Simulation, optimization and control of a thermal cracking furnace

M.E. Masoumia, S.M. Sadramelia,*, J. Towfighia, A. Niaeib

aChemical Engineering Department, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, IranbDepartment of Applied Chemistry, University of Tabriz, 51666-14766 Tabriz, Iran

Received 2 November 2003

Abstract

The ethylene production process is one of the most important aspect of a petrochemical plant and the cracking

furnace is the heart of the process. Since, ethylene is one of the raw materials in the chemical industry and the

market situation of not only the feed and the product, but also the utility is rapidly changing, the optimal operation

and control of the plant is important. A mathematical model, which describes the static and dynamic operations of

a pilot plant furnace, was developed. The static simulation was used to predict the steady-state profiles of

temperature, pressure and products yield. The dynamic simulation of the process was used to predict the transient

behavior of thermal cracking reactor. Using a dynamic programming technique, an optimal temperature profile

was developed along the reactor. Performances of temperature control loop were tested for different controller

parameters and disturbances. The results of the simulation were tested experimentally in a computer control pilot

plant.

q 2005 Elsevier Ltd. All rights reserved.

1. Introduction

The bulk of the worldwide annual commercial production of ethylene is based on thermal cracking of

petroleum hydrocarbons with steam; the process is commonly called pyrolysis or steam cracking.

Hydrocarbon feed mixed with process steam is introduced into the tubular reactors (cracking coils) with

short residence time and at a high temperature. Steam is used to increase the olefin selectivity and to

reduce the coke formation by decreasing the hydrocarbon partial pressure.

Energy 31 (2006) 516–527

www.elsevier.com/locate/energy

0360-5442/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.energy.2005.04.005

* Corresponding author. Visiting Faculty: Chemical Engineering, University of Florida, Chemical Engineering Building,

Gainesville, FL 32611-6005, USA. Tel.: C1 352 392 0862; fax: C1 352 392 9513.

E-mail address: sadrameli@che.ufl.edu (S.M. Sadrameli).

Nomenclature

Ci concentration of coke precursors, mole/m3

Cp heat capacity, J/mole K

dt tube diameter, m

F molar flow rate, mole/h

Fr friction factor

G total mass flux of the process gas, kg/m2s

DH heat of reaction, J/mole

Kc proportional constant

Mm average molecular weight, kg/mole

Pt total pressure, kPa

PI performance index

PI proportional integral control

PID proportional integral derivative control

Q heat flux, W/m2

Rb radius of the tube bend, m

Re reynolds number

r tube radius, m

rc coking reaction rate, kg/m3s

rri reaction rate in pyrolysis process, mole/m3s

tc coke thickness, m

t time, h

Td derivative control constant

TI integral Control constant

sij stoichiometry factor

T temperature, K

z axial reactor coordinate, m

Greek letters

a coking factor

L angle of bend 0

rc coke density, kg/m3

h unit conversion factor

Abbreviations

COT coil outlet temperature

XOT cross over temperature

S/HC steam to hydrocarbon ratio

IAE integral of absolute value of error

M.E. Masoumi et al. / Energy 31 (2006) 516–527 517

The paraffinic feedstock is thermally cracked into mainly olefins, aromatics, methane and hydrogen.

The homogeneous cracking reactions are endothermic and energy input is required in order to reach the

gas temperature as high as 800–900 8C at the coil outlet. The required energy is supplied by a thermal

cracking furnace. In fact, hydrocarbon feed is mixed with steam in the convection section of the furnace

M.E. Masoumi et al. / Energy 31 (2006) 516–527518

and the temperature of the mixture is raised to the cracking temperature. The mixture is then fed into the

radiant section of the furnace, where the temperature of the gas mixture increases rapidly to the desired

cracking temperature. In the radiant section, the hydrocarbon is cracked to a combination of olefins,

aromatics, pyrolysis fuel oil and other heavier hydrocarbons. Upon leaving the radiant section of the

furnace the cracked gas is cooled rapidly to stop the undesired reactions [1].

Coil Outlet Temperature (COT) is an important parameter affecting yields of ethylene production

thus, should be controlled. Since, furnaces are the first step of the production process, the entire process

is affected by disturbances that occur due to the furnace operation. The heat input to the furnace reactor is

manipulated and controlled by measuring the cracked gas temperature in the coil outlet (COT). This loop

is one of the most important loops in the control of thermal cracking furnaces.

