Wang - Mass Flow Controller Gas Conversion Factors MSC 2014

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

[email protected]

Long Beach, CA

March 2014

mailto:[email protected]

mailto:[email protected]

http://www.brunson.us/ImagesProducts/MicTarget.jpg



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



THERMAL MASS FLOW CONTROLLER



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



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)



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



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.



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



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)



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



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 !



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



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



Thermal Mass Flow Sensor



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



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



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



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:



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)



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



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



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



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

⇒



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



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



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



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



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



H ld th i f t



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



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



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



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



Thank You

Wang - Mass Flow Controller Gas Conversion Factors MSC 2014

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