Modeling method for flow model of industrial dehydrogenation double-ring radial reactor

Abstract

The invention provides a modeling method for a flow model of an industrial dehydrogenation double-ring radial reactor, which comprises the following steps of: deducing the flow model of the industrial dehydrogenation reactor according to a modified momentum equation, an Ergun equation and a continuity equation, and simulating fluid mechanics behaviors of reactant flow in a main runner and a catalyst bed layer; a modeling method for solving the mathematical model of the double-ring radial reactor by adopting a numerical algorithm; a numerical algorithm is adopted to solve a mathematical model of the double-ring radial reactor, accurate mathematical description of fluid mechanics behaviors in the industrial dehydrogenation reactor is achieved, and quantitative reference is provided for optimization selection of the structural size of the industrial double-ring radial reactor on the basis. A newly-built industrial dehydrogenation reactor based on the method can realize more balanced utilization of the catalyst at different parts, so that the treatment capacity of the dehydrogenation reactor and the overall utilization efficiency of the catalyst are improved.

Description

Technical Field

[0001] The present invention relates to the field of petrochemical industry, and more particularly to a flow modeling method for an industrial dehydrogenation double-ring radial reactor. Background Art

[0002] Alkane dehydrogenation processes include long-chain alkane dehydrogenation and low-carbon alkane dehydrogenation. Typically, the dehydrogenation reaction is carried out in an axial or radial plug-flow adiabatic reactor in the presence of hydrogen. Linear alkanes undergo dehydrogenation over a platinum catalyst supported on alumina or zeolite to produce linear monoolefins. The dehydrogenation process is accompanied by side reactions such as isomerization, cracking, and dimerization. The gas velocity and pressure distribution within the reactor affect the conversion and selectivity of the dehydrogenation reaction. Therefore, studying the hydrodynamic behavior of alkanes and hydrogen within the reactor has high industrial application value and can also provide a reference for improving dehydrogenation equipment.

[0003] A radial flow reactor is a gas-solid catalytic reactor in which reactants pass radially through a catalytic bed. It generally consists of a central flow channel, an annular catalyst bed, and an annular flow channel. Fluid enters the reactor axially from the central channel (or annular channel), flows axially and radially simultaneously, passing through the annular catalyst bed and converging into the annular channel (or central channel), exiting the reactor axially at either the same or the other end. Compared to axial flow reactors, radial flow reactors offer a larger flow area, lower flow rates, shorter flow paths, and lower bed pressure.

[0004] Radial flow reactors are currently widely used in fields such as petrochemicals, chemical synthesis, energy, and the environment, achieving excellent results. Years of research and production practice have deepened our understanding of the fluid flow, gas distribution, heat transfer, mass transfer, stability, and operational control within radial reactors. It is believed that their performance is primarily determined by the axial distribution of the fluid along the catalytic bed. Uneven fluid distribution can affect the bed temperature and concentration profiles, reactor stability, and reaction conversion and selectivity. Therefore, the study of reactor fluid dynamics is fundamental and crucial to its design.

[0005] In 2016, Jiang Hongbo et al. published a one-dimensional flow model for a double-ring radial reactor, using a one-dimensional model based on ideal reactor conditions to simulate the flow of fluid in the reactor. The establishment of the one-dimensional model is based on the ideal assumption that the fluid passes through the catalyst bed in a strictly radial direction. However, the gas phase fluid does not flow in an ideal one-dimensional direction when passing through the catalyst bed. In actual reactors, there is axial gas flow in the catalyst bed. In 2017, Jiang Hongbo et al. published a two-dimensional flow model for a double-ring radial reactor. However, in this model, the distribution ratio of the flow rate of the inner annular gap fluid to the inner and outer catalyst beds is given by an artificially defined distribution function, which may differ from the actual situation. A more reasonable two-dimensional flow model and a more efficient numerical calculation method are yet to be studied. In view of this, it is necessary to improve the existing technology to solve the above problems. Summary of the Invention

[0006] The object of the present invention is to disclose a flow modeling method for an industrial dehydrogenation double-ring radial reactor, which derives the flow model of the industrial dehydrogenation reactor from a modified momentum equation, an Ergun equation, and a continuity equation, simulates the fluid mechanics behavior of the reactant flow in the main channel and the catalyst bed, and uses a numerical algorithm to solve the mathematical model of the double-ring radial reactor.

