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Nov 6, 2012 - A numerical simulation for the flue gas and process sides of a coking furnace with floor gas burners was conducted. The computational fl...
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Numerical Simulation of the Flue Gas and Process Side of Coking Furnaces Junwei Yang, Ningning Tai, Lanjuan Wang, Jiazhi Xiao,* and Chaohe Yang State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266580, China S Supporting Information *

ABSTRACT: A numerical simulation for the flue gas and process sides of a coking furnace with floor gas burners was conducted. The computational fluid dynamics (CFD) approach was employed to simulate flow, combustion, and heat transfer in the furnace. The process-side conditions were calculated with a special program. The simulation provides detailed information about the flue gas velocity, temperature fields, and process conditions for this type of coking furnace. Good agreement is obtained between industrial measurement and simulated excess air coefficient, outlet temperature of flue gas, and outlet pressure on the process side. Moreover, the simulated results indicate that there are hot spots on the tubes, located at the height of 1.5−2.5 m. That is consistent with the actual phenomenon of industrial coking furnaces. To investigate the effect of furnace structure on physical field distribution and process-side conditions, a comparative simulation case with more wide spacing of burners to walls was conducted. Results indicate that the comparative case improves the uniformity of heat flux distribution, obviously, which is beneficial for the run length of coking furnaces. (DTM)21 are all radiation heat transfer models, which have been used for simulation of industrial furnaces. However, the standard k−ε model is the most adopted flow model in furnace simulation and shows good predictive ability and stability.22−24 As the processes of thermal reaction, phase equilibria, and two-phase flow coexist on the process side, it is difficult to simulate the process side by the CFD method. Many researchers25−27 have simplified the process side as a nonadiabatic plug flow reactor model with two-phase flow, and the heat flux distribution on the tubes was simulated by zero-dimensional or one-dimensional models. However, the coarse heat flux distribution may affect the process side conditions directly. In the present work, a coupled simulation for the flue gas and process sides of a coking furnace with floor gas burners was conducted. The CFD method was employed to simulate the processes of turbulence, combustion, and heat transfer, to obtain the heat flux distribution on the tubes. The process-side conditions were calculated with a special program, PSS, developed by our research group.28 Moreover, the effects of furnace structure on physical field distribution and process-side conditions were discussed.

1. INTRODUCTION Delayed coking is an important process for upgrading petroleum residues, which is the only process in the refinery that produces coke. The feed to the delayed coker can be any undesirable heavy stream containing high metal content.1 A common feed is vacuum residue, but it can also accept fluid catalytic cracking slurry. In delayed coking processing, the heat required to complete the coking reaction is supplied by the coking furnace, while coking itself takes place in drums. The coking furnace with burners in the floor is the core equipment in this process. Therefore, accurate modeling of the flue gas and process side conditions is important in the design and operation of coking furnaces. Numerical simulation, as an alternative, has become a powerful tool to predict the operating parameter distributions. The simulation of a coking furnace can be divided into two parts generally. One is the flue gas-side simulation, including turbulent flow, fuel combustion, and heat transfer processes. The other is the process-side simulation, including the processes of heat transfer, thermal reaction, phase equilibria, and two-phase flow. The modeling of industrial furnaces evolves from zero-dimensional models, for example, the Lobo− Evans method,2 over multidimensional models,3 to the computational fluid dynamics (CFD) models developed recently.4−7 With the development of CFD, numerical simulation is widely employed in the modeling of industrial furnaces, such as ethane cracking furnaces,8−13 glass melting furnaces,14 and steam boilers.15 The main differences in the reported studies are combustion model and radiation heat transfer model. For nonpremixed industrial combustion systems with gas fuel, the finite rate/eddy-dissipation model,16,17 presumed probability-density-function (PDF) model,18 and eddy dissipation concept (EDC) model10 are always used and show appropriate results. The P1 model,19 discrete ordinate model (DO),20 and discrete transfer model © 2012 American Chemical Society

2. MATHEMATICAL MODELS 2.1. Furnace Model. 2.1.1. Governing Equation. The simulation of the flow field, temperature field, and species concentrations on the flue gas side is based on Reynoldsaveraged Navier−Stokes equations (RANS). Due to the time averaging of the equations, a closure model is required to account for turbulence, in addition to continuity, momentum, Received: Revised: Accepted: Published: 15440