A pilot plant is designed and set up to investigate the effects of different parameters on the products

yields. A computer program simulates the parameters of the furnace before running the pilot plant. In

this work, the effect of furnace parameters on the reactor yields is studied.

2. Pilot plant

The schematic diagram of the pilot plant is shown in Fig. 1. The reactor feed contains at least two

streams: the hydrocarbon and the dilution steam. Liquid hydrocarbons and water, used to produce

dilution steam, are fed by means of two dosing pumps. The feed flow rates and S/HC (steam to

hydrocarbon) ratio can be altered between 5–15 g/min and 0.3–0.8, respectively.

The furnace preheaters consist of two electrical coils for heating water and hydrocarbon feeds. The

reaction section is divided into eight zones, which can be heated independently to achieve the desired

temperature profile. The reactor is a tube of 1 m lengths, and 0.01 inside diameter made of Inconel (alloy

600 HS 2). Temperature of different parts is measured by eight thermocouples as shown in Fig. 1.

After cooling, the reactor effluent to the appropriate temperature in a double pipe heat exchanger,

liquids and tars are separated from the cracked gas. A fraction of the product gas is then withdrawn for

the on-line analysis via a gas chromatograph, while the rest is sent directly to the flare. The system is

connected to a personal computer through the interface cards for monitoring and control purposes.

3. Static simulation

The heart of an ethylene plant is the cracking furnace. For finding an optimal operating strategy, it is

necessary to investigate the influences of the operating parameters, which can be satisfactorily calculated

through the rigorous modeling. Rao et al. [2] simulated the reactor and the radiant box simultaneously.

Several packages were developed by other researchers [3–6].

In almost all of the ethylene plants in Europe, naphtha is the most widely used feed material for the

thermal cracking furnaces. Naphtha is a mixture of complex hydrocarbon materials, which ranges mostly

from C5 to C10 paraffins. In the reactor, numerous cracking reactions occur to produce ethylene and

propylene. The reaction mechanism of thermal cracking of hydrocarbons is free-radical chain reaction

[7]. In this work, a free-radical reaction set with the kinetic parameters for 90 species and 543 reactions

has been used.

LIQUIDFEED

BALANCE PUMP

TT TT

TT TT

WATER

BALANCE PUMP

TT

TT

WATER

PRE HEA TER

FEED

PRE HEA TER

CE

NA

UR

FN

EZ

O8

EX

CH

AN

GE

R

EXCHANGER

WATERCONDENSATE

H.C.CONDENSATE

GASCOUNTOR

GASEOUS FEED

VENT

AIR FILTER

COMPRESSOR

AIR FOR DECOKING

TT

TT

TT

TT

TT

TT

TT

TT

TT

TT

TT

TT

G.C.

FLARE

8

7

6

5

4

3

2

11

2

3

4

6

7

8

5

INTERFACE CARD

INPUTSIGNALS

OUTPUTSIGNALS

TT

SAFETYVALVE

WTWT

GasFlowmeter

Fig. 1. Schematic diagram of the thermal cracking pilot plant.

M.E. Masoumi et al. / Energy 31 (2006) 516–527 519

3.1. Reactor model

The geometry of the model configuration for the reactor tube is shown in Fig. 2. The following

assumptions have been considered for the mathematical model:

1.

One dimensional flow

2.

Plug flow and laminar regime

3.

Radial concentration gradients and axial dispersion are negligible

4.

Ideal gas behavior

5.

Inertness of the steam diluents in feed

6.

No hydrodynamic or thermal entrance region effects

7.

Quasi steady-state in Coke deposition model.

In this form, the coking rate model is pseudo steady-state with respect to time. In other words, coking

rate is assumed to be constant over a time step and the effect of coke formation through coking equation

Fig. 2. Differential element of a cracking coil.

M.E. Masoumi et al. / Energy 31 (2006) 516–527520

is updated explicitly at the end of each time step. This pseudo steady-state assumption would be indeed

valid as long as the coke formation rate does not change appreciably over a sufficiently small time step.

