TWO SIMULATION ALGORITHMS FOR INDUSTERIAL CRACKING …58).pdf · IChEC9 Part 6: Modelling and...

Abstract

Keywords: Simulation algorithms, cracking furnace, Coke formation, Ethylene yield.

TWO SIMULATION ALGORITHMS FOR

INDUSTERIAL CRACKING FORNACES

Babak Maghbooli* and Hossein Amani

Department of Chemical Engineering, Arak University, Arak, Iran [email protected]

The Pyrolysis of naphtha and other hydro carbons, witch is of primary importance in the manufacture of olefins, is always accompanied by formation of coke. This article suggests two simulation procedures that contain the information about coke formation and ethylene yield as a function of time. One is an old and time consuming but reliable algorithm and the other one is a fast simulation method we compare this two algorithms and discuss about their benefits.

9th Iranian Chemical Engineering Congress

Iran University of Science and Technology

23-25 November, 2004

mailto:[email protected]

IChEC9

Part 6: Modelling and Simulation

9th Iranian Chemical Engineering Congress (IChEC9), Iran University of Science and Technology (IUST), 23-25 Nov., 2004

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Old simulation procedure (Hendricks Method) Simulation need. Thermal cracking of hydrocarbons to olefins is an endothermal process accompanied by the formation of coke on the inner surface of the cracking coils suspended in a pyrolysis furnace. Fouling of the cracking coils has major consequences on the operation of the furnace. First of all, the coke layer reduces the heat transfer from the furnace to the process gas, since coke is a very poor heat conductor. If the feed conversion is to be maintained, a higher heat input to the furnace is required, resulting in a rise of the external tube skin temperature and a decrease of the thermal efficiency of the furnace. The tube skin temperature, gradually increasing in time, reaches a maximum value imposed by the tube metallurgy. The cracking run has to be stopped to decoke the reactor tubes by controlled combustion of the coke layer with a steam/air mixture. Second, the growing coke layer on the internal tube skin reduces the cross section of the reactor tube. With a constant feed rate to the reactor coil, the pressure drop over the reactor tube increases. Since the process gas outlet pressure is normally imposed, the feed inlet pressure increases during the run length of the furnace, and this is detrimental for the ethylene selectivity. Too high an inlet pressure can also cause the cracking run to be stopped for decoking the tubes. Reactor geometry, operating conditions, and feedstock composition deter-mine which of the two described effects causes the production cycle to be stopped. Decoking of the reactor tubes involves a significant loss in production capacity and should be limited to a minimum. This can only be obtained by reducing the rate of coke formation. The coking rate is determined by the interface temperature between the process gas and the coke layer (Sundaram and Froment, 1979). Limiting the interface temperature results in lower coking rates and a longer run length of the furnace. Simulation results have shown that significant circumferential nonuniformities in heat flux, tube skin, and coking rate profiles exist, due to the presence of "front" sides and "shadow" sides on the tubes (Heynderickx and Froment, 1996). It was also shown that circumferential coking rates can be reduced up to 30gc by replacing cylindrical tubes by tubes with an elliptical cross section. Model Equations and Simulation Procedure Reactor Model. The set of continuity equations for the various species is solved simultaneously with the energy equation and the pressure drop equation (Froment and Bischoff, 1990):

with the friction factor (Knutzen and Katz, 1958)

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for the straight parts of the reactor coils and

for the tube bends, with (Nekrasov, 1969)

For the tubes of elliptical cross section, the tube diameter dt is replaced by the equivalent (hydraulic) tube diameter de:

A detailed radical reaction scheme is combined with a one-dimensional plug-flow model to simulate the cracking reactions in the reactor coil. Reynolds numbers on the order of 250 000 are calculated in the reactor tubes. The turbulence wipes out temperature profiles in the process gas over the cross section of the reactor tubes. The kinetic scheme is based on a complete reaction network for the decomposition of the ethane feed. The CRACKSIM reaction network contains 1054 reactions: 56 initiation reactions, 572 H-abstractions, 126 radical additions, 126 decomposition reactions, 6 isomerization reactions, 56 termination reactions, and a number of molecular Diels-Alder cyclizations (Sundaram and Froment, 1978; Willems and Froment, 1988a, b). Coke formation at any time during the cracking run and at any position in the reactor tube is calculated from the continuity equation (Plehiers et al., 1990):

Rate expressions Rc for the coke formation in the thermal cracking of ethane and propane have been derived by Sundaram and Froment (1979) and Sundaram et al. (1981). A number of coke precursors were found to contribute to the formation of coke:

Furnace Model. The furnace model is based upon the zone method of Hottel and Sarofim (1967). The furnace wall, the tube skin, and the flue gas volume are divided into a number of isothermal elements with uniform properties. For each of these elements, named zones, the energy balance is set up, taking into account the contributions of convective, conductive, and radiative heat transfer.

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The contributions of radiative transfer are obtained through Monte Carlo simulation (Plehiers and Froment, 1989), calculating the view factors between the different zones in the furnace. From these view factors, the total exchange areas ZiZj between the zones Zi and Zj in the furnace are determined. The total exchange area ZiZj is the amount of radiative energy emitted by the zone Zi in the direction of the zone Zj, divided by the blackbody emissive power of the zone Zi. The emissive power of a blackbody with temperature T, is calculated from the Stefan-Boltzmann law:

The determination of ZiZj is discussed in detail by Rao et al. (1988) and by Plehiers and Froment (1989). The set of energy balances for the furnace can be written as

where Qi represents the nonradiative heat flux emitted by the zone Zi with area Ai. Solving this set of energy equations yields the heat flux and temperature profiles n the furnace. To calculate the circumferential temperature distribution in the tube wall, the tubes are discretized along the tube perimeter and over the tube skin. By constructing and solving the energy balance for each element in the tube skin, circumferential heat flux and temperature profiles are calculated in the tube skin. The form of these energy balances for the zones in the tube skin is discussed by Heynderickx et al. (.1992). They are obtained by discretizing the conduction equation for each zone in the reactor tube slain. Accounting for the appropriate boundary conditions:

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Simulation Procedure A simplified flowchart of the iterative calculation scheme is given in Figure 1. Predicting the run length of the cracking furnace requires the simultaneous solution of the set of differential and algebraic equations (1)-(3), (8), (11), and (12). By assuming an incremental pseudo steady state for thee cracking reactions (coking reactions are much slower than cracking reactions), the run time of the cracking furnace can be augmented in a stepwise manner (outer loop in Figure 1). For each time increment a coupled furnace and reactor simulation has to be performed by simultaneously solving the set of equations (1)-(3), (11), and (12). For that purpose, a double iterative scheme is used. Starting from initial estimates for temperatures and fluxes, the energy balances (11) are constructed and solved. This provides better estimates for the zone temperatures. From the tube skin and process gas temperatures, new flux estimates are calculated. Based on these new fluxes, the process gas composition, temperature, and pressure are calculated from equations (1)-(3). By solving (12), new zone temperatures are obtained which are compared to the previously obtained values. The cycle is repeated until convergence is reached for the time increment. Time increments of 60 h of furnace run time were found to be sufficiently small to justify pseudo steady state

A total of 20-28 time steps were taken for each of the three run length simulations that have been performed. The three run length simulations reported here each required around 8 h of CPU time on an IBM/RS6000/375 computer For each run length simulation, the crossover temperature of the process gas was kept constant at a value of 600 °C. However, the process gas inlet temperature is determined by the heat transfer in the convection section of the furnace, and thus by the flue gas outlet temperature in the radiation section of the furnace. The flue gas outlet temperature differs for both coil types and rises with time. Accounting for these variations in crossover temperature requires the calculation of the convection section of the furnace and would introduce an additional iteration loop in the calculations. Simulation time would be augmented by a factor of 2, without adding meaningful precision to the calculation results.

