CN103150433B - The Coupled Numerical modeling method of cracking reaction in industry dichloroethane cracking furnace hearth combustion and boiler tube - Google Patents

Abstract

The invention provides the Coupled Numerical modeling method of cracking reaction in a kind of industrial dichloroethane cracking furnace hearth combustion and boiler tube, dichloroethane cracking furnace is divided into hearth model and furnace tube model by the method in modeling, and respectively to burner hearth boiler tube grid division.The tube wall temperature that burner hearth provides using furnace tube model is as boundary condition, and utilize combustion model, flow model, heat transfer model calculates chamber flue gas temperature, speed, the important burner hearth parameter distribution such as concentration of component; The boiler tube thermoflux that boiler tube then calculates with burner hearth is for boundary condition, utilize cracking reaction model in pipe, consider the mass conservation in pipe, momentum conservation, energy conservation relation calculates the Process Gas temperature along pipe range direction, pressure, CONCENTRATION DISTRIBUTION, thus under favourable analysis current operational conditions, ethylene dichloride cracking conversion ratio, selectivity, the principal economic indicators such as unit consumption, are conducive to guide field process optimization.And this modeling method is applicable to all kinds of high-temperature cracking furnace, there is adaptability widely.

Description

Coupling Numerical Modeling Method of Furnace Combustion and Cracking Reaction in Furnace Tube of Industrial Dichloroethane Cracking Furnace

technical field

The invention relates to a process device modeling method, in particular to a coupled numerical modeling method for furnace combustion and cracking reaction in a furnace tube of an industrial dichloroethane cracking furnace.

Background technique

Ethylene dichloride cracking furnace is the core unit and large energy consumer of vinyl chloride production plant. The benefit of the entire vinyl chloride plant is closely related to the design and operation level of the cracking furnace. The key to improving the economic efficiency of vinyl chloride production plant lies in high-level design and how to optimize it. Operating conditions of the cracking furnace. At present, most of the ethylene dichloride cracking technologies and devices in my country are imported from abroad. The introduction of advanced and mature vinyl chloride devices provides a higher starting point for the development of my country's vinyl chloride industry. However, my country's dichloroethane cracking operation level generally lags behind the world's advanced level. The dichloroethane cracking conversion rate is low, the selectivity is low, and the unit consumption is high. However, the licensors kept the key technology secret, so that my country's grasp of the dichloroethane cracking process mechanism is not deep enough, and it is difficult to achieve a substantive breakthrough in the technical level. Domestic understanding of material fluid flow, heat transfer, mass transfer, and chemical reactions inside the cracking furnace is not clear enough, and lacks sufficient theoretical support, so that the transformation of cracking furnaces and the design of domestic cracking furnaces mainly imitate foreign technologies without theoretical basis , often make the modification and design inappropriate, or when the cracking raw material and operating conditions change, the operating parameters can only be determined by experience, so there is a certain blindness in the design and operation, and the potential of the device has not been fully utilized. Therefore, if we blindly introduce complete sets of foreign technologies and imitate them, but do not pay attention to digesting, absorbing and re-innovating the fundamental and basic technologies, then my country's vinyl chloride cracking production technology will always lag behind the world's leading level and lack international competitiveness. .

In order to fully grasp the operation mechanism of the dichloroethane cracking furnace, master the heat coupling relationship between the furnace and the furnace tube, and understand the operating cycle of the dichloroethane cracking furnace, the conversion rate, selectivity, and unit consumption of dichloroethane cracking, etc. It is particularly important to carry out mechanism modeling on the dichloroethane cracking furnace for key parameters that have an important impact on important performance indicators. In the past, the research and development of the mathematical model of the dichloroethane cracking furnace focused on the description of the cracking reaction kinetics, without taking into account the interaction between the cracking reaction and the flow and heat transfer. The process has been greatly simplified. In the simulation research of the furnace, it is mainly the simulation of the radiation heat transfer process. They use simplified methods such as the Rob-Evans method, the Belocon method, and the area method to calculate the radiation heat transfer process in the furnace. The fuel combustion mechanism process is simulated, but the heat release rate of the fuel is simply used to estimate the composition and temperature of the flue gas, and the influence of the combustion and flue gas flow process on the heat transfer is ignored.

With the sharp increase in computer computing power, complex and time-consuming Computational Fluid Dynamics (CFD) has become an important method in solving various fields involving fluid flow, such as machinery manufacturing, chemical industry and many other fields. CFD is a branch of fluid mechanics. It uses detailed numerical simulation methods instead of analytical methods to solve nonlinear partial differential equations, and solves many problems that cannot be solved by theoretical fluid mechanics. The nonlinear momentum, heat, mass and component conservation equations in the flow, heat transfer, mass transfer and reaction process of most engineering problems can be discretized by CFD, and the original continuous in space coordinates The fields of physical quantities (velocity field, temperature field, concentration field, etc.) are replaced by a collection of variable values at many discrete points, and an algebraic equation system about the relationship between field variables at these discrete points is established. Closed discrete equations under certain conditions, numerical solution is carried out to obtain the approximate solution of the physical quantity field, and the distribution of each physical quantity (such as: velocity, temperature and concentration, etc.) in the entire research system is given. Accurate details of processes such as flow, heat transfer, mass transfer, and reactions. In a narrow sense, CFD only studies fluid flow phenomena, but with the continuous development of other research fields (such as: combustion, radiation and chemical reactions, etc.), the tentacles of CFD are getting longer and longer, and the coverage is getting wider and wider. For example, in the field of chemical industry, the reaction model describing the chemical reaction can be combined with the flow model to simulate the reactor; effectively simulate the reaction and flow conditions in the reactor and other equipment. Therefore, theoretically speaking, wherever there is fluid flow, the CFD method can work effectively. Therefore, the introduction of CFD technology into the mechanism modeling of dichloroethane cracking furnace will help to understand more clearly important information such as heat coupling of dichloroethane cracking furnace furnace tube, flow field distribution, etc. This will further provide strong theoretical and data support for the design and transformation of ethylene cracking furnaces, optimized operation and the development of new technologies, thus providing technical support for the localization and old transformation of dichloroethane cracking furnaces.

Contents of the invention

In order to solve the shortcomings of the above-mentioned existing models, the present invention comprehensively and systematically analyzes the complex flow, heat transfer, mass transfer and cracking reaction in the reaction tube of the dichloroethane cracking furnace and the flow, heat transfer, mass transfer and combustion reaction in the furnace. At the same time, the strong coupling between these complex processes is analyzed. Based on the turbulent flow model of fluid mechanics, the radiation heat transfer model, the combustion model and the cracking reaction kinetics model, the transfer in the cracking furnace reaction tube and the cracking reaction process are compared with those in the furnace. Combustion heat transfer process is coupled, and a numerical modeling method for the coupling of furnace combustion and cracking reaction in the furnace tube of industrial dichloroethane cracking furnace is designed.

