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TABLE OF CONTENT

BIL CONTENT PAGE NUMBER

1 ABSTRACT 2

2 INTRODUCTION 3

3 LITERATURE REVIEW 5

4 OBJECTIVE 6

5 METHODOLOGY 7

6 RESULT AND DISCUSSION 10

7 CONCLUSION AND RECOMMENDATIONS 22

8 REFERENCES 23

9 APPENDICES 24

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ABSTRACT

The experiment conducted is to study on dynamics of first order system using furnace.

The objectives of experiment are to demonstrate the properties of a first order system for

various values of the system gain and time constant and also to illustrate the dynamicresponse of a first order to different input signals. Firstly, software Mat lab must be open, and

then Furnace module was selected. The input and output graphs and furnace process

flowsheet window is opened. The simulation was started. The fuel gas purity was decrease

from 1.0 to 0.95, and then output was changing with time. The fuel gas purity was change to

its original value. The initial state values for each inputs and outputs were recorded. The air

flow rate was set to 17.9 and allowed the system reach steady state. Reading value at the

hydrocarbon outlet temperature and oxygen exit concentration was recorded at 40 simulation

minutes. The step repeated for air flow rate 18.1, 18.3, 18.5 and 18.7. After that, the fuel gas

flow rate was set at 1.21 and the hydrocarbon outlet temperature and oxygen exit

concentration was recorded after reach steady state. The step repeated for 1.22, 1.23, 1.24 and

1.25. Next, the hydrocarbon flow rate was set at 0.0350 and the reading of hydrocarbon outlet

temperature and oxygen exit concentration was recorded after reach steady state. The step was

repeated for 0.0355, 0.0360, 0.0365 and 0.0370. Last but not least, the fuel gas purity was set

at 1.00, the hydrocarbon outlet temperature and oxygen exit concentration was recorded after

reach steady state. The step repeated for fuel gas purity at 0.99, 0.98. 0.97 and 0.95. The

nominal Air Flow Rate by was increased to 20% and the whole procedure was repeated. As a

conclusion, a change in the fuel gas flow rate resulting by the highest hydrocarbon outlet

temperature and also the exit oxygen temperature. In other hand, by increasing 20% of the

nominal flow rate would causes the increasing of the exit oxygen concentration but on the

same time will reduces the peak or patern of the hydrocarbon outlet temperature.

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INTRODUCTION

In the study of transfer function models, the dynamic models derived can be put into standard

transfer function typically first order and second order processes. The unit operation in this

experiment was represented by a furnace fueled by natural gas which preheats high molecular

weight hydrocarbon feed to a cracking unit at a petroleum refinery. The assumed combustion

of the fuel followed the following mechanism:

22

224

2

1

22

3

COOCO

OHCOOCH

There are a few inputs to be manipulated and outputs to be controlled so that the combustion

inside the furnace is complete and the stream delivered at the desired temperature. To be able

to obtained the desired output, the furnace inputs was manipulated. The output was recorded.

The system gain for all the manipulated inputs were calculated and substituted into the stadard

transfer function. From the function, the desired output was determined and the input

according to the function was obtained. The obtained inputs were the values to allow the

furnace to achieve its objective.

In this section, you will obtain steady state models for a process system to determine the

effect of manipulated and load variables on the controlled variables of a process.This data is

useful for approximating the changes in the manipulated variablesnecessary to keep the

controlled variables at their desired setpoints.The steady state gain of a system characterizes

the effect that a change in aninput variable has upon an output variable. The gain is

mathematically described as follows:

It is important to note that the gain is defined on the basis of the incremental change in the

respective variables. An implicit assumption in such a calculation is that changes in the

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controlled variables can be calculated by summing the changes in all the manipulated and

load variables multiplied by constant gain coefficients.This is known as the principle of

superposition and is strictly valid only for linear processes. The furnace and column are

nonlinear systems; consequently, this approximation is valid only over a small region around

the operating point where the system behaves in a nearly linear manner.The steady state gains

can be used for many purposes, some of which are listed below:

(a) to determine the value of a manipulated variable necessary to change the setpoint of a

controlled variable

(b) to predict the effect of a change in a load variable upon a controlled variable

(c) to predict the change in a manipulated variable necessary to counteract a

load variable change

The first order transfer function is:

G(s) = K/(s + 1)

Time behavior of a system is important. When design a system, the time behavior may well

be the most important aspect of its' behavior. The points :

1. How quickly a system responds is important. If control system that'scontrolling a temperature, how long it takes the temperature to reach a new

steady state is important.

