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

Modeling Case Study: Surge Tanks, Valves, Level sensors, and modeling By Peter Woolf (pwoolf@umich.edu) University of Michigan Michigan Chemical Process Dynamics and Controls Open Textbook version 1.0 Creative commons

Surge tank P&ID and model from previous lectures.. ODE model: dh dt = F " k 1v 1 h h[0] = h 0

What level sensor? LC1 What control line? What valve?

Manual valve Angle valve Ball valve Bleed port ball valve Plug valve Bleed port plug valve Butterfly valve Type not specified On/off, reliable, inexpensive On/off, easy clean, see valve position Similar to ball valve, more $$, but more rugged High capacity, economical, can have good flow control Diaphragm valve Used for abrasive, sanitary, & corrosive environments Flush bottom valve Gate valve Globe valve Needle valve Drain tanks w/o dead space High press. and high temp. environments Good flow control, hard to clean Best flow control, low flow Images courtesy of B. Barkel Check valve Allows flow only in 1 direction

Name that valve! (c) Need good rangability, flow resistance okay, robust shutoff needed (a) Need to regulate the flow and robustly shut off if needed Needle valve? Globe valve? Gate valve? (b) Low flow resistance when open, infrequently used but need reliability

Name that valve! (e) Not a control valve, but vents if pressure is too high Safety valve (f) Prevent backflow Check valve (d) Low flow resistance with good control abilities Butterfly valve

Air operated control valve (Globe, needle, ball valves) Air operated butterfly valve (circle in middle indicates butterfly) Air operated shut off valves (ball, plug, etc) * Solenoid operated valves (all valves except butterfly) Motor operated valves (all valves except butterfly) Specify fail safe condition: FO: Fail Open FC: Fail Closed FL: Fail last position Images courtesy of B. Barkel

Automatic solenoid valve

Name that valve! Answer: Motor operated (hydraulic) ball valve Movie from ChemE Visual Encyclopedia

How to pick a valve? Type: Many kinds work, but some work better than others for specific applications. Materials: Can it withstand the pressure, temperature, ph, abrasiveness? Can it be cleaned? Does it leach? Size: Is the valve big enough?

Valve Sizing For liquids, valves are characterized by their Cv factor: G t Cv = F max "P Note: Units are important! F max = maximum flow through valve in gallons per minute ΔP = pressure drop across valve in psi G t =liquid s specific gravity.

Example table for a particular valve from a valve catalog Table from http://www.thevalveshop.com/menu/auto/triaca/triacda/triac88da.pdf G t Cv = F max "P Note: Units are important! F max = maximum flow through valve in gallons per minute ΔP = pressure drop across valve in psi G t =liquid s specific gravity.

Valve Sizing Example You are to design a system to load 50% sodium hydroxide into a carbon steel tank in your plant. Sodium hydroxide is considered a hazardous material. It is not recommended to move 50% sodium hydroxide at velocities over 6 ft/sec in carbon steel piping. The supply pump at the plant can generate a flow of up to 250 gpm. The recommended maximum pressure drop across the valves in the system is 3 psi. Specific gravity of the sodium hydroxide solution is 1.52. Please specify a control valve for this service. Fmax=250 GPM Gt=1.52 ΔP=3 psi Cv = F max G t "P = 250 1.52 3 =178

You are to design a system to load 50% sodium hydroxide into a carbon steel tank in your plant. Sodium hydroxide is considered a hazardous material. It is not recommended to to move 50% sodium hydroxide at at velocities over 6 6 ft/sec in in carbon steel steel piping. The supply pump at the plant can generate a flow of up to 250 gpm. The recommended maximum pressure drop across the valves in the system is 3 psi. Specific gravity of the sodium hydroxide solution is 1.52. Please specify a control valve for this service. Cv =178 Result: 5 inch valve or for a little bit more range, 6 inch valve Table from http://controls.engin.umich.edu/wiki/index.php/valvetypesselection

You are to design a system to load 50% sodium hydroxide into a carbon steel tank in your plant. Sodium hydroxide is considered a hazardous material. It is not recommended to move 50% sodium hydroxide at velocities over 6 ft/sec in carbon steel piping. The supply pump at the plant can generate a flow of up to 250 gpm. The recommended maximum pressure drop across the valves in the system is 3 psi. Specific gravity of the sodium hydroxide solution is 1.52. Please specify a control valve for this service. What diameter pipe would correspond to a flow of 6ft/sec? d = 4F max = 4 #.557 ft 3 /s =.344 ft = 4.1 in "v " # 6 ft /s Fmax=A*v A=πr 2 = π *(d/2) 2 A pipe with a diameter over v=6 ft/sec 4.1 inches should not exceed Fmax=250 gpm=0.557 ft 3 /sec the 6 ft/sec requirement Specification: 5 inch ball valve

Characterizing valve flows Test 1: With constant pressure feed, open valve to many positions and measure flow rate through valve Different shapes depending on fluid properties and valve geometry Saturating effect Quarter turn No effect until threshold

Characterizing valve flows Test 1: With constant pressure feed, open valve to many positions and measure flow rate through valve Finite possible valve turns quick opening valve Near linear valve Two turns

Modeling valve flows Linear: flow = k 1 x Quick opening flow = k 1 x Equal % flow = k 1 R x"1 Image from http://controls.engin.umich.edu/wiki/index.php/valvemodeling flow = Linear w/ threshold IF( x > x min,,k 1 (x " x min ),0)

What level sensor? LC1 What control line? What valve?

Images courtesy of B. Barkel Pneumatic line Electrical or thermocouple leads 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

What level sensor? LC1 What control line? What valve?

Level Sensors Visual: sight tubes, inexpensive but not automatic Float: inexpensive but requires clean fluids and calm fluids Electronic: point detection, accurate, but may require regular cleaning Image from http://controls.engin.umich.edu/wiki/index.php/levelsensors

Non-contact sensors Ultrasonic/microwave: accurate, works in harsher environments, needs smooth surface & moderately expensive Nuclear: read levels through walls, but very expensive Level Sensors

Level Sensors Alternatives: Mass sensor: Weigh the tank Pressure sensor: Measure pressure at bottom of tank Temperature: thermal imaging of tank to detect liquid level Cooler Warmer Thermal image Normal image Cold Approximate liquid level

Pressure relief valve What level sensor? Three electronic sensors LC1 Pneumatic What control line? What 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! Air driven ball valve, characterized experimentally

(1) Parameterize valve What kind of model to use? Maybe equal percentage? Thresholds at ~3 and 15 psi?

(1) Parameterize valve Equal % k 1 flow = k 1 R x"1 Modified Equal %: flow = IF p < p min,0,if( p > p max,k 1,k 1 R x"1 ) where ( ) p min p max x = p " p min p max " p min Estimate values from graph: P min ~4, p max ~14, k 1 ~10, R=?? Find parameters with regression! See tank.model.xls

(2) Create a sensor model Elected to use 3 electronic sensors. Sensors report 1 if immersed in fluid or 0 if dry. s3 LC1 s2 s1 IF(vol>20, s1=1,s1=0) IF(vol>50, s2=1,s2=0) IF(vol>80, s3=1,s3=0) Note: Sensor details often not provided in 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 is process and application specific It is possible to develop accurate quantitative models of a process using numerical integration, IF..THEN.. statements, experimental data, and numerical optimization.