The model of the present invention is composed of a furnace model and a furnace tube model, wherein: in the furnace model, a full premixed mode is adopted according to the mixing degree of fuel and air; the combustion of fuel gas adopts a simplified one-stage series combustion model; the combustion chemical reaction adopts The turbulence-chemical reaction interaction model—the eddy dissipation model; the furnace flue gas flow adopts the Reynolds average model, and the standard k-ε double equation model is used to close the turbulence term; the furnace flue gas radiation heat transfer model adopts the discrete coordinate model , and the multi-ash gas weighted model is used to calculate the flue gas radiation characteristics. In the furnace tube model, a simplified series cracking reaction of dichloroethane is adopted; the process gas flow model is consistent with the flue gas flow model. The iterative variables of the coupled simulation of the furnace model and the furnace tube model are the outer wall temperature and heat flux of the furnace tube. From this, the temperature, velocity, and component concentration distribution of the flue gas in the furnace, the temperature distribution of the inner and outer walls of the furnace tube, the heat flux distribution of the furnace tube, and the temperature, velocity, and component concentration distribution of the cracked gas in the tube can be used to understand the cracking of dichloroethane more accurately. The inherent characteristics of the furnace provide theoretical support for the operation optimization, process transformation, and new process design of the cracking furnace.

A method for numerical modeling of industrial dichloroethane cracking furnace hearth and furnace tube coupling, comprising the following steps:

Step 1: Determine the furnace tube size of the dichloroethane cracking furnace to be simulated, for the furnace and furnace

Grid division of the pipe; determine the boundary conditions according to the process parameters, including: the combustion chamber of the side wall burner

Gas inlet flow, air inlet flow and reaction tube inlet gas flow and temperature, furnace wall heat

Loss coefficient, furnace flue gas outlet pressure and furnace tube cracking gas outlet pressure;

Step 2: Build the furnace model:

Step 2.1: The flue gas flow model in the furnace adopts the standard k-ε based on the Reynolds average equation

Two-equation model builds a closed model;

Step 2.2: The fuel gas in the furnace adopts a one-stage serial combustion reaction model, and flows during combustion

The model adopts the finite rate/eddy dissipation model;

Step 2.3: The radiation heat transfer model in the furnace adopts the discrete coordinate model, and the furnace flue gas adopts

Multi-ash gas weighted model to calculate its radiation characteristics;

Step 3: Build the furnace tube model:

Step 3.1: The cracking reaction of dichloroethane in the furnace tube adopts a first-order series reaction model, and the cracking

The reaction kinetics conform to the Arenlius formula;

Step 3.2: Determine the gas density, heat capacity, viscosity, thermal conductivity and expansion in the furnace tube model

The parameters of the dispersion coefficient calculation formula;

Step 4: Based on the serious thermal coupling relationship between the furnace and the furnace tube and the results obtained in step 1

The initial conditions and boundary conditions, the outer wall temperature of the furnace tube and the heat flux of the furnace tube are used as the furnace model

Iterative coupling variables with the numerical solution of the furnace tube model, and the furnace and furnace tube model

The loop iterates until the model converges, and the parameters involved in the model are obtained.

Further, in the step 1, the furnace and the furnace tube are meshed, and the burner area and the furnace tube area in the furnace are divided into grids by tetrahedron units; other areas of the furnace are divided into grids by hexahedron units; the furnace tube model Hexahedron elements are used to divide the grid for the straight tube wall of the middle furnace tube; hybrid elements are used for the bent tube to divide the grid.

Further, in the steps 2 and 3, the furnace tube and the wall surface of the furnace are regarded as non-slip boundaries; in the viscous bottom layer near the wall, the flow and heat transfer of the actual process are approximated by the standard wall function; the thermal boundary on the wall of the furnace The heat flux boundary condition is given by heat loss; the wall boundary of the furnace tube is assigned to the tube wall by a custom function. In the furnace tube model, the heat flux custom function of the outer wall of the furnace tube is defined as Q(x)=a ₁ +b ₁ x+c ₁ x ² +d ₁ x ³ +e ₁ x ⁴ +f ₁ x ⁵ , in the furnace model, the custom function of the outer wall temperature of the furnace tube is defined as T(x)=a ₂ +b ₂ x+c ₂ x ² +d ₂ x ³ +e ₂ x ⁴ +f ₂ x ⁵ , where a ₁ , b ₁ , c ₁ , d ₁ , e ₁ , f ₁ , a ₂ , b ₂ , c ₂ , d ₂ , e _2. f2 is the parameter to be fitted, x is the coordinate along the radial direction of the furnace tube _; Q is the heat flux, and T is the temperature of the outer wall of the furnace tube;

Further, the first-stage series combustion model in the step 2.2 is:

Applying the finite rate model, the chemical source term is calculated using the Arrhenius formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}$

M _w,i is the molecular weight of component i, _NR is the number of reaction equations, R _i is the net production rate of component i caused by the chemical reaction, is the production/decomposition rate of the i-th substance in the r-th reaction, and its expression is:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>$

Among them, the net effect of the Γ third object on the reaction rate, ν′ _{i, r} , ν″ _{i, r} is the stoichiometric coefficient, k _{f, r} is the forward reaction rate constant, C _{j, r} is the molar concentration, η′ _{j, r} , η″ _{j, r} is the rate index, and N is the total number of substances participating in the reaction;

Applying the eddy dissipation model, the production rate R _i,k of substance k in reaction r is determined by the smaller of the two items in the following formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; A\&rho;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; R</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; AB\&rho;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}$

Among them, ν′ _{i, k} , ν′ _{R, k} , ν″ _{j, k} are stoichiometric coefficients, M _{w, i} , M _{w, R} , M _{w, j} are molecular weights, A, B are empirical coefficients, ρ gas density , is the Leonard-Jones potential energy parameter, Y _R , Y _P is the mass fraction of the product.

Further, in step 2.1, a closed mathematical model is established based on the standard k-ε double-equation model of the Reynolds-averaged Navier-Stokes equation, and the mass, momentum, turbulent kinetic energy, dissipation rate of turbulent kinetic energy, energy and component transport equations are expressed as follows :

Continuity equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left({\mathrm{\&rho;U}}_i\right)=0$

Momentum equation: $\frac{\&PartialD;}{{\&PartialD;x}_j}\left({\mathrm{\&rho;\; U}}_i{u}_j\right)=\frac{{\&PartialD;p}_{\mathrm{eff}}}{{\&PartialD;x}_i}+\frac{\&PartialD;}{{\&PartialD;x}_j}\left[{\mathrm{\&mu;}}_{\mathrm{eff}}(\frac{{\&PartialD;u}_i}{{\&PartialD;x}_j}+\frac{{\&PartialD;u}_j}{{\&PartialD;x}_i}-\frac{2}{3}{\mathrm{\&delta;}}_{\mathrm{ij}}\frac{{\&PartialD;u}_l}{{\&PartialD;x}_l})\right]$

k-equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left(\mathrm{\&rho;}{k}_i\right)=\frac{\&PartialD;}{{\&PartialD;x}_i}\left[(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_k})\frac{\&PartialD;k}{{\&PartialD;x}_j}\right]+G_k-\mathrm{\&rho;\&epsiv;}$

