wang - mass flow controller gas conversion factors msc 2014
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8/13/2019 Wang - Mass Flow Controller Gas Conversion Factors MSC 2014
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“ACHIEVING COMPETITIVE ADVANTAGE THROUGH MEASUREMENT INNOVATION”
THERMAL MASS FLOW CONTROLLERGAS CONVERSION FACTORS
Jim Chiun Wang, Ph.D.
CareFusion Respiratory Technologies
Yorba Linda, CA 92887
Long Beach, CA
March 2014
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Agenda
• Introduction• Thermal mass flow controllers and their calibration
• The gas conversion factors & FAQs
• Review of the thermal flow sensor scaling relation• Review of laminar flow element scaling relation
• Derive the linearized gas conversion factors
• Answers to the FAQs
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THERMAL MASS FLOW CONTROLLER
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Semiconductor Ultra-Clean Processes
• Particulates contaminate the silicon wafers – They destroy the
nanometer-sized line features of the micro-electronic circuit
• Corrosion generates contaminants
− Moisture adsorbed in gas lines, process vessel walls− Gases such as Cl2 or HCl or SiH4 ..Interacts with water
Corrosion ⇒ Rust
− Rust adsorbs more moisture
More Corrosion ⇒ More Rust … etc.
• Contaminants breaks loose⇒ particulates
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MFC Calibration ..
• Not “OK” to calibrate MFC‟s directly with theprocess gases• Some gases are corrosive – once exposed to these gases the
MFCs are contaminated
• Some gases are Toxic
• Ultra-pure gases are rare and expensive
• Some gases may be proprietary
• MFCs are usually calibrated with nitrogen (N2)
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MFC Calibration …
• Not “OK” to calibrate MFC‟s with the processgases• Some gases are corrosive – once exposed to these gases the
MFCs are contaminated
• Some gases are Toxic
• Some gases are rare and expensive
• Some gases may be proprietary
• MFCs are usually calibrated with nitrogen (N2)
• Must Guarantee Process Gas Accuracy• 1% of reading accuracy (covering 10% to 100% of full scale)
Conflicting Requirements
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CALIBRATION OPTIONS
• Characterize multiple MFC samples with process gases toestablish empirical models. Use the empirical model as thecalibration curve for production MFCs
• Costly & time consuming: MFCs are nonlinear devices
• Individual calibration curves are needed for hundreds of processgases
• Manufacturing tolerance: One model does not fit all MFC‟s
• Insufficient accuracy
• Exact similarity scaling from calibration gas to process gases – Method not available until recently
• Gas Conversion Factors – Linear scaling used by nearly allconventional MFC manufacturers. Easy to apply but insufficientaccuracy (Issues). Sometimes enhanced by using surrogate gaseschosen by experience.
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Gas Conversion Factors
• Gas Conversion Factors are numerical constants used to relate theprocess gas flow rate to the calibration gas flow rate corresponding to the
same mass flow sensor output:
• To determine the process gas flow rate, simply multiply the N2 flow
rate by the gas conversion factor (not very accurate)
• Gas Conversion Factors are conventionally estimated by taking the
ratio of the molar specific heat of nitrogen, to that of the process gas:
(Subscript in CFC stands for the conventional , estimated, conversion factor)
PG
p
N
p
C
C
C
CF
2 heatspecifcmolargasfor thestands
pC
2 E q u a l F lo w S e n s or O u t p u t
P r o c e s s G a s F l o w R a t e
C a l ib r a ti o n G a s ( N ) F lo w R a teG a s C o n v e r s i o n F a c t o r
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Gas Conversion Factors - conti
•Gas Conversion Factors are conventionally estimated by taking the
ratio of the molar specific heat of nitrogen, to that of the process gas:
(Subscript in CFC stands for the conventional , estimated, conversion factor)
PG p
N
p
C
C
C
CF
2 heatspecifcmolargasfor thestands
pC
• Empirical „fudge factors‟ are also used to tweak the CF
2
2
p N
N
C
p PG
PG
C N
CF
C N
N - “Spin Factors”
??!!
(Nothing but fudge factors)
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Conventional Gas Conversion Factors-Issues
Insufficient accuracy
• Accuracy is usually fair at lower flow rates
• Accuracy degrades when flow rate increases,indicative of sensor nonlinearity
• Overall accuracy is gas-dependent - OK forsome gases but poor for most other gases
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Conventional Gas Conversion FactorsIssues - conti
Nonlinearity Error• Gas-dependent: For gases with poor thermal
conductivity the gas conversion factor errors cansometimes exceed 10%
Design / Model Dependent• Gas conversion factor for MFCs made by different
manufacturers or models may differ by a few percent
⇒ MFCs from different vendors are generally
speaking non-interchangeable !
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Frequently Asked Questions (FAQ)
• What are the gas conversion factors?• Are they intrinsic gas properties?
• If so, how could they be hardware design dependent?
• If they are design dependent, how could they correlate (more or
less) with the gas specific heat?• If gas specific heat is not the only thing important, what else may
influence the gas conversion factors, and in what way?
