Kyle Fennel
Justin Hosp
Omar Khan
Garrett Steiger
Derek Weidlein
Overview
•
Coriolis flow meters are one of very few types of flow
meters that directly measure mass flow rate through a
pipe.
•
The pipes in a Coriolis flow meter are vibrated by an
electro-magnetic drive system, or an actuator.
•
The mass flow rate is calculated based on the vibration
lag between the upstream and downstream ends of the
meter. The lag is shown on the next slides
•
The density of the liquid can also be calculated based
on the vibrations. The resonant frequency of the pipes
is used to calculated the exact mass in the pipes at any
given time, and because the pipes have a constant
volume, the density can be found.
http://www.redsealmeasurement.com/how-does-a-mass-flowmeter-work/
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Types
•
Coriolis flow meters are generally either composed of two parallel tubes, or one small tube
within a larger tube.
•
In the case of two parallel tubes, the two tubes vibrate towards and away from one another.
Increasing the bend and length of these tubes increases the accuracy of the flow meters
•
Meters with both a large and small degree of bend are depicted below, one showing vibration
of empty pipes.
http://en.wikipedia.org/wiki/Mass_flow_meter
http://research.che.tamu.edu/groups/Seminario/numerical-topics/mass%20flow.pdf
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Types
•
In the case of the concentric pipes, only the inner pipe carries fluid, while the outer pipe acts as
a reference pipe. These types of Coriolis flow meters are generally not as accurate as the
parallel tubes type.
http://www3.emersonprocess.com/micromotion/tutor/39_flowoper
atingprincipalSTcorflow.html
http://research.che.tamu.edu/groups/Seminario/numerical-topics/mass%20flow.pdf
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Advantages
•
Coriolis flow meters are very accurate, within ± 0.25% error.
•
Because mass is measured directly, changing other conditions such
as pressure or temperature does not change the calculations.
•
Coriolis flow meters can be used to measure flow in either direction.
•
Coriolis flow meters can be used to calculate mass flow rate, fluid
density, and often include a thermometer.
•
Coriolis flow meters have very low maintenance costs compared to
other flow meters due to their lack of moving parts. A mass flow
meter with moving parts is depicted to the right.
•
Coriolis flow meters can be used for sterile processes.
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
http://www.bellflowsystems.co.uk/news.html
Turndown
Ratios
Costs of
Alternatives
Disadvantages
•
Coriolis flow meters are generally not accurate in
measuring steam flow, or gas density.
•
Coriolis flow meters lose accuracy when measuring
fluids with multiple phases.
•
Because the measurements are based on vibrations,
ambient vibrations from other processes can interfere
and decrease accuracy .
•
Coriolis flow meters may require a higher pressure drop
than other methods of measuring flow rate and have a
relatively low maximum operating pressure.
•
Coriolis flow meters can be very large, and
comparatively more expensive, as shown in the table to
the right.
Background
Coriolis
Calculations
http://www.coleparmer.com/TechLibraryArticle/667
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Measuring the Mass Flow rate of Coriolis Meter




V-velocity
Ω-angular velocity
Small section of the fluid that is on the inlet side away from
the point of flexture at distance “r”
The Coriolis force on the small fluid section δ m is

δḞc =δm*ac =δm*2ΩxV

Fc,Ω,V are all vectors in the above equation





To simply the problem, assume the tube is a perfect U shape.
Cross Section Area-A
Length- L
Width- d
Twisting moment - Tc




Tc = Fc*d= m*ac*d=ρAL*2ΩV*d
A K factor can be introduced to compensate for the more
generalized U-shape
Tc=2KΩρAVdL=2KΩQmdL
Where Qm=ρAV
Please note that the amplitudes of the vibration and twist are extremely
small compared to the size of the U-shaped tube. The above graphics
are highly exaggerated for illustration purposes.
http://www.efunda.com/designstandards/sensors/fl
owmeters/flowmeter_cor.cfm
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Measuring the Mass Flow rate of Coriolis Meter
𝑑2 𝜃
𝑑𝜃

𝐼𝑢 𝑑𝑡 2 + 𝐶𝑢 𝑑𝑡 + 𝐾𝑢 𝜃 = 𝑇𝑐

Iu - the inertia of the U-shaped tube
Cu – coefficient
Ku –stiffness
Θ –twist angle
T- time
Since the Coriolis meters are vibrating the U-shaped to
generate the rotation, the real angular velocity Ω is a
function of vibrating frequency ω:
Ω = Ω0 cos 𝜔𝑡
Assume that the damping term Cu is negligible, the
equation of twisting becomes