ε-equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left(\mathrm{\&rho;\&epsiv;}{u}_i\right)=\frac{\&PartialD;}{{\&PartialD;x}_j}\left[(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}})\frac{\&PartialD;\mathrm{\&epsiv;}}{{\&PartialD;x}_j}\right]+\frac{\mathrm{\&epsiv;}}{k}(C_{1\mathrm{\&epsiv;}}{G}_k-C_{2\mathrm{\&epsiv;}}\mathrm{\&rho;\&epsiv;})$

Energy equation:

$\frac{<span\; class="notranslate">\; \&PartialD;</span>}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&rho;E</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; eff</span>}}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; T</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; eff</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}$

Component transport equation: $\frac{{\&PartialD;\mathrm{\&rho;\; U}}_j{Y}_i}{{\&PartialD;x}_j}=\frac{\&PartialD;}{{\&PartialD;x}_j}\left[({\mathrm{\&rho;D}}_{i,m}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{sc}}_t})\frac{{\&PartialD;Y}_i}{{\&PartialD;x}_j}\right]+R_i$

Where U _i , U _j , U _l are velocity components in i, j, k directions, x _i , x _j , x _l are coordinates in i, j, k directions, ρ is gas density, p _eff is effective pressure, μ _eff is the effective viscosity, δ _ij is the Kronecker function, k is the turbulent kinetic energy, μ is the viscosity of gas molecules, μ _t is the turbulent viscosity, G _k is the generation item of turbulent kinetic energy, ε is the dissipation rate of turbulent kinetic energy, S _h is the source term in the energy equation, C _μ , C _1ε , C _2ε , σ _k , σ _ε are the standard k-ε model parameters, E is the total energy per unit mass, p is the pressure, k _eff conductivity, is the diffusion flux of the component, h _j is the enthalpy of component j, Y _j is the mass fraction of component j, D _i,m is the mass diffusion coefficient of component i in the mixture, Sc _t is the turbulent Schmidt number , R _i is the net production rate of component i caused by the chemical reaction.

Further, the radiation heat transfer model in step 2.3 adopts a discrete coordinate model, and its mathematical expression is:

$<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;n</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>$

where I is the radiation intensity, is the position vector, is the direction vector, α is the absorption coefficient, σ _s is the scattering coefficient, n is the refractive index, σ is the Stefan-Boltzmann constant, T is the flue gas temperature Φ is the phase function, Ω′ is the solid angle;

The flue gas in the furnace uses a multi-ash weighted model to calculate the radiation characteristics of the flue gas. This model approximates the blackness of the real gas as the weighted sum of the blackness of several gray gases:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; ps</span>}}<span\; class="notranslate">\; )</span>$

Where α _{ε, i} is the emissivity weighting factor of the i-th virtual gray gas, then the total absorption coefficient of the smoke can be expressed as:

When s>10 ^-4 m, $\mathrm{\&alpha;}=-\frac{\ln (1-\mathrm{\&epsiv;})}{\mathrm{the\; s}};$ When s≤10 ^-4 m, $\mathrm{\&alpha;}=\underset{i=0}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{\&epsiv;},i}{k}_{i}p.$

Further, step 3.1 dichloroethane cracking gas cracking reaction in series is

Its kinetics conform to the Arenlius formula, and the chemical reaction rate is expressed by the following formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>$

in is the production/decomposition rate of the i-th substance in the r-th reaction, ν′ _i,r , ν″ _i′r is

Stoichiometric coefficient, η′ _j,r , η″ _j,r is the reaction rate index, k _f,r is the forward reaction rate constant,

k _b,r is the rate constant of the reverse reaction, and C _j,r is the molar concentration of component j.

Furthermore, the convergence condition of the furnace model is that a new set of heat flux on the tube wall obtained by the furnace model is compared with the heat flux on the tube wall calculated in the previous time to reach a preset accuracy.

Further, the convergence condition of the furnace tube model is that a set of new tube wall temperatures obtained by the furnace tube model and the temperature of the outer wall of the furnace tube calculated in the previous calculation reach a preset accuracy.

The invention provides a coupled numerical modeling method for furnace combustion and cracking reaction in the furnace tube of an industrial dichloroethane cracking furnace. In the modeling, the dichloroethane cracking furnace is divided into a furnace model and a furnace tube model, and respectively Furnace tubes are meshed. The furnace takes the outer wall temperature given by the furnace tube model as the boundary condition, and uses the combustion model, flow model, and heat transfer model to calculate the distribution of important furnace parameters such as the furnace flue gas temperature, velocity, and component concentration; the furnace tube is calculated based on the furnace The heat flux of the furnace tube is used as the boundary condition, and the temperature, pressure, and concentration distribution of the process gas along the tube length direction are calculated by using the cracking reaction model in the tube, considering the mass conservation, momentum conservation, and energy conservation relationships in the tube, so as to facilitate the analysis of the current operating conditions Under such circumstances, important economic indicators such as dichloroethane cracking conversion rate, selectivity, and unit consumption are helpful to guide on-site process optimization. Moreover, this modeling method is applicable to various high-temperature cracking furnaces and has wide adaptability.

Description of drawings

Fig. 1 Grid division diagram of dichloroethane cracking furnace.

Fig. 2 Block diagram of iterative solution for furnace tube coupling of dichloroethane cracking furnace.

Figure 3 Furnace flue gas flow velocity field distribution diagram (y=0.0485m)

Fig. 4 Furnace flue gas temperature field distribution diagram (y=0.0485m)

Fig.5 O2 concentration distribution in furnace flue gas (y=0.0485m)

Figure 6 CO concentration distribution map in furnace flue gas (y=0.0485m)

Figure 7 CO2 concentration distribution in furnace flue gas (y=0.0485m)

Figure 8 The heat flux distribution of the furnace tube along the length direction of the furnace tube

Figure 9 Distribution of cracked gas temperature in the furnace tube along the length direction of the furnace tube

Figure 10 Distribution diagram of cracking gas velocity in the furnace tube along the length direction of the furnace tube

Figure 11 Distribution of cracked gas pressure in the furnace tube along the length direction of the furnace tube

Figure 12 Distribution diagram of cracked gas molar flow along the length of the furnace tube in the furnace tube

detailed description

The complete dichloroethane cracking furnace includes a convection section and a radiation section. The main function of the convection section is to preheat and vaporize the liquid dichloroethane and send it to the radiation section. The radiation section further uses the high-temperature flue gas released by fuel combustion to heat the dichloroethane. ethane, and make it crack rapidly, vinyl chloride and by-products form cracking gas. Therefore the present invention mainly considers the radiant section with cracking reaction, and assumes that the dichloroethane vapor temperature entering the radiant section is constant. Although in the cracking furnace, the heat transfer tightly couples various physical and chemical processes in the furnace and the furnace tube, but from the perspective of the research object, the two are relatively independent. Therefore, from the modeling point of view, the mathematical model of the furnace and the mathematical model of the furnace tube can be established separately. The interface between the furnace and the furnace tube is the outer wall of the furnace tube. The furnace model and the furnace tube model can be combined to form a complete mathematical model of the radiant section of the cracking furnace through the temperature of the heat flux on the outer wall of the tube. .

