CHE 185 – PROCESS CONTROL AND DYNAMICS

OPTIMIZATION AND PRIMARY LOOP ELEMENTS

TYPES OF CONTROL • OPTIMIZATION – INTENTION IS TO GET THE “BEST” ECONOMIC/QUALITY CONDITIONS – CONTROL IS THE MORE GENERAL FORM OF RESPONDING TO CHANGE

CONTROL & OPTIMIZATION • FOR A BIOREACTOR http://www.automation.siemens.com/wcmsnewscenter/details.aspx?xml=/conte nt/10001666/en/as/Pages/PN-200201-06 Alles_unter_Kontrolle.xml?NoRedirect=true&xsl=publication-en-www4.xsl

EXAMPLE OF OPTIMIZATION • OPTIMIZATION AND CONTROL OF A CSTR

EXAMPLE OF OPTIMIZATION • ECONOMIC OBJECTIVE FUNCTION  

Q C A V A



Q C B V B



Q C C V C



Q C A

0

V AF

• Φ = $/𝑡𝑖𝑚𝑒 •

ECONOMIC VALUES ,

V B > V C , V A , OR V AF • AT LOW T, LITTLE FORMATION OF B • AT HIGH T, TOO MUCH OF B REACTS TO FORM C • SO THERE EXISTS AN OPTIMUM REACTOR TEMPERATURE, T*

OPTIMZATION EXAMPLE • METHOD OF SOLUTION • 1. SELECT INITIAL GUESS FOR REACTOR TEMPERATURE, T* • 2. EVALUATE

C A

,

C B

, AND

C C

• 3. EVALUATE  • 4. CHOOSE NEW REACTOR TEMPERATURE AND RECYCLE THROUGH STEP 2 UNTIL

T

* IS IDENTIFIED.

EXAMPLE OF OPTIMIZATION

A



B



C

Mole

Q C A

0 balance 

Q C A

on A : 

k

1 exp[ 

E

1 /

RT

]

C A V r

Solving for

C A C A

 1 

k

1

C

exp[ 

A

0

E

1 /

RT

]

V r Q

Likewise,

C B

and

C C

are calculated from mole balances.

EXAMPLE OF OPTIMIZATION • GRAPHICAL SOLUTION OF OPTIMUM REACTOR TEMPERATURE, T*

OTHER TYPES OF CONTROL • SUPERVISORY – RESPONDS TO THE SIGNAL FROM THE OPTIMIZATION CONTROLLER – SENDS A SIGNAL TO THE REGULATORY CONTROL LOOP

TYPES OF CONTROL • REGULATORY – RECEIVES A SIGNAL FROM THE SUPERVISORY CONTROLLER – ACTUALLY ADJUSTS A PROCESS VARIABLE TO MAKE NECESSARY CHANGES FOR OPERATION.

REGULATORY CONTROL EXAMPLE • TEMPERATURE CONTROL FOR A HEAT EXCHANGER

Steam Setpoint TC Product Stream TT Feed Condensate

CATEGORIES OF LOOP COMPONENTS • FEEDBACK LOOP THE PRIMARY COMPONENTS ARE SHOWN SCHEMATICALLY

LOOP COMPONENTS - SENSORS • MEASURE THE VALUE OF THE TARGET AND MANIPULATED VARIABLES – TYPICALLY P, T, L, D, ρ,Μ, COMPOSITION, MASS – LOCATED “IN-LINE”, EVEN IF THEY DO NOT CONTACT PROCESS FLUIDS

LOOP COMPONENTS - SENSORS • TYPICALLY ANALOG DEVICES WITH FULL SCALE RANGES: – 20 MA CURRENT SIGNAL – mV VOLTAGE SIGNAL – 3 - 15 PSIG PNEUMATIC SIGNAL

LOOP COMPONENTS TRANSMITTERS • ANALOG DEVICES – CONVERT SIGNAL INTO A VALUE THAT CAN BE TRANSMITTED WITHOUT SIGNIFICANT LOSS IN VALUE – TYPICAL OUTPUT IS 4 - 20 MA CURRENT FULL SCALE RANGE

LOOP COMPONENTS TRANSDUCERS • CONVERT THE ANALOG SIGNAL FROM THE TRANSMITTER INTO A DIGITAL SIGNAL – LABELED A/D FOR ANALOG TO DIGITAL – LABELED D/A FOR DIGITAL TO ANALOG • CAN TRANSFER ELECTRONIC TO PNEUMATIC

LOOP COMPONENTS CONTROLLERS • RECEIVES DIGITAL SET/POINT AND MEASURED SIGNALS FOR A VARIABLE • MAKES A COMPARISON BETWEEN THE SIGNALS USING A BRIDGE • PRODUCES A DIGITAL OUTPUT SIGNAL TO ADJUST THE MEASURED VALUE TO THE SET/POINT VALUE

LOOP COMPONENTS - ACTUATORS • RECEIVES THE OUTPUT SIGNAL FROM THE CONTROLLER, VIA THE TRANSDUCER • ADJUSTS THE POSITION OF A DEVICE (FINAL CONTROL ELEMENT) TO CHANGE A PROCESS VARIABLE