[0007] To achieve the above-mentioned object, the present invention provides a flow modeling method for an industrial dehydrogenation double-ring radial reactor. The method is based on a double-ring radial reactor, wherein an inner annular gap and an outer annular gap are coaxially arranged in sequence from the inside to the outside around a central tube. When the material enters the reactor axially from the inner annular gap flow channel of the reactor, the fluid in the inner annular gap is radially divided into two streams. One part of the fluid flows radially through the outer catalyst bed and flows out along the outer annular gap flow channel; the other part flows radially through the inner catalyst bed and flows out along the central tube. Finally, the two parts of the fluid merge and flow out of the reactor. The method comprises the following steps:

[0008] Step 1: Input the structural parameters and reactor feed parameters of the double-ring radial reactor into the program;

[0009] Step 2: determine the number of axial and radial grids according to the structural parameters of the double-ring radial reactor and initialize the bed pressure field;

[0010] Step 3, calculating the pressure and velocity fields of the inner and outer catalyst beds;

[0011] Step 3.1, based on the initial pressure field, describe the pressure field and velocity field of the bed gas phase using the Ergun equation, and calculate the two-dimensional velocity field;

[0012] Step 3.2: Determine whether the two-dimensional velocity field meets the requirements of the continuity equation residual. If so, jump to step 4. If not, obtain the pressure correction field by solving the finite difference linear equations based on the velocity field, update the pressure field, and return to step 3.1.

[0013] Step 4, calculating the velocity distribution of the flow channel according to the gas linear velocity at the inlet and outlet boundaries of the catalyst bed according to the law of flow conservation;

[0014] Step 5: Calculate the flow channel pressure distribution based on the flow channel velocity distribution using the flow channel momentum equation, and calculate the through-hole pressure drop using the air distribution hole pressure drop formula;

[0015] Step 6: Calculate the pressure at the bed inlet and outlet boundaries based on the flow channel pressure distribution and the through-hole pressure drop, and adjust the boundary conditions. Determine whether the boundary adjustment amplitude meets the accuracy. If not, return to step 3. If it meets the requirements, calculate the pressure drop and axial gas distribution uniformity.

[0016] As a further improvement of the present invention, when the material flows inside the double-ring radial reactor, the modified momentum equation is:

[0017]

[0018] In the formula, the ± term is - in case of converging flow and + in case of diverting flow;

[0019] P is the pressure in the flow channel; z is the axial coordinate consistent with the flow direction of the flow channel; K is the momentum exchange coefficient; U is the gas flow velocity in the flow channel; λ is the gas flow friction coefficient; ρg is the gas density; De is the hydraulic diameter of the flow channel; the value of the subscript i is 0 for the inner annular gap flow channel, 1 for the outer annular gap flow channel, and 2 for the center tube flow channel; K i The value is the momentum exchange coefficient; when i = 0, it means the flow of fluid in the inner annular gap flow channel is a diversion flow.

[0020]

[0021] When i=1 or 2, it indicates that the fluid flows in the outer annular gap and the center tube flow channel, which is a concentrated flow.

[0022]

[0023] As a further improvement of the present invention, the formula for calculating the gas flow friction resistance coefficient λ is:

[0024]

[0025] Where Re is the Reynolds number.

[0026] As a further improvement of the present invention, the expression for the pressure drop of the gas distribution hole is:

[0027]

[0028] Where, ξ is the through-hole resistance coefficient; ω is the gas through-hole velocity;

[0029]

[0030]

[0031] Where f is the correction factor related to the wall thickness and aperture of the gas pipe, and its formula is:

[0032]

[0033] The expression of gas passing through the hole velocity is:

[0034]

[0035] in is the opening ratio of the flow channel; F is the cross-sectional area of ​​the flow channel.

[0036] As a further improvement of the present invention, in the catalyst bed, the resistance of the gas passing through the catalyst bed causes a change in gas pressure. In step 3.1, the pressure field and velocity field in the bed can be specifically described by the following formula:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] P bi is the inner catalyst bed pressure; v bi is the radial velocity of the inner catalyst bed; u bi is the axial velocity of the inner catalyst bed; P bo is the outer catalyst bed pressure; v bo is the radial velocity of the outer catalyst bed; u bo is the axial velocity of the outer catalyst bed; α, β are related to the properties of the bed particles. p is the catalyst particle diameter; ε is the particle bed porosity; μ is the gas viscosity; and r is the radial coordinate of the reactor.

