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, 2016

June 15, 2016

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Is a Flow Pressure Calculator Needed?

June 15, 2016

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• Reversed-flow modulator incorporates a vent restrictor.

• Calculation of vent restrictor dimensions to prevent pre-modulator 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.

Differential Flow Modulation

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Loading

* J.V. Seeley, F. Kamp, C.J. Hicks, Anal. Chem, 72 (2000), 4346-4352

Simple design easy to use but susceptible to break-through if modulator channel is overfilled.

First Generation: Forward-Fill/Forward-Inject Modulator*

Injection

Differential Flow Modulation

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Second Generation: Forward-Fill/Reverse-Inject Modulator*

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),

Loading Injection

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Pre-Modulator Channel Flow SplittingOptimized System

Inlet

Monitor FID (or Vent)

Column 1

Column 2

Vent Restrictor

AnalyticalFID

Collection Channel

Flow Modulator

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Pre-Modulator Channel Flow SplittingOptimized System

Inlet

Monitor FID (or Vent)

Column 1

Column 2

Vent Restrictor

AnalyticalFID

Collection Channel

Flow Modulator

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Pre-Modulator Channel Flow SplittingUnoptimized System

Inlet

Monitor FID (or Vent)

Column 1

Column 2

Vent Restrictor

AnalyticalFID

Collection Channel

Flow Modulator

Too restrictive

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Pre-Modulator Channel Flow SplittingUnoptimized System

Inlet

Monitor FID (or Vent)

Column 1

Column 2

Vent Restrictor

AnalyticalFID

Collection Channel

Flow Modulator

Too restrictive

Flow through vent restrictor > Flow through column 2 during collection

Modeling the System

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• 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.

Fluid Circuit

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𝐶𝐶 =𝜋𝜋𝑟𝑟4

16𝜂𝜂𝜂𝜂𝜂𝜂

Column Constant

“Resistance/ Conductance”

∆𝑃𝑃 = 𝑃𝑃12 − 𝑃𝑃22

Differential Pressure

“Potential” “Current”

𝐹𝐹

Flow Rate

Ohm’s Law Equivalent

𝐹𝐹 = 𝐶𝐶∆𝑃𝑃

P2P1

C

FV2V1

R

I

𝐹𝐹𝑜𝑜𝑜𝑜𝑜𝑜 = 𝐹𝐹1_𝑖𝑖𝑖𝑖 + 𝐹𝐹2_𝑖𝑖𝑖𝑖

Kirchhoff’s Law Equivalent

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Fluid Circuit

GCxGC System

GCxGC-FID/FID System Model – Collect Cycle

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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

• Carrier gas type

• Detector outlet pressures

• Flow through the vent restrictor (greater than column 1 flow)

Unknowns:

• Pressures to achieve desired flows (column 1 and column 2)

• Restrictor dimensions

• Modulator holdup time

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Outlet Flow Equations

𝐹𝐹1 = 𝐶𝐶1 𝑃𝑃12 − 𝑃𝑃22

𝐹𝐹2 = 𝐶𝐶2 𝑃𝑃22 − 𝑃𝑃32

𝐹𝐹3 = 𝐶𝐶3 𝑃𝑃22 − 𝑃𝑃42

𝐹𝐹4 = 𝐶𝐶4 𝑃𝑃42 − 𝑃𝑃52

𝐹𝐹1,𝐹𝐹2

𝐹𝐹3= 1.1𝐹𝐹1

𝐹𝐹4 = 𝐹𝐹3

𝐶𝐶1,𝐶𝐶2,𝐶𝐶3,

𝑃𝑃3,𝑃𝑃4

Knowns

𝑃𝑃1,𝑃𝑃2, 𝑃𝑃4

𝐶𝐶4

Unknowns

Define Variables

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Step 1: find PCM pressure:

𝑃𝑃2 = ⁄𝐹𝐹2 𝐶𝐶2 + 𝑃𝑃32

Step 2: find inlet pressure

𝑃𝑃1 = ⁄𝐹𝐹1 𝐶𝐶1 + 𝑃𝑃22

Step 3: find restrictor constant:

𝐶𝐶4 =1.1𝐹𝐹1

𝑃𝑃22 − 𝑃𝑃52 − 1.1 ⁄𝐹𝐹1 𝐶𝐶3

Step 4: find modulator outlet pressure:

𝑃𝑃4 = ⁄1.1𝐹𝐹1 𝐶𝐶4 + 𝑃𝑃52

Explicit Solutions

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𝛼𝛼1 = ⁄𝑃𝑃1 𝑃𝑃2 𝑗𝑗1= 32

𝛼𝛼12−1𝛼𝛼13−1

𝑣𝑣1 = 𝐹𝐹1𝐿𝐿1𝑉𝑉1

𝑗𝑗1 𝑡𝑡1 = 𝐿𝐿1𝑣𝑣1

𝛼𝛼3 = ⁄𝑃𝑃2 𝑃𝑃4 𝑗𝑗3 = 32

𝛼𝛼32−1𝛼𝛼33−1

𝑣𝑣3 = 𝐹𝐹3𝐿𝐿3𝑉𝑉3

𝑗𝑗3 𝑡𝑡3 = 𝐿𝐿3𝑣𝑣3

𝛼𝛼2 = ⁄𝑃𝑃2 𝑃𝑃3 𝑗𝑗2 = 32

𝛼𝛼22−1𝛼𝛼23−1

𝑣𝑣2 = 𝐹𝐹2𝐿𝐿2𝑉𝑉2

𝑗𝑗2 𝑡𝑡2 = 𝐿𝐿2𝑣𝑣2

𝛼𝛼4 = ⁄𝑃𝑃4 𝑃𝑃5 𝑗𝑗4 = 32

𝛼𝛼42−1𝛼𝛼43−1

𝑣𝑣4 = 𝐹𝐹4𝜂𝜂4𝑉𝑉4

𝑗𝑗4 𝑡𝑡4 =𝜂𝜂4𝑣𝑣4

Column 1 Column 2 Modulator Restrictor

Average Velocities and Holdup Times

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Fluid Circuit

GCxGC System

GCxGC-FID/FID System Model – Inject Cycle

In Silico Validation

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Compare MathCAD Calculations to Agilent Pressure Flow Calculator

Flow Pressure Calculator GCxGC Calculator DifferencePCM Pressure (Column 2) 23.615 psi 23.731 psi -0.116 psiInlet Pressure (Column 1) 28.807 psi 28.928 psi -0.121 psiModulator Outlet pressure NA 23.730 psi NARestrictor Length 5.13 m* 5.120 m 0.010 m

Flow Pressure Calculator (min) GCxGC Calculator (min) DifferenceColumn 1 holdup time 2.04 2.053 -0.013Column 2 holdup time 0.02 0.016 0.004Restrictor holdup time 0.10* 0.102 -0.002Modulator holdup time NA 0.150 NA* Estimated from PCM pressure

Length (m) Diameter (um)Column 1 20 180Column 2 5 250Restrictor TBD 100Modulator 0.195 535

Conditions

Temperature = 140 °C

Gas = H2

Flow (mL/min)Column 1 0.5Column 2 20Restrictor 0.55

Results

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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.

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Experimental ValidationRestrictor Holdup Time

FID

Uncoated5.020 m x 0.100 mm

SSL

Conditions

Temperature 140 °C

Pressure 34.577 psi

Marker Methane

Carrier Gas Hydrogen

Split Flow 600 mL/min

Calculated Holdup Time

Nominal 0.069 min (100 µm ID)

Maximum 0.073 min (97 µm ID)

Minimum 0.065 min (103 µm ID)

Measured Holdup Time

to = 0.0839 min

Calculated Length

Nominal 5.533 m (100 µm ID)

Minimum 5.367 m (97 µm ID)

Maximum 5.699 m (103 µm ID)

Measured to the nearest mm!

