Process Control Homework 2

Process Control Homework 2 CHEN 461-Fall 2012 Team Members: Cristancho Dahiyana Leon Paola Instructor: Jorge Seminario Date: 09/17/2012

Team Number: 29

Question 1.2 Review the equipment sketches in Figure 1(a) and (b) and explains whether each is or is not a level feedback control system. In particular, identify the four necessary components of feedback control, if they exist. (a) The flow is a function of the connecting rod position. Solution: Figure 1(a) represents a level feedback control system where the fours elements (1. Process, 2. Sensor, 3. Controller and 4 Final element) are identified: Figure 1(b) does not represent a clearly process and it is no possible to identify the four control elements

(a)

(b)

Figure 1. (a) Level feedback control system and (b) An example of a not level feedback control system. Question 1.5 Review the processes sketched in Figure 1.7a through d in which the controlled variable is to be maintained at its desired value. (a) From your chemical engineering background, suggest the physical principle used by the sensor. (a) Continuous stirred-tank reactor with composition control

Solution: Composition is the variable sensed in the CSTR, which is controlled by the valve in the heating medium. With an increase in the temperature, the control system would sense a decrease in the outlet composition of reactant. In response, the control system would adjust the heating coil valve, closing slightly, until the outlet composition returned to its desired value. (b) Flow controller Solution: Flow is the variable sensed in the pipe, which is controlled by the valve that is located after the pump. With an increase in the pressure drop, the control system would sense an increase in the fluid flow. In response, the control system would adjust the valve, opening slightly, until the fluid flow returned to its desired value. (c) Tank level with controller Solution: Level is the variable sensed in the tank, which is controlled by the valve that is located after the pump. With an increase in the pressure drop, the control system would sense an increase in the fluid flow. In response, the control system would adjust the valve, opening slightly, until the fluid flow returned to its desired value.

( d) Mixing process Solution: Composition of B is the variable sensed in the tank, which is controlled by the valve in the pipe of the feed of B. With an increase in the fluid of B, the control system would sense an increase in the composition of B. In response, the control system would adjust the valve, decreasing slightly, until the composition of B returned to its desired value. (b) Explain the causal relationships between the manipulated and controlled variables Solution: Flow control

Figure 2. Schematic of flow through valve, where P is the pression at different points in the pipe.

Sensor: The most often used flow sensor for vapors and liquids is an orifice plate. The relationship between the flow and pressure can be derived by applying Bernoulli equation with Janna. (

)

+

(

)

(1)

P1= upstream pressure P2= Pressure at the narrowest flow F= volumetric flow rate = density A= cross sectional area This can be arranged to give √

(1)

(2)

With K depending on the diameters of the pipe and the orifice, along with same friction losses. It is determined empirically. The pressure difference can be measured with the manometer, but this would not provide a signal the computer. A pieza electric device generates a s signal voltage proportional to pressure, and this signal can used for transmission to a computer. Notice that the equation also contains the fluid density. Since density is more expensive to measure, it is common practice to assume that density is constant, then, √

with

(3)

Density can be measured if a very accurate measurement is required Notice that the square root of the measure variable is proportional to flow rate. The measurement of is noisy, ie, it has high frequency interference, because of the turbulence around the orifice plate. Also, almost the entire pressure drop from P1 to P2 is recovered when the flow enlarges to the entire pipe diameter at P3. Thus, P1 P3, although P3 must be slightly lower Final element: The final element is the dominant restriction in the system, so that adjusting the value (the way we adjust a facet) influences the flow. Bernoulli equation for flow in a pipe with friction factors and fittings is equation ( 5.30) is Janna ( )

∑

( )

∑

( ) (4)

f=friction factor which depends on Re ∑

( ) = Minor losses which are due to elbow, expansions and values3

The term minor is unfortunate, since the flow goes to zero (K ) when the value is completely closed. For the simplest case with Pin=P1=constant=Pout=P4=constant, and other friction losses in the pipe and (non-recoverable) in the orifice

√

(5)

The term depends on the value design and the percentage open- see Table 5.4 for typical values.

For initial modeling, we will assume that the relationship between value opening ( 0100%) is linear with flow. √

(6)

Figure 3.Graphic representation of the equation (6). Flow is linearly proportional to valve opening.

(c ) Explain whether the control valve should be opened or closed to increase the value of the controlled variable.