Figure 1. Flow diagram of the calculations.

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Figure 2. Top view of the ethane furnace

Furnace Description The main dimensions and operating conditions of the ethane cracking furnace are summarized in Table 1. Two reactor coils, with 8 passes each, are suspended in the furnace which is heated by means of 64 radiation burners positioned in 8 rows of 4 burners in the front and in the rear wall of the furnace. A top and front view of the furnace is shown in Figures 2 and 3. The internal cross section of the elliptical tubes was taken to be equal to that of the circular tube, allowing for hydrocarbon feed and steam rates identical for the reactor coils of both types, and thus for identical furnace capacity. The process gas pressure drop in both tube types can easily be compared (eq 3). The external major axis-of the elliptical tube was taken to exceed the external diameter of the circular tube by 40%. Based on the results of Heynderickx and Froment (1996), simulation results for elliptical tubes of lower eccentricity can be expected to vary between the simulation results presented for circular and elliptical tubes in this paper. The dimensions of both tube types are compared in Table 2. The perimeters of the elliptical tubes were determined by numerical integration of the elliptical integral of the second kind:

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Table 1.Furnace dimensions & operating conditions

Figure 3. Front view of the ethane furnace.

Table 2. Tube Dimensions

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In this expression, ф represents the angle of the parameter equation of the ellipse (Figure 4)

with a and b the semimajor and semiminor axes of the ellipse. For identical cross sections of both tube types, the perimeter of the elliptical tube exceeds that of the circular tube by 9%. Since the surface-to-volume ratio of the elliptical tube is larger, this results in higher friction losses for the process gas. Two run length simulations for furnaces with elliptical tubes were performed. For the first simulation the coil length was taken equal to that of the coil with circular tubes. This result in a 9% rise of the total heat-exchanging surface: For the second simulation, the length of the coil with elliptical tubes was reduced to obtain a total heat exchanging surface equal to that of the coil with circular tubes. The center-to-center distance (pitch) between the tubes was the same for both tube types in order to retain the furnace length. For the elliptical coil of reduced length, the furnace height is reduced by 1 m. This implies an 8% reduction of the furnace volume. The furnace was divided into zones by means of four planes parallel to the furnace bottom plate. The five axial zones on the fourth, fifth, and sixth pass of the reactor coil through the furnace were circumferentially divided into 16 zones of equal area, as presented in Figure 4 for the tube with elliptical cross section. Accounting for symmetry in the furnace, a total of 162 zones are obtained: 145 (external) tube skin zones, 12 furnace wall zones, and 5 flue gas volume zones.

Figure 4. Circumferential division of the tube.

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Part 2: A fast simulation algorithm A new simulation algorithm for industrial cracking furnaces significantly increases simulation speed with satisfactory accuracy. The energy-balance equations of cracking furnaces were transformed to the temperature differential equation by directly solving a quartic equation of the tube wall temperature. One set of new continuity equations for various reactants, temperature and pressure was formed. The new algorithm greatly reduces the number of complex iterations during the actual simulation, and simulation speed is fast enough to accomplish a periodic simulation of a cracking furnace in just a few minutes with a personal computer (PC). An industrial cracking furnace demonstrates this. Fast Algorithm need. Improving operation of steam cracking furnaces by implementing real-time optimization (RTO) or online dynamic optimization is a popular trend to increase economic benefits of an ethylene plant. To implement these advanced technologies, a fast and accurate simulation for the entire periodic furnace operation is necessary. To simulate periodic furnace operation, the incremental pseudo steady state for the run time augmented in a stepwise manner is usually assumed because coking reactions are much slower than cracking reactions. About 20-30 recycled time-steps are used to simulate a furnace. Simulation speed of each time step controls total simulation speed. Previous methods coupled with complex furnace and reaction models mainly carry out strict simulations. But these simulation methods were so time-consuming that usually several CPU hours were needed to complete a whole periodic simulation, making it impossible for them to be used in RTO. This was the motivation for us to develop a simulation algorithm fast enough to be applied in RTO that has enough rigor and is a compromise between the precise models and calculation load. New set of continuity equations. For a given kinetic reaction model, the reaction network for reactants could be reformulated with respect to tube length as follows:

where Vim was the stoichiometric coefficient of reactant m in the ith reaction. Momentum balance in the reactor tube is mainly concerned with calculating pressure drop. We established the local pressure drop model to calculate pressure drop of each tube section individually. The momentum equation is:

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Figure 5 : Simulation strategy for periodic cracking furnace operation

To derive the formulation of d dT/dL, the energy-balance equations need to be reconsidered. For one piece of tube section, the amount of energy transferred from the flue gas to tube wall can be formulated according to the one-dimensional Lobo-Evans equation as:

Energy-balance in each section is described in the flowing equations:

Qradia = Qtrans = Qreact (20)

where Qtrans represents the heat transferred from tube wall to the oil gas and Qreact represents the heat used by oil gas for the reaction and temperature increment. From Qtrans = Qreact, the dT/dL formula can be easily derived:

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Figure 7 : Pressure drop increased with run time.

To eliminate parameter Tw (L) in the above equation, the following two simplified measures were employed: 1. The second item in Eq. 17:

Figure 6 : Tube wall temperature distribution was a quadratic curve.

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Denotes the convection heat transformed from flue gas to tube wall. Compared to the value of the first item which was the radiant heat from flue gas, Qc only makes up 4% of the other at most. So we designated Qc as 2% of value of first item on average for initial simulation. 2. In Eq. 18, the total heat transfer coefficients, k, can be expressed as:

(22)

where λw = a + b * Tw(L). In the initial simulation, we use φ (L) to approximate Tw(L) as λw = a + b φ(L) , which makes k independent with Tw(L) temporarily. From these two assumptions, according to Qradia = Qtrans a quartic equation could be derived as follows:

Where

The analytical solution is:

Where

It should be noted that Eq. 24 suggests Tw(L) is the function of flue temperature of Tg(L) and oil gas temperature of T. By substituting Eq. 24 in Eq. 21, the energy-balance equations were finally transformed to the dT/dL formula,

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(25)

From Eqs. 15, 16 and 25, a new set of continuity equations was established and adopted as our simulation model. It should be noted that in previous research, a lot of complex iterations for solution procedure were employed because the reaction and furnace radiant models were separately formulated. While the proposed new set of equations has integrated the traditional reactor and furnace models, the whole pyrolysis process in a cracking furnace could be easily accomplished by simultaneously solving the set of equations with a usual ordinary differential equation (ODE) solver. The calculation speed for integrating Eqs. 15, 16 and 25 is fast. A Fast Simulation Algorithm. For simulating an industrial cracking furnace, the coil outlet temperature (COT) and pressure (COP) are usually fixed, which is typically adopted at actual operation. As in previous methods, some iterations that were used to adjust the flue gas temperature, Tg(L) and inlet pressure, were used in our simulation procedure to match the calculated COT and COP with the fixed ones. There are about three or five iterations for a time-step simulation. Here, a method is proposed for compensating the rough effects from the simplified measures mentioned previously. That is, before each next iteration, the values of. λw and Qc are renewed by using the formulas

which is based on Tw(L) and Tg(L) calculated in the last iteration. From the previous discussion, we established the fast simulation strategy for naphtha pyrolysis in industrial cracking furnaces. Fig. 5 shows the algorithm diagram.Simulating periodic operation of a cracking furnace requires undergoing dozens of pseudo steady-state simulations (outer loop) as shown in Fig. 5. Between two outer loops, the coke formation model should be employed to update the heat transfer coefficient and actual reactor tube inlet diameter.