𝑑2 𝜃

𝐼𝑢 𝑑𝑡 2 + 𝐾𝑢 𝜃 = 2K𝑄𝑚 𝑑𝐿Ω0 cos 𝜔𝑡

The particular solution (steady-state) solution of the twist
angle is:

http://www.efunda.com/designstandards/sensors/flowmete
rs/flowmeter_cor.cfm
𝜃 = 𝜃0 cos ω𝑡 =
Background
2𝐾𝑄𝑚 Ω0 𝑑𝐿
cos(ω𝑡)
𝐾𝑢 −𝐼𝑢 𝜔2
Coriolis
Calculations
http://en.wikipedia.org/wiki/File:Coriolis_meter_vibrating_noflow_256x256.gif
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Measuring the Mass Flow rate of Coriolis Meter
 Furthermore, the velocity of the
turning corners of the U-shaped
tube are ΩL and the displacement
difference between the 2 corners is
θd/2. So the time lag is:
 𝑡=
𝜃𝑑
Ω𝐿
=
𝜃0 𝑑
Ω0 𝐿
=
2𝐾𝑄𝑚 𝑑2
𝐾𝑢 −𝐼𝑢 𝜔2
 By measuring the time lag t, the
mass flow rate can be expressed as:
 𝑄𝑚 =
𝐾𝑢 −𝐼𝑢 𝜔2
𝑡
2𝐾𝑑2
http://www3.emersonprocess.com/micromotion/t
utor/46_densityoptubefreq.html
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Measuring the Mass Flow rate of Coriolis Meter
Matlab Code for the final equation
function Qm = flowrate( Ku,Iu,w,K,d,t )
%Qm - the mass flow rate of the system
%Ku - stiffness coefficient given by the manufacturer
%
depending on the size of the Coriolis meter
%Iu - the inertia of the U-shaped tube given by the manufacturer
%
depending on the size of the Coriolis meter
%w - vibrating frequency; dependent on type of liquid flowing
%
through the meter
%K - factor to compensate for the more generalized U-shape
%
this is also given by the manufacturer
%d - diameter of the tube
%t - time lag between the two corners
Qm=(Ku-Iu*w^2)/(2*K*d^2)*t
end
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Orifice Meters
•
•
•
•
•
http://www.engineeringexcelspreadsheets.com/wpcontent/uploads/2011/03/Orifice-and-Venturi-Meter.jpg
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
An orifice meter uses differential
pressure and diameter to calculate
flow rate. Works similarly to a
simple Venturi meter
Although they are less accurate
than Coriolis meters, DP orifice
meters can withstand higher
temperatures
Pressure is measured at the before
and after the orifice, and the
diameters of your orifice plates, D1
and D2, are known
A probe measures the temperature
of the fluid, which is used to
calculate the fluid density
P1, P2, D1, D2, and ρ are substituted
into a modified Bernoulli’s
equation to solve for the mass flow
rate of the fluid
Turndown
Ratios
Costs of
Alternatives
Mass Flow Calculations for Orifice Meter
Calculations
Bernoulli’s Equation with pressure and kinetic
energy terms
−∆𝑃
ρ
http://www.efunda.com/formulae/fluids/images/DP_O
rificePlate_cal.gif
Definition of variables
𝑄𝑚 - mass flow rate
A – cross sectional area
Di – diameter at first orifice plate
D0 – diameter at second orifice plate
𝜌 – density of fluid
ūi – average velocity of fluid at Di
ū0 – average velocity of fluid at D0
∆𝑃 – pressure drop P1-P2
Important Relationships
𝜋
•
𝑄𝑚 = 𝐴 ∗ 𝜌 ∗ ū = 4 𝐷 2 ∗ 𝜌 ∗ ū
•
−∆𝑃
ρ
2
ū02 − ū𝑖2 = 0
+
1
2
16𝑄𝑚
2
𝜋2 𝐷04 𝜌2
−
2
16𝑄𝑚
𝜋2 𝐷𝑖4 𝜌2
=0
𝟐
Factor out 𝑸𝒎
∆𝑃
ρ
=
2
8𝑄𝑚
1
𝜋 2 𝜌2
𝐷04
−
1
𝐷𝑖4
Solve for 𝑸𝒎
𝑄𝑚 =
16𝑄 2
Background
1
Substitute for ū𝟐
ū2 = 𝜋2 𝐷4𝑚𝜌2 (use in substitutions)
Coriolis
Calculations
+
Calculations
for Alternative
Meters
𝜋 2 𝜌∆𝑃
1
1
8( 4 − 4 )
𝐷0 𝐷𝑖
Turndown
Ratios
Costs of
Alternatives
Using Matlab to Calculate Mass Flow
function dporificemeter(D1,D2,P1,P2,rho)
%Inputs
%D1 = larger diameter (m)
%D2 = smaller diameter (m)
%P1 = pressure at D1 (Pa)
%P2 = pressure at D2 (Pa)
%rho = fluid density (kg/m^3)
%
%Output
%Qm = mass flow rate (kg/s)
