Modeling Case Study:Surge Tanks, Valves,Level sensors, and modeling

By Peter Woolf (pwoolf@umich.edu)University of Michigan

Michigan Chemical ProcessDynamics and ControlsOpen Textbook

version 1.0Creative commons

!

dh

dt= F " k

1v1h

!

h[0] = h0

ODE model:

Surge tank P&ID and model from previous lectures..

LC1

Whatvalve?

Whatcontrolline?

What level sensor?

On/off, reliable, inexpensiveOn/off, easy clean, seevalve position

Similar to ball valve, more$$, but more ruggedHigh capacity, economical,can have good flow control

Used for abrasive, sanitary, & corrosive environments

Drain tanks w/o dead space

High press. and high temp. environmentsGood flow control, hard to clean

Best flow control, low flow

Allows flow only in 1 directionImages courtesy of B. Barkel

Angle valve

Plug valveBleed port plug valveButterfly valve

Diaphragm valve

Flush bottom valve

Gate valveGlobe valve

Needle valve

Check valve

Bleed port ball valve

Ball valve

Manual valve Type not specified

(b) Low flow resistancewhen open, infrequentlyused but need reliability

(a) Need to regulate theflow and robustly shutoff if needed

(c) Need goodrangability, flowresistance okay, robustshutoff needed

Globe valve?

Gate valve?

Needle valve?

Name that valve!

(e) Not a control valve,but vents if pressure istoo highSafety valve

(d) Low flow resistancewith good controlabilitiesButterfly valve

Check valve(f) Prevent backflow

Name that valve!

Solenoid operated valves(all valves exceptbutterfly)

Motor operated valves(all valves exceptbutterfly)

Air operated controlvalve(Globe, needle, ballvalves)

Air operated butterflyvalve (circle in middleindicates butterfly)

Air operated shut offvalves (ball, plug, etc)

Specify fail safe condition:FO: Fail OpenFC: Fail ClosedFL: Fail last position

*

Images courtesy of B. Barkel

Automatic solenoid valve

Name that valve!

Movie from ChemE Visual Encyclopedia

Answer:Motoroperated(hydraulic)ball valve

How to pick a valve?

• Type: Many kinds work, but some workbetter than others for specificapplications.

• Materials: Can it withstand thepressure, temperature, pH,abrasiveness? Can it be cleaned?Does it leach?

• Size: Is the valve big enough?

Valve Sizing

• For liquids, valves are characterized bytheir Cv factor:

!

Cv = Fmax

Gt

"P

Note: Units are important! Fmax = maximum flow through valve ingallons per minute ΔP = pressure drop across valve in psi Gt =liquid’s specific gravity.

!

Cv = Fmax

Gt

"P

Note: Units are important! Fmax = maximum flow through valve ingallons per minute ΔP = pressure drop across valve in psi Gt =liquid’s specific gravity.

Table from http://www.thevalveshop.com/menu/auto/triaca/triacda/triac88da.pdf

Exampletable for aparticularvalve from avalve catalog

Valve Sizing Example

!

Cv = Fmax

Gt

"P= 250

1.52

3=178

You are to design a system to load 50% sodium hydroxide into acarbon steel tank in your plant. Sodium hydroxide is considereda hazardous material. It is not recommended to move 50%sodium hydroxide at velocities over 6 ft/sec in carbon steelpiping. The supply pump at the plant can generate a flow of upto 250 gpm. The recommended maximum pressure drop acrossthe valves in the system is 3 psi. Specific gravity of the sodiumhydroxide solution is 1.52. Please specify a control valve for thisservice.

Fmax=250 GPMGt=1.52ΔP=3 psi

You are to design a system to load 50% sodium hydroxide into acarbon steel tank in your plant. Sodium hydroxide is considereda hazardous material. It is not recommended to move 50%sodium hydroxide at velocities over 6 ft/sec in carbon steelpiping. The supply pump at the plant can generate a flow of upto 250 gpm. The recommended maximum pressure drop acrossthe valves in the system is 3 psi. Specific gravity of the sodiumhydroxide solution is 1.52. Please specify a control valve for thisservice.

You are to design a system to load 50% sodium hydroxide into acarbon steel tank in your plant. Sodium hydroxide is considereda hazardous material. It is not recommended to move 50%sodium hydroxide at velocities over 6 ft/sec in carbon steelpiping. The supply pump at the plant can generate a flow of upto 250 gpm. The recommended maximum pressure drop acrossthe valves in the system is 3 psi. Specific gravity of the sodiumhydroxide solution is 1.52. Please specify a control valve for thisservice.

!

Cv =178

Table from http://controls.engin.umich.edu/wiki/index.php/ValveTypesSelection

Result:5 inch valveor for a littlebit morerange, 6inch valve

You are to design a system to load 50% sodium hydroxide into acarbon steel tank in your plant. Sodium hydroxide is considereda hazardous material. It is not recommended to move 50%sodium hydroxide at velocities over 6 ft/sec in carbon steelpiping. The supply pump at the plant can generate a flow of upto 250 gpm. The recommended maximum pressure drop acrossthe valves in the system is 3 psi. Specific gravity of the sodiumhydroxide solution is 1.52. Please specify a control valve for thisservice.