Furnace Mathematical Model

In the hearth of the dichloroethane cracking furnace, fuel and air are sprayed out from each row of the side wall, and burn rapidly, academically, it will be a fluid flow with chemical reaction. From this definition, combustion is a complex transfer and reaction process. Therefore, as long as the chemical reaction process of the flow can be accurately described, the distribution of various physical quantities in the furnace can be clearly expressed in the furnace space. Using the CFD method, the furnace can first describe the flow in the furnace, and then consider the chemical reaction and radiation and convective heat transfer on the basis of the flow. But in fact, there is no strict sequence relationship among these, but mutual causality and mutual influence: fluid flow affects the concentration distribution of components, thereby affecting chemical reactions, and changes in chemical reactions will affect heat transfer, The transfer of heat back affects the flow, and these processes are interdependent and inseparably coupled. Therefore, the establishment of the mathematical model of the furnace should organically reflect the relationship between them. Careful analysis of the physical and chemical process of combustion can also be decomposed, and the various sub-processes after decomposition can be described by several mathematical models: (1) Fluid flow model, the key is turbulence model; (2) Each component (3) Heat transfer model, including convective heat transfer and radiation heat transfer, the key of which is the radiation heat transfer model.

(1) Fluid flow model

In the cracking furnace, it is assumed that the flue gas flow is embodied in a turbulent flow mode, so the flue gas flow is described in the Reynolds average conservation equation assumed by the turbulent transport item, so that the simultaneous equations are closed. Because the burner installed in the furnace of the cracking furnace sprays the fuel at a high speed, and burns and releases heat in the furnace, the flow rate of the formed flue gas is very fast, so the flow in the furnace is basically in a turbulent state, and its flow law is relatively complicated. The existing influential turbulence models include: zero equation model, single equation model, double equation model, algebraic stress model, Reynolds stress model and other multi-equation models. Among these models, the two-equation model is more commonly used. Previous research results show that the algebraic stress model and the Reynolds stress model are the best, but they are the most difficult to implement and require high computer performance; the k-ε model is a two-equation model, which has a wide range of applications, high precision, and relatively easy solution. The advantages. Therefore, the present invention selects a standard k-ε double-equation model based on the Reynolds-averaged Navier-Stokes (RANS) equation to establish a closed mathematical model. Mass, momentum, turbulent kinetic energy, dissipation rate of turbulent kinetic energy, energy and component transport equations are expressed as follows:

Continuity equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left({\mathrm{\&rho;U}}_i\right)=0$

Momentum equation: $\frac{\&PartialD;}{{\&PartialD;x}_j}\left({\mathrm{\&rho;U}}_i{u}_j\right)=\frac{{\&PartialD;p}_{\mathrm{eff}}}{{\&PartialD;x}_i}+\frac{\&PartialD;}{{\&PartialD;x}_j}\left[{\mathrm{\&mu;}}_{\mathrm{eff}}(\frac{{\&PartialD;u}_i}{{\&PartialD;x}_j}+\frac{{\&PartialD;u}_j}{{\&PartialD;x}_i}-\frac{2}{3}{\mathrm{\&delta;}}_{\mathrm{ij}}\frac{{\&PartialD;u}_l}{{\&PartialD;x}_l})\right]$

k-equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left(\mathrm{\&rho;}{k}_i\right)=\frac{\&PartialD;}{{\&PartialD;x}_j}\left[(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_k})\frac{\&PartialD;k}{{\&PartialD;x}_j}\right]+G_k-\mathrm{\&rho;\&epsiv;}$

ε-equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left(\mathrm{\&rho;\&epsiv;}{u}_i\right)=\frac{\&PartialD;}{{\&PartialD;x}_j}\left[(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}})\frac{\&PartialD;\mathrm{\&epsiv;}}{{\&PartialD;x}_j}\right]+\frac{\mathrm{\&epsiv;}}{k}(C_{1\mathrm{\&epsiv;}}{G}_k-C_{2\mathrm{\&epsiv;}}\mathrm{\&rho;\&epsiv;})$

Energy equation: $\frac{\&PartialD;}{{\&PartialD;x}_i}\left[u_i(\mathrm{\&rho;E}+p)\right]=\frac{\&PartialD;}{{\&PartialD;x}_j}(k_{\mathrm{eff}}\frac{\&PartialD;T}{{\&PartialD;x}_j}-\underset{j}{\mathrm{\&Sigma;}}{h}_j{\stackrel{\&Right\; Arrow;}{J}}_j+u_i{\mathrm{\&mu;}}_{\mathrm{eff}}[(\frac{{\&PartialD;u}_j}{{\&PartialD;x}_i}+\frac{{\&PartialD;u}_i}{{\&PartialD;x}_j})-\frac{2}{3}\frac{{\&PartialD;u}_l}{{\&PartialD;x}_l}{\mathrm{\&delta;}}_{\mathrm{ij}}\left]\right)+S_h$

Component transport equation: $\frac{{\&PartialD;\mathrm{\&rho;U}}_j{Y}_i}{{\&PartialD;x}_j}=\frac{\&PartialD;}{{\&PartialD;x}_j}\left[({\mathrm{\&rho;D}}_{i,m}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{sc}}_t})\frac{{\&PartialD;Y}_i}{{\&PartialD;x}_j}\right]+R_i$

in $p_{\mathrm{eff}}=p+\frac{2}{3}\mathrm{\&rho;k},$ μ _eff =μ+μ _t , ${\mathrm{\&mu;}}_t={\mathrm{\&rho;C}}_{\mathrm{\&mu;}}\frac{k^2}{\mathrm{\&epsiv;}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1(i=j)\\ 0(i\&NotEqual;j)\end{array}\right.,$ $G_k={\mathrm{\&mu;}}_t[(\frac{{\&PartialD;\mathrm{\&mu;}}_i}{{\&PartialD;x}_j}+\frac{{\&PartialD;\mathrm{\&mu;}}_j}{{\&PartialD;x}_i})-\frac{2}{3}\frac{{\&PartialD;\mathrm{\&mu;}}_l}{{\&PartialD;x}_l}{\mathrm{\&delta;}}_{\mathrm{ij}}]\frac{{\&PartialD;u}_i}{{\&PartialD;x}_j},$ k _eff =k+k _t , $\mathrm{E.}=h-\frac{p}{\mathrm{\&rho;}}+\frac{u^2}{2}$ $h=\underset{j}{\mathrm{\&Sigma;}}{Y}_j{h}_j,$ $h_j={\&Integral;}_{T_{\mathrm{ref}}}^T{c}_{p,j}\mathrm{dT},$ The parameters of the standard k-ε model are C _μ =0.09, σ _k =1.0, σ _ε =1.3, C _1ε =1.44 and C _2ε =1.92. For the calculation of component enthalpy, T _ref is set to 298.15K.

(2) Combustion model

The industrial dichloroethane cracking furnaces currently established all adopt the side wall burner heating combustion mode. The simulated object of the present invention is a dichloroethane cracking furnace of a Mitsui device, which also adopts side wall burners for heating, and two rows of premixed burners are respectively arranged on both sides of the cracking furnace wall, and a total of 136, i.e. fuel It is pre-mixed with air and sprayed out for combustion.