Solution: the valve must be opened to increase the volumetric flow according to the following equation: √

(6)

(d) Identify possible disturbances that could influence the controlled variable. Also, describe how the process equipment would have to be sized to account for the disturbances Solution: Disturbances Decrease in P1 and Increase in P4 The value opening would have to be large enough to allow the desired flow at the lowest P1-P4 Change in density The measured will be maintained but the actual volumetric flow will change

Question 1.6 The preliminary process designs have been prepared for the system in Figure 4. The key variables to be controlled are (a) flow rate, temperature, composition, and pressure for the flash system and (b) composition, temperature, and liquid level for the CSTR. For both processes, disturbances occur in the feed temperature and composition. Answer the following questions for both processes. Determine which sensors and final elements are required so that the important variables can be controlled. Sketch them on the figure where they should be located Solution: Flash drum in figure 4 will have control added in this question:

Figure 4. Control system for a drum in which it is included final elements such as valves, heat exchangers and pumps to keep the process to the desire conditions of performing

(a) Sensors: Flow rate: orifice meter in the inlet pipe Temperature: thermocouple in the vapor space of the drum Pressure: bourbon tube in the vapor space of the drum Composition: The sensor depends on the components in the flash. A typical sensor would be a gas chromatograph Final Elements Flowrate: valve in inlet pipe Temperature: valve in one of the heat exchanger flows. The second heat exchanger flow is chosen here Pressure: the valve in the exit vapor pipe is a natural selection to control the pressure Note that this system must also have a level controller so that the liquid entering the drum for the flash exits via the pipe at the bottom of the drum. (b)The heat exchangers should be sized for the (i) largest process flow, (ii) lowest heating medium temperature, and highest flash temperature. The flash drum should provide sufficient volume for good vapor-liquid separation and sufficient volume for good vaporliquid separation sufficient liquid inventory for level control. The values should accommodate the largest expected flow, including disturbances conditions. (c ) The selected controller pairings are shown in the figure. Note that a causal relationship exists between each manipulated and controlled variable pairing. However, the manipulated variable also influences other controlled variables; thus, interaction exits. Chemical Reactor- The chemical reactor in figure 5 will have control added in this question

Figure 5. Control system for a CSTR.

(a) Sensors Temperature: a thermocouple located in the reactor liquid. It would be protected with a metal sleeve or thermo-well Level: The level can be sensed by a float whose position is sensed Composition: with the temperature maintained pipe could be used to influence the heat transfer rate Level: a valve in either the feed or effluent pipes is required. Here the effluent pipe is selected Composition: with the temperature maintained at a specified, the feed composition is selected to influence the exit composition. Here, the flow rate of the reactant is manipulated. Note that the flow of the solvent must be determined; thus, a valve is added to the solvent inlet pipe, and its value is maintained constant

(b) Describe how the equipment capacities should be determined Solution: The heat exchanger should be sized for the maximum cooling rate at the highest coolant temperature. The values should allow the maximum flow, including disturbed conditions. (c ) Select controller pairings; that is, select which measured variable should be controlled by adjusting which controlled variable.

Solution:The variable pairings are shown in the figure. A causal relationship exists between the manipulated and controlled variable. However, the manipulated variable also influences other controlled variables; thus, interaction exits. Question 1.9 Evaluate the potential feedback control designs in Figure Q1.9. Determine whether each is a feedback control system. Explain why or why not, and explain whether the control system will function correctly as shown for disturbances and changes in desired value. (a) Sensor: measured pressure drop

Figure 6. Level control for a tank.

This sensor measures the position if a rod connected to a float Manipulated: there must be a caudal relationship =

-∑

(7)

The flow out influences the level: Disturbances in and influences the level, and can compensate for their disturbances as long as it has the “range”, i.e, the needed flow of can be achieved, 0≤ ≤max (b) Sensor: the sensor indicates the level to the left of the Xwhich will always remain at the top of the X The level of interest is to the right of the x which should be measured as shown in figure 7.

Figure 7. Level control

(c) Sensor: For the weight fraction of A (Xa) Manipulated variable: The inlet flow influences the amount of A entering the tank. Thus, there may be a causal relationship which appears to exist. A material balance as the component A gives ) (8) Adjusting F influences the rate of change but does not influence the steady-state which is , ie, the outlet concentration equals the inlet, for any F(≠0). Thus , although the flow is an input to the system, it is not possible to control composition in the tank to a desired steady-state value by adjusting F. Note, a feedback control system would be possible if the inlet concentration could be manipulated

Figure 8. Composition control without chemical reaction

(c) Temperature control The temperature in the tank is measured by a sensor, eg, thermocouple, at the exit. The energy balance in the tank gives

(9) Where The control system shown influences the temperature driving force for the heat transfer by mixing some warmer coolant recycle with the fresh constant. Thus, a causal relationship exists between the valve change and the tank temperature. Question 2.1 For each of the following processes, identify at least one control objective in each of the seven categories introduced in Section 2.2. Describe a feedback approach appropriate for achieving each objective. Solution: (a) Reactor-Separator in Figure 1.8 (see book)-. Table 1. Seven control objectives for a reactor-separator Control objective process example

1. safety

vessels at high pressure are dangerous.

control design Add feedback PC to control valve 8 on top of the vessel based on the P1 indicator

2. environmental

sufficient air to combust theHydrocarbons are harmful to the atmosphere

Release system to flare in the overhead vapour line

3. equipment

running pump should have flow at all times, to prevent cavitation

Add feeback LC to control valve 5 based on the L1 indicator

4. smooth operation

Constant flow rate

add a feedback FC to control valve V6 based on the F3 indicator

5. product quality

6. efficiency

7. monitoring and diagnosis

Monitor composition of vapour

add feedback AC that measures composition to the products streams to adjust valve 1 on the inlet feed.