[0044] As a further improvement of the present invention, the (13) and (14) are transformed into mathematical models:

[0045]

[0046]

[0047]

[0048]

[0049] As a further improvement of the present invention, a fixed boundary cannot be used for the catalyst bed boundary of the radial reactor. Therefore, radial airflow exists at the boundary, and axial airflow also exists in the axial direction due to the pressure gradient. Therefore, the boundary conditions of the model are: first, at the fixed boundary, the fluid complies with the no-slip condition on the wall, and the pressure gradient is zero:

[0050]

[0051] Secondly, in the open area, the Ergun equation is used to calculate the pressure drop at the catalyst bed boundary to determine the boundary conditions:

[0052]

[0053]

[0054] As a further improvement of the present invention, in step 6, the precise value of the flow field is u, v, P; the initial field of the iteration is u * , v * , P * ; The correction field is u′, v′, P′;

[0055] Then we have: u′=uu * , v′=vv * ,P′=PP *

[0056] First, the momentum equation (11) is discretized to obtain:

[0057] P C -P N =-(a+b|u n |)u n Δz (24);

[0058] In order to derive the equation of the iterative correction field, it is assumed that the iterative initial field u * , v * , P * It also satisfies the momentum equation, namely:

[0059] PC * -P N * =-(a+b|u n * |)u n *Δz (25);

[0060] Quasi-linearize equation (25), |u n |=|u n * |, then subtract equations (24) and (25) to obtain the momentum equation consisting of the correction amount:

[0061] P C ′-P N ′=-(a+b|u n * |)u n ′Δz (26);

[0062] The corrected velocity field can be obtained from formula (26):

[0063]

[0064] Similarly, we get:

[0065]

[0066] Applying the same treatment to formula (10) yields:

[0067]

[0068] Similarly, we can get:

[0069]

[0070] Then discretize the continuity equation (12), namely:

[0071]

[0072] Assuming that the initial field of the iteration satisfies the momentum equation, it does not necessarily satisfy the continuity equation at the same time. Therefore, the continuity equation of the initial field of the iteration will have a residual S m ,Right now:

[0073]

[0074] Subtracting (31) from (32), and considering the relationship between the initial field, the precise field, and the correction field, we can obtain:

[0075]

[0076] Finally, the correction velocity field equations (27) to (30) are substituted to obtain the pressure correction equation shown in equation (34):

[0077] A C P C’ -A N P N’ -A S P S’ -A E P E’ -A W P W’ =-S m (34);

[0078] The coefficient A in the above formula C 、A N 、A S 、A E and A W , respectively:

[0079]

[0080] The specific calculation method is: according to the initial u * , v * and P * , and then obtain the corrected pressure field P ij ′, and then update the pressure field:

[0081] P ij =P ij * +P ij ′ (36);

[0082] Based on the new pressure field obtained above, the new velocity fields u and v are obtained using equations (10) and (11). The above steps are repeated until the residual of the continuity equation obtained by substituting the calculated velocity fields u and v into equation (32) is less than the tolerance, that is, the pressure field and velocity field that satisfy both the momentum equation and the continuity equation are obtained.

[0083] As a further improvement of the present invention, in step 6, a staggered grid is used to discretize the control equation of the flow field.

[0084] As a further improvement of the present invention, the axial gas distribution uniformity in step 6 is specifically obtained by:

[0085]

[0086] Where: Δp is the static pressure difference at the same position of the axial opening area of ​​the two main channels. Compared with the prior art, the beneficial effects of the present invention are:

[0087] A two-dimensional flow modeling method for a double-ring radial reactor is proposed. A numerical algorithm is used to solve the mathematical model of the double-ring radial reactor, achieving an accurate mathematical description of the fluid mechanics behavior in the industrial dehydrogenation reactor. On this basis, a quantitative reference is provided for the optimal selection of the structural dimensions of the industrial double-ring radial reactor. New industrial dehydrogenation reactors built on this basis can achieve more balanced utilization of catalysts in different parts, thereby improving the processing capacity of the dehydrogenation reactor and the overall utilization efficiency of the catalyst. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a schematic diagram of a double-ring radial reactor;

[0089] Figure 2 is the cylindrical coordinate diagram of the reactor;

[0090] Figure 3 is a staggered grid graph;

[0091] Figure 4 It is an iterative calculation flow chart;

[0092] Figure 5 These are the velocity and pressure field diagrams of the main channel, a is the velocity field diagram, and b is the pressure field diagram;

[0093] Figure 6 The velocity field and pressure field diagrams of the inner ring catalyst bed are shown in Figure 1. a is the radial velocity field diagram, b is the axial velocity field diagram, and c is the pressure field diagram.