What diameter pipe would correspond to a flow of6ft/sec?

Fmax=A*vA=πr2= π *(d/2)2

!

d =4F

max

"v=

4 # .557 ft3/s

" # 6 ft /s= .344 ft = 4.1 in

v=6 ft/secFmax=250 gpm=0.557 ft3/sec

A pipe with a diameter over4.1 inches should not exceedthe 6 ft/sec requirement

Specification: 5 inch ball valve

Characterizing valve flowsTest 1: With constant pressure feed, open

valve to many positions and measureflow rate through valve

Quarter turn

No effectuntilthreshold

Saturating effectDifferent shapesdepending on fluidproperties and valvegeometry

Characterizing valve flowsTest 1: With constant pressure feed, open

valve to many positions and measureflow rate through valve

Two turns

“quickopening” valve

Nearlinearvalve

Finite possiblevalve turns

!

flow =

IF x > xmin,,k1(x " xmin ),0( )

Modeling valve flows

Image from http://controls.engin.umich.edu/wiki/index.php/ValveModeling

Linear w/ threshold

Linear:

!

flow = k1x

Quick opening

!

flow = k1x

Equal %

!

flow = k1Rx"1

LC1

Whatvalve?

Whatcontrolline?

What level sensor?

Electrical or thermocouple leadsPneumatic line

Multiplexed signal

Pneumatic controls:•Spark free control•Control signal also provides power for valve•Relatively short range and slower acting•Common pressure signal range: 3 to 15 Psi

Electrical controls:•Fast and long range•May pose a spark hazard•Can be multiplexed to address many controllers at once•Common signal range: 4-20 mA

Images courtesy of B. Barkel

LC1

Whatvalve?

Whatcontrolline?

What level sensor?

Image from http://controls.engin.umich.edu/wiki/index.php/LevelSensors

Level Sensors• Visual: sight tubes,

inexpensive but notautomatic

• Float: inexpensive butrequires clean fluids andcalm fluids

• Electronic: pointdetection, accurate, butmay require regularcleaning

Non-contact sensors• Ultrasonic/microwave:

accurate, works inharsherenvironments, needssmooth surface &moderately expensive

• Nuclear: read levelsthrough walls, butvery expensive

Level Sensors

Alternatives:• Mass sensor: Weigh the

tank• Pressure sensor: Measure

pressure at bottom of tank• Temperature: thermal

imaging of tank to detectliquid level

Level SensorsNormalimage

Thermalimage

Cooler

Warmer

ColdApproximate liquid level

LC1

Whatvalve?

Whatcontrolline?

What level sensor?

Air drivenball valve,characterizedexperimentally

Pneumatic

Three electronicsensors

Pressurerelief valve

Bring it all together in a model!(1) Parameterize valve(2) Create sensor model(3) Create feed model(4) Create physical model(5) Simulate!

Modeling Case Study:Surge Tanks, Valves,Level sensors, and modeling

By Peter Woolf (pwoolf@umich.edu)University of Michigan

Michigan Chemical ProcessDynamics and ControlsOpen Textbook

version 1.0Creative commons

LC1

Whatvalve?

Whatcontrolline?

What level sensor?

Air drivenball valve,characterizedexperimentally

Pneumatic

Three electronicsensors

Pressurerelief valve

Bring it all together in a model!(1) Parameterize valve(2) Create sensor model(3) Create feed model(4) Create physical model(5) Simulate!

(1) Parameterize valve

What kind of model to use?Maybe equal percentage?Thresholds at ~3 and 15 psi?

(1) Parameterize valve

Estimate values from graph:Pmin~4, pmax~14, k1~10, R=??

Find parameterswith regression!

See tank.model.xls

Equal %

!

flow = k1Rx"1

Modified Equal %:

!

flow = IF p < pmin,0,IF p > p

max,k1,k1Rx"1( )( )

where

x =p " p

min

pmax

" pmin

pmin pmax

k1

(2) Create a sensor model

s1

s2

s3

IF(vol>20, s1=1,s1=0)IF(vol>50, s2=1,s2=0)IF(vol>80, s3=1,s3=0)

Elected to use 3 electronic sensors. Sensorsreport 1 if immersed in fluid or 0 if dry.

LC1

Note: Sensordetails oftennot providedin P&ID!

Modeling continued

(1)Parameterize valve(2)Create sensor model(3)Create feed model(4)Create physical model(5)Simulate!

See tank.model.xls

Take home messages

• Your choice of instrumentation isprocess and application specific

• It is possible to develop accuratequantitative models of a process usingnumerical integration, IF..THEN..statements, experimental data, andnumerical optimization.