The set of continuity equations for the various process gas species is solved simultaneously with the

energy, momentum and the coking rate equations required [11]. These equations are as follows:

Mass balance:

dFj

dzZ

Xi

sijrri

!pd2

t

4(1)

Energy balance:

Xj

Fjcpj

dT

dzhQðzÞpdt C

pd2t

4

Xi

rriðKDHÞi (2)

Momentum balance:

1

MmPt

KPt

hG2RT

� �dpt

dzZ

d

dz

1

Mm

� �C

1

Mm

1

T

dT

dzCFr

� �(3)

With the friction factor:

Fr Z 0:092ReK0:2

dt

Cz

pRb

(4)

And for the tube bends as:

z Z 0:7 C0:35L

900

� �0:051 C0:19

dt

Rb

� �(5)

where Rb and L are tube bend radius and bend angle, respectively. Since, the coking is slow, quasi

steady-state conditions may be assumed, so that, we can write the rate of coke formation:

vC

vtZ ðdt K2tcÞ

arc

rc

(6)

Table 1

Specification of naphtha feed (wt%)

Carbon no. n-Paraffins Iso-paraffins Naphthenes Aromatics

4 0.22 2.67 – –

5 25.22 17.94 4.19 –

6 14.88 23.41 2.82 2.0

7 1.67 3.27 – 0.97

8 – 0.57 – 0.2

Total 41.99 47.83 7.01 3.17

M.E. Masoumi et al. / Energy 31 (2006) 516–527 521

Using the mathematical model, the amount of coke deposited on the internal wall of the reactor tubes

has been calculated with a limiting value for tube skin temperature (1100 8C). The governing mass,

energy, and momentum balance equations for the cracking coil constitute the two-point boundary value

problem, which is highly stiff. The implicit Euler method [8] is used for solving the equations. The rate

of coke formation has been taken into account [9–11]. The tuning parameters, such as overall heat

transfer coefficient and coking rate factor can be adjusted to make the model prediction close to the

actual data [12]. The developed software receives the feed specifications and provides products yield and

gas temperature profile. Details of the static simulation were published recently by Masoumi et al. [13].

3.2. Simulation results

Specifications of naphtha feed and operating conditions are given in Tables 1 and 2, respectively.

After running, the program under these conditions, furnace temperature, gas temperature and product

yield profiles are obtained along the reactor. Different temperature profiles were applied to the reactor

and the simulation results at the reactor outlet are presented in Table 3. Fig. 2 shows that increasing COT

will increase the ethylene yield while decreasing the propylene yield. The gas temperature profiles

resulted from the simulation are illustrated in Fig. 3.

3.3. Optimal reactor temperature

During a production period, coke is formed and deposited on the inner tube surface of the cracking

coil. The coke formation reduces the olefin selectivity mainly due to the pressure drop increase in the

cracking coil. The coke formation also leads to excitation of one or more of the furnace operational

constraints at the end of production period. Coke is burned-off with steam and air during a 1–4 days

Table 2

Operating variables

Inlet temperature (8C) 600

Inlet pressure (atm. abs.) 3

Feed flow rate (g/min) 10

Inlet pressure (atm. abs.) 3

COT (8C) 830–70

S/HC ratio 0.7

Table 3

Static simulation/experimental results

COT (8C) C2H4 yield (wt%) C3H6 yield (wt%) Furnace temp. (8C)

800 –/19.76 –/18.32 –870

810 –/21.15 –/18.74 –/880

820 –/21.42 –/18.73 –/890

830 26.79/22.00 11.80/18.63 913.0/900

840 28.81/22.61 12.07/18.77 924.5/910

850 30.66/23.42 12.17/18.63 935.5/920

860 32.15/24.02 12.10/18.59 945.5/930

870 33.43/24.83 11.86/18.52 954.0/940

880 34.40/23.97 11.51/18.35 962.0/950

890 35.18/26.43 11.02/17.55 970.0/960

900 35.68/27.72 10.48/16.99 977.0/970

M.E. Masoumi et al. / Energy 31 (2006) 516–527522

decoking period. The decoking operation has to be done every 30–80 days depending on furnace design

and operating philosophy [14,15].