August 22, 2012 October 15, 2012 November 6, 2012 November 6, 2012 dx.doi.org/10.1021/ie302248m | Ind. Eng. Chem. Res. 2012, 51, 15440−15447

Industrial & Engineering Chemistry Research

Article

H 2 + 0.5O2 → H 2O

enthalpy, and species equations. As described above, the standard k−ε model was used. Then, the general form of the governing equation can be written as

with corresponding intrinsic reaction rate expressions: rCH4 = (1.5 × 1013)e−125604/ RT CCH4 −0.3CO21.3

∂ (ρϕ) + div(ρuϕ) = div(Γϕ grad ϕ) + Sϕ ∂t

(1)

rCO = (3.98 × 1020)e−167472/ RT CCOCO2 0.25C H2O0.5

The meanings of φ, Γϕ, and Sϕ for each equation are summarized in Table 1. The radiation source term in the energy equation was described by a radiation model, and the chemical source terms in species equations were determined by combustion models.

rH2 = (1.0 × 1013)C H2CO2 0.5

2.1.3. Radiation Model. Radiation is the predominant mode of heat transfer in a coking furnace, because of the high temperatures of flue gas and furnace walls. Therefore, a reasonable radiation model is important to predict the heat transfer process in the furnace. In this work, the discrete transfer model29 (DTM) was employed. The DTM is based on tracing the domain by multiple rays leaving from the bounding surfaces, and it depends upon the discretization of the radiative transfer equation (RTE) along rays. The physical quantities in each element are assumed to be uniform. The RTE of the DTM can be written as

Table 1. Meanings of φ, Γϕ, and Sϕ in Governing Equationsa equation continuity equation momentum equations

φ

Γϕ

1 ui

0 μ + μt

Sϕ 0

− enthalpy equation

h

species equations

Ys

turbulent kinetic energy equation

k

dissipation rate equation of turbulent kinetic energy

ε

a

λ+ (μt/ σh) D+ (μt/ σY) μ+ (μt/ σk) μ+ (μt/ σε)

∂P ∂ ⎛ ∂μj ⎞ ⎜⎜μ ⎟⎟ + ρg + i ∂xi ∂xi ⎝ i ∂xi ⎠

Sh

∇[I( r ⃗ , s ⃗) s ⃗] + (α + σs)I( r ⃗ , s ⃗)

Rs

= αn 2

Gkρε

σ σT 4 + s π π

I( r ⃗ , s ⃗′)ϕ( s ⃗ , s ⃗′) dΩ′

(5)

The weighted sum of gray gases model (WSGGM) was used to calculate the absorption coefficient of flue gas. The emissivity of the real gas is expressed as the weighted sum of the emissivities of a number of gray gases:

(ε/k)(C1Gk − C2ρε)

I

ε=

∑ αε ,i(T )[1 − e−k ps] i

0

2.1.2. Combustion Model. The combustion process of gas fuel in a coking furnace is turbulent diffusion combustion, which is a diffusion-limited combustion process. In this work, the turbulent chemistry interaction model based on the work of Magnussen and Hjertager,16 called the finite rate/eddydissipation model, was employed. In the finite-rate model, the chemical source term is calculated from an Arrhenius expression, in which the Arrhenius molar rate of creation/ destruction of species i in reaction r is given by ⎡ ⎤ N (ηi″, r − ηi′, r )⎥ ⎢ ̂ R i , r = Γ(νi″, r − νi′, r ) κ f, r ∏ Cj , r ⎢⎣ ⎥⎦ j=1

⎛ ε ⎞ ⎛ YR ⎞ ⎟ R i , r = νi′, r M w, i Aρ⎜ ⎟min⎜⎜ ⎝ κ ⎠ ⎝ νR,′ r M w,R ⎟⎠

(6)