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Figure 9 : Ethylene yield decreased with run time

Figure 8 : Coke thickness increased with run time.

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Example. With the proposed algorithm, we simulated 54 days of operation for an industrial cracking furnace with COT equal to 821'C and coking refresh time, At = 48 hr. This means 27 recycled time steps were executed in the procedure. The molecular kinetic model and coke formation mode developed by Kumar and Kunzru were applied in our simulation. All the other parameters for simulation such as feed rate, water oil ratio, etc.., were derived from the real plant. The simulation results are exciting. All the pyrolysis information for periodic operation of the cracking furnace was obtained with an IBM PC (PIII 800/256M). The CPU time consumed for the whole periodic simulation was only five minutes. Figs. 6-8 give the 3-D profiles of oil gas temperature, pressure and coke layer thickness, respectively. In Fig. 6, tube wall temperature distribution was a quadratic curve. As we maintain COT in our periodic simulation, the tube wall temperature gradually increased with run time, because the increasing radiant box temperature should compensate for the heat resistance increase from coke accumulation. Thus, tube wall temperature increased slowly to 1,100°C-which was the upper limit of the reactor tube for operating safely-such that the cracking furnaces have to be shut down to decoke. The pressure profile in Fig. 7 shows that the pressure drop increased with run time because coke accumulation made the actual reactor tube sectional area become gradually smaller. From the coke thickness profile (Fig. 8), the increasing trend of coke deposition along the tube length and with run time is obvious. The places of sudden change of thickness corresponded to the tee joints of the branch coils, where the pressure drop was much greater than the other tube sections. The changing parameters mentioned in periodic operation o the cracking furnace eventually resulted in the yield changing with time. Fig. 9 illustrates ethylene yield decreasing with time. Ethylene yield reduced approximately 0.35 wt%, which suggested that reaction selectivity was descending with run time. The simulation results showed good agreement with the data from the real ethylene plant. ACKNOWLEDGEMENTS The authors wish to thank A. Moghadasi (PhD), whom helped us in gathering information and calculating the final results and Mr. Saeed Mohammadi who spent hours for typing the final text.

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NOMENCLATURE in Part 1 Ai area of zone i (m^2) α semimajor axis of the ellipse (m) b semiminor axis of the ellipse (m)

Cc concentration of coke (mol/m^3) Cp heat capacity (J/mol . k) de equivalent (hydraulic) diameter of the elliptical tube(m) dt tube diameter (m) E blackbody emissive power (W/m^2) F molar flow rate (mol/hr) G total mass flux of the process gas (kg/m^2.s)

hp process gas convection coefficient (W/m^2•K) ΔH heat of reaction (J/mol) Mm average molecular weight (kg/mol)

n stoichiometric coefficient O wetted perimeter (m) P perimeter of the ellipse (m)

Pt total pressure (Pa) Q heat flux (W/m^2) q heat flux (W/m^2) r radius (m)

rc,i coking reaction rate of precursor i (mol/m^3.s) Re Reynolds number Rc coking reaction rate (mol/m^3.s) Rb radius of the tube bend (m) rr reaction rate (mol/m^3.s) S wetted area (m2) s tube pitch (m) t time (s)

T temperature (K) Tp process gas temperature (K)

Z axial reactor coordinate (m) ZiZj total exchange area between zones ii and j (m^2)

α unit conversion factor Є eccentricity of the ellipse θ polar coordinates angle (Figure 4) (rad) Ф angle in the parameter equation of the ellipse (Figure 4) (rad)

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NOMENCLATURE in Part 2 Acp equivalent flat area

As convective heat-transfer area, M2 Cpm heat capacity, kJ/mol

Di actual reactor inlet diameter, m Do reactor outlet diameter, m

E equivalent reduced factor F total exchange coefficient G total process gas mass flux, kg/m2s L reactor length, m

Nm molar flow rate of reactant m, mol/hr P oil gas pressure, Pa S actual inlet area, m2 T oil gas temperature, K