While the reactor is in production, the thickness of the carbon deposit increases monotonically. At the

same time, the instantaneous net earning from the operation decreases. For chemical and petrochemical

plants, it seems that maximizing the operating profit would always give a satisfactory solution. The

objective function must combine the favorable effect of higher valuable product yield with the negative

effect of the coking rate on the profit.

Increasing the reactor gas temperature increases the ethylene yield and consequently the income. On

the other hand, increasing temperature will also increase the rate of coke deposition as shown in Fig. 4

which results in higher cost. By maximizing the defined objective function using dynamic programming

technique, the optimal temperature profile along the reactor is obtained. The objective function proposed

by Towfighi [16] is used as follows

PI Z Income Kcost

Income Z Ethylene mass flow rate � ethylene price � yearly operating time;

Cost Z L � ethylene mass flow rate � ethylene price � yearly decoking period;

10

20

30

40

800 820 840 860 880 900

Yield (wt%)

C2H4, Ex p.C2H4, Sim.C2H6, Ex p.C2H6, Sim.

Coil outlet Temperature (C)

Fig. 3. Effects of COT on the product yields.

600

700

800

900

0 0.2 0.4 0.6 0.8 1Reactor Length (m)

Gas Temperature (C)

900˚C

830˚C

Fig. 4. Gas temperature profiles along the reactor tube at different COT’s.

M.E. Masoumi et al. / Energy 31 (2006) 516–527 523

The labor and utility costs necessary for decoking, are expressed as a fraction, L, of term representing

the benefit lost due to the interruptions. The iterative dynamic programming procedure using systematic

region contraction is used for the optimization. The optimization criteria are the maximization of benefit,

since increasing COT, increase the coke and ethylene production. Increasing of ethylene production,

increases the income, but subsequently increases coke production, that results increase of decoking cost.

The details of the optimization procedure are discussed in [13]. The optimal gas temperature profile

obtained through simulation is shown in Fig. 5. As can be seen, the optimal COT is 877.34 8C. At this

condition the ethylene yield in the reactor effluent, is 33.737%.

4. Dynamic simulation

In order to investigate the performance of a control scheme, it is necessary to have a dynamic model

of the process. By applying conservation laws, such a model can be obtained. For simulating the system,

the unsteady mass and energy balances must be solved simultaneously with pressure drop equation. It is

difficult to measure the gas temperature inside the reactor due to the coke deposition. If the desired

furnace wall temperature corresponding to desired reactor temperature is known, it would be much

easier to measure and control the furnace wall temperature than the reactor temperature. Therefore, if

0

0.004

0.008

0.012

0.016

830 840 850 860 870 880 890 900Coil outlet temperature (C)

Coke deposition (gr/min)

Fig. 5. Effect of COT on the coke deposition.

M.E. Masoumi et al. / Energy 31 (2006) 516–527524

the gas temperature in the reactor is known then furnace wall temperature can be obtained by back

calculation. Using the optimal temperature profile obtained in Section 3, furnace wall temperature is

calculated. Furnace is divided into eight thermal zones. The desired optimal furnace wall temperature

can be approximated by eight step functions. Electrical heaters are used to provide necessary heat. The

transfer function between electrical voltage of element and related temperature of each zone is assumed

a first order plus lag dynamic and it’s parameters are obtained experimentally as: KZ100, TZ5,

TdZ2 min. Detail of the dynamic simulation are presented by Shahroki and Nedjati [17].

4.1. Furnace wall temperature control

As mentioned, the furnace wall temperature can be obtained from the optimal reactor gas temperature

using by-back calculation. Discretization of this profile provides the desired temperature of each zone.

For temperature control of each zone, a PI controller can be used. The controller parameters are

calculated based on open loop response and minimizing the integral of absolute value of the error (IAE).

In this research controller parameters, Kc and TI are set to 0.1 and 0.004, respectively.

4.2. Reactor temperature control

It is almost impossible to measure the gas temperature inside the reactor due to the coke deposition. In

this case, the gas temperature measurement is available at the end of each zone. The set point of each

controller is the temperature at the outlet of corresponding zone. To evaluate the performance of control

system, the reactor temperature is changed and the controllers activate one at a time. In this case the

temperature overshoot is high. To get a better transient response, it is proposed to activate the first zone

controller and freeze the output of the other controllers. When the temperature error in the first zone

becomes less than a predetermined value, the second controller is activated and so on. In this case the

temperature overshoot is considerably smaller than the previous case. This control strategy cannot be

applied to the pilot plant due to the impossibility of the temperature measurement in the end of each

zone. Therefore, only simulation studies have been done and the results are published by Shahrokhi and

Nedjati [17].

