Essentials of Process Control phần 3 pdf

f (VIAIWX 1. Conventional Control Systems and Hardware 101 Conventional FIGURE P3.8 II II II II II II II II II II II II II II II II ,, I, ,lA Tube-in-shell II Ii Ii II condenser II II ,I 11 Dcphlegmator since they eliminate a separate condenser shell, a reflux drum, and a reflux pump. Com- ment on the relative controllability of the two process systems sketched above. 3.9. Compare quantitatively by digital simulation the dynamic performance of the three cool- ers sketched on the next page with countercurrent flow, cocurrent flow, and circulating water systems. Assume the tube and shell sides can each be represented by four perfectly mixed lumps. Process design conditions are: Flow rate =50,000 lb,,/hr - Inlet temperature = 250°F Outlet temperature = 130°F Heat capacity =OS Btu/lb,,, “F Cooling-water design conditions are: A. Countercurrent: Inlet temperature = 80°F Outlet temperature = 130°F B. Cocurrent: Inlet temperature = 80°F Outlet temperature = 125°F C. Circulating system: Inlet temperature to cooler = 120°F Outlet temperature from cooler = 125°F Makeup water temperature to system = 80°F Neglect the tube and shell metal. Tune PI controllers experimentally for each system. Find the outlet temperature deviations for a 25 percent step increase in process flow rate. rm’r ONI:.: Time 1)omain l~ynaniics and Control Process - Water Comment II I rrocess -Y- vessel Q- Makeup 1 water FIGURE P3.9 3.10. The overhead vapor from a depropanizer distillation column is totally condensed in a water-cooled condenser at 120°F and 227 psig. The vapor is 95 mol% propane and 5 mol% isobutane. Its design flow rate is 25,500 lb,/hr, and average latent heat of vaporization is 125 Btu/lb,. Cooling water inlet and outlet temperatures are 80°F and lOS’F, respectively. The condenser heat transfer area is 1000 ft2. The cooling water pressure drop through the condenser at design rate is 5 psi. A linear-trim control valve is installed in the cooling water line. The pressure drop over the valve is 30 psi at design with the valve half open. The process pressure is measured by an electronic (4-20 mA) pressure transmit- ter whose range is 100-300 psig. An analog electronic proportional controller with a gain of 3 is used to control process pressure by manipulating cooling water How. The FIGURE P3.10 electronic signal from the controller (CO) is converted to a pneumatic signal in the I/P transducer. (N) Calculate the cooling water flow rate (gprn) at design conditions. (/I) Calculate the size coefficient (C,,) of the control valve. (c) Specify the action of the control valve and the controller. (d) What are the values of the signals PV, CO, SP, and P,.;,,,, at design conditions? (e) Suppose the process pressure jurnps IO psi. How much will the cooling water Row rate increase? Give values for PV, CO, and Pvi,lvc at this higher pressure. Assume that the total pressure drop over the condenser and control valve is constant. 3.11. A circulating chilled-water system is used to cool an oil stream from 90 to 70°F in a tube-in-shell heat exchanger. The ternperature of the chilled water entering the process heat exchanger is maintained constant at 50°F by pumping the chilled water through a refrigerated cooler located upstream of the process heat exchanger. The design chilled-water rate for normal conditions is 1000 gpm, with chilled water leaving the process heat exchanger at 60°F. Chilled-water pressure drop through the process heat exchanger is 15 psi at 1000 gpm. Chilled-water pressure drop through the refrigerated cooler is 15 psi at 1000 gpm. The heat transfer area of the process heat exchanger is I 143 ft*. The temperature transmitter on the process oil stream leaving the heat exchanger has a range of 50 to 150°F. The range of the orifice differential-pressure flow transmitter on the chilled water is 0 to 1500 gpm. All instrumentation is electronic (4 to 20 mA). Assume the chilled-water pump is centrifugal with a flat pump curve. (~1) Design the chilled-water control valve so that it is 25 percent open at the 1000 gpm design rate and can pass a maximum flow of 1500 gpm. Assume linear trim is used. (b) Give values of the signals from the temperature transmitter, temperature controller, and chilled-water flow transrnitter when the chilled-water flow is 1000 gpm. (c) What is the pressure drop over the chilled-water valve when it is wide open? (cl) What are the pressure drop and fraction open of the chilled-water control valve when the chilled-water How rate is reduced to 500 gpm? What is the chilled-water flow transmitter output at this rate’? (e) If electric power costs 2.5 cents/kilowatt-hour, what are the annual pumping costs for the chilled-water pump at the design 1000 gpm rate’! What horsepower motor is required to drive the chilled-water pump? (I hp = 550 ft-lbtkec = 746 W.) 104 l’:\lU ONI!. Time f>(~rllain L)ynilrnics irrtd C’0111roi Elcvalion 20’ TanA aI ;~lmosplwic Elevation IS’ Circulating cliillccl watei __ 1 Refrigerant I