• How could the gas thermal conductivity affect MFC nonlinearity,when it is not even included in the conversion factor formula ?
There is a void in the understanding of how the thermalmass flow meters & controllers work
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Thermal Mass Flow Controller ScalingRelations (Recent Studies)
• Exact scaling relations were obtained by using similaritytransforms
1. Thermal Mass Flow Sensor**
2. Laminar Flow Element**
3. Flow Control Valve
Ref : “Thermal Mass Flow Controller Scaling Relations” Wang, C. Measurement Science Conference,March 2012.
Combine these scaling relations to re-examine the gasconversion factors
Review the scaling relations for the thermal mass flowsensor and the laminar flow element
Reconsider the gas conversion factor issues
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Thermal Mass Flow Sensor
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Thermal Mass Flow SensorScaling Relation
k
c DV W W
p
D
Pr Re
k
S
Pr Re
1
Pr Re
2
Pr Re
10
11
0
θθPr)(ReS D D
L
D D
L
D D
L dx
dr
d dx
dr
d T T GkD
r r
DW
where
S - thermal mass flow sensor output (see below)
K - thermal conductivity of the gas
cp – gas specific heat V – mean flow velocity
D – sensor tube diameter
ReD, Pr are the Reynolds number and the Prandtl number, resp. andReD·Pr together as a product is also known as the Pèclet number
Ref: "A Similarity theory for Thermal Mass Flow Sensor and Its Gas Conversion Factors", Wang, C.
Measurement Science Conference, Jan. 25, 2007, Long Beach, CA.
Sensor similarity scaling relation derived from heat transfer theory
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Raw Sensor Output vs. Flow
Raw data from a typical thermal mass flow sensor
0.0
0.5
1.0
1.5
0 5 10 15 20 25 30 35 40 45
S e n s o r O u t p u t
Actual Gas Flow (sccm)
Ar
CF4
SF6
CO2
CH4
CHF3
He
N2
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Sensor Output Scaled by usingSimilarity Theory
0
20
40
60
80
100
0 1000 2000 3000 4000 5000 6000
( S e n s o r O u t ) / ( k * E k
)
F Re Pr *Ec
Sensor Output in Similarity Variables N2
He
Ar
CF4
SF6
CO2
CH4
CHF3
HBr
Cl2
NH3
CH3F
C2H4
BCl3
SiCl4
C2F6
C4F8
CH2F2
C4F6
Xe
Ref: “Thermal Mass Flow Sensor Similarity Theory - Comparison with Experiments” Wang, C.
Measurement Science Conference, March 2008, Long Beach, CA.
Data correlated by using the similarity model
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Sensor-Alone Gas Conversion Factor
• Very low-flow MFCs (~5 sccm N2) uses no LFE bypass• MFC conversion factor the same as sensor conversion factor
• S-ṁ curve slope proportional to Cp at equal Φ
• Linear approximation ⇒ conventional gas conversion factor CFC
• Gas conversion factors explained for the first time
)(Pr)(Re Dk
C mW k W k S
p
D
)()( '' FF
W D
C
kD
C W k
md
S d p p
)()(
)()(
]/[
]/[
2
'
2
'
2 N N p
PG PG p
N
PG
W C
W C
md dS
md dS
F
F
RePr F
2
2222
)(
)(
]ˆ/[
]ˆ/[
N p
PG p
PG PG
N N
PG PG
N N
C
C
QT R PM
QT R PM
Q
Q
^
2 2 2
^
2
( ) ( )
( ) ( )
N p N p N PG
PG p PG p PG N
FC
M C C Q
M C Q C
C
22
)(
)(
]/[
]/[
N p
PG p
N
PG
C
C
mS
mS
2
2
)(
)(
][
][
N p
PG p
PG
N
C
C
m
m
Qm
At equal sensor output S:
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Laminar Flow Element
A typical LFE
• Consists of multiple round tubes of finite length
• Installed in parallel to the flow sensor
• Experiences the same pressure drop as the sensor
• Serves as the “flow divider” – (Not necessarily linear)
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Laminar Flow Element Scaling Relation
• Without the entrance effect, the pressure drop should be linearlydependent on flow by Poiseuille‟s law:
4
128 QL P
D
• Entrance Effect⇒ Nonlinearity in pressure-flow relation
• Nonlinear scaling achieved by similarity transform2
Re½ ~ D
u f
P
D
L
•Each LFE passage is a shortcapillary tube
•Laminar flow in short tubes
suffers from “Entrance Effect”
•Sensitive to the exact shape
at the tube entrance
Ref : “Calibration of Nonlinear Laminar Flow Elements for Multi-gas Applications” Wang, C.
Measurement Science Conference, Long Beach, CA. March 2009
VD D Re
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Laminar Flow Element Data inPrimitive Variables
0
1
2
3
4
5
6
0 10 20 30 40 50 60
P r e s s u r e D r o p ( m m H g )
Mean Flow Velocity (ft/sec)
Laminar Flow Element LFE-C
He
Ar
H2
N2
CO2
CH4
CHF3
CF4
SF6
Raw LFE Data
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Laminar Flow Element DataScaled by Similarity Method
Ref : “Calibration of Nonlinear Laminar Flow Elements for Multi-gas Applications” Wang, C.