Fuel and air are ejected from the nozzle to form a high-speed jet and react quickly. The present invention uses a turbulence-chemical reaction interaction model, ie, a vortex dissipation model, to describe the combustion of the wall burner. In the finite rate model, the chemical source term is calculated by the Arrhenius formula, and the chemical reaction net source term of the chemical substance i is calculated by the sum of the Arrhenius reaction sources of the N _R chemical reactions in which it participates:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}$

where M _w,i is the molecular weight of the i-th substance, is the production/decomposition rate of the i-th substance in the r-th reaction, and its expression is:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>$

In the eddy dissipation model, the production rate R _i,k of species k in reaction r is given by the smaller of the following two expressions:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; A\&rho;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; R</span>}}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; AB\&rho;</span>}\frac{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}$

In this model, liquefied petroleum gas (LPG) is used as the fuel gas of the ethylene dichloride cracking furnace, and the main components include C ₃ H ₈ /C ₄ H ₆ /C ₄ H ₈ /C ₄ H ₁₀ . The present invention adopts a one-stage serial combustion reaction model.

C ₃ H ₈ +3.5O ₂ →3CO+4H ₂ O

C ₄ H ₆ +3.5O ₂ →4CO+3H ₂ O

C ₄ H ₈ +4O ₂ →4CO+4H ₂ O

C ₄ H ₁₀ +4.5O ₂ →4CO+5H ₂ O

CO+0.5O ₂ →CO ₂

(3) Radiation model

Since the discrete coordinate model can be applied to media of any optical depth, it can not only calculate the radiation heat transfer between gas and particles, but also allow the use of the gray belt model to calculate non-gray body radiation, not only considering the influence of scattering, but also allowing specular reflection and radiation in translucent media, especially for problems with localized heat sources. In addition, the discrete coordinate algorithm has been widely used because of its simplicity, reliability, and small amount of calculation. The radiation heat transfer model of this patent applies the discrete coordinate model (DiscreteOrdinates) to solve the radiation propagation equation issued by a finite number of discrete solid angles. The number of radiation propagation equations is the same as the appropriate number of neutralization directions in the space coordinate system, and its mathematical expression is :

$<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;n</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$

The furnace is filled with a large amount of flue gas, which (especially CO, CO ₂ and H ₂ O) participates in radiative heat transfer. In these flue gases, CO ₂ and H ₂ O have different absorption broadband. The multi-grey gas weighted model (WSGGM) was used in this simulation to calculate the radiative properties of the flue gas. This model divides the blackness of real gas into the weighted sum of several gray gas blacknesses, the expression is as follows:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; ps</span>}}<span\; class="notranslate">\; )</span>$

For the open area, due to its high spectral absorptivity, the absorption coefficient of the i=0 component is set to 0, and the weighted value of its absorption coefficient is:

${\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}$

The temperature-dependent a _ε,i can be approximated (fitted) by any function, but generally takes the following form:

${\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

The total absorption coefficient of the mixed gas is calculated as follows:

When s>10 ^-4 m, $\mathrm{\&alpha;}=-\frac{\ln (1-\mathrm{\&epsiv;})}{\mathrm{the\; s}};$ When s≤10 ^-4 m, $\mathrm{\&alpha;}=\underset{i=0}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{\&epsiv;},i}{k}_{i}p.$

Furnace Tube Mathematical Model

In the reaction tube, the cracking raw material is undergoing complex cracking reactions while undergoing fluid flow, heat transfer and mass transfer. From the point of view of the transfer process, the furnace tube and the furnace are both fluid flows with chemical reactions. The only difference is that there is one less radiation heat transfer process in the tube. From the perspective of chemical reaction, although the cracking reaction mechanism of raw materials in the tube is different from the combustion reaction mechanism in the furnace, the equations that need to be solved for both are similar, and both are component equations. Therefore, the equations involved in each model in the tube are basically the same as those in the furnace, except for one radiation heat transfer equation.

(1) Kinetic model of pyrolysis reaction

For the cracking reaction process of dichloroethane, it is treated with a first-order series reaction model:

(2) Mathematical model of in-tube transfer reaction

When using the first-order series reaction model to calculate the composition distribution in the tube, CFD needs to solve the composition process, and the most important thing is to determine the source term in the equation, and this source term reflects the influence of chemical reactions. The kinetics of the cleavage reaction conforms to the Arenlius formula, therefore, the chemical reaction rate is expressed by the following formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>$

In CFD simulations, this formula is also called the finite rate model (FRC). When calculating the transfer reaction process in the tube, in addition to calculating the four component equations, it is also necessary to solve the above-mentioned fluid flow equation and energy equation. The form of the equation is the same as that in the furnace, so it will not be described again. The total 11 equations. Finally, to make these partial differential equations have definite solutions, the corresponding boundary conditions must be given to close the entire system of equations.

(3) Material properties

Gas physical properties such as density, heat capacity, viscosity, thermal conductivity and diffusion coefficient in the mathematical model of the reaction tube are calculated by the following formulas.

The process gas in the reaction tube is under high temperature and low pressure, and the density of the mixed gas is calculated by the ideal gas state equation.

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; RT\&Sigma;</span>}\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}$

One-component viscosity is calculated by kinetic theory: in,

The viscosity of the cracked mixed gas is obtained by the weighting technique of the viscosity formula of one component:

in,

Single-component gas heat capacity: C _pi =A _i +B _i T+C _i T ² +D _i T ³ , then the mixed gas heat capacity:

In the formula, A _i , B _i , C _i , D _i are the heat capacity calculation coefficients of component i.

The single-component thermal conductivity is calculated by kinetic theory: then mixed

Gas thermal conductivity:

The diffusion coefficient between the two components is calculated from kinetic theory: in, ${\mathrm{\&Omega;}}_{\mathrm{D.}}={\mathrm{\&Omega;}}_{\mathrm{D.}}\left(\frac{T}{{(\mathrm{\&epsiv;}/k)}_{\mathrm{ij}}}\right),$ ${(\mathrm{\&epsiv;}/k)}_{\mathrm{ij}}=\sqrt{{(\mathrm{\&epsiv;}/k)}_i{(\mathrm{\&epsiv;}/k)}_j},$ ${\mathrm{\&sigma;}}_{\mathrm{ij}}=\frac{1}{2}({\mathrm{\&sigma;}}_i+{\mathrm{\&sigma;}}_j).$ From this, the diffusion coefficient of the mixed gas can be obtained:

Coupling Simulation of Dichloroethane Furnace and Furnace Tube

meshing

Due to the symmetry of the dichloroethane cracking furnace, in order to reduce the amount of CFD calculations, only half of the dichloroethane cracking furnace is used for simulation along the width direction. Mesh division of the furnace: Tetrahedral elements are used to divide the grids of the burner area and the furnace tube area; hexahedral elements are used to divide the grids of other areas of the furnace. Grid division of the furnace tube: the hexahedron unit is used to divide the grid of the wall of the furnace tube; the hybrid unit is used to divide the grid of the connection part of the furnace tube. The mesh division of the furnace and furnace tube is shown in Figure 1:

Boundary conditions

(1) Inlet boundary conditions: Determine the gas inlet flow rate of the side wall burner, the air inlet flow rate, and the gas flow rate and temperature at the reaction tube inlet according to the process parameters.