[0094] Figure 7 These are the velocity field and pressure field diagrams of the outer ring catalyst bed, a is the radial velocity field diagram, b is the axial velocity field diagram, and c is the pressure field diagram. DETAILED DESCRIPTION

[0095] The present invention is described in detail below with reference to the various embodiments shown in the accompanying drawings, but it should be noted that these embodiments are not limitations of the present invention, and any equivalent transformations or substitutions in functions, methods, or structures made by ordinary technicians in this field based on these embodiments are all within the scope of protection of the present invention.

[0096] The present invention provides a flow model for an industrial dehydrogenation reactor derived from a modified momentum equation, Ergun equation, and continuity equation. This model simulates the fluid dynamics of the reactant flow in the main flow channel and catalyst bed, and uses a numerical algorithm to solve the mathematical model of a double-ring radial reactor. The steps are as follows:

[0097] Step 1: Input the structural parameters and reactor feed parameters of the double-ring radial reactor into the program;

[0098] For a double-ring radial reactor, the material enters the reactor axially from the inner annular gap flow channel. In the inner annular gap, the fluid is radially divided into two streams. One stream flows radially through the outer catalyst bed and flows out along the outer annular gap flow channel; the other stream flows radially through the inner catalyst bed and flows out along the central pipe. Finally, the two streams merge and flow out of the reactor. The structure is as follows: Figure 1 shown.

[0099] Step 2: Determine the number of axial and radial grids based on the structural parameters of the double-ring radial reactor and initialize the bed pressure field. Use the modified momentum equation to describe the fluid dynamics behavior of the variable mass flow in the main channel. The modified momentum equation is in the form of:

[0100]

[0101] In the formula, for the items marked with “±”, take “-” for converging flow and take “+” for diverting flow.

[0102] Where P is the pressure in the flow channel, in Pa;

[0103] z is the axial coordinate consistent with the flow direction of the channel, in meters;

[0104] K is the momentum exchange coefficient;

[0105] U is the gas velocity in the flow channel, in m·s -1 ;

[0106] λ is the friction resistance coefficient of gas flow;

[0107] ρ g is the gas density, in kg·m -3 ;

[0108] De is the hydraulic diameter of the flow channel, in m;

[0109] The subscript 0 represents the inner annular gap flow channel, 1 represents the outer annular gap flow channel, and 2 represents the center tube flow channel.

[0110] In the above formula, K is the momentum exchange coefficient, which directly affects the static pressure distribution in the flow channel between the diverter and collector within the reactor. Song et al. at Tsinghua University conducted experiments using a large-scale experimental device under industrial conditions, and the K value obtained by regression is close to industrial practice. This study shows that the K value is mainly related to the relative change in the kinetic energy of the fluid in the main channel, as shown by the formula:

[0111]

[0112]

[0113] When the value of i is 1 or 2, it indicates that the fluid flows in the outer annular gap and the center tube flow channel, which is a collecting flow; when the value of i is 0, it indicates that the fluid flows in the inner annular gap flow channel, which is a diverging flow.

[0114] λ is the friction coefficient of gas flow, which is related to laminar and turbulent flow and can be calculated by the Reynolds number (Re). The formula is as follows:

[0115]

[0116] The modified momentum equation explains that changes in the flow channel's pressure are caused by changes in the fluid's dynamic pressure and frictional resistance losses. In the diverter channel, the fluid's velocity decreases continuously due to lateral diversion, and the fluid's dynamic pressure is continuously converted into static pressure. Therefore, the fluid pressure in the diverter channel increases continuously along the flow direction. In the converging channel, the fluid's velocity increases continuously due to the lateral inflow of fluid, and the dynamic pressure increases continuously, which in turn consumes the system's static pressure, causing the fluid pressure in the converging channel to decrease continuously along the flow direction. Frictional resistance losses, on the other hand, cause the fluid pressure to decrease continuously along the flow direction. During fluid flow, the effect of dynamic pressure exchange on pressure changes is far greater than the effect of flow frictional resistance. The combined effect of the two causes the pressure of the reactant flow to increase along the flow direction when flowing in the diverter channel, and the pressure of the reactant flow to decrease along the flow direction when flowing in the converging channel.

[0117] The expression for the pressure drop of the gas distribution hole is:

[0118]

[0119] Where ξ is the via resistance coefficient;

[0120] ω is the gas velocity passing through the hole.

