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Ind. Eng. Chem. Res. 2006, 45, 3574-3582
PROCESS DESIGN AND CONTROL Modeling and Control of a Naphtha Thermal Cracking Pilot Plant Miresmaeil Masoumi,† Mohammad Shahrokhi,*,‡ Mojtaba Sadrameli,† and Jafar Towfighi† Department of Chemical Engineering, Tarbiat Modarres UniVersity, P.O. Box 14155-4838, Tehran, Iran, and Department of Chemical and Petroleum Engineering, Sharif UniVersity of Technology, P.O. Box 11365-9465, Tehran, Iran
A computer-controlled pilot plant has been constructed to study the dynamical behavior and control of the thermal cracking furnace. The governing equations that describe the furnace dynamics are presented, and, based on these equations and a kinetic model, software that simulates the steady-state behavior of the system has been developed. The furnace is divided into eight zones that can be heated independently, and, therefore, any desired temperature profile can be applied. The variables to be measured are the furnace zone temperature, coil outlet temperature (COT), and product yield. Two different control strategies (namely, COT control and furnace wall temperature control) are applied using digital proportional-integral-differential (PID) controllers. The results show that, by applying a predetermined temperature profile along the furnace wall in the wall temperature control strategy, the same yield that is obtained by COT control can be achieved with the lower maximum furnace wall temperature. Finally, based on a performance index, the optimal temperature profile has been obtained and it is applied to the pilot through the designed control system. 1. Introduction Ethylene is one of the most important industrially produced organic materials. Current worldwide ethylene production is ∼180 billion pounds per year, and it is projected to increase at a rapid pace. Feedstock to ethylene plants ranges from gaseous ethane/propane to heavy naphtha and vacuum gas oils. The heart of an ethylene plant with a huge economic impact is the cracking furnace. The essential factor of the optimal design is the precise prediction of yield and furnace performance. Control systems are designed to achieve many objectives, including safety, good product quality, and high profit. Because the control design determines the controlled and manipulated variables, it affects the steady-state operating conditions that are encountered as disturbances occur. Therefore, the control design can have a profound effect on the profit. Several processes may be used in ethylene production; however, the process that is favored in modern practice involves the cracking reactions (this process is also called steam cracking or pyrolysis). Hydrocarbon feedstock mixed with process steam is introduced into tubular reactors (cracking coils) with short residence times and high temperatures. Steam is used to increase the olefin selectivity and reduce the coke formation by decreasing the hydrocarbon partial pressure. The paraffinic feedstock is thermally cracked into mainly olefins, aromatics, methane, and hydrogen. The homogeneous cracking reactions are endothermic and require energy input to reach gas temperatures as high as 800-900 °C at the coil outlet. The required energy is supplied by a thermal cracking furnace. Because furnaces are the first step in the production process, * To whom correspondence should be addressed. Tel.: +98-21-66 16 54 19. Fax: +98-21-66 02 28 53. E-mail address: shahrokhi@ sharif.edu. † Department of Chemical Engineering, Tarbiat Modarres University. ‡ Department of Chemical and Petroleum Engineering, Sharif University of Technology.