if D1<=D2
error('The second orifice plate should have a smaller diameter')
elseif P2>=P1
error('Pressure should drop from P1 to P2')
else
Qm = sqrt(((P1-P2)*pi^2*rho)/(8*((1/D2^4)-(1/D1^4))))
end
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
•
Turbine Meters
•
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦(ν)
𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒(𝑄)
•
𝐾=
•
Each turbine has a unique K value that
will need to be calibrated
At high flow rates K is relatively constant
and will yield accurate flow rate results.
At low flow rates, fluid friction on the
turbine makes results inaccurate.
If the turbine meter has been calibrated
and there is a large flow rate, flow rate
ν
can be calculated as: 𝑄 =
•
http://www.globalspec.com/ImageRepository/LearnMore/20129/T
urbine2c3d99fe6296b4920b1d692bc121a21a2.gif
In order to calculate flow, a turbine
meter uses a sensor to calculate the rate
of rotation of the turbine blades
The measured spin frequency is related
to the fluid flow in the pipe by a K-factor
•
𝐾
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Turndown Ratio
•
Compare the range of flow measuring devices
• The ratio of top-end to low-end flow rates
• Indicates the range in which flow meter can accurately measure the fluid
qmax = maximum flow rate, qmin = minimum flow rate
•
Large turndown ratios
beneficial to
• Batch reactors
• Multiproduct financial transfer
• Process startup applications
http://research.che.tamu.edu/groups/S
eminario/index-1.html
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Turndown Ratio
•
Technique to determine turndown ratio:
1.
Minimum accuracy is defined, to set low-end flow rate
𝑀𝑖𝑛𝐹𝑙𝑜𝑤 =
•
𝑍𝑒𝑟𝑜𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦
Zero Stability – limits within which the meter zero may drift during operation and is
constant over the operating range
•
Percentage of nominal mass flow or value of flow rate units
•
Limiting factor when establishing turndown ratio
•
Achievable when the Coriolis meter is installed and re-zeroed at operating
conditions
•
Coriolis meter must be zeroed at normal process temperature conditions, due to
zero stability dependence on temperature
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Turndown Ratio
2.
Maximum pressure is defined, to determine top-end flow rate
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Turndown Ratio
function [ Qvb ] = Untitled( Pag,pfr,Prg,pfa,Qvf,pfa,pba )
%Pag = differential pressure across coriolis meter with
application gas
%pfr = density of reference gas at flowing conditions
%Prg = differential pressure across coriolis meter with
reference gas
%pfa = density of application gas at flowing conditions
%Qvf = volume flow rate of reference gas at flowing conditions
%pfa = density of application gas at base conditions
%pba = volume flow rate of application gas at bas conditions
Qvb = [sqrt((Pag*pfr)/(Prg*pfa))*Qvf*pfa]/pba
end
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
•
Pressure drop is proportional to the flowrate squared. High Flowrates result in higher
pressure drops but greater accuracies. At lower flowrates (high turndown), pressure drop
is lower, but accuracy is lower as well.
http://www.documentation.emersonprocess.com/groups/public_public_mmisami/documents/articles_articlesreprints/jds030705naturalgas.pdf
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Prices of Coriolis Meters VS. Other Flow Measurement Devices
•