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Experimental ValidationRestrictor Holdup Time

Problem: minor contributions to holdup time can be significant for small volumes

to_measured = to_inject + to_syringe + to_inlet + to_column + to_detector + to_DAS + to_other

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Experimental ValidationSystem Delay Time – Reduce complexity

to_measured = to_system+ to_inlet + to_column

to_system = (to_inject + to_syringe + to_detector + to_DAS + to_other)

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Experimental Validation

Measure holdup time with restrictor

of known dimensions

Subtract holdup time contribution

from inlet

Subtract holdup time contribution

from restrictor

System Holdup Time Measurement

System holdup time

Measured or Calculated

Calculated

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Experimental ValidationLiner Contribution - Zero Liner Volume Calibration Method

Extrapolate holdup time at zero liner volume: 0.08231 min = to_system+ to_column

y = (1.6352x10-6 min/µL) x + 0.08231 min

0,08220,08240,08260,08280,08300,08320,08340,08360,08380,08400,0842

0 200 400 600 800 1000 1200

Hol

dup

Tim

e (m

in)

Inlet Liner Volume (µL)

t inlet = liner volume / split flow

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Experimental ValidationLiner Contribution – Liner Contribution Subtraction Method

Subtract calculated inlet residence time from measured holdup: 0.08229 min

LinerDiameter

(mm)

Liner Volume (µL)

Split Flow (mL/min)

Calculated InletResidence Time (min)

Measured Holdup (min) System + Column (min)

0.75 34.6 600 0.000058 0.08237 0.08227

1.0 61.65 600 0.000103 0.08242 0.08230

1.5 138 600 0.000230 0.08250 0.08226

2.0 247 600 0.000412 0.08275 0.08234

4.0 986 600 0.001643 0.08392 0.08227

to_inlet = liner volume/split flow

Average

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Experimental ValidationSystem Delay Time

Based upon calibration with restrictor with known dimensions.

Length (m) Diameter (µm)5.020 ± 0.002 100 ± 3

Temperature 140 °C

Pressure 34.577 psi

Marker Methane

Carrier Gas Hydrogen

Split Flow 600 mL/min

Conditions

Restrictor

Nominal 0.069 min (100 µm ID)

0.073 min (97 µm ID)

0.065 min (103 µm ID)

Calculated Holdup Time

to_system = (to_measured - to_inlet) - to_column = (0.08229 min) – 0.06906 min = 0.01323 min

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Experimental ValidationIn Situ Calibration Method – Eliminate Inlet Effects

Methane

FID B

Column 2

Vent Restrictor

FID A

PCM

(Hydrogen)

pA

Time

pA

Time

Collection Cycle

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Experimental ValidationIn Situ Calibration Method – Eliminate Inlet Effects

Methane

FID B

Column 2

Vent Restrictor

FID A

PCM

(Hydrogen)

pA

Time

pA

Time

Injection Cycle

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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)

NominalLength

HoldupTime

MeasuredLength

CorrectedHoldup

In SituHoldup

-5

-4

-3

-2

-1

0

1

2

3

4

5

Perc

ent E

rror

Collect Cycle

Inject Cycle

HoldupTime

MeasuredLength

Corrected Holdup

In SituHoldup

NominalLength

-0,12

-0,08

-0,04

0,00

0,04

0,08

0,12

Diff

eren

ce in

Hol

dup

Tim

e (m

in)

(Pre

dict

ed -

Mea

sure

d)

Collect Cycle

Inject Cycle

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Experimental Validation

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.

y = -10,986x + 26,653R² = 0,9973

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

2,20 2,30 2,40 2,50 2,60

Nor

mal

ized

Pea

k Ar

ea

Modulation Time (min)

Modulated Peak

Measured Holdup Time = 2.381 min

Calculated Holdup Time = 2.386 min

Difference = 0.005 min

Error = 0.23 %

Prediction Accuracy

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GC×GC-FID/FID Calculator ExampleFlow Splitting

If vent restrictor too restrictive compared to column 2, flow splitting can occur

0.505 mL/min

0.33 mL/min

0.17 mL/min-0.05 mL/min

0,00

0,20

0,40

0,60

0,80

1,00

1,20

0,35 0,4 0,45 0,5 0,55 0,6 0,65

Split

Fra

ctio

n

Restrictor Length (m)

Calculated Flow Ratio - Restrictor

Calculated Flow Ratio - Column 2

Measured Peak Area Ratio - Restrictor

Measured Peak Area Ratio - Column 2

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GCxGC-FID/FID Calculator ImplementationTranslated 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) 0.18 20.68 0.09 Unit ConversionColumn 2 (second dimension) 0.25 5.815 0.125 1 mL/min = 1.66667E-08 m3/sModulator Channel 0.535 0.196 0.2675 1 psia = 6894.757 PaRestrictor 0.1 6.00 0.05