Elevation 0’ c FIGURE P3.11 90°F I Hot oil Cooled oil I 70°F 3.12. Tray 4 temperature on the Lehigh distillation column is controlled by a pneumatic PI controller with a 2-minute reset time and a 50 percent proportional band. Tempera- ture controller output (COT) adjusts the setpoint of a steam flow controller (reset time 0.1 minutes and proportional band 100 percent). Column base level is controlled by a pneumatic proportional-only controller that sets the bottoms product withdrawal rate. Transmitter ranges are: Tray 4 temperature Steam flow Bottoms flow Base level 60-l 20°C O-4.2 lb,/min (orificelAP transmitter) O-l gpm (orificelAP transmitter) O-20 in Hz0 PVL c Bottoms 1 'OF &-, pvF 75 psig steam SP FIGURE P3.12 (~ll~iw:~~ 3 C’onvcntional Control Systems and tlardwarc I OS Srcxly-slate operating conditions arc: Tray 4 tcnipcrati~rc 13asc lcvcl Stcnlll flow Ho~tolns flow 83°C 55% full 3.5 Ib,,,/niin 0.6 gpm Prcssurc drop over the control valve on the bottoms product is constant at 30 psi. This control valve has linear trim and a C,, of 0.5. The formula for steam flow through a control valve (when the upstream pressure P,Y in psia is greater than twice the down- stlxam pressure) is where W = steam flow rate (Ib,,,/hr) c,, = 4 X = valve fraction open (linear trim) (a) Calculate the control signals from the base level transmitter, temperature transmit- ter, steam flow transmitter, bottoms flow transmitter, temperature controller, steam flow controller, and base level controller. (b) What is the instantaneous effect of a +S’C step change in tray 4 temperature on the control signals and flow rates? 3.13. A reactor is cooled by a circulating jacket water system. The system employs a double cascade reactor temperature control to jacket temperature control to makeup cooling water flow control. Instrumentation details are as follows (electronic, 4-20 mA): Reactor temperature transmitter range: 50-250°F Circulating jacket water temperature transmitter range: 50-l 50°F Makeup cooling water flow transmitter range: O-250 gpm (orifice plate + differential pressure transmitter) Control valve: linear trim, constant 35-psi pressure drop Normal operating conditions are: Reactor temperature = 140°F Circulating water temperature = 106” Makeup water flow rate = 63 gpm Control valve 25% open (u) Specify the action and size of the makeup cooling water control valve. (b) Calculate the milliampere control signals from all transmitters and controllers at normal operating conditions. (c) Specify whether each controller is reverse or direct-acting. (d) Calculate the instantaneous values of all control signals if reactor temperature in- creases suddenly by 10°F. Proportional band settings of the reactor temperature controller, circulating jacket water temperature controller, and cooling water flow controller are 20, 67, and 200, respec- tively. Reactor ::; I- f Cooling jacket Pump Makeup cooling water FIGURE P3.13 3.14. Three vertical cylindrical tanks ( IO feet high, 10 feet in diameter) are used in a process. Two tanks are process tanks and are level-controlled by manipulating outflows using proportional-only level controllers (PB = 100). Level transmitter spans are 10 feet. Control valves are linear, 50 percent open at the normal liquid rate of 1000 gpm, and air-to-open, with constant pressure drop. These two process tanks are 50 percent full at the normal liquid rate of 1000 gpm. I Process I Process vessel 2 i Surge tank (‘IIWI I I< 1 (‘onvcntional Control Systems antf Hardware IO7 ‘l‘hc third tallk is ;I surge tank wl~osc lcvcl is uncontrolled. Liquid is pumped from this tank to the lirst process vessel, on to the second tank in series, and then back to the surge tank. If the surge tank is half full when 1000 gpm of liquid are circulated, how full will the surge tank be, at the new steady state, when the circulating rate around the system is cut to 500 gpm? 3.15. Liquid (sp gr = I ) is pumped from a tank at atmospheric pressure through a heat exchanger and a control valve into a process vessel held at 100 psig pressure. The system is designed for a maximum flow rate of 400 gpm. At this maximum flow rate the pressure drop across the heat exchanger is SO psi. A centrifugal pump is used with a performance curve that can be approximated by the relationship AP,, = 198.33 - 1.458 x 10P”F2 where AP,, = pump head in psi F = fIow rate in gpm The control valve has linear trim. (cl) Calculate the fraction that the control valve is open when the throughput is reduced to 200 gpm by pinching down on the control valve. (0) An orifice-plate differential-pressure transmitter is used for flow measurement. If the maximum full-scale flow reading is 400 gpm, what will the output signal from the electronic flow transmitter be when the flow rate is reduced to I50 gpm? 3.16. Design liquid level control systems for the base of a distillation column and for the vaporizer shown. Steam flow to the vaporizer is held constant and cannot be used to control level. Liquid feed to the vaporizer can come from the column and/or from the surge tank. Liquid from the column can go to the vaporizer and/or to the surge tank. Liquid feed FIGURE P3.16 Vapor 108 PARTONE: Time Domain Dynamics and Control Since the liquid must be cooled if it is ~ellt to the SllrgC tank and then rcheatcd in the vaporizer, there is an energy COSt penalty aSWciated with SClldillg 111WC INaterial (0 the surge tank than is absolutely necessary. Your level control system should therefore hold both levels and also minimize the amount of material sent to the surge tank. (If;rlt: One way to accomplish this is to make sure that the valves in the lines to and from the surge tank cannot be open simultaneously.) 3.17. A chemical reactor is cooled by a circulating oil system as shown. Oil is circulatctl through a water-cooled heat exchanger and through control valve VI. A portion of the oil stream can be bypassed around the heat exchanger through control valve VI. The system is to be designed so that at design conditions: l The oil flow rate through the heat exchanger is 50 gpm (sp gr = I) with a IO-psi pressure drop across the heat exchanger and with the VI control valve 25 percent open. l The oil flow rate through the bypass is 100 gpm with the VI control valve SO percent open. Both control valves have linear trim. The circulating pump has a fat pump curve. A maximum oil flow rate through the heat exchanger of 100 gpm is required. (a) Specify the action of the two control valves and the two temperature controllers. (b) Calculate the size (C,) of the two control valves and the design pressure drops over the two valves. (c) How much oil will circulate through the bypass valve if it is wide open and the valve in the heat exchanger loop is shut? Y2 Circulating oil FIGURE P3.17 3.18. The formula for the flow of saturated steam through a control valve is w = 2. K,.f&) J(P, 4 f-q(P, - P2) where W = Ib,/hr steam PI = upstream pressure, psia P2 = downstream pressure, psia FIGURE P3.18 The temperature of the steam-cooled reactor shown is 285°F. The heat that must be transferred from the reactor into the steam generation system is 2.5 X IO” Btu/hr. The overall heat transfer coefficient for the cooling coils is 300 Btu/hr ft’ “F. The steam dis- charges into a 25psia steam header. The enthalpy difference between saturated steam and liquid condensate is 1000 Btu/lb,,,. The vapor pressure of water can be approxi- mated over this range of pressure by a straight line. T(“F) = 195 + f.8P(psia) Design two systems, one where the steam drum pressure is 40 psia at design and another where it is 30 psia. (a) Calculate the area of the cooling coils for each case. (b) Calculate the C,, value for the steam valve in each case, assuming that the valve is half open at design conditions: fix, = 0.5. (c) What is the maximum heat removal capacity of the system for each case‘? 3.19. Cooling water is pumped through the jacket of a reactor. The pump and the control valve must be designed so that: (a) The normal cooling water flow rate is 250 gpm. (b) The maximum emergency rate is 500 gpm. (c) The valve cannot be less than IO percent open when the flow rate is 100 gpm. Pressure drop through the jacket is IO psi at design. The pump curve has a linear slope of -0. I psi/gpm. Calculate the C,, value of the control valve, the pump head at design rate, the size of the motor required to drive the pump, the fraction that the valve is open at design, and the pressure drop over the valve at design rate. 3.20. A CZ splitter column uses vapor recompression. Because of the low temperature re- quired to stay below the critical temperatures of ethylene and ethane, the auxiliary condenser must be cooled by a propane refrigeration system. (u) Specify the action of all control valves. (b) Sketch a control concept diagram that accomplishes the following objectives: Level in the propane vaporizer is controlled by the liquid propane flow from the refrigeration surge drum. 110 PARTONE: Time Domain Dynamics and COII~~()~ Cohnn compressor d q&- H.P. stcanl - Flash valve - Propane surge vaporizer drum Auxiliary condenser Distillate FIGURE P3.20 Column pressure is controlled by adjusting the speed of the column compressor through a steam flow control-speed control-pressure control cascade system. Reflux is flow controlled. Reflux drum level sets distillate flow. Base level sets bottoms flow. Column tray 10 temperature is controlled by adjusting the pressure in the propane vaporizer, which is controlled by refrigeration compressor speed. High column pressure opens the valve to the flare. (c) How effective do you think the column temperature control will be? Suggest an improved control system that still achieves minimum energy consumption in the two compressors. 3.21. Hot oil from the base of a distillation column is used to reboil two other distillation columns that operate at lower temperatures. The design flow rates through reboilers 1 and 2 are 100 gpm and 150 gpm, respectively. At these flow rates, the pressure drops through the reboilers are 20 psi and 30 psi. The hot oil pump has a flat pump curve. Size the two control valves and the pump so that: l Maximum flow rates through each reboiler can be at least twice design. l At minimum turndown rates, where only half the design flow rates are required, the control valves are no less than 10 percent open. [...]... make pH control ideal for on-line adaptive control methods Several instrument vendors have developed commercial on-line adaptive controllers Seborg, Edgar, and Shah (AIChE Journal 32 :88 1, 1986) give a survey of adaptive control strategies in process control 4.6 VALVE POSITION (OPTIMIZING) CONTROL Shinskey [Chem Erg Prog 72(5): 73, 1976; Chem Eng Prog 74(5): 43, 19781 proposed the use of a type of control. .. CASCADE CONTROL One of the most useful concepts in advanced control is cascade control A cascade control structure has two feedback controllers, with the output of the primary (or master) controIlcr changing the sctpoint of the secondary (or slave) controller The output of the secondary goes to the valve, as shown in Fig 4.2 There arc two purposes for cascade control: ( I ) to eliminate the effects of some... lhc C,, value of the control valve (c*) Calculate the PV signal from the pressure transmitter and the CO signal from the pressure controller under steady-state conditions ((1) If the proportional band of the controller is 75 and the pressure in the sterilizer suddenly drops by 5 psi, calculate the instantaneous value of the controller output and the new value of the steam flow rate 3. 33 Design a centrifugal... 100 percent of scale) or a minimum (usually 0 percent) This is called reset windup A sustained error signal can occur for a number of reasons, but the use of override control is one major cause If the main controller has integral action, it will wind up when the override controller has control of the valve And if the override controller is a PI controller, it will wind up when the normal controller... recognized and solved This is accomplished in a number of different ways, depending on the controller hardware and software used In pneumatic controllers, reset windup can be prevented by using external reset feedback (feeding back the signal of the control valve to the reset chamber of the controller instead of the controller output) This lets~the controller integrate the error when its output is going... controller is setting the valve Similar strategies are used in analog electronics In computer control systems, the integration action is turned off when the controller does not have control of the valve 4.5 NONLINEAR AND ADAPTIVE CONTROL Since many of our chemical engineering processes are nonlinear, it would seem advantageous to use nonlinear controllers in some systems The idea is to modify the controller... in some cases, significantly improve the performance of a control system These structures include ratio control, cascade control, and override control 4.1 RATIO CONTROL As the name implies, ratio control involves keeping constant the ratio of two or more flow rates The flow rate of the “wild” or uncontrolled stream is measured, and the flow rate of the manipulated stream is changed to keep the two... broad overview of how to go about finding an effective control structure and designing an easily controlled process A consideration of dynamics should be factored into the design of a plant at an early stage,- preferably as early as the conceptual design stage It is often easy and inexpensive in the early stages of a project to design a piece of process equipment so that it is easy to control If the... ~OIl~lI~l Another type of nonlinear control can bc achieved by using nonlinear transformations of the controlled variables For example, in chemical reactor control the rate of reaction can be controlled instead of the temperature The two are, of course, related through the exponential temperature relationship In high-purity distillation columns, a logarithmic transformation of the type shown below... variable affects both the primary and the secondary controlled variables directly Thus, the two processes are basically different and result in different dynamic characteristics We quantify these ideas later 4 .3 COklPUTED VARIABLE CONTROL One of the most logical and earliest extensions of conventional control was the idea of controlling the variable that was of rea’l interest by computing its value from . 100 -30 0 psig. An analog electronic proportional controller with a gain of 3 is used to control process pressure by manipulating cooling water How. The FIGURE P3.10 electronic signal from the controller. band of the controller is 75 and the pressure in the sterilizer suddenly drops by 5 psi, calculate the instantaneous value of the controller output and the new value of the steam flow rate. 3. 33. . performance of a control system. These structures include ratio control, cascade control, and override control. 4.1 RATIO CONTROL As the name implies, ratio control involves keeping constant the ratio of