It is true that the capital costs of Coriolis meters are higher than that of other Flow
meters.
However it is worth mentioning that their maintenance costs are minimum since they
have such few parts. (Stappert)
(Flo-Corp,2013)
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Prices of a few Coriolis Meters
Name: DMF- series Micro Coriolis Flow Meter
Price: US $200 – 5000/unit ( Depending on Size and
Weight)
Company: Beijing Automation Equipment Co.Ltd
Name: Coriolis Mass Flow Meter
Price: US $1000 – 20,000 / set
Company: Liaoning MEC Group Co.Ltd
(Ali-baba Showroom)
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Capital Costs
Capital Cost, $
Engineering Cost, $
Installation Cost, $
Maintence Costs
(over 10-yr life), $
Total
*Periodic meter zoning
Meter
Straight Pipe runs
Filter/strainer
Pressure sensor
Temperature Sensor
Flow Computer
Wiring
Flow Meter
Flow Computer
Wiring, etc
Meter
Straight pipe runs
Filter/Strainer
Pressure sensor
Temperature Sensor
Flow Computer
Wiring
Meter repair*
Meter flow calibration
Pressure
Temperature
Flow computer
Coriolis
DP/Orifice
5,000-8,000
1,200
0
1,000
0
0
0
500
0
250
0
1,000
500
2,300
500
1,000
0
200
200
200
500
1,000
0
500
0
500
0
100
0
100
0
200
500
400
1,000
2,000
0
2,000
0
1,000
0
500
0
500
$7,900-10,900 $14,350
7,900
10,900
Turbine
2,500
1,000
500
400
250
1,000
200
1,000
200
200
1,000
500
500
100
100
200
400
5,000
5,000
1,000
500
500
$26,850
•
This table compares the
capital costs of a 1 in.
diameter Coriolis, Orifice,
and Turbine meters over a
10-year span
http://research.che.tamu.edu/groups/Seminario/numerical-topics/mass%20flow.pdf
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Capital Costs
•
This gives a visual
representation of
the difference in
costs of a 1 in.
diameter Low end
Coriolis, High end
Coriolis, Orifice,
and Turbine meters
over a 10-year span
http://research.che.tamu.edu/groups/Seminario/numericaltopics/mass%20flow.pdf
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
A Wise Investment?
•
Though at the end of the day the initial price of buying Coriolis meters may be
great, it justifies its cost in the long run
•
Provides much more accurate readings than its competitors
No need for a field operator since it unlike its competitors, it automatically
accounts for Pressure and Temperature. (O’Bannon,2013)
•
Background
Coriolis
Calculations
Calculations
for Alternative
Meters
Turndown
Ratios
Costs of
Alternatives
Conclusion
• In conclusion, Coriolis meters measure mass flow rate extremely
accurately for a large range of fluids and volume flow rates. While
they are more expensive to start up than conventional flow
measurement devices, they are much more cost efficient in the
long run after maintenance and additional costs are considered.
• Future work could include making Coriolis meters more accurate
over a wider range of flow rates, finding ways to make them
smaller and lighter with different materials and further compare
parallel and concentric type Coriolis meters.
References
•
•
•
•
•
•
•
•
http://www.engineeringexcelspreadsheets.com/wp-content/uploads/2011/03/Orifice-and-Venturi-Meter.jpg
http://www.ematem.org/Dokumente/2008_lau_calculat.pdf
http://www.documentation.emersonprocess.com/groups/public_public_mmisami/documents/articles_articlesreprint
s/jds-030705naturalgas.pdf
http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_cor.cfm
http://www.efunda.com/formulae/fluids/images/DP_OrificePlate_cal.gif
http://www.globalspec.com/ImageRepository/LearnMore/20129/Turbine2c3d99fe6296b4920b1d692bc121a21a2.gif
http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_cor.cfm
http://www3.emersonprocess.com/micromotion/tutor/46_densityoptubefreq.html
"Showroom Measurement & Analysis Instruments Flow Measuring Instruments Flow Meters Coriolis Flow Meter: 1,561
Products Found from 53 Suppliers Manufacturers." Coriolis Flow Meter, Coriolis Flow Meter Products, Coriolis Flow
Meter Suppliers and Manufacturers at Alibaba.com. N.p., n.d. Web. 27 Nov. 2013.
<http://www.alibaba.com/showroom/coriolis-flow-meter.html>.
•
Bannon, Tom O. "Coriolis: The Direct Approach to Mass Flow Measurement." Back to Basics (2013): 41-46. Print.
•
"FLO-CORP: Choosing The Correct Flow Meters For Hydraulic Fracturing." FLO-CORP: Choosing The Correct Flow
Meters For Hydraulic Fracturing. N.p., 25 July 2013. Web. 27 Nov. 2013.
<http://flowlineoptions.blogspot.com/2013/07/choosing-correct-flow-meters-for.html>.
•
•
Stappert, Karl. "Coriolis Mass Flow Meters For Natural Gas Measurements." (n.d.): n. pag. Print.
http://en.wikipedia.org/wiki/File:Coriolis_meter_vibrating_no-flow_256x256.gif