LOOP COMPONENTS - FINAL CONTROL ELEMENT • CHANGES A PROCESS VARIABLE TO OBTAIN A CORRECTION TO THE MEASURED VARIABLE • FOR CHEMICAL PLANTS, MOST OF THE TIME THESE DEVICES ARE VALVES

SOURCE OF SET/POINTS • FOR A SIMPLE PROCESS, THESE MAY BE ENTERED MANUALLY • FOR CONTEMPORARY SYSTEMS, THESE SIGNALS COME FROM A COMPUTER – PLC - PROGRAMMABLE LOGIC CONTROLLER – DCS COMPUTER - DISTRIBUTED CONTROL SYSTEM COMPUTER

DCS FUNDAMENTALS • DCS HAS THE FOLLOWING GENERAL COMPONENTS – LOCAL CONTROLLERS – INPUT/OUTPUT PANELS (I/O PANELS) TO RECEIVE PROCESS VARIABLE VALUES FROM THE CONTROLLER AND SEND SET/POINT VALUES – DATA HIGHWAY/MULTIPLEXER TO SAMPLE THE VALUES ON A REGULAR FREQUENCY

DATA HIGHWAY/MULTIPLEXER

DCS FUNDAMENTAL COMPONENTS • HOST COMPUTER TO ENTER SET/POINTS • ALARM COMPUTER - PLC’S TO INITIATE ALARMS AND/OR INTERLOCKS • DATA STORAGE COMPUTER – KEEPS TREND DATA – LOGS ALARMS – OTHER COMPUTERS THAT HAVE ACCESS

FINAL CONTROL ELEMENT CHARACTERIZATION - VALVES • VALVES ARE USED FOR EITHER ON/OFF OR THROTTLING OPERATION SEE PERRY’S 7TH PAGE 8-64 • ON/OFF VALVE CHARACTERISTICS – HAVE A COMPLETELY OPEN AND COMPLETELY CLOSED POSITION – HAVE A TIGHT SHUT-OFF CAPABILITY – HAVE LIMITED VALUE FOR THROTTLING

PLUG VALVES AND BALL VALVES • 90° RANGE FROM OPEN TO CLOSED • USE PNEUMATIC OR MOTOR ACTUATORS

GATE VALVES • TYPICALLY USED FOR ISOLATION VALVES - FOR MAINTENANCE AND AS BACK-UP FOR CLOSED THROTTLING VALVES

GATE VALVES • MAY HAVE SEVERAL TURNS BETWEEN OPEN AND CLOSED • MAY HAVE MOTOR OPERATORS – BUT MORE FREQUENTLY USE MANUAL OPERATION

THROTTLING (CONTROL) VALVES • VARIOUS FLOW CHARACTERISTICS BASED ON THE SHAPE OF THE PLUG AND THE SEAT • FLOW THROUGH THE VALVE DEPENDS ON THE FRACTION OPEN AND THE NET PRESSURE DROP • HAVE COMPLETELY OPEN AND COMPLETELY CLOSED POSITION, BUT DESIGNED FOR INTERMEDIATE POSITION FOR CONTINUOUS OPERATION - NOT TIGHT SHUT OFF • GENERAL REFERENCE HTTP://WWW.DOCUMENTATION.EMERSONPROCES

S.COM/GROUPS/PUBLIC/DOCUMENTS/BOOK/CVH99 .PDF

GLOBE (THROTTLING) CONTROL VALVE

CROSS-SECTION OF A GLOBE VALVE

THROTTLING (CONTROL) VALVES • BASIC FLOW EQUATION IS THE SAME AS FOR AN ORIFICE: 𝑄 𝑓𝑙𝑜𝑤 = 𝐾𝐶 𝑣 (𝑥) 𝑃 1 − 𝑃 2 𝜌 • C V IS SIMILAR TO AN ORIFICE COEFFICIENT, HOWEVER IT VARIES WITH VALVE POSITION • K IS EQUAL TO UNITY WHEN  IS EXPRESSED AS SPECIFIC GRAVITY, FLOWRATES ARE IN gpm AND PRESSURE DROP IS IN psi

GLOBE VALVE TYPES • • •

QUICK OPENING-

FOR SAFETY BY-PASS APPLICATIONS WHERE QUICK OPENING IS DESIRED

EQUAL PERCENTAGE-

FOR ABOUT 90% OF CONTROL VALVE APPLICATIONS SINCE IT RESULTS IN THE MOST LINEAR INSTALLED CHARACTERISTICS

LINEAR

- WHEN A RELATIVELY CONSTANT PRESSURE DROP IS MAINTAINED ACROSS THE VALVE

GLOBE VALVE FLOW CHARACTERISTICS

GLOBE VALVES - LINEAR • PLUGS/SEATS DESIGNED TO HAVE THE FRACTION OF FLOW BE LINEAR WITH THE VALVE STEM POSITION FOR A CONSTANT Δp • f(x) = x WHERE x IS VALVE POSITION • DESIGN POSITION IS ABOUT 50% OPEN