I

∑ αε ,i = 1 0

(7)

where αε,i is a weighting factor and the bracketed quantity in eq 6 is the ith fictitious gray gas emissivity. 2.2. Tubular Reactor Model. As high-pressure steam is injected into each of the furnace coils to suppress coke formation in the tubes, the processes of thermal reaction, phase equilibria, and two-phase flow coexist on the process side. Therefore, the plug flow model has been used in this work. Because the heavy oil begins to crack at 350 °C33 (the outlet temperature of residue is 490−500 °C), there is a partial thermal cracking reaction on the tube side. That is necessary to take into account in the design of the coking furnace, because the apparent velocity and residence time in the tube are all critical parameters for the design and operation of the coking furnace.34 However, the product distribution of thermal cracking reaction affects these parameters directly, so it is important to establish an accurate model for the product distribution in thermal cracking of heavy oil, which is suitable for the calculation of apparent velocity and residence time in the furnace tubes. There are many kinetic models proposed for different processes and conditions.35−39 In this work, a 12-lump kinetic model was employed to describe the thermal cracking process.40 Since the partial vaporization of the liquid feed in furnace tubes plays an important role for the flow conditions and chemical reactions, it was decided at an early stage to model the phase equilibria. The SRK equation of state was used to model the phase equilibria, and the two-phase pressure drop in the

(2)

In the eddy-dissipation model, the net rate of production of species i due to reaction r (Ri,r) is given by the smaller of the two following expressions:

(3)

and R i,r

4π

30−32

Here μt = Cμρk2/ε and Gk = μt∂ui/∂xj(∂ui/∂xj + ∂uj/∂xi).

∑ pY P ⎛ε⎞ p = νi′, r M w, i ABρ⎜ ⎟ N ⎝ κ ⎠ ∑ ν″ M w, j j j,r

∫0

(4)

The following reaction scheme is considered for the combustion of CH4/H2/air mixture: CH4 + 1.5O2 → CO + 2H 2O CO + 0.5O2 → CO2 15441

dx.doi.org/10.1021/ie302248m | Ind. Eng. Chem. Res. 2012, 51, 15440−15447

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tubes was calculated by the Baker method. All the physical properties used in the process simulation were estimated by established methods.41 The flow and coking process is complex on the tube side. Especially, the coking rate on the tube side under actual operating conditions is very slow: the thickness of coke is only 5−15 mm for 6−12 months. It is difficult to estimate an accurate coking model by experiment or correlation based on industrial data. So the coking process in the tube has been neglected. 2.3. Boundary Conditions. The standard wall functions were used as turbulent wall boundary conditions. At the burner inlets, the velocity, temperature, and mixture composition were imposed. At the furnace exit, the outlet pressure was imposed as −50 Pa. The possibility of reverse flow at the outlet boundary during the solution process was taken into account. The no-slip boundary condition was imposed on the tubes and furnace walls. The tube skin temperature was obtained from industrial measurements by interpolation, the furnace walls were set to adiabatic boundaries, and the emissivity of tubes and furnace walls is 0.8. The wall surface temperature was calculated from the following equation while imposing qout: qout = (1 − εw )qin + n2εw σTw 4

(8)

Here 4π

qin =

∫s ⃗n⃗ >0 Iins ⃗n⃗ dΩ

where Iin is the intensity of the incoming ray, Ω is the hemispherical solid angle, and n⃗ is the normal pointing out of the domain. 2.4. Meshing and Numerical Method. The hexahedral unit was adopted in furnace domain, and the O-grid method was applied to the tube system. Due to the complex structure of burners, a local refinement of tetrahedral mesh strategy was adopted. The number of grid cells for the furnace is 898 881. The mesh independence of our simulation results has been verified; when the number of refined grid cells increased from 898 881 to 1 797 762, the results show almost no difference. Therefore, the original grid was used in the coupled calculation. The governing equations were integrated over each control volume, such that the relevant quantity is conserved in a discrete sense for each control volume. The convection items were discretized by a second-order upwind scheme. A coupled solver supplied in CFX was used, which solved the hydrodynamic equations (for u, v, w, p) as a single system. This solution approach used a fully implicit discretization of the equations at any given time step. For steady-state problems, the time-step behaves like an “acceleration parameter”, to guide the approximate solutions in a physically based manner to a steadystate solution. 2.5. Coupled Solution of Coking Furnaces. The coupled calculation algorithm is shown in Figure 1. First, the tube skin temperature from industrial measurement was assigned as the tube skin boundary of the furnace, and the solution of firebox was carried out to obtain the heat flux distribution on the tubes. Then the resulting heat flux was applied to the simulation of process inside tubes, yielding improved tube skin temperature and process-side conditions. The coupled solution had to be continued until the difference of tube skin temperature between the estimated value of the furnace model and the improved

Figure 1. Flow chart of coupled solution.

value of the tubular reactor model was less than a predefined threshold value (e.g., 1 K).