Step 2 - Select Conditions: Column Temperature, Reference Temperatures and Pressures, and Gas Viscosity

Column temperature 50 CReference temperature 25 CReference pressure 14.696 psi

Viscosity Table (From Temperature-Program Gas Chrom Viscosity at standard temperature (ηs t) 8.362E-06 Pa*s (select from table ) Gas He H2 N2

Gas-dependent exponent (ξ) 0.698 (select from table ) ηs t (µPa*s) 18.69 8.362 16.24Viscosity 9.4030E-06 Pa*s ξ 0.685 0.698 0.71

Step 3 - Pick Flows

Column 1 (first dimension) 0.5 mL/minColumn 2 (second dimension) 22 mL/minRestrictor 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 14.696 psiaRestrictor oulet 14.696 psia

Calculated Column ConstantsColumn 1 (first dimension) 6.032E-19 m5s3/kg2

Column 2 (second dimension) 7.983E-18 m5s3/kg2

Modulator Channel 4.967E-15 m5s3/kg2

Restrictor 1.981E-19 m5s3/kg2

Calculated PressuresHead pressure for column 2 (PCM) 32.312 psia 17.62 psigHead pressure for column 1 36.402 psia 21.71 psigModulator outlet pressure 32.311 psia 17.62 psig

Calculated Restrictor LengthRestrictor 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 FlowsActual restrictor column constant 1.98064E-19 m5s3/kg2

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GCxGC-FID/MSD CalculatorSame approach to modeling – add purged splitter

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GCxGC-FID/MSD Calculator ImplementationTranslated 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 ConversionColumn 1 (first dimension) 0.18 21.115 0.09 1 mL/min = 1.66667E-08 m3/sColumn 2 (second dimension) 0.25 3.572 0.125 1 psia = 6894.757 PaModulator Channel 0.45 0.14 0.225Monitor Restrictor 0.1 4 0.05Split Restrictor 0.25 0.2 0.125MSD Restrictor 0.15 1.08 0.075

Step 2 - Select Conditions: Column Temperature, Reference Temperatures and Pressures, and Gas Viscosity

Column temperature 60 CReference temperature 25 C Viscosity Table (From Temperature-Program Gas Chromatography, Reference pressure 14.696 psi Gas He H2 N2 Ar

ηs t (µPa*s) 18.69 8.362 16.24 21.35Viscosity at standard temperature (ηs t) 1.87E-05 Pa*s (select from table ) ξ 0.685 0.698 0.71 0.75Gas-dependent exponent (ξ) 0.685 (select from table )Viscosity 2.14E-05 Pa*s

Step 3 - Pick Flows

Column 1 (first dimension) 0.5 mL/minColumn 2 (second dimension) 22 mL/minMSD 2 mL/min

Step 4 - Pick Pressures

Monitor Detector (FID) 14.696 psiaAnalytical Detector (FID) 14.696 psiaAnalytical Detector (MSD) 2.707E-07 psia

Step 5 - Pick AuxEPC Pressure and Percent Flow Increase

AuxEPC Pressure 2.5 psigPercent flow increase 10 % (a minimum flow increase of 10% is recommended )Split channel outlet flow 22.2 mL/min

Calculated Column ConstantsColumn 1 (first dimension) 2.515E-19 m5s3/kg2

Column 2 (second dimension) 5.533E-18 m5s3/kg2

Modulator Channel 1.482E-15 m5s3/kg2

Monitor Restrictor 1.265E-19 m5s3/kg2 Actual

Split Restrictor 9.76207E-17 m5s3/kg2 9.88631E-17 m5s3/kg2

MSD Restrictor 2.3713E-18 m5s3/kg2 2.37271E-18 m5s3/kg2

Calculated Pressures

Conclusions

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• 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.

Acknowledgements

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• Jim McCurry, Agilent Technologies

• Roger Firor, Agilent Technologies

• Gaelle Jousset, Total Research & Technology Gonfreville

• John Romesburg, Agilent Technologies