[0121] The ξ in the above equation is an important parameter describing the fluid dynamics of radial reactors. Zhang Chengfang and others at the East China University of Chemical Technology conducted experiments and concluded that the through-hole resistance coefficient is related to the ratio of the through-hole velocity to the main channel velocity. Wang Jinfu and others at Tsinghua University derived a computational correlation based on regression of experimental data:

[0122]

[0123]

[0124] Where f is the correction coefficient related to the wall thickness and aperture of the air distribution pipe, and its value is calculated by formula (8):

[0125]

[0126] The expression of gas passing through the hole velocity is:

[0127]

[0128] in is the flow channel opening ratio;

[0129] F is the cross-sectional area of ​​the flow channel, in m 2 .

[0130] Step 3.1, based on the initial pressure field, describe the pressure field and velocity field of the bed gas phase using the Ergun equation, and calculate the two-dimensional velocity field;

[0131] Step 3.2: Determine whether the two-dimensional velocity field meets the requirements of the continuity equation residual. If so, jump to step 4. If not, obtain the pressure correction field by solving the finite difference linear equations based on the velocity field, update the pressure field, and return to step 3.1.

[0132] In the catalyst bed, the resistance of the gas passing through the catalyst bed causes changes in gas pressure. In the case of gas-solid cross-flow, the pressure field and velocity field of the gas phase in the bed can be described by the following Ergun equation and continuity equation:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Among them: P bi is the inner catalyst bed pressure, in Pa;

[0140] v bi is the radial velocity of the inner catalyst bed, in m·s -1 ;

[0141] u bi is the axial velocity of the inner catalyst bed, in m·s -1 ;

[0142] P bo is the outer catalyst bed pressure, in Pa;

[0143] v bo is the radial velocity of the outer catalyst bed, in m·s -1 ;

[0144] ubo is the axial velocity of the outer catalyst bed, in m·s -1 ;

[0145] α and β are parameters related to the properties of bed particles;

[0146] d p is the catalyst particle diameter, in m;

[0147] ε is the porosity of the particle bed;

[0148] μ is the gas viscosity;

[0149] r is the radial coordinate of the reactor, in m.

[0150] For the parameters in the Ergun equation, under real catalyst and high temperature and high pressure conditions, Ergun obtained specific numerical values ​​through experimental correlation formulas. The calculated values ​​of α and β were 150 and 1.75, respectively.

[0151] make Then (10), (11), (13) and (14) are transformed into:

[0152]

[0153]

[0154]

[0155]

[0156] Equations (1), (5), (10), (11), (12), (13), (14) and (15) constitute the mathematical model of the double-ring radial reactor. As long as the physical parameters and the structural parameters of the reactor are known, combined with the exact boundary conditions, numerical calculations can be performed using the above mathematical model.

[0157] Step 4, calculating the velocity distribution of the flow channel according to the gas linear velocity at the inlet and outlet boundaries of the catalyst bed according to the law of flow conservation;

[0158] For radial reactors, the catalyst bed boundary cannot be a fixed boundary because there is radial airflow at the boundary and axial airflow due to the axial pressure gradient. Therefore, the boundary conditions need to be set dynamically.

[0159] Cylindrical coordinates are used for the double-ring radial reactor, such as Figure 2 As shown, the boundary conditions of the model are:

[0160] 1. At a fixed boundary, the fluid obeys the no-slip condition on the wall and the pressure gradient is zero:

[0161]

[0162] 2. In the open area, the Ergun equation is used to calculate the pressure drop at the catalyst bed boundary to determine the boundary conditions:

[0163]

[0164]

[0165] Step 5: Calculate the flow channel pressure distribution based on the flow channel velocity distribution using the flow channel momentum equation, and calculate the through-hole pressure drop using the air distribution hole pressure drop formula;

[0166] In order to quantitatively describe the uniformity of the axial gas distribution of the reactant flow, the following formula is defined to calculate and determine the axial gas distribution uniformity of the reactor:

[0167] A rough estimate based on the static pressure difference between the flow channels. Since the radial flux of gas is proportional to the square root of the static pressure difference between the flow channels, the axial gas distribution uniformity can be expressed as:

[0168]

[0169] Where: Δp—static pressure difference at the same position in the axial opening area of ​​the two main channels;

[0170] Step 6: Calculate the pressure at the bed inlet and outlet boundaries based on the flow channel pressure distribution and the through-hole pressure drop, and adjust the boundary conditions. Determine whether the boundary adjustment amplitude meets the accuracy. If not, return to step 3. If it meets the requirements, calculate the pressure drop and axial gas distribution uniformity.