3. FURNACE DESCRIPTION An industrial coking furnace was simulated by use of the comprehensive mathematical model developed above to investigate its physical fields and process-side conditions. Because of structural similarity, only a representative segment of one-fourth of the industrial coking furnace was simulated. The furnace contains 52 tubes with two parallel passes in the firebox. Namely, the two parallel passes, which have 26 tubes in one pass, are identical in geometric structure and variance profiles. In the furnace floor, between the walls and tubes, 48 gas burners are located in four rows. Each burner includes six nozzles arranged around the air inlet. The high-pressure steam is injected into the inlet of the furnace coils. The configuration of one-fourth of the coking furnace is depicted in Figure 2. The configuration parameters and main operating conditions are given in the Supporting Information. 15442

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Industrial & Engineering Chemistry Research

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Figure 3. Flue gas velocity fields on the cross section at z = 2.9 m: (case a) industrial furnace, Lm = 0.5 m; (case b) comparative case, Lm = 1.0 m. Figure 2. Configuration of one-fourth of coking furnace: (a) front view of the simulated segment of coking furnace; (b) gas burner configuration. (Units = millimeters.)

industrial furnace in case a. However, that is about 3.5 m for the furnace in case b. As the furnace walls and tubes are all no-slip boundary conditions, the flue gas velocity near the furnace walls and tubes is very small. A wide range of recirculation is formed at both sides of the tubes due to the entrainment effect of the highvelocity jet of the burners. These recirculation zones start from the furnace floor toward the tubes and expand to the middle of the furnace, circulating the high-temperature flue gas of the flame into the low-temperature part of the furnace, thereby increasing the residence time of the high-temperature flue gas in the furnace. Hence, this recirculation zone improves the uniformity of the heat flux on the tubes. However, there are some differences in the characteristics of the recirculation zone for cases a and b. For case a, as the spacing of burners to walls Lm = 0.5 m, and the spacing of burners to tubes is 1.0 m, the recirculation mainly exists between the burners and tubes due to the geometric asymmetry. For case b, the recirculation is approximately symmetric, as the spacing of burners to walls is equal to the spacing of burners to tubes. It will be seen in the next section that these differences also have obvious effects on the heat flux distribution. 4.2. Flue Gas Temperature Field and Heat Flux Profile. Figure 4 shows the flue gas temperature fields on the cross section at z = 2.9 m. For both cases a and b, it can be observed that the flue gas temperature is high near the furnace wall and the zone where the burners are located. On the other hand, the temperature is relatively low on the furnace floor, the top of the furnace, and in the neighborhood of the tubes. However, the outlet flue-gas temperature in case a is lower than in case b. Figure 5 shows the flue-gas temperature distribution at different sections along the height of the furnace. It shows that the flue gas temperature at the bottom of the furnace is low. The flue gas temperature gradually increases from bottom to top and reaches its peak value at the range of 1.5−2.5 m. Above this height the flue gas temperature begins to decrease. It is worth nothing that the peak value of flue gas temperature in case a is about 40 K higher than in case b. However, on the top of the furnace, the flue gas temperature in case a is about 60 K lower than in case b.