disturbances that occur due to the furnace operation will affect the entire process. The coil outlet temperature (COT) is an important parameter that affects the yield of ethylene production, and, therefore, it must be controlled. COT is controlled by measuring the cracked gas temperature at the coil outlet and manipulating the heat input to the furnace. This loop is the most important loop in controlling the thermal cracking furnaces. It has been observed that the temperature profile in the reactor also has significant effects on the coke formation and the product yield. A temperature profile should be applied along the reactor to minimize the coke formation and obtain an appropriate product yield. This matter has already been treated in the literature where the optimal temperature trajectory has been considered. Such optimal profiles have been obtained for ethane, propane, and naphtha thermal cracking.1,2 The main output variable of the cracking furnace is the product composition, which must be measured at regular intervals. If this composition deviates from a prescribed value, control action must be taken. Therefore, the product yield control is another objective in thermal cracking furnaces. Because the analysis of the products via gas chromatography (GC) may take ∼30-40 min, the control performance of the cracking reactor may be poor. The inferential control strategy could be very useful for this situation. In this work, the dynamic behavior and control of thermal cracking reactions are studied using a pilot plant. The paper is organized as follows. First, the thermal cracking pilot plant is described. The governing equations that describe the furnace dynamics then are discussed. Next, the different control strategies are explained, and, finally, the experimental results are presented. 2. Thermal Cracking Pilot Plant A schematic diagram of the pilot plant is shown in Figure 1. The reactor feed is supplied from two separate streams: the
10.1021/ie050630f CCC: $33.50 © 2006 American Chemical Society Published on Web 04/12/2006
Ind. Eng. Chem. Res., Vol. 45, No. 10, 2006 3575
Figure 1. Schematic diagram of the pilot plant. Table 1. Basic Data of the Pilot Plant section
length (cm)
diameter (cm)
number of zones
number of thermocouples
power (kW)
feed preheater water preheater furnace reactor
100 100 100 100
10 10 10 1
1 1 8
1 1 8 2
13.2 13.2 17.6
dowsing pumps
Qmax ) 3 L/h, Pmax ) 10 bar
0.1
hydrocarbon and the dilution steam. Liquid hydrocarbons and water are fed into the preheaters by means of two dosing pumps. The feed flow rate and steam to hydrocarbon (S/HC) ratio can vary in the range of 5-15 g/min and 0.3-0.8, respectively. There are two electrical preheaters for heating water and hydrocarbon feeds. The reaction section is divided into eight zones, which can be heated independently to apply the desired temperature profile. The reactor is a tube that is 1 m long, composed of Inconel (alloy 600 HS 2), and has an internal diameter of 10 mm. The temperatures of different sections are measured as shown in Figure 1. Detail specifications of the pilot plant are presented in Table 1. The reactor cross section is shown in Figure 2. After the reactor effluents are cooled to the appropriate temperature in a double-pipe heat exchanger, liquids and tars are separated. A fraction of the product gas is then withdrawn for the analysis via GC, whereas the remainder is sent directly to the flare. The system is connected to a computer through interface cards for monitoring and control purposes. For on-line monitoring, control and data logging of the pilot plant a software is developed. Trends of all variables can be shown and saved. The proportional-integral-differential (PID) or user-defined control algorithm can be implemented.
Figure 2. Furnace zones and the cross section of each zone.
3. Furnace Dynamic Model For control purposes, modeling of the cracking unit can be divided into two parts, namely, chemical and thermal.3 The chemical part describes the cracking reactions and relates the concentrations of products at the reactor outlet to the temperature and pressure profiles along the coil. The thermal part describes the relationship between the temperature profile along the coil and the heat input to the furnace.