[0171] In the process of solving the two-dimensional flow field, the pressure and radial velocity of the fluid passing through the catalyst bed need to be solved simultaneously. First, use Figure 3 The governing equations of the staggered grid discretized flow field are shown, and then the correction formulas for the iterative process are derived as follows, taking the inner catalyst bed as an example.

[0172] Assume: The exact values ​​of flow field u, v, P

[0173] The initial field of the iteration is u * , v * , P *

[0174] The correction field is u′, v′, P′

[0175] Then we have: u′=uu * , v′=vv * ,P′=PP *

[0176] First, the momentum equation (11) is discretized as:

[0177] P C -P N =-(a+b|u n |)u n Δz (24)

[0178] In order to derive the equation of the iterative correction field, it is assumed that the iterative initial field u * , v * , P * It also satisfies the momentum equation, namely:

[0179] P C * -P N * =-(a+b|u n * |)u n *Δz (25)

[0180] Quasi-linearize equation (25), |u n |=|u n * |, then subtract equations (24) and (25) to obtain the momentum equation consisting of the correction amount:

[0181] P C ′-P N ′=-(a+b|u n * |)u n ′Δz (26) The corrected velocity field can be obtained from equation (26):

[0182]

[0183] Similarly, we can get:

[0184]

[0185] Applying the same treatment to equation (10) yields:

[0186]

[0187] Similarly, we can get:

[0188]

[0189] Then discretize the continuity equation (12), that is:

[0190]

[0191] Since the iterative initial field is assumed to satisfy the momentum equation, it does not necessarily satisfy the continuity equation at the same time, otherwise the exact solution of the two-dimensional flow field would have been calculated. Therefore, the continuity equation of the iterative initial field will have a certain residual S m ,Right now:

[0192]

[0193] Subtracting (31) from (32), and considering the relationship between the initial field, the precise field, and the correction field, we can obtain:

[0194]

[0195] Finally, by substituting the corrected velocity field equations (27) to (30), we can obtain the pressure correction equation shown in (34):

[0196] A C P C’ -A N P N’ -A S P S’ -A E P E’ -A W P W’ =-S m (34)

[0197] The coefficient A in the above formula C 、A N 、A S 、A E and A W , respectively:

[0198]

[0199] The specific calculation method is: according to the initial u * , v * and P * , use the linear equation solver to solve, and then find the corrected pressure field P ij ′, and then update the pressure field:

[0200] P ij =P ij * +P ij ′ (36)

[0201] Based on the new pressure field obtained above, use equations (10) and (11) to calculate the new velocity fields u and v. Repeat the above steps until the residual of the continuity equation obtained by substituting the calculated velocity fields u and v into equation (32) is less than the tolerance, that is, the pressure field and velocity field that satisfy both the momentum equation and the continuity equation are obtained.

[0202] The above is the calculation of the internal circulation of the catalyst bed flow field.

[0203] The main loop performs iterative calculations through the sequential quadratic programming (SQP) algorithm. The initial values ​​of the boundary pressures at the inlets and outlets of the inner and outer catalyst beds are used to simultaneously calculate the pressure field and velocity field of the two beds. The velocity distribution of the main channel is then calculated based on the velocity field boundaries of the two beds. The pressure distribution and the through-hole gas velocity and pressure drop of the gas distribution channels are obtained from the main channel velocity distribution. Finally, the inlet and outlet boundary pressures of the two beds are updated based on the channel pressure distribution and the through-hole pressure drop.

[0204] The calculated boundary pressure is equal to the boundary pressure obtained in the previous iteration, and the outlet pressure of the central tube and the outer annular gap are equal as the equality constraint. The boundary pressure of the bed inlet is greater than the outlet pressure as the inequality constraint. The SQP algorithm is used to solve such a constrained optimization problem, and finally the reactor flow field and outlet parameters that satisfy all equations are obtained. The specific iterative calculation flow chart is as follows: Figure 4 .

[0205] Establishment of flow model for double-ring radial reactor

[0206] When establishing the reactor model, the fluid is assumed to be an ideal gas due to the high temperature and low pressure of the reaction system. The pressure drop across the inner and outer annular gaps is ignored compared to the pressure drop across the catalyst bed. The gas is isothermal and incompressible, with constant viscosity, volume flow rate, and density. The mathematical equations for the double-ring radial reactor are derived from the modified momentum equation, Ergun equation, and continuity equation, as shown in Equations (1), (5), (10), (11), (12), (13), (14), and (15).

[0207] Solving the model equations

[0208] The above-mentioned mathematical model of the reactor involves a series of differential equations, which are discretized using staggered grids through the finite difference method.

