process control homework

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)

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

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

(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

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


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.

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


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


proper operation of

equipment which could

change due to fouling


coefficients of reboiler and

condenser

(d) Fired Heater

Table 4.Seven control objectives for a Fired Heater


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%


monitor the heat transfer in

the convective heat

exchangers


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:

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 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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