Tg(L) flue gas temperature, K Tw(L) reactor tube wall temperature

f friction factor ΔHf heat of formation, kJ/mol

α view factor ρ oil gas density, kg/m3

λw tube wall conductivity factor, kW/m^2|K δw tube wall thickness, m δc coke thickness, m σ Stefan-Boltzmann constant, 5.7 * 10^8 W/m^2|K^4 χ oil gas heat-transfer coefficient, kW/m2|K

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References

1. Heyndericks, G. J. and G. F. Froment, "Simulation and comparison of the run length of an ethane cracking furnace with reactor tubes of circular and elliptical cross sections," Ind. Eng. Chem. Res., 1998, 37, 914-922.

2. Froment, G. F. and K. B. Bischoff, Chemical reactor analysis and design, John Wiley and Sons, New York, 1990.

3. Ravi, N. and A. Zak, "Proceedings of the 7th international symposium on process systems engineering," Comput. & Chem. Eng., 2000 (24), 533-538.

4. Kumar, P and D. Kunzru, "Modeling of Naphtha Pyrolysis," Ind. Eng. Chem. Process Des. Dev., 1985, 24(3), 774-782.

5. Kumar, P and D. Kunzru, "Kinetics of Coke Deposition in Naphtha Pyrolysis," Can. J. Chem. Eng, 1985, 63(8), 598-603.

6. Heynderickx, G. J.; Froment, G. F. A Pyrolysis Furnace with Reactor Tubes of Elliptical Cross Section. Ind. Eng. Chem. Res.1996, 35 (7), 2183.

7. Heynderickx, G. J.; G. Cornelis. G.: Froment, G. F. Circumferential Tube Skin Temperature Profiles in Thermal Cracking Coils. AIChE J. 1992, 38, 1905.

8. Hottel, H. C.; Sarofim. A. F. Radiative Heat Transfer: McGraw-Hill: New York, 1967. 9. Knutzen. J. G.; Katz, D. L. Fluid Dynamics and Heat Transfer; McGraw-Hill: New

York, 1958. 10. Nekrasov, B. B. Hvdra.ulics: Peace Publishers: Moscow. 1969. 11. Plehiers. P. M.: Froment, G. F. Firebox Simulation of Olefin Units. Chem. Eng.

Commun. 1989, 80. 81. 12. Plehiers. P. M.: Reyniers. G. C.: Froment. G. F. Simulation of the Run Length of an

Ethane Cracking Furnace. Ind. Eng. Chem. Res. 1990. 29, 636-641. 13. Rao. M. V. R.: Plehiers, P. M.: Froment, G. F.'Simulation of the Run Length of an

Ethane Cracking Furnace. Ind. Eng. Chem. Sci. 1988. 43. 1223. 14. Sundaram. K. M.: Froment. G. F. Modeling of Thermal Cracking Kinetics. 3. Radical

Mechanisms for the Pyrolysis of Simple Paraffins. Olefins and Their Mixtures. Ind. Eng. Chem. Fundamn. 1978. 17 (3). 174-182.

15. Sundaram. K. M.; Froment. G. F. Kinetics of Coke Deposition in the Thermal Cracking of Propane. Chem. Eng. Sci. 1979, 34. 635-644.

16. Sundaram, K. M.; Van Damme, P. S.; Froment. G. F. Coke Deposition in the Thermal Cracking of Ethane. AIChE J. 1981. 27, 946-951.

17. Willems. P.; Froment, G. F. Kinetic Modeling of the Thermal Cracking of Hydrocarbons, Part 1: Calculation of Frequency Factors. Ind. Eng. Chem. Res. 1988a. 27. 1959.

18. Willems. P.: Froment. G. F. Kinetic Modeling of the Thermal Cracking of Hydrocarbons, Part 2: Calculation of Activation Energy. Ind. Eng. Chem. Res. 1988b, 27. 1966.

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