2. Control systems designers worry about overshoot and how close a systemcomes to instability.

Many different aspects of time behavior of a system those are important in

control system design. The examples above really are talking about aspects

like:

1. Speed of response2. Relative stability of the system3. Stability of the system

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Literature Review

The experiment is about the study on dynamics of first order system using furnace. The

properties of first order system are shown by altering the values of the system gain and time

constant. The dynamic response of first order to different input signals is determined. The inputs

are hydrocarbon flow rate, hydrocarbon inlet temperature, air flow rate, air temperature, fuel gasflow rate, fuel gas temperature and fuel gas purity. The inputs variables can classify as

manipulated or disturbance variables. The inputs may change continuously or at discrete

intervals of time. The outputs are hydrocarbon outlet temperature, furnace temperature, exhaust

gas flow rate and oxygen exit concentration. The outputs variables can classify as measured or

unmeasured variables which measurements may be made continuously or at discrete intervals of

time.

Figure 1: Input/output representation

Figure 2: Control representation

A manipulated input can be adjusted by the control system or the process operator. A

disturbance input can affect the process outputs but cannot adjust by the control system. Thecontrol can be classified to two classes which are feed forward and feedback. A feed forward

controller measures the disturbance variable and transmit the value to the controller which

adjusts the manipulated variable. A feedback control system measures the output variable and

compares the value to desired output value and uses the information to adjust the manipulated

variable. In figure below shown that the process is a first-order process when the responses of the

process variable to a step change in the manipulated variable.

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According Seaborg et al. (2011), the transfer functions can be used conveniently to obtain

output responses to any type of input. By manipulating the input values in this experiment, the

output values can be obtained. When theoretical models are not available or are very

complicated, empirical models providing a viable alternative. Experimental data obtained is

sufficient to develop a model for the control system design. In this experiment, we obtain the

experiment data by manipulating the input. The data obtained then is analyzed and model is

developed to fit the data.

First order transfer function model can be obtained by analyzing the data graphically or

nonlinear regression. To be able to develop a model for the furnace, the system gain and time

constant were calculated then the models were developed. Doyle et al. (1999) also stated that

the steady gain obtained can be used for various purposes. First, the value of manipulated

variable can be determined to change the set point of a controlled variable. Second, the effect

changes in load variables can be predicted upon controlled variables. Lastly, the changes in

load variable can be counteracted to predict the changes in manipulated variables. Nonlinear

systems can behave in a nearly linear manner when the principle of superposition is applied.

The steady gain for the nonlinear system can be gained.

OBJECTIVE

The purpose of the experiment is to demonstrate the properties of a first order system for

various values of the system gain and time constant. This module also illustrates the dynamic

response of a first order to different input signals.

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METHODOLOGY

Select the distillation column from the Main Menu for starting. Clicking the left mouse button

once on the furnace modules. This opens the menu window for the furnace modules. On the

Furnace button, Click the left mouse button. Two additional windows should open, one for the

input and output graphs and one for the furnace process flow sheet.

Under the Simulation menu, select Start. This command should be executed once during a lab

session. It is the simulated equivalent to a perfect process start-up. The process output graphs

are located on the window labelled Furnace Process Monitor. Notice how the outputs remain

unchanged with time.

Next, try decreasing the fuel gas purity. This will act as a disturbance to the system. By

double clicking on the Fuel Gas Purity box, change the value from 1.0 to 0.95 by clicking on

the value box and using the backspace key to erase the old value. When you have entered a

new value, click on the Close button. Again, notice how the outputs on the process monitor

are changing with time. Now return the Fuel Gas Purity to 1.0 by double clicking on Fuel GasPurity box and adjusting the value as done before.

Start the furnace. Record the initial steady state values for each of the inputs and outputs of

the furnace:

Make the following sequence of increases in the air flow rate by double clicking the left

mouse button on the Air Flow Rate box. The remaining inputs (the six other inputs) should be

kept at their initial steady state values. After each change in the air flow rate, allow the system

to reach a new steady state (approximately 40 simulation minutes) and then record the values

of the output variables obtained using the pointers on the output graphs. Record the steady

state values: Return the Air Flow Rate to its initial value allows the furnace to reach steady

state

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Make the following sequence of increases in the fuel gas flow rate by double clicking the left

mouse button on the Fuel Gas Flow Rate box. The remaining inputs (the six other inputs)

should be kept at their initial steady state values. After each change in the fuel gas flow rate,

allow the system to reach a new steady state (approximately 40 simulation minutes) and then

record the values of the output variables obtained using the pointers on the output graphs.

Record the steady state values: Return the Fuel Gas Flow Rate to its initial value allows the

furnace to reach steady state.