(2) Wall boundary conditions: the reaction tube and the furnace wall are assumed to have no slip, that is, the values of all physical quantities on the wall are 0; the flow and heat transfer in the viscous bottom layer near the wall are approximated by standard wall functions; The thermal boundary of the heat flux is assigned to the boundary condition of heat flux through heat loss; the temperature boundary of the furnace tube wall is assigned to the tube wall by adopting the temperature initially assumed by the actual working conditions of the factory and operating experience, and can be assigned by a user-defined function (UDF). The outer wall heat flux UDF function is defined as: Q(x)=a ₁ +b ₁ x+c ₁ x ² +d ₁ x ³ +e ₁ x ⁴ +f ₁ x ⁵ , in the furnace model, the temperature of the outer wall of the furnace tube UDF is defined as T(x)=a ₂ +b ₂ x+c ₂ x ² +d ₂ x ³ +e ₂ x ⁴ +f ₂ x ⁵ ;.

(3) Outlet boundary conditions: Determine the outlet pressure of the cracking furnace flue gas and the cracking gas outlet pressure of the furnace tube according to the process conditions.

Coupled simulation solver

The mathematical models of the above-mentioned transfer and reaction in the furnace and tube are respectively established on the computational fluid dynamics platform Ansys14.0 (fluent). However, we say that these two sets of mathematical models do not exist in isolation, but are interconnected and coupled together. The "link" of this connection is the temperature and heat flux of the tube wall, so the two must be coupled through the thermal boundary The calculation can get the final result, the specific algorithm is as follows:

(1) The present invention selects a group of tube wall temperatures actually measured as the initial value, assigns it to the tube wall boundary in the furnace model, thereby calculates the combustion and flow process of the fuel gas in the furnace, and obtains a group of verification furnaces A set of heat flux data distributed along the length of the tube. This group of heat flux data is compared with the heat flux data calculated last time, if the difference between the two reaches the specified accuracy.

(2) Assign the heat flux calculated in (1) to the tube wall boundary of the established tube model, and obtain a new set of tube wall temperatures by calculating the heat transfer of the furnace tube and the cracking process in the tube. (3) compare the temperature of a group of new tube walls calculated in (2) with the temperature of the outer wall of the furnace tube calculated in the previous time, if the difference between the two reaches the specified accuracy (the accuracy of the present invention is less than 1°C ), the calculation stops, otherwise, repeat steps (1) and (2) to continue iterating until the calculation accuracy is satisfied.

The coupled solution process of the furnace combustion heat transfer model and the in-pipe transfer reaction model of the dichloroethane cracking furnace is shown in Figure 2.

Result analysis

Determine the boundary conditions, close the degrees of freedom of CFD calculation, and through CFD simulation, the detailed distribution of important variables in the furnace and furnace tube can be obtained. Fig. 3 to Fig. 7 show the velocity field, temperature field, CO, O2, and CO2 concentration field distribution of the furnace flue gas on the tangent plane in the direction of the furnace width direction y=0.0485m respectively. Figures 8 to 12 show the distribution curves of the heat flux of the furnace tube, the temperature of the cracked gas in the tube, the velocity of the cracked gas in the tube, the pressure of the cracked gas in the tube, and the components of the cracked gas in the tube along the length of the furnace tube. From the data analysis in Table 1, it can be seen that the key data simulated by this CFD method has a small error with the field measured data, so it can be seen that the modeling of dichloroethane cracking furnace using the above CFD method is very accurate.

Table 1 Comparison table of key data between CFD modeling and one-dimensional modeling methods

Appendix Symbol Table

A empirical constant

B empirical constant

C _j,r is the molar concentration of component j in reaction r, kgmol/m ³

C _pi heat capacity of single component i, J/kg/K

D _i, the mass diffusion coefficient of component i in a mixture of m, m ² /s

D _ij Binary mass diffusion coefficient of component i in j, m ² /s

D _t Effective mass diffusion coefficient due to turbulent flow, m ² /s

E total energy per unit mass, J/kg

Generation term of G _k turbulent kinetic energy, J/m ³ /s

hSensible enthalpy, J/kg

h _j enthalpy of component j, J/kg

I Radiation intensity, J/m ² /s

Diffusion flux of components, kg/m ² /s

k Turbulent kinetic energy, m ² /s ^-2

k _eff effective conductivity, W/m/K

k _f,r forward rate constant of reaction r, 1/s

Reverse rate constant of k _b,r reaction r, 1/s

k _i The absorption coefficient of the i-th gray gas, 1/m

k _t Turbulent thermal conductivity, W/m/K

_{Mw, the molecular weight of i} component i, g/mol

nRefractive index

The number of chemical species in the N system

The sum of the p pressure and the partial pressure of all absorbed gases, Pa

p _eff effective pressure, Pa

position vector

R ideal gas constant, R=8.314J/mol/K

R _i Net production rate of component i caused by chemical reaction, gmol/m ³ /s

R _j j is the reaction rate in which j participates, kmol/m/s

direction vector

Scattering Direction Vector

s path length

Sc _t turbulent Schmidt number

Source term in S _h energy equation, J/m ³ /s

T local temperature and oil gas temperature, K

Velocity components in U _i , U _j , U _l i,j,k directions, m/s

x _i , x _j , x _l i, j, k coordinates, m

Mole fraction of X _i component i

Mass fraction of Y _j component j

Mass fraction of Y _P product P

Mass fraction of Y _R reactant R

α absorption coefficient, 1/m and conversion factors dependent on _pt units

α _ε,i is the emissivity weighting factor of the i-th virtual gray gas

δ _ij Kronecker function

Dissipation rate of ε turbulent kinetic energy, m ² /s ³ and emission rate

ε/k Leonard-Jones potential energy parameter, K

μ Viscosity of gas molecules, kg/m/s

μ _eff effective viscosity, kg/m/s

μ _t turbulent viscosity, kg/m/s

ρgas density, kg/m ³

Γ The net effect of the third object on the reaction rate

ν′ _i,r stoichiometric coefficient of reactant i in reaction r

ν″ _{i, the stoichiometric coefficient of product i in r} reaction r

η′ _j,r velocity exponent of reactant j in reaction r

η″ _j,r velocity index of product j in reaction r

σStefan-Boltzmann constant, σ=5.672×10 ^-8 W/m ² K ⁴

σi Leonard-Jones collision diameter of component _i , angstrom

σ _S scattering coefficient, 1/m

Φ phase function

Ω′ solid angle

Ω _D diffusion collision integral

Ω _μi Viscosity collision integration number of component i

The above descriptions are illustrative only, not restrictive. Any equivalent modifications or changes made without departing from the spirit and scope of the present invention shall be included in the appended claims.