4. RESULTS AND DISCUSSION Table 2 shows a comparison between simulation results and industrial data. The excess air coefficient, outlet temperature of Table 2. Comparison of Simulation Results and Industrial Data items

industrial data

simulation data

temperature of outlet flue gas (K) excess air coefficient tube inlet temperature (K) tube outlet temperature (K) tube inlet pressure (MPa) tube outlet pressure (MPa)

943 1.15 633 773 1.30 0.45

938 1.16 633 779 1.30 0.49

flue gas, and outlet pressure on the process side are in agreement with the industrial data. It shows that the simulation results are reliable. The results can be used to analyze the velocity, temperature, and heat flux distributions in coking furnaces. Furthermore, in order to investigate the effect of furnace structure on physical field distribution and process-side conditions, a comparative simulation case with the spacing of burners to walls Lm = 1.0 m (in Figure 2) was conducted. As the flue gas concentration profile is not concerned in industrial application, it will not be discussed here. 4.1. Flue Gas Velocity Field. Figure 3 shows the flue gas velocity fields in the plane at z = 2.9 m of the furnaces. Because of structural similarity, only 9 m length of the coking furnace was simulated. A typical cross-section (z = 2.9 m), which is 2.9 m away from the center of furnace, was used to analyze. It can be seen that the velocity above the burners is higher than any other place in the furnace, as a consequence of the high velocity of the fuel entering the furnace through the small burner nozzles. Two jets are observed above the burners, with a strong increase in velocity in the flame region due to the temperature rise and expansion effect. The height of high-velocity zone above the burners in the y-direction is about 3 m, for the 15443

dx.doi.org/10.1021/ie302248m | Ind. Eng. Chem. Res. 2012, 51, 15440−15447

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Figure 4. Flue gas temperature fields on the cross section at z = 2.9 m: (a) industrial furnace, Lm = 0.5 m; (b) comparative case, Lm = 1.0 m.

Figure 5. Average temperature distribution of flue gas in the ydirection of furnaces. (Lm = spacing of burners to walls in Figure 2.)

Figure 6. Tube skin temperature distribution in coking furnaces. (Lm = spacing of burners to walls in Figure 2.)

In the furnace floor, the fuel gas injected from the burners has a very high velocity so that it is improperly mixed with ambient air, without enough combustion and much heat release; hence, the flue gas temperature is low. With the development of jet, the fuel gas and air further mix and the combustion reaction intensely goes on, which leads to a large amount of heat. Therefore, the flue gas temperature gradually increases along the furnace height, and it reaches the highest value about the range of 1.5−2.5 m. When the height continues to increase, because the fuel gas and air gradually consume and the tubes continuously absorb the heat, the temperature will gradually drop. Moreover, Figure 4 shows the 1200 K isosurface of flame temperature; it is obvious that the flames in case a have a tendency to impinge on the tubes, while the flames in case b improve this phenomenon, which is beneficial for avoiding hot spots on the furnace tubes. As shown in Figures 6 and 7, due to the differences of flue gas temperature fields, both the tube skin temperature and heat flux distributions in case b are more uniform than in case a; the numeral order of the furnace tubes is from top to bottom. Figure 7 shows that the maximum/minimum ratio of heat flux is 3.05 in case a, and the maximum/minimum ratio of heat flux

Figure 7. Heat flux distribution in coking furnaces. (Lm = spacing of burners to walls in Figure 2.)

is just 1.78 in case b. The uniform heat flux distribution is beneficial for the run length of coking furnaces. 4.3. Process-Side Conditions. Figure 8 shows the process temperature profiles inside the tube. The process temperature in case a is lower than that in case b at the entrance section, while the tendency is reversed after the 20th furnace tube. The maximum temperature difference between cases a and b is 10.6 15444

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5. CONCLUSIONS A coupled simulation for the flue gas and process sides of a coking furnace with floor gas burners was conducted, via a computational fluid dynamics (CFD) approach. Good agreement was obtained between industrial measurements and simulated excess air coefficient, outlet temperature of flue gas, and outlet pressure on the process side, and therefore this approach provides a proper theoretical basis for gaining better insight into the behavior of industrial coking furnaces. The optimal design of a coking furnace requires the combination of firebox design, coil design, and layout of burners and can be conducted by coupled CFD simulations on the fire gas side with process-side simulation on the tube side. To investigate the effect of furnace structure on physical field distribution and process-side conditions, two comparative simulation cases with the spacing of burners to walls Lm = 0.5 and 1.0 m were conducted. Result indicates that the case with Lm = 1.0 m improves the uniformity of heat flux distribution obviously, which is beneficial for the run length of coking furnaces.

Figure 8. Process temperature profiles inside the tubes. (Lm = spacing of burners to walls in Figure 2.)