Make the following sequence of increases in the hydrocarbon flow rate by double clicking the

left mouse button on the Hydrocarbon Flow Rate box. The remaining inputs (the six other

inputs) should be kept at their initial steady state values. After each change in the hydrocarbon

flow rate, allow the system to reach a new steady state (approximately 40 simulation minutes)

and then record the values of the output variables obtained using the pointers on the output

graphs. Record the steady state values: Return the Hydrocarbon Flow Rate to its initial value

allows the furnace to reach steady state.

Make the following sequence of increases in the fuel gas purity by double clicking the left

mouse button on the Fuel Gas Purity box. The remaining inputs (the six other inputs) should

be kept at their initial steady state values. After each change in the fuel gas purity, allow the

system to reach a new steady state (approximately 40 simulation minutes) and then record the

values of the output variables obtained using the pointers on the output graphs. Record the

steady state values: Return the Fuel Gas Purity to its initial value allows the furnace to reachsteady state.

Increase the nominal Air Flow Rate by 20% and repeat Procedure 4-8.

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For the ended of this session, select Stop under the Simulation menu, then select Yes under

the Quit menu from the Main Menu window. This will return you to the MATLAB prompt.

At this prompt, type quit to exit MATLAB.

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RESULTS AND DISCUSSION

Initial steady state values for each of the input and output of the furnace

Inputs

Hydrocarbon Flow Rate 0.035 m3/min

Hydrocarbon Inlet Temperature 310 K

Air Flow Rate 17.9 m /min

Air Temperature 310 K

Fuel Gas Flow Rate 1.21 m /min

Fuel Gas Temperature 310 K

Fuel Gas Purity 1.0 mol CH4/mol total

Outputs

Hydrocarbon Outlet Temperature 610.1316 K

Furnace Temperature 1426.0309 K

Exhaust Gas Flow Rate 43.2895 m3/min

Oxygen Exit Concentration 0.9190 mol O2/min

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Change in Air Flow Rate:

Air Flow Rate Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

17.9 (nominal) 610.2136 0.9190

18.1 607.2863 0.95066

18.3 605.4827 0.97961

18.5 601.9637 1.0078

18.7 600.3682 1.0335

Change in Fuel Gas Flow Rate:

Fuel Gas Flow

Rate

Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

1.21 (nominal) 609.8684 0.9204

1.22 612.2368 0.9000

1.23 615.1316 0.8796

1.24 616.9737 0.85855

1.25 618.9962 0.8390

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Change in Hydrocarbon Flow Rate:

Hydrocarbon

Flow Rate

Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

0.0350 (nominal) 610.1316 0.9207

0.0355 605.9610 0.9207

0.0360 602.7225 0.9207

0.0365 599.3346 0.9207

0.0370 595.3203 0.9207

Change in Fuel Gas Purity:

Fuel Gas Purity Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

1.00 (nominal) 610.1316 0.9230

0.99 607.2368 0.9493

0.98 604.3421 0.9743

0.97 601.1842 1.0032

0.95 595.3947 1.0585

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Results after nominal Air Flow rate increased by 20%:

Initial steady state values for each of the input and output of the furnace

Inputs

Hydrocarbon Flow Rate 0.035 m3/min

Hydrocarbon Inlet Temperature 310 K

Air Flow Rate 21.48 m /min

Air Temperature 310 K

Fuel Gas Flow Rate 1.21 m /min

Fuel Gas Temperature 310 K

Fuel Gas Purity 1.0 mol CH4/mol total

Outputs

Hydrocarbon Outlet Temperature 568.2675 K

Furnace Temperature 1273.2717 K

Exhaust Gas Flow Rate 45.0563 m3/min

Oxygen Exit Concentration 1.4379 mol O2/min

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Change in Air Flow Rate:

Air Flow Rate Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

21.48 (nominal) 568.2675 1.4379

21.72 564.9672 1.4534

21.96 562.5378 1.4965

22.20 561.8265 1.5278

22.44 558.4472 1.5735

Change in Fuel Gas Flow Rate:

Fuel Gas FlowRate

Hydrocarbon OutletTemperature

Oxygen ExitConcentration

1.21 (nominal) 568.2675 1.4379

1.22 570.2837 1.4129

1.23 572.1929 1.3931

1.24 574.0650 1.3670

1.25 575.8970 1.3429

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Change in Hydrocarbon Flow Rate:

Hydrocarbon

Flow Rate

Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

0.0350 (nominal) 568.2675 1.4379

0.0355 565.2574 1.4379

0.0360 561.5518 1.4379

0.0365 559.0314 1.4379

0.0370 556.0783 1.4379

Change in Fuel Gas Purity:

Fuel Gas Purity Hydrocarbon Outlet

Temperature

Oxygen Exit

Concentration

1.00 (nominal) 568.2675 1.4379

0.99 565.3581 1.4774

0.98 562.3821 1.5058

0.97 560.1134 1.5309

0.95 555.4262 1.6033

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DISCUSSION

1. Using the information from Procedure 5-8, calculate the steady state gain for

each of the following input-output pairings. This can be accomplished by graphically by

plotting the output versus input values from the tables and calculating the best linear fit

to the data.

