A heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery

Abstract

The present invention relates to the technical field of energy recovery and biomass conversion, and specifically discloses a heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery. First, a heat transfer model between biomass particles and high-temperature metallurgical slag particles in a rotary kiln is established. A three-parallel pyrolysis reaction model is used to define the three components of biomass particles, and decomposition is performed according to a single Arrhenius-type reaction to describe the kinetic behavior of the biomass pyrolysis reaction. This comprehensively covers the multi-component reaction paths and characteristics of biomass pyrolysis, and accurately characterizes the pyrolysis behavior of biomass in contact with high-temperature metallurgical slag and its impact on the heat transfer process. By effectively combining these two models, numerical simulation calculations of the biomass-high-temperature metallurgical slag heat transfer process are realized, and the changing patterns of key parameters such as temperature distribution, heat flow transfer, and pyrolysis conversion distribution in the system can be accurately obtained. This contributes to a deeper understanding of the complex mechanism of heat transfer between biomass and high-temperature metallurgical slag.

Description

Technical Field

[0001] The present invention relates to the technical field of energy recovery and biomass conversion, and in particular to a heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery. Background Art

[0002] The large amount of high-temperature slag produced during non-ferrous metal smelting is a potential energy resource. However, due to its complex phase composition and high-temperature properties, efficient recovery of slag waste heat has been a challenge for the industry. Meanwhile, biomass, as a renewable energy source, has enormous potential for thermochemical conversion. However, traditional biomass pyrolysis and slag waste heat recovery technologies suffer from low heat transfer efficiency and high energy losses, limiting the feasibility of combining the two.

[0003] Rotary reactors have been increasingly used in slag waste heat recovery and biomass thermochemical conversion in recent years due to their excellent mixing characteristics and high heat transfer efficiency. However, the mixing and heat exchange between biomass and slag in rotary reactors involves complex multiphase flow, heat transfer, and chemical reactions. A systematic model and calculation method are still lacking to effectively describe and optimize this process. Therefore, an effective heat transfer model calculation method is proposed, which is of great significance for improving the efficiency of slag waste heat recovery and biomass energy utilization. Summary of the Invention

[0004] In order to solve or partially solve the problems existing in the related art, the present invention provides a heat transfer calculation method for coupling biomass pyrolysis and metallurgical slag waste heat recovery, which can accurately describe the heat transfer characteristics and energy exchange process between slag and biomass particles in a rotary reactor as well as the biomass pyrolysis reaction process, thereby providing a theoretical basis and technical support for improving the slag waste heat recovery and biomass thermochemical conversion efficiency.

[0005] The present application describes a heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery. A heat transfer model is established between biomass particles and high-temperature metallurgical slag particles in a rotary kiln. A three-parallel pyrolysis reaction model is used to define the three components of the biomass particles, which are then decomposed according to a single Arrhenius-type reaction. The heat transfer model calculation method specifically includes the following steps:

[0006] S1: Calculate the total heat input Q of the rotary kiln pyrolysis system in,all ;

[0007] S2: Calculate the contact heat transfer coefficient h1 between biomass particles and metallurgical slag particles in the rotary kiln;

[0008] S3: Calculate the contact heat transfer coefficient h2 between the biomass particles in the rotary kiln and the inner wall of the kiln;

[0009] S4: Calculate the contact heat transfer coefficient h3 between biomass particles, air film and metallurgical slag particles in the rotary kiln;

[0010] S5: Calculate the contact heat transfer coefficient h4 between the biomass particles, the air film, and the inner wall of the rotary kiln;

[0011] S6: Calculate the convection heat transfer coefficient h5 between the biomass particles on the upper surface of the rotary kiln and the gas;

[0012] S7: Calculate the convection heat transfer coefficient h6 between the rotary kiln wall and the gas;

[0013] S8: Calculate the radiation heat transfer coefficient h7 between the rotary kiln wall and the biomass particles on the upper surface of the kiln;

[0014] S9: Calculate the radiation heat transfer coefficient h8 between the gas and the rotary kiln wall;

[0015] S10: Calculate the biomass pyrolysis conversion rate q based on the three-parallel pyrolysis reaction model r ;

[0016] S11: Calculate the heat Q generated by chemical reaction or phase change i,c ;

[0017] S12: Calculate the heat transfer Q of the rotary kiln pyrolysis system transfer ;

[0018] S13: Calculate the change ΔQ of the internal energy of the rotary kiln pyrolysis system.