Measurement Science Conference, Long Beach, CA. March 2009
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0 2 4 6 8 10 12 14
ρ V 2 / ( 2 Δ P )
Re D/L
Laminar Flow Element LFE-C
He
Ar
H2
N2
CO2
CH4
CHF3
CF4
SF6
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Laminar Flow ElementBypass Split-Ratio
• Using the similarity method, the split-ratio of the LFE was derivedand shown to be gas dependent
• LFE and sensor under the same P
2
Re½ ~ D
V f
P
D
L
2 2
S S B B
S S S S B B B B
B BS S
V V
V D D V D D f f
L L
• Similarity Scaling for LFE is nonlinear but nonlinearity is mild
• Explicit solution after linearization using Peusuille‟s law
4
128
D
QL P
D L
VDVL
V
P
DRe6464
2
1 22
4 4
4
4;
S S S B B B
S B
S S B BS B
S B B S
Q L Q L
D D
L DQQ L D
• The bypass split-ratio is affected by the gas viscosity temp-co
⇒
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Mass Flow Controller Gas ConversionFactor
• Assume tube number n >> 1, and/or DB4>> DS
4 , or both.
• Linearized GCF for the total MFC flow
2 2
2 2 2 2
^
2. . . . . . . .
^
. . . .
( )
( )
B B N S S N S p N T P G P G P G P G
T N B S S B S P G N N P G N p PG
Q C Q
Q Q C
• Here [Qs]P.G / [Qs]N2 is the sensor-alone Gas Conversion Factor
⇒ Total MFC Gas Conversion Factor, Linearized
2
2
^
2. .
^
. .
( )
( )
B N S p N P G L
B S P G N p PG
C CF
C
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Compare CFL against CFC
• The linearized CFL vs. the conventional CFC
2
2
^
2. .
^
. .
( )
( )
B N S p N P G L
S B N P G p PG
C CF
C
PG
p
N
p
C
C
C
CF
2
• Gas specific heat dominates the Gas Conversion
Factor
• The viscosity temperature-coefficient affects the gas
conversion factors• The gas Cp and gas viscosity must be enumerated at
the right operating temperature for the sensor and for the
bypass respectively
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Additional Discussions
• The linearized gas conversion factors CFL arevalid only in the “linear range” of the MFC. Accuracy depends on how the “linear range” isdefined
• To achieve the best accuracy, the full nonlinearscaling method of similarity transform must beused.
• The similarity transforms also provide insightinto the gas conversion factor related issues
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What are the gas conversion factors?
• Gas Conversion Factors are numerical constantsused to relate the process gas flow rate to the
calibration gas flow rate corresponding to the same
mass flow sensor output:
2 EqualFlowSensorOutput
Process Gas Flow Rate
Galibration Gas (N ) Flow RateGasConversion Factor
A G C i F i i i
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Are Gas Conversion Factors intrinsicgas properties?
• No. Gas conversion factors are not intrinsic gasproperties
• The exact scaling of the mass flow rate involves
• The gas specific heat• The gas thermal conductivity
• The gas viscosity and viscosity temp-co
• MFC design parameters such as LS, DS, LB, DB
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H ld th i f t
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How could the gas conversion factorsvary from unit to unit?
• The exact scaling depends not only on the gas thermal physicalproperties but also on the design of the MFC
Sensor
Bypass / LFE
• Manufacturing tolerances in LS, DS, LB, DB, etc.. can affect the gasconversion factors
• This explains why GCFs can vary somewhat from unit to unit
Pr Re
1
Pr Re
2
Pr Re
10
11
0
θθPr)(ReS D D
L
D D
L
D D
L dx
dr
d dx
dr
d T T GkD
r r
DW
k
c DV W W
p
D
Pr Re
k
S
2
Re½ ~ D
u f
P
D
L
VD D Re
H ld th i f t
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How could the gas conversion factorscorrelate with the gas specific heat?
• The linearized gas conversion factors aredominated by gas specific heat
• The conventional gas conversion factors areOK in the “linear range”
• The nonlinearity of the mass flow controllers arestrongly influenced by the gas thermalconductivity.
• The gas conversion factors do not work well forgases with poor thermal conductivity
Wh t l i fl th
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What else may influence the gasconversion factor? How?
• MFC design factors that affect the GCF• Sensor tube length
• Sensor heated tube length
• Sensor tube diameter
• Sensor temperature profile• Bypass LFE tube length and diameter
• Bypass tube count
• Bypass temperature
• Exact scaling can only be achieved by usingthe similarity transform method
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CONCLUSIONS
• Thermal mass flow controller gas conversionfactors are reviewed in the light of the similarityscaling method
• Linearized gas conversion factors are derived
and improves the conventional gas conversionfactors
• Frequently asked questions about gas
conversion factors are answered• The similarity scaling theory successfully
explained how the thermal mass flow meters &controllers work
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