process control homework
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Process Control Homework 2 Team Number: 29
CHEN 461-Fall 2012
Team Members: Cristancho Dahiyana
Leon Paola
Instructor: Jorge Seminario
Date: 09/17/2012
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
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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.
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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)
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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 ( 0-
100%) 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.
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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:
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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 vapor-
liquid 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
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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.
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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.
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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
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(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 control design
1. safety vessels at high pressure are
dangerous.
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
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5. product quality Monitor composition of
vapour
add feedback AC that
measures composition to
the products streams to
adjust valve 1 on the inlet
feed.
6. efficiency 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
7. monitoring and diagnosis 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 process example control design
1. safety
safe combustion, always
sufficient air to combust the
fuel
measure % oxygen and
achieve desired value by
adjusting air flow in
2. environmental prevent smoke in the flue
gas same as above
3. equipment
prevent over heating the
metal due to lack of water
circulation
have emergency control
stop
fuel in water level is too
low
4. smooth operation water flow
introduce water in a
smooth
manner, rather than on-off
5. product quality
The steam temperature
(super heat) should be
constant.
Adjust the "spray" water
that
cools the steam.
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6. efficiency utilize the lowest amount of
fuel possible
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
7. monitoring and diagnosis
monitor the heat transfer in
the convective heat
exchangers
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 column
Control objective process example control design
1. safety
maintain pressure below
upper mechanical limit
measure pressure and open
vent to containment when
pressure too high
2. environmental contain hazardous material
ensure large capacity of
containment
3. equipment protection
prevent large changes in
vapor
flow rate which could
damage
trays
smooth manipulation of
the
reboiler flow (duty)
4. smooth operation
relatively constant product
flow rates to downstream
units
level controllers that are
designed to introduce slow
changes to the flows
5. product quality
off key components in
products, eg., heavy key in
distillate
measure the product
composition and adjust the
reflux flow
6. efficiency
operate with minimum
utility
consumption
control the distillation
pressure
at conditions that
maximize
the relative volatility for
the
components
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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 Heater
Control objective process example control design
1. safety
fully combust all fuel at
flame
measure % oxygen and
control by adjusting the air
flow
2. environmental prevent smoke in flue gas same as above
3. equipment protection
prevent overheating the
metal
emergency controls that
stop
the fuel flow when the
flow of
feed is too low
4. smooth operation
smooth adjustments to the
fuel
design temperature
controller
to implement gradual
adjustments to the fuel,
when
possible
5. product quality
temperature of the process
fluid
design controls to reduce
effects of process variation
6. efficiency use minimum fuel
maintain % oxygen at
good
value, 1-2%
7. monitoring and diagnosis
monitor the heat transfer in
the convective heat
exchangers
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 850C. 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:
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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
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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 XBave XB (Perf)ave A 0.75 0.177 -22.3
B 2.06 0.967 -9.2 Nearly same Xbave, but broader distribution
C 4.00 0.71 -28 D 2.17 0.63 -4.67 Best performance
The analysis and results highlight the importance of having a tight distribution around the
best operation for this process.
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