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Cal Poly Pomona CHE 426 - Problem Set #9

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_______________________ Last Name, First CHE426: Problem set #91. A circulating chilled-water system is used to cool an oil stream from 90 to 70oF in a tube-in-shell heat exchanger. The temperature of the chilled water entering the process heatexchanger is maintained constant at 50oF by pumping the chilled water through a coolerlocated upstream of the process heat exchanger.The design chilled-water for normal conditions is 1000 gpm, with chilled waterleaving the process heat exchanger at 60oF. Chilled-water pressure drop through the processheat exchanger is 15 psi at 1000 gpm. Chilled-water pressure drop through the refrigeratedcooler is 15 psi at 1000 gpm. The heat exchanger area of the process heat exchanger is 1143ft2.The temperature transmitter on the process oil stream leaving the heat exchanger hasa range of 50-150oF. The range of the orifice-differential pressure flow transmitter on thechilled water is 0-1500 gpm. All instrumentation is electronic (4 to 20 mA). Assume thechilled-water pump is centrifugal with a flat pump curve (total pressure drop across thesystem is constant).1) Assuming linear trim determine Cv for the chilled-water control valve that is 25percent open at the 1000 gpm design rate and has a maximum flow of 1500 gpm.2) Determine values of the signals from the temperature transmitter, temperaturecontroller, and chilled-water flow transmitter when the chilled-water flow is 1000gpm.3) Determine the pressure drop over the chilled-water valve when it is wide open.4) Determine the pressure drop and fraction open of the chilled-water control valvewhen the chilled-water flow rate is reduced to 500 gpm. Determine the chilled-waterflow transmitter output at this rate.T TT CF TE l e v a t i o n 0 'E l e v a t i o n 1 5 'E l e v a t i o n 2 0 'T a n k a t a t m o s p h e r i cp r e s s u r eC i r c u l a t i n g c h i l l e d w a t e rH e a te x c h a n g e rC o o l e r9 0 FoH o t o i lC o o l e d o i l 7 0 FoR e f r i g e r a n t5 0 Fo2. Consider the two-tank, interacting liquid-level system shown below and its block diagram.The data for the system are: A1 = 1 ft2, A2 = 0.5 ft2, R1 = 0.5 ft/cfm, R2 = 2 ft/cfm, and R3 = 1ft/cfm. R1R2A1A2c1c2m2m1R3G ( s )1 1G ( s )2 1G ( s )1 2G ( s )2 2++++M2M1C1C2The transfer functions G11, G21, G12, and G22 are given as:G11 = 5( 1)( 7)ss s++ +G12 = 4( 1)( 7)s s+ + G21 = 4( 1)( 7)s s+ +G22 = 3( 1)( 7)ss s++ + Use Simulink to obtain the response of c1 and c2 for (a) M1 = 1/s, M2 = 0, and (b) M1 = 0, M2 = 1/s.3.1 A tank is heated by steam condensing inside a coil. A PID controller is used to control thetemperature in the tank by manipulating the steam valve position. Derive the complete blockdiagram and the closed-loop transfer function from the following design data.Process. The feed has a density  of 68.0 lb/ft3 and a heat capacity cp of 0.80 Btu/lboF. Thevolume V of liquid in the reactor is maintained constant at 120 ft3. The coil consists of 205 ftof 4-in. schedule 40 steel pipe that weighs 10.8 lb/ft and has a heat capacity of 0.12 Btu/lboFand an outside diameter of 4.5 in. The overall heat transfer coefficient U, based on theoutside are of the coil, has been estimated as 2.1 Btu/minft2oF. The saturated steam isavailable at 30 psia; it can be assumed that its latent heat of condensation  is constant at 966Btu/lb. It can also be assumed that the inlet temperature Ti is constant.Design Conditions. The feed flow F at design condition is 15 ft3/min, and its temperature Tiis 100oF. The contents of the tank must be maintained at a temperature T of 150oF. Possibledisturbances are changes in feed rate and temperature.Temperature Sensor and Transmitter. The temperature sensor has a calibrated range of 100to 200oF and a time constant T of 0.75 min. Control Valve. The control valve is to be designed for 100% overcapacity, and pressure dropvariation can be neglected. The valve is an equal percentage valve with a rangeabilityparameter  of 50, f(x) = x-1 = 50x-1. The actuator has a time constant v of 0.20 min. a) Determine the parameters listed in the following tableParameters for stirred tank heater.A 241.5 ft24.93 minCM265.7 Btu/oFc0.524 minKF 2.06 oF/(ft3/min) Kw1.905 oF/(lb/min)Ks0.383 oF/ oF KT1.0 %TO/ oFKv1.652 (lb/min)/ %COv0.20 minT0.75 minb) Use simulink to simulate the temperature response to a step change in both set pointand flow rate with a PID controller for two reset rates of 0.5 min-1 and 1.0 min-1, Kc =2, and D = 1 min.4. A liquid stream enters tank 1 at a volumetric flow rate F in cfm and contains reactant A ata concentration of C0 [mol A/ft3]. Reactant A decomposes in the tanks according to theirreversible chemical reactionA  BThe reaction is first order with reaction rate constant k1 and k2 for tank 1 and tank 2respectively. The reaction is to be carried out in a series of two continuous stirred-tankreactors. The tanks are maintained at different temperatures with tank 2 at a highertemperature. We will neglect any changes in physical properties due to chemical reaction.The purpose of the control system is to maintain C2, the concentration of A leaving tank 2 atsome desired value in spite of variations in the inlet concentration C0. This will beaccomplished by adding a stream of pure A to tank 1 through a control valve using aproportional controller. A portion of the liquid leaving tank 2 is continuously withdrawnthrough a sample line at a rate of 0.1 cfm. The sample line has a length of 50 ft and the cross-sectional area of the line is 0.001 ft2.C o n t r o l l e r( S e t p o i n t )V , TC , k11 1V , TC , k22 2C o m p o s i t i o nm e a s u r i n ge l e m e n tS a m p l e s t r e a mP r o d u c t s t r e a mF , C0H e a t i n g c o i lP u r e AF + m /AData: MwA = 100, A = 0.8 lbmol/ft3, C0s = 0.1 lbmol/ft3, F = 100 cfm, ms = 1.0 lbmol/min, k1= 1/6 min-1, k2 = 2/3 min-1, V = 300 ft3,  = V/F = 3 min.Kv = 16 cfm/psi, Km = 400 3mAlbmol/ft, KT = 0.75 psi/mA, d = 0.5 mina) Use simulink to obtain the response to a unit step change in both the set point and the inlet


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Cal Poly Pomona CHE 426 - Problem Set #9

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