[0209] In the solution area, such as Figure 2 , divided into M equal parts in radial direction and N equal parts in axial direction. i , R j ) (abbreviated as (i, j)), equation (34) is a five-point difference format, which is converted into a finite difference equation:

[0210]

[0211] The residual on the right side of the equation Calculated from equation (38):

[0212]

[0213] The linsolve function in MATLAB is used to solve (37) and obtain the pressure correction field of the catalyst bed. First, rewrite (37) as A·X=b, where X is the pressure P of each grid point. i,j, The solution vector is arranged in order, and A is the coefficient A corresponding to each grid point. C 、A N 、A S 、A E and A W According to the corresponding arrangement, the coefficient matrix is ​​formed, and b is the residual The linsolve function can be used to quickly and accurately solve the pressure correction field of the bed.

[0214] The main loop is iteratively calculated using the Sequential Quadratic Programming (SQP) algorithm:

[0215] The objective function is a constant function with a value of 0; the equality constraint is that the difference between the catalyst bed boundary pressure before and after is equal to 0 and the inner annular gap inlet flow rate is equal to a given value; the inequality constraint is that the bed inlet boundary pressure is greater than the outlet pressure.

[0216] This method allows the optimal solution x to be found, satisfying all constraints. x includes the boundary pressures at the bed inlet and outlet, as well as the outlet pressure of the flow channel. This information is then used to sequentially calculate the bed pressure and velocity fields, and the velocity and pressure distributions in the flow channels. Thus, given the flow channel inlet pressure and flow velocity, the flow field distribution in the reactor, as well as the pressure and velocity at the flow channel outlet, can be determined.

[0217] The structural dimensions of a reactor are shown in Table 1.

[0218] Table 1 Structural dimensions of the double-ring radial reactor

[0219]

[0220] The simulation results show that the bed pressure drop is 6kPa, the axial gas distribution uniformity of the inner ring is 0.12, and the axial gas distribution uniformity of the outer ring is 0.13. Figure 5 , the flow field of the bed is as follows Figure 6 , Figure 7 .

[0221] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A flow modeling method for an industrial dehydrogenation double-ring radial reactor, characterized in that: Based on a double-ring radial reactor, the reactor is coaxially provided with an inner annular gap and an outer annular gap from the inside to the outside around a central tube. When the material enters the reactor axially from the inner annular gap flow channel of the reactor, the fluid in the inner annular gap is radially divided into two fluids, one part of the fluid flows radially through the outer catalyst bed layer and flows out along the outer annular gap flow channel; the other part flows radially through the inner catalyst bed layer and flows out along the central pipe. Finally, the two parts of the fluid merge and flow out of the reactor, including the following steps: Step 1, inputting the structural parameters and reactor feed parameters of the double-ring radial reactor into the program; Step 2, determining the number of axial and radial grids according to the structural parameters of the double-ring radial reactor, and initializing the bed pressure field; Step 3, calculating the pressure and velocity field of the inner and outer catalyst beds; Step 3.1, based on the initial pressure field, the pressure field and velocity field of the gas phase in the bed are described by the Ergun equation, and the two-dimensional velocity field is calculated; Step 3.2, determine whether the two-dimensional velocity field meets the requirements of the continuity equation residual. If so, jump to step 4. If not, obtain the pressure correction field based on the velocity field by solving the finite difference linear equations, update the pressure field, and return to step 3.1; Step 4, according to the gas linear velocity at the inlet and outlet boundaries of the catalyst bed, the velocity distribution of the flow channel is calculated according to the law of flow conservation; Step 5, according to the flow channel velocity distribution, the flow channel pressure distribution is calculated by the flow channel momentum equation, and the through-hole pressure drop is calculated by the air distribution hole pressure drop formula; Step 6, calculate the pressure at the inlet and outlet boundaries of the bed layer based on the flow channel pressure distribution and the through-hole pressure drop, and adjust the boundary conditions; and judge whether the boundary adjustment amplitude reaches the accuracy. If not, return to step 3. If it meets the requirements, calculate the pressure drop and axial gas distribution uniformity.

2. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 1, characterized in that: When the material flows inside the double-ring radial reactor, the modified momentum equation is: The ± term in the formula is - in case of concentrator flow and + in case of diverter flow; P is the pressure in the flow channel; z is the axial coordinate consistent with the flow direction of the flow channel; K is the momentum exchange coefficient; U is the gas flow rate in the flow channel; λ is the gas flow friction coefficient; ρg is the gas density; De is the hydraulic diameter of the flow channel; the value of the subscript i is 0 for the inner annular gap flow channel, 1 for the outer annular gap flow channel, and 2 for the center tube flow channel; K i The value is the momentum exchange coefficient; When i=0, it indicates that the fluid flows in the inner annular gap flow channel, which is a split flow. When i=1 or 2, it means the flow of fluid in the outer annular gap and the center tube flow channel is a collecting flow.

3. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 2, characterized in that: The formula for calculating the gas flow friction resistance coefficient λ is: Where Re is the Reynolds number.

4. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 2, characterized in that: The expression for the pressure drop of the gas distribution hole is: Among them, ξ is the through-hole resistance coefficient; ω is the gas through-hole velocity; Where f is the correction factor related to the wall thickness and hole diameter of the air distribution pipe, and its formula is, The expression of gas passing through the hole velocity is: in is the opening ratio of the flow channel; F is the cross-sectional area of ​​the flow channel.

5. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 1, characterized in that: In the catalyst bed, the resistance of the gas passing through the catalyst bed causes a change in gas pressure. In step 3.1, the pressure field and velocity field in the bed can be specifically described by the following formula: P bi is the inner catalyst bed pressure; v bi is the radial velocity of the inner catalyst bed; u bi is the axial velocity of the inner catalyst bed; P bo is the outer catalyst bed pressure; v bo is the radial velocity of the outer catalyst bed; u bo is the axial velocity of the outer catalyst bed; α, β are related to the properties of the bed particles. p is the catalyst particle diameter; ε is the particle bed porosity; μ is the gas viscosity; r is the radial coordinate of the reactor.

6. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 5, characterized in that: Said (10), (11), (13) and (14) are transformed into mathematical models:

7. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 5, characterized in that: The catalyst bed boundary of the radial reactor cannot be fixed, so there is radial airflow at the boundary, and there is also axial airflow due to the pressure gradient. Therefore, the boundary conditions of the model are: First, at the fixed boundary, the fluid obeys the no-slip condition at the wall, and the pressure gradient is zero: Secondly, in the open area, the Ergun equation is used to calculate the pressure drop at the catalyst bed boundary to determine the boundary conditions:

8. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 5, characterized in that: In step 6, the exact value of the flow field is u, v, P; the initial field of iteration is u * , v * , P * ; The correction field is u′, v′, P′; Then we have: u′=uu * , v′=vv * ,P′=PP * First, the momentum equation (11) is discretized to obtain: P C -P N =-(a+b|u n |)u n Δz (24); In order to derive the equations of the iterative correction field, it is assumed that the iterative initial field u * , v * , P * It also satisfies the momentum equation, namely: P C * -P N * =-(a+b|u n * |)u n * Δz (25); Quasi-linearize equation (25), n |=|u n * |, then subtract equation (24) from (25) to obtain the momentum equation consisting of the correction amount: P C ′-P N ′=-(a+b|u n * |)u n ′Δz (26); The corrected velocity field can be obtained by equation (26): Similarly, we get: Applying the same treatment to equation (10) yields: Similarly, we can get: Then discretize the continuity equation (12), namely: Assuming that the initial field of the iteration satisfies the momentum equation, it does not necessarily satisfy the continuity equation at the same time. Therefore, the continuity equation of the initial field of the iteration will have a residual S m ,Right now: Subtracting equations (31) and (32), and considering the relationship between the initial field, the precise field, and the correction field, we can obtain: Finally, the correction velocity field equations (27) to (30) are substituted to obtain the pressure correction equation shown in equation (34): A C P C’ -A N P N’ -A S P S’ -A E P E’ -A W P W’ =-S m (34); The coefficient A in the above formula C , A N , A S , A E and A W , respectively: The specific calculation method is: according to the initial field u * , v * and P * , and then obtain the corrected pressure field P ij ′, and then update the pressure field: P ij =P ij * +P ij ′ (36); Based on the new pressure field obtained above, the new velocity fields u and v are obtained using equations (10) and (11). The above steps are repeated until the residual of the continuity equation obtained by substituting the calculated velocity fields u and v into equation (32) is less than the tolerance, that is, the pressure field and velocity field that satisfy both the momentum equation and the continuity equation are obtained.

9. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 1, characterized in that: In step 6, a staggered grid is used to discretize the control equation of the flow field.

10. The method for modeling a flow model of an industrial dehydrogenation double-ring radial reactor according to claim 1, characterized in that: The axial air distribution uniformity in step 6 is specifically obtained by: Where: Δp is the static pressure difference at the same position of the axial opening area of ​​the two main channels.

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