Claims (7)

1. A coupled numerical modeling method for combustion of a hearth of an industrial dichloroethane cracking furnace and cracking reaction in the furnace tube is characterized by comprising the following steps:

step 1: determining the size of a furnace tube of a hearth of the dichloroethane cracking furnace to be simulated, and performing grid division on the hearth and the furnace tube; determining boundary conditions according to process parameters, including: the gas inlet flow and the air inlet flow of the side wall burner, the inlet gas flow and the temperature of the reaction tube, the heat loss coefficient of the furnace wall, the outlet pressure of the hearth flue gas and the outlet pressure of the furnace tube cracking gas;

the mesh division is carried out on the hearth and the furnace tube, wherein a burner area and a furnace tube area in the hearth adopt tetrahedral units for dividing meshes; other areas of the hearth adopt hexahedral units for dividing grids; the wall surface of a straight pipe of the furnace tube in the furnace tube model adopts hexahedral units to divide grids; the bent pipe adopts a mixture unit to divide grids;

step 2: establishing a hearth model:

step 2.1: a flue gas flow model in the hearth adopts a standard k-double-stroke model based on a Reynolds average equation to establish a closed model;

step 2.2: a first-stage series combustion reaction model is adopted for fuel gas in a hearth, and a finite rate/vortex dissipation model is adopted for a flow model during combustion;

step 2.3: the radiation heat transfer model in the hearth adopts a discrete coordinate model, and the hearth flue gas adopts a multi-ash gas weighting model to calculate the radiation characteristic of the hearth flue gas;

and step 3: establishing a furnace tube model:

step 3.1: the ethylene dichloride cracking reaction in the furnace tube adopts a first-stage series reaction model, and the cracking reaction kinetics conforms to an Allen-Raeus formula;

step 3.2, determining parameters of a gas density, heat capacity, viscosity, heat conductivity coefficient and diffusion coefficient calculation formula in the furnace tube model;

and 4, step 4: based on the serious heat coupling relationship between the hearth and the furnace tube and the initial condition and the boundary condition obtained in the step 1, the outer wall temperature and the heat flux of the furnace tube are used as mutual iterative coupling variables when numerical values of the hearth model and the furnace tube model are solved, and the hearth model and the furnace tube model are circularly iterated until the model converges to obtain the model related to each parameter;

in the step 2 and the step 3, the furnace tube and the wall surface of the hearth wall are regarded as non-slip boundaries; in the viscous bottom layer near the wall surface, a standard wall surface function is adopted to approximate the flow and heat exchange in the actual process; the heat boundary on the hearth wall gives a heat flux boundary condition through heat loss; the boundary of the wall surface of the furnace tube is assigned to the wall surface by a self-defined function, and in the model of the furnace tube, the self-defined function of the heat flux of the outer wall of the furnace tube is defined as Q (x) a₁+b₁x+c₁x²+d₁x³+e₁x⁴+f₁x⁵In the furnace chamber model, the furnace tube outer wall temperature customized function is defined as T (x) a₂+b₂x+c₂x²+d₂x³+e₂x⁴+f₂x⁵Wherein a is₁、b₁、c₁、d₁、e₁、f₁、a₂、b₂、c₂、d₂、e₂、f₂X is a coordinate along the radial direction of the furnace tube as a parameter to be fitted; q is the heat flux, and T is the furnace tube outer wall temperature.

2. The coupled numerical modeling method for furnace chamber combustion and in-furnace cracking reaction of an industrial dichloroethane cracking furnace according to claim 1, characterized in that the first-stage series combustion model in step 2.2 is:

$C_x{H}_y+(\frac{x}{2}+\frac{y}{4})O_2=xCO+\frac{y}{2}{H}_{2}O$

$CO+\frac{1}{2}{O}_2={\mathrm{CO}}_2;$

using a finite rate model, the chemical source term is calculated using the Arrhenius formula:

$R_i=M_{w,i}\underset{r=1}{\overset{N_R}{\&Sigma;}}{\hat{R}}_{i,r}$

M_w,iis the molecular weight of component i, N_RFor the number of equations, R_iThe net production rate of component i caused by the chemical reaction,the production/decomposition rate of the ith substance in the r reaction is expressed as:

${\hat{R}}_{i,r}=\mathrm{\&Gamma;}({\mathrm{\&nu;}}_{i,r}^{\&prime;\&prime;}-{\mathrm{\&nu;}}_{i,r}^{\&prime;})\left(k_{f,r}\underset{j=1}{\overset{N}{\&Pi;}}{\&lsqb;C_{j,r}\&rsqb;}^{({\mathrm{\&eta;}}_{j,r}^{\&prime;}+{\mathrm{\&eta;}}_{j,r}^{\&prime;\&prime;})}\right)$

wherein the net effect of the third object on the reaction rate, v'_i,r，ν″_i,rIs the stoichiometric coefficient, k_f,rForward reaction rate constant, C_j,rIs molar concentration, η'_j,r，η″_j,rIs the rate index, N is the total number of substances participating in the reaction;

using a vortex dissipation model, the rate of production R of a substance k in a reaction R_i,kThe smaller of the two terms in the following formula:

$R_{i,k}=min\&lsqb;{\mathrm{\&nu;}}_{i,k}^{\&prime;}{M}_{w,i}A\mathrm{\&rho;}\frac{\mathrm{\&epsiv;}}{k}min\left(\frac{Y_R}{{\mathrm{\&nu;}}_{R,k}^{\&prime;}{M}_{w,R}}\right),{\mathrm{\&nu;}}_{i,k}^{\&prime;}{M}_{w,i}AB\mathrm{\&rho;}\frac{\mathrm{\&epsiv;}}{k}\frac{{\mathrm{\&Sigma;}}_P{Y}_P}{{\mathrm{\&Sigma;}}_j^N{\mathrm{\&nu;}}_{j,k}^{\&prime;\&prime;}{M}_{w,j}}\&rsqb;$

v 'therein'_i,k，ν′_R,k，ν″_j,kIs a stoichiometric coefficient, M_w,i，M_w,R，M_w,jMolecular weight, A, B are empirical coefficients, ρ gas density,is the Lonned-Jones potential energy parameter, Y_R，Y_PIs the mass fraction of the product.

3. The method for modeling the coupling value of the furnace chamber combustion and the in-furnace cracking reaction of the industrial dichloroethane cracking furnace according to claim 1, wherein a closed mathematical model is established based on a standard k-two-equation model of the Reynolds average Navier-Stokes equation in step 2.1, and the mass, momentum, turbulence energy, dissipation ratio of the turbulence energy, energy and component transport equations are expressed as follows:

continuity equation: $\frac{\&part;}{\&part;x_i}\left({\mathrm{\&rho;U}}_i\right)=0$

the momentum equation: $\frac{\&part;}{\&part;x_j}\left({\mathrm{\&rho;U}}_i{U}_j\right)=\frac{\&part;p_{eff}}{\&part;x_i}+\frac{\&part;}{\&part;x_j}\&lsqb;{\mathrm{\&mu;}}_{eff}(\frac{\&part;U_i}{\&part;x_j}+\frac{\&part;U_j}{\&part;x_i}-\frac{2}{3}{\mathrm{\&delta;}}_{ij}\frac{\&part;U_l}{\&part;x_l})\&rsqb;$

k-equation: $\frac{\&part;}{\&part;x_i}\left({\mathrm{\&rho;kU}}_i\right)=\frac{\&part;}{\&part;x_j}\&lsqb;(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_k})\frac{\&part;k}{\&part;x_j}\&rsqb;+G_k-\mathrm{\&rho;}\mathrm{\&epsiv;}$

