ensures comprehensive analysis - Allows operation without second FID detector Model prediction accuracy error is 1% for calibrated columns and 5% nominal column lengths. Flow model extended to include splitter for interfacing to mass spectrometer. 34

35 Acknowledgements Jim McCurry, Agilent Technologies Roger Firor, Agilent Technologies Gaelle Jousset, Total Research & Technology Gonfreville John Romesburg, Agilent Technologies 35