K, which is obviously related to the difference in heat flux and tube skin temperature profiles. At the entrance section of tubes, the process temperature rapidly increases because of the low process temperature and limited heat consumption. The temperature rapidly increases from 360 °C at the entrance of the inlet tube to about 460 °C at the 20th tube. With increasing process temperature, the light distillate inside the tubes begins to vaporize and crack, obviously. Both of these are endothermic process, hence, the slope of the process temperature is slowed down. Figure 9 shows the process pressure and apparent velocity profiles inside the tubes. The apparent velocity gradually

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ASSOCIATED CONTENT

S Supporting Information *

One table listing configuration parameters and operating conditions of the simulated furnace. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +86-532-8698-1812. Fax: +86-532-8698-1787. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out with financial support from the China Petroleum and Chemical Corp. (Project X0500022). Figure 9. Process pressure and apparent velocity profiles inside the tubes. (Lm = spacing of burners to walls in Figure 2.)

increases along the length of the tubes, due to expansion of the process medium caused by temperature rise and partial vaporization. In inlet tube, the process apparent velocity increases from 6.5 m/s at the entrance of inlet tube to about 14.4 m/s at the 20th tube. The slope of the apparent velocity accelerates obviously after the 20th tube, which is mainly caused by more vaporization of light distillate. The maxima of apparent velocity in cases a and b are 34 and 43 m/s, respectively. From the obtained average velocity, the residence time of the process medium inside the tubes has been calculated as 47 and 40 s for cases a and b, respectively. As shown in Figure 9, the process pressure decreases gradually from the inlet tube to the 20th tube, the slope of the pressure profile is approximately linear. At the 20th tube, the slope of the pressure profile changes and the process pressure decreases rapidly, which is consistent with the velocity profiles. The outlet pressures in cases a and b are 0.5 and 0.45 MPa, respectively. In addition, the pressure decreases rapidly, also caused by the flow pattern transition. The flow pattern inside the tubes changes from single-phase flow gradually into twophase flow. 15445

NOMENCLATURE A, B = empirical constants C1, C2, Cμ = constants of k−ε turbulent model Cj,r = molar concentration of species j in reaction r, kg·mol/ m3 D = diffusion coefficient, m2/s gi = gravity component, m/s2 Gk = generation of turbulent kinetic energy, J/(m3/s) h = total enthalpy per unit mass, J/kg I = radiation intensity, J/(m2/s) k = turbulent kinetic energy, m2/s2 kf,r = forward rate constant for reaction r, 1/s ki = absorption coefficient of the ith gray gas, 1/m Mw,i = molecular mass of species i, g/mol n = refractive index N = number of chemical species in the system p = pressure and sum of partial pressures of all absorbing gases, Pa r ⃗ = position vector R = ideal gas constant, 8.314 J/(mol/K) Ri = net rate of production of species i by chemical reaction, g·mol/(m3/s) Rj = rate of reaction in which j participates, kmol/(m/s) s ⃗ = direction vector dx.doi.org/10.1021/ie302248m | Ind. Eng. Chem. Res. 2012, 51, 15440−15447

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s = path length Sh = source term in the enthalpy equation, J/(m3/s) T = local temperature and process side temperature, K Ui = velocity component in the i direction, m/s xi = coordinate direction in the i-direction, m YP = mass fraction of product P YR = mass fraction of reactant R Greek Letters

α = absorption coefficient, 1/m αε,i = emissivity weighting factors for fictitious gray gas ε = dissipation rate of turbulent kinetic energy, m2/s3, and emissivity μ = dynamic viscosity, kg/(m·s) μt = turbulent viscosity, kg/(m/s) ρ = density, kg/m3 Γϕ = diffusion coefficient of φ ν′i,r = stoichiometric coefficient for reactant i in reaction r νi,r″ = stoichiometric coefficient for product i in reaction r ηj,r ′ = rate exponent for reactant species j in reaction r η″j,r = rate exponent for product species j in reaction r σ = Stefan−Boltzmann constant, 5.672 × 108 W/(m2·K4) σh = Prandtl number of enthalpy equation σk, σε = turbulent Prandtl number σY = Schmidt number of species equation σs = scattering coefficient, 1/m ϕ = phase function Ω′ = solid angle

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