GLOBE VALVES - EQUAL PERCENTAGE • EQUAL PERCENTAGE CHANGE IN VALVE POSITION RESULT IN EQUAL PERCENTAGE CHANGE IN FLOW • 𝑓 𝑥 = 𝑅 𝑥−1 WHERE 20 < R < 50 IS VALVE OPENING AND x • DESIGN POSITION IS ABOUT 70% OPEN

GLOBE VALVES - QUICK OPENING • TRIM IS DESIGNED TO HAVE LARGE INCREASE IN FLOW WITH SMALL CHANGE IN VALVE OPENING • 𝑓 𝑥 = 𝑥 • DESIGN POSITION IS OPEN OR CLOSED

GLOBE VALVES - OTHER TYPES • ECCENTRIC PLUG VALVES – COMBINATION OF PLUG AND GLOBE IN THEIR CHARACTERISTICS – CLAIM TO BE TIGHT SHUT OFF – REFERENCE: http://www.millikenvalve.com/pdf/plug2011 .pdf

CHARACTERIZATION OF CONTROL ELEMENTS • TIME CONSTANTS – TIME IT TAKES FOR A UNIT TO RESPOND TO A SIGNAL AND COMPLETE A CHANGE – FOR VALVES THIS IS THE TIME TO STROKE TO A NEW POSITION • DEADBAND – RANGE OF SIGNAL THAT REQUIRED TO INDICATE AN ACTUAL CHANGE

CHARACTERIZATION OF CONTROL ELEMENTS • POSITION – DEADBAND – RANGE OF SIGNAL THAT REQUIRED TO INDICATE AN ACTUAL CHANGE – FOR THERMOCOUPLES THIS MIGHT BE +1 C.

CHARACTERIZATION OF CONTROL ELEMENTS • TURNDOWN RATIO – SPECIFIES THE RANGE OF STABLE OPERATION FOR THE DEVICE, MINIMUM TO MAXIMUM – NORMAL OPERATING RANGE SHOULD NOT BE AT EITHER EXTREME POSITION

CONTROL VALVE DESIGN • EVALUATE C V AT THE MAXIMUM AND MINIMUM FLOW RATE 𝐶 𝑣 𝑥 = 𝐾 𝑄 𝑓 𝑃1 − 𝑃2 𝜌 • DETERMINE WHICH VALVES CAN EFFECTIVELY PROVIDE THE MAX AND MIN FLOW RATE – THE VALVE POSITION SHOULD BE GREATER THAN ABOUT 15% OPEN FOR THE MINIMUM FLOW RATE – AND LESS THAN 85% OPEN FOR THE MAXIMUM FLOW RATE.

CONTROL VALVE DESIGN • CHOOSE – SMALLEST VALVE THAT MEETS THE RANGE CRITERION FOR THE MINIMUM CAPITAL INVESTMENT – THE LARGEST VALVE TO ALLOW FOR FUTURE THROUGHPUT EXPANSION.

• C V VERSUS % OPEN FOR DIFFERENT VALVE SIZES.

• AVAILABLE PRESSURE DROP ACROSS THE VALVE VERSUS FLOW RATE FOR EACH VALVE. NOTE THAT THE EFFECT OF FLOW ON THE UPSTREAM AND DOWNSTREAM PRESSURE MUST BE KNOWN.

http://www.norriseal.com/files/comm_id_47/Valve_Size_Manual.pdf

CONTROL VALVE DESIGN EXAMPLE • SIZE A CONTROL VALVE FOR MAX 150 GPM OF WATER AND MIN OF 50 GPM.

• USE THE VALVE FLOW EQUATION TO CALCULATE C V • FOR D P, USE PRESSURE DROP VERSUS FLOW RATE (E.G., TABLE ON PAGE 82)

CONTROL VALVE DESIGN EXAMPLE • EQUATION AT LIMITS

VALVE POSITION FOR MAX AND MIN FLOWS BASED ON SIZE

ANALYSIS OF RESULTS • 2-INCH VALVE APPEARS TO BE BEST OVERALL CHOICE: LEAST EXPENSIVE CAPITAL AND IT CAN PROVIDE UP TO A 50% INCREASE IN THROUGHPUT.

• 3-INCH AND 4-INCH VALVE WILL WORK, BUT NOT RECOMMENDED BECAUSE THEY WILL COST MORE TO PURCHASE. THE 2-INCH VALVE WILL PROVIDE MORE THAN ENOUGH EXTRA CAPACITY (I.E., SOMETHING ELSE WILL LIMIT CAPACITY FOR IT)

ADJUSTABLE SPEED PUMPS FOR FLOW CONTROL • USED EXTENSIVELY IN THE BIO PROCESSING INDUSTRIES TO MAINTAIN STERILE CONDITIONS AND RELATIVELY LOW FLOW RATES.

• FAST AND PRECISE.

• DO REQUIRE AN INSTRUMENT AIR SYSTEM (I.E., 4-20 MA SIGNAL GOES DIRECTLY TO PUMP).

• MUCH HIGHER CAPITAL COSTS THAN CONTROL VALVES FOR LARGE FLOW RATE APPLICATIONS .