[0019] In some embodiments, the total heat input to the rotary kiln pyrolysis system comes from the metallurgical slag particles and the constant temperature of the rotary kiln wall. The total heat input to the rotary kiln pyrolysis system is Q in,all The calculation formula is:

[0020] Q in,all =Q in,kiln +Q in,slag

[0021] Where Q in,all is the total heat input to the pyrolysis system, Q in,kiln is the heat input to the rotary kiln wall, Q in,slag It is the heat input of metallurgical slag.

[0022] In some embodiments, the contact heat transfer coefficient h1 between biomass particles and metallurgical slag particles in the rotary kiln is calculated as follows:

[0023]

[0024] Where k b-s is the effective thermal conductivity between biomass particles and metallurgical slag particles, r bRadius of biomass particle, r s Radius of metallurgical slag particles, k b is the thermal conductivity of biomass particles, k s is the thermal conductivity of metallurgical slag particles, is the volume fraction of biomass particles in the rotary kiln, It is the volume fraction of metallurgical slag particles in the total volume of the rotary kiln.

[0025] In some embodiments, the calculation formula for the contact heat transfer coefficient h2 between the biomass particles in the rotary kiln and the kiln inner wall is,

[0026]

[0027] Where k b is the thermal conductivity of biomass particles, k w is the thermal conductivity of the rotary kiln wall, r b is the radius of the biomass particle, r w is the inner radius of the rotary kiln.

[0028] In some embodiments, the calculation formula for the contact heat transfer coefficient h3 between biomass particles, air film and metallurgical slag particles in the rotary kiln is:

[0029]

[0030] Nu1=2+0.6Re 1 / 2 Pr 1 / 3

[0031]

[0032] Where k g is the gas thermal conductivity, Nu1 is the Nusselt number of the gas film between biomass particles-gas film-metallurgical slag particles, d1 is the distance between biomass particles and high-temperature metallurgical slag particles, Re is the Reynolds number, Pr is the Prandtl number, C p is the specific heat capacity of the gas, ν is the gas flow rate, and μ is the gas dynamic viscosity.

[0033] In some schemes, the calculation formula of the contact heat transfer coefficient h4 between biomass particles, air film and kiln inner wall in the rotary kiln is:

[0034]

[0035] Nu2=2+0.6Re 1 / 2 Pr 1 / 3

[0036] Where d2 is the distance between the biomass particles and the rotary kiln wall, k gis the thermal conductivity of gas, and Nu2 is the Nusselt number of the gas film between biomass particles-gas film-rotary kiln wall.

[0037] In some embodiments, the convective heat transfer coefficient h5 between the biomass particles on the upper surface of the rotary kiln and the gas is calculated as follows:

[0038]

[0039] Nu3=C(GrPr) n

[0040]

[0041] Where k g is the thermal conductivity of gas, Nu3 is the Nusselt number of gas around biomass particles on the upper surface of the rotary kiln, d b is the diameter of the biomass particle, Gr is the Grashof number, Pr is the Prandtl number, C is the empirical correction constant in the heat transfer coefficient correlation, n is the empirical power exponent characterizing the nonlinear relationship of heat transfer, g is the acceleration of gravity, β is the gas volume expansion coefficient, and ΔT1 is the temperature difference between the gas and the biomass particle.

[0042] In some schemes, the calculation formula of the convection heat transfer coefficient h6 between the rotary kiln wall and the gas is as follows,

[0043]

[0044] Nu4=0.023Re 0.8 Pr 0.4

[0045] Where Nu4 is the Nusselt number of the gas in the rotary kiln that forms convective heat transfer with the wall, k g is the thermal conductivity of gas, d w is the inner diameter of the rotary kiln, Re is the Reynolds number, and Pr is the Prandtl number.

[0046] In some embodiments, the radiation heat transfer coefficient h7 between the rotary kiln wall and the biomass particles on the upper surface of the kiln is calculated as follows:

[0047]

[0048] Where q7 is the heat flux density of radiation heat transfer between the rotary kiln wall and the biomass particles on the upper surface of the kiln, T w is the temperature of the kiln wall, T b is the temperature of the biomass particles, ε w-b is the effective radiation coefficient between biomass particles and kiln wall, and σ is the Stefan-