*Hint: There are 8 steady state gain.

K = ( y2y1 ) / (x2x1 )

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Air Flow Rate versus Hydrocarbon Outlet Temperature

Gain, K = 12.182

Air Flow Rate versus Oxygen Exit Concentration

Gain, K = 0.146

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Fuel Gas Flow Rate versus Hydrocarbon Temperature

Gain, K = 220.43

Fuel Gas Flow Rtae versus Oxygen Exit Concentration

Gain, K = 2.132

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Hydrocarbon Flow Rate versus Hydrocarbon Outlet Temperature

Gain, K = 7425.65

Hydrocarbon Flow Rate versus Oxygen Exit Concentration

Gain ,K = 0

Fuel Gas Purity versus Hydrocarbon Outlet Temperature

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Gain, K = 301.34

Fuel Gas Purity vesus Oxygen Exit Concentration

Gain, K = 2.823

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2. Compared with results from (1), is the nonlinear behavior of the furnaceapparent? How this behavior manifested?

-The nonlinear behavior of the furnace is not obvious and mostly linear. According to

the graph, the value of R2

is mostly almost 0.99. Thus, the nonlinear behavior of the

furnace is not apparent.

3. Using the gains obtained in (1), determine the values of the Air Flow Rate andFuel Gas Flow Rate that are necessary to increase the Hydrocarbon Outlet

Temperature by 7 C and decrease the Oxygen Exit Concentration by 0.05 mol

O2/m3

by assuming the load variables remain constant. Calculate the new value of

the Fuel Gas Flow Rate and Air Flow Rate.

- The increase of Air Flow Rate causes the temperature to decrease and the Exit

Oxygen Concentration to increase. Therefore, the air flow rate is remain at steady state

which is 17.9 m3/min.

- By increasing the Hydrocarbon Outlet Temperature by 70C and decreasing the

Oxygen Exit Concentration by 0.05 mol O2/ m3, Hence, to manipulate both outlet

variables the inlet variable must be changed as below calculated value ;

Increase of hydrocarbon outlet temperature

235 = T / Fuel Gas Flow Rate

235 = 7/ (X1.21)

X = 7/235 + 1.21

X = 1.2397 m3/min

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Decrease of Oxygen Exit Concentration

2.145 = Exit Oxygen Concentration / Fuel Gas Flow Rate

2.145 = 0.05 / (X1.21)

X = 0.05/2.145 + 1.21

X = 1.2333 m3/min

- the value for both Fuel gas Flow rate is 1.2397 m3/min and 1.2333 m3/minrespectively. Which is approximately equal to 1.23 m

3/min.

CONCLUSION

As a conclusion, a change in the fuel gas flow rate resulting by the highest

hydrocarbon outlet temperature and also the exit oxygen temperature. Besides that, any other

factors almost give similar in values or effect. Furthermore, hydrocarbon flow rate gives the

smallest change of value to the hydrocarbon outlet temperature and to the exit oxygen

concentration. Thus, the manipulated of the fuel gas flow rate should be done to give a great

impact to the yield. In other hand, by increasing 20% of the nominal flow rate would causes

the increasing of the exit oxygen concentration but on the same time will reduces the peak or

patern of the hydrocarbon outlet temperature. Lastly, the higher input of air causes the higher

remaining oxygen in the exit and increasing the air flow rate causes cooling to the

hydrocarbon.

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RECOMMENDATION

For the recommendation to get better result the excess air can be increase more up than 20%

in order to make the reaction to be complete combustion. The second recommendation is we

should decrease the oxygen exit concentration to increase the air flow rate as we know that

more air flowrate will make the reaction complete.

REFERENCES

1. Seborg, D. E., Edgar, T. F. and Mellichamp, D. A. (2004).Process Dynamic andControl (2

nded.). United States: John Wil

2. F.J.Doyle III , E.P.Gatzke , R.S.Parker , Process Control Design, 1996.3. Seborg, D.G,Edgar, Process Dynamics and Control , 1989.4. Bequett, B.W., Process Dynamics: Modelling,Analysis and Simulation ,1998.5. Mahoney,D.P., A Real-Time Approach to Process Control,2006.