-the equation: $\frac{\&part;}{\&part;x_i}\left({\mathrm{\&rho;\&epsiv;U}}_i\right)=\frac{\&part;}{\&part;x_j}\&lsqb;(\mathrm{\&mu;}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}})\frac{\&part;\mathrm{\&epsiv;}}{\&part;x_j}\&rsqb;+\frac{\mathrm{\&epsiv;}}{k}(C_{1\mathrm{\&epsiv;}}{G}_k-C_{2\mathrm{\&epsiv;}}\mathrm{\&rho;}\mathrm{\&epsiv;})$

energy equation:

$\frac{\&part;}{\&part;x_i}\&lsqb;U_i\left(\mathrm{\&rho;}E+p\right)\&rsqb;=\frac{\&part;}{\&part;x_j}\left(k_{eff}\frac{\&part;T}{\&part;x_j}-\underset{j}{\&Sigma;}{h}_j{\stackrel{\&RightArrow;}{J}}_j+U_i{\mathrm{\&mu;}}_{eff}\&lsqb;\left(\frac{\&part;U_j}{\&part;x_i}+\frac{\&part;U_i}{\&part;x_j}\right)-\frac{2}{3}\frac{\&part;U_l}{\&part;x_l}{\mathrm{\&delta;}}_{ij}\&rsqb;\right)+S_h$

component transport equation: $\frac{\&part;{\mathrm{\&rho;U}}_j{Y}_i}{\&part;x_j}=\frac{\&part;}{\&part;x_j}\&lsqb;({\mathrm{\&rho;D}}_{i,m}+\frac{{\mathrm{\&mu;}}_t}{{\mathrm{Sc}}_t})\frac{\&part;Y_i}{\&part;x_j}\&rsqb;+R_i$

wherein U is_i,U_j,U_lIs the velocity component in the i, j, k direction, x_i,x_j,x_lIs the coordinate in the i, j, k direction, p is the gas density, p_effEffective pressure, mu_effIn order to be of an effective viscosity,_ijis a function of kronecker, k is the kinetic energy of turbulence, μ is the viscosity of the gas molecule, μ_tFor turbulent viscosity, G_kFor the generation term of turbulent kinetic energy, for the dissipation ratio of turbulent kinetic energy, S_hAs a source term in the energy equation, C_μ,C₁,C₂,σ_k，σ Is a standard k-model parameter, E is the total energy per unit mass, p is the pressure, k_effThe conductivity of the water is measured by the conductivity meter,is the diffusion flux of the component, h_jIs the enthalpy of component j, Y_jIs the mass fraction of component j, D_i,mIs the mass diffusion coefficient of component i, Sc, in the mixture_tIs the turbulent Schmitt number, R_iIs the net production rate of component i caused by the chemical reaction.

4. The coupled numerical modeling method for combustion of the furnace chamber of the industrial dichloroethane cracking furnace and the cracking reaction in the furnace tube as recited in claim 1, characterized in that the radiation heat transfer model in step 2.3 adopts a discrete coordinate model, and the mathematical expression of the model is as follows:

$\&dtri;\&CenterDot;\left(I\right(\stackrel{\&RightArrow;}{r},\stackrel{\&RightArrow;}{s}\left)\stackrel{\&RightArrow;}{s}\right)+(\mathrm{\&alpha;}+{\mathrm{\&sigma;}}_s)I(\stackrel{\&RightArrow;}{r},\stackrel{\&RightArrow;}{s})={\mathrm{\&alpha;n}}^2\frac{{\mathrm{\&sigma;T}}^4}{\mathrm{\&pi;}}+\frac{{\mathrm{\&sigma;}}_s}{4\mathrm{\&pi;}}{\&Integral;}_0^{4\mathrm{\&pi;}}I(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{s}}^{\&prime;})\mathrm{\&Phi;}(\stackrel{\&RightArrow;}{s}\&CenterDot;{\stackrel{\&RightArrow;}{s}}^{\&prime;}){\mathrm{d\&Omega;}}^{\&prime;};$

wherein I is the intensity of radiationThe degree of the magnetic field is measured,in the form of a position vector, the position vector,is a direction vector, α is an absorption coefficient, σ_sThe scattering coefficient is n, the refractive index is n, the sigma is a Stefan-Boltzmann constant, T is the flue gas temperature phi which is a phase function, and omega' is a solid angle;

the radiation characteristic of the flue gas in the hearth is calculated by adopting a multi-ash-gas weighted model, and the model approximately processes the blackness of the real gas into the weighted sum of the blackness of a plurality of ash gases:

$\mathrm{\&epsiv;}=\underset{i=0}{\overset{I}{\&Sigma;}}{\mathrm{\&alpha;}}_{\mathrm{\&epsiv;},i}\left(T\right)(1-e^{-k_{i}ps})$

α therein_,iThe emissivity weighting factor of the ith kind of virtual ash gas, the total absorption coefficient of the flue gas can be expressed as:

when s > 10^-4m, $\mathrm{\&alpha;}=-\frac{ln(1-\mathrm{\&epsiv;})}{s};$ When s is less than or equal to 10^-4m， $\mathrm{\&alpha;}=\underset{i=0}{\overset{I}{\&Sigma;}}{\mathrm{\&alpha;}}_{\mathrm{\&epsiv;},i}{k}_{i}p.$

5. The coupled numerical modeling method for combustion of industrial dichloroethane cracking furnace and cracking reaction in furnace according to claim 1, characterized in that the step 3.1 of first-stage series cracking reaction of dichloroethane cracking gas is

The kinetics of the method accord with an Allen-Raeus formula, and the chemical reaction rate is represented by the following formula:

${\hat{R}}_{i,r}=\mathrm{\&Gamma;}({\mathrm{\&nu;}}_{i,r}^{\&prime;\&prime;}-{\mathrm{\&nu;}}_{i,r}^{\&prime;})(k_{f,r}\underset{j=1}{\overset{N}{\&Pi;}}\&lsqb;C_{j,r}\&rsqb;{\mathrm{\&eta;}}_{j,r}^{\&prime;}-k_{b,r}\underset{j=1}{\overset{N}{\&Pi;}}\&lsqb;C_{j,r}\&rsqb;{\mathrm{\&eta;}}_{j,r}^{\&prime;\&prime;})$

whereinIs the production/decomposition rate of the ith substance in the r-th reaction, v'_i,r，ν″_i,rIs stoichiometric coefficient, η'_j,r，η″_j,rIs a reaction rate index, k_f,rIs a forward reaction rate constant, k_b,rAs a reverse reaction rate constant, C_j,rIs the molar concentration of component j.

6. The coupled numerical modeling method for furnace combustion and in-furnace cracking reactions of an industrial dichloroethane cracking furnace according to claim 1, characterized in that the furnace model convergence condition is that the heat flux on the tube wall obtained by the furnace model for a new group of tube walls reaches a preset accuracy compared with the heat flux on the tube wall obtained by the previous calculation.

7. The coupled numerical modeling method for furnace chamber combustion and in-furnace cracking reactions of an industrial dichloroethane cracking furnace according to claim 1, characterized in that the furnace model convergence condition is that a new set of wall temperatures obtained by the furnace model reaches a preset accuracy compared with the previously calculated furnace wall temperature.