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A special feature of the cracking furnace is that the product residence time in the coil is short (typically 1000 s).4 Therefore, a static relationship between temperature and concentration can be considered. In the following, the furnace energy balance and the kinetic model are discussed. 3.1. Energy Balance. To model the thermal part of the system, the energy balance equation is used for the furnace wall, the reactor tube, and the gas inside the reactor as follows. Assuming the uniform temperature for each furnace zone, applying the energy balance yields the following equations. 3.1.1. Energy Balance on the Furnace Wall. The energy balance on the furnace wall can be described as
dTwin(t)
(mCp)wn
dt
πdt2 ∂Cin 4
where the subscript n denotes the furnace zone number, En(t - τdn) the electrical heat input for the nth zone, and QLn(t) the heat loss for the nth zone. The term QLn(t) is given by the relation
2πLn ln(R5/R4) ln(R6/R5) 1 + + kw kis R6ham
(mCp)tn
dt
πdt2
[ () Ptn
∂Fin
4R FTnTgn ∂t
[Tton(t) - Tgn(t)] (4) ln(R3/R2) ln(R2/R1) 1 + + kt kc R1hgn
πdt2∆zn dTgn(t) dt
∆zn
) QCn(t)
Nc
FiCpiTg (t)|z ∑ i)1
n + ∆zn
n
+
Nc
+
FiCpiTg (t)|z ∑ i)1
n
n
Ln
πdt2∆zn Nr 4
rj(-∆Hj)|T ∑ j)1
(t) (5)
gn
(FCp)gn
∂t
)
RTgn
[
4 QCn(t) πdt2
Ln
Nc
+
FiCpi ∑ i)1
( )] ∂Tgn(t)
+
∂zn
Nr
rj(-∆Hj)|T ∑ j)1
)
(t) (6)
gn
3.2. Kinetic Model. Mass balance and pressure drop equations are required to solve eq 6. Numerous cracking reactions occur to produce ethylene and propylene. The reac-
(7)
+ Fi n
dPtn dzn
]
∂t
)
dzn
+
FinPtn
(8)
FTnRTgn
)-
∂Fin
+
(
-
Sjirj ∑ j)1 (9)
1 1 dTgn + Fr Mmn Tgn dzn
1
πdt2 Nr 4
∂zn
)
(10)
Pt n γG2RTgn
where
Fr )
0.092Re-0.2 dt
(11)
Nc Using the definition Mmn ) ∑i)1 yinMin, eq 11 can be written as
dPtn
{
)
dzn 1
Nc
Mi ∑ 2 i)1
FTn
(
n
dFin
FTn
dzn
Mm2
Nc
)
dFin
∑ i)1 dz
- Fin
n
+
(
1
(
1 dTgn
Mmn Tgn dzn 1
MmnPtn
where ∆Hj is the heat of reaction of the jth reaction. Dividing eq 5 by ∆zn and allowing ∆znf 0, we have
∂Tgn(t)
RTgn
yinPtn
MmnPtn
2πLn
4
)
d(1/Mmn)
3.1.3. Energy Balance on Gas inside the Reactor. The energy balance on the gas inside the reactor yields
(FCp)gn
Pin
∂(Ptn/FTnTgn)
where the heat transfer through conduction in the nth zone (QCn(t)) is given by the relation
QCn(t) )
Sjirj ∑ j)1
4
Momentum balance:
[Twin(t) - Tam] (2)
) σFAwn[Twin4(t) - Tton4(t)] - QCn(t) (3)
+
∂zn
Substituting eq 8 into eq 7 yields
3.1.2. Energy Balance on the Tube Wall. The energy balance on the tube wall can be described by the equation
dTton(t)
)-
πdt2 Nr
Using the ideal gas law, we have
) En(t - τdn) (for n ) 1, ..., 8) (1)
∂Fin
∂t
Cin )
σFAwn[Twin4(t) - Tton4(t)] - QLn(t)
QLn(t) )
tion mechanism of thermal cracking is a free-radical chain reaction. Several kinetic models have been proposed in the literature, and based on these models, different software has been developed.5-11 The governing mass and momentum balance equations are as follows. Mass balance:
-
+ Fr
Ptn γG2RTgn
}
)
)
÷
(12)
To obtain the furnace dynamic, eqs 1, 3, 6, 9, and 12 should be solved simultaneously. Several attempts have been made to model the system behavior. In one research study, the chemical part of the model for a steam gas reformer has been solved and the thermal part approximated by a second-order plus lag dynamic.12 In other research, by assuming a lump parameter system and linearizing the endothermic reaction dynamics around the reference temperature, eqs 1, 3, and 6 are simplified and a first-order plus lag model is obtained between the gas temperature and heat input to the system.13 To model the propane thermal cracking, a first-order plus lag dynamic also is considered for the thermal part and the governing equations
Ind. Eng. Chem. Res., Vol. 45, No. 10, 2006 3577
for the chemical part have been solved.2 For control application, usually equations that describe the thermal part can be approximated by a first-order plus lag dynamic. Because of the short residence time of the chemical part (