4.3. COT control

One of the main objectives of this work is COT control. Therefore, furnace wall temperature will be

constant in all zones and furnace acts as a single zone furnace. The transfer function between electrical

voltage of element and COT is assumed a second order plus lag dynamic and it’s parameters are obtained

experimentally as: KZ100, TZ5, TdZ2 min. A PID controller, which was tuned by open loop

response, is used for system controlling. Controller parameters are 0.1 for proportional gain, 0.004 min

for integral time and 0.0001 for derivative time.

4.4. Ethylene yield control

Control of ethylene yield can be achieved by measuring of ethylene yield directly in coil outlet or by

measuring of COT and then evaluation of ethylene yield from COT (inferential control). If there is a

relation between COT and ethylene yield, or system is observable, then inferential control is practical.

600

700

800

900

0 0.2 0.4 0.6 0.8 1

Reactor Length (m)

Gas temperature (C)

Fig. 6. Optimal gas temperature profile along the reactor.

M.E. Masoumi et al. / Energy 31 (2006) 516–527 525

In this work, the GC run time for cracked gas analysis is about 35 min that makes the on-line ethylene

yield control impossible. Therefore, this control strategy is eliminated from this work.

5. Experimental studies

Experiments are performed with typical naphtha as feed, which was supplied from Arak

Petrochemical Company (APC). The feed flow rates and S/HC ratio are 10 g/min and 0.7, respectively.

Preheaters and the furnace temperatures are set to desired values by using PID digital controllers. To set

the XOT to 600 8C, water and hydrocarbon preheater set points are set at 750 8C. By changing the

furnace set point, different COT values will be achieved. This enables different temperature profiles to be

applied to the reactor.

While running the pilot under these conditions, the effluent cracked gas is sent to the GC for the

analysis. The experimental results of this investigation are shown in Table 3 and Figs. 3–8. As can be

seen from Fig. 2, increasing COT, increases the ethylene and at the same time decreases the propylene

yield. XOT, COT, furnace temperature, and furnace set point are given in Figs. 7 and 8. As can be seen

800

850

900

950

1000

0 1 2 3 4 5 6 7 8 9

setpointfurnace temp.

Time (hr)

Temperature (C)

Fig. 7. Temperature control of zone 8.

500

600

700

800

900

1000

0 1 2 3 4 5 6 7 8 9

XOTCOT

Temperature (C)

Time (hr)

Fig. 8. Reactor inlet (XOT) and COT temperature diagrams.

M.E. Masoumi et al. / Energy 31 (2006) 516–527526

from the figures the performance of control system in keeping constant XOT and tracking the set point

by changing COT and furnace wall temperature is fairly well. On the other hand, results of Fig. 3 show

that increasing COT, increases ethylene yield while decreases propylene yield which is confirmed by

the literature data. The XOT is approximately constant about 600 8C. Furnace temperature tracks furnace

set points with good competition.

6. Conclusions

A computer program for simulating the behavior of a thermal cracking pilot is developed based

on a kinetic model. This kinetic model consists of 543 radical reactions. The developed software is

used to simulate the static behavior of the process and find the effects of different parameters on

product yields. Simulation results indicate that increasing COT increases the ethylene yield and the

rate of coke deposition. A thermal cracking pilot plant including eight zoned electrical furnace was

designed and set up to investigate the influence of the furnace parameters on the product yields.

Finally the new developed optimal temperature profile for naphtha cracking was obtained in the

range of COT between 800 and 900 8C which have not been reported before in the literature.

Simulation results were tested experimentally by the pilot. Comparison of the simulation and

experimental results show similar trends. The discrepancies between the simulation and experimental

results are due to the nonlinear and unknown furnace dynamic model, and some measurement

experimental errors.

Acknowledgements

The authors are grateful to Dr M. Pishvaei and Mr A. Nedjati for the preparation of the control

software. The financial support by APC is also gratefully acknowledged.

M.E. Masoumi et al. / Energy 31 (2006) 516–527 527

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