least costly heating

Add AC to liquid product of vessel and have it control valve 7 on the hot oil line into the heat exchanger

Calculate and plot key parameters such as heat exchangers

(b) The boiler in Figure 14.17 (from the class book) and steam superheat Table 2.Seven control objectives for a boiler

Control objective 1. safety 2. environmental

process example safe combustion, always sufficient air to combust the fuel prevent smoke in the flue gas

3. equipment

prevent over heating the metal due to lack of water circulation

4. smooth operation

water flow

5. product quality

The steam temperature (super heat) should be constant.

control design measure % oxygen and achieve desired value by adjusting air flow in same as above have emergency control stop fuel in water level is too low introduce water in a smooth manner, rather than on-off Adjust the "spray" water that cools the steam.

6. efficiency

utilize the lowest amount of fuel possible

7. monitoring and diagnosis

monitor the heat transfer in the convective heat exchangers

i. prevent large excess air by measuring and controlling 7o oxygen ii. ensure good mixing by adjusting the burner and injecting steam to improve mixing calculate the heat transfer coefficient and when too low, clean surface mechanically with steam

(c) Distillation column Table 3.Seven control objectives for a distillation

Control objective

column process example

1. safety

maintain pressure below upper mechanical limit

2. environmental

contain hazardous material

5. product quality

prevent large changes in vapor flow rate which could damage trays relatively constant product flow rates to downstream units off key components in products, eg., heavy key in distillate

6. efficiency

operate with minimum utility consumption

3. equipment protection

4. smooth operation

control design measure pressure and open vent to containment when pressure too high ensure large capacity of containment

smooth manipulation of the reboiler flow (duty) level controllers that are designed to introduce slow changes to the flows measure the product composition and adjust the reflux flow control the distillation pressure at conditions that maximize the relative volatility for the components

7. monitoring and diagnosis

proper operation of equipment which could change due to fouling

calculate the heat transfer coefficients of reboiler and condenser

(d) Fired Heater Table 4.Seven control objectives for a Fired

Control objective

1. safety 2. environmental

3. equipment protection

4. smooth operation 5. product quality

6. efficiency

7. monitoring and diagnosis

Heater process example

fully combust all fuel at flame prevent smoke in flue gas

control design measure % oxygen and control by adjusting the air flow same as above

prevent overheating the metal

emergency controls that stop the fuel flow when the flow of feed is too low

smooth adjustments to the fuel temperature of the process fluid

use minimum fuel monitor the heat transfer in the convective heat exchangers

design temperature controller to implement gradual adjustments to the fuel, when possible design controls to reduce effects of process variation maintain % oxygen at good value, 1-2% calculate the heat transfer coefficients of reboiler and condenser

Question 2.4 Sometimes there is no active hard constraint. Assume that the fired heater in Figure 2.11 (from textbook) has no hard constraint, but that a side reaction forming undesired products begins to occur significantly at 850C. This side reaction has activation energy with larger magnitude than the product reaction. Sketch the shape of the performance function for this situation. How would you determine the best desired (average) value of the temperature and the best temperature distribution? Solution:

Soft constraint For this situation, the performance curve would have a maximum, beyond which the losses due to side reaction would involve be greater than the gain due to increased feed conversion.

Figure 9. Performance curve of fired heater versus temperature (T)

The best value average depends on the performances curve and the distribution of T. If the distribution represented no variation, the dashed line would be the best average temperature. Otherwise, the (Fj) distribution which maximized ∑

(10)

It would be used to calculate the average temperature. Question 2.8 The performance function for a distillation tower is given in Figure Q2.8 in terms of lost profit from the best operation as a function of the bottoms impurity, xB (Stout and Cline, 1978). Calculate the average performance for the four distributions (A through D) given Table Q2.8 along with the average and standard deviation for the concentration, xB. Discuss the relationship between the distribution and the average performance Solution: Process performance To calculate the average, use equation (2-3) ∑ (11) ∑ (12) Where Paverage= average process performance Fj= fraction of data in interval j=Nj/NT M= number of intervals in the frequency distribution Pj= performance measured at the midpoint of interval j

The standard deviation can be calculated from the frequency distribution ∑

(13)

i=individual data n=number of points Sx = Standard deviation This can be rearranged to give ∑

∑ [ ∑

=

] (14) (15)

With ∑

(16)

∑

∑ ∑

(17) ∑

(17) For large NT

The calculations are easily performed with a spread sheet, and the results are: Table 5. The average performance for the four distributions (A through D) Case A B C D

XBave XB (Perf)ave 0.75 0.177 -22.3 2.06 4.00 2.17

0.967 0.71 0.63

Nearly same Xbave, but broader -9.2 distribution -28 -4.67 Best performance

The analysis and results highlight the importance of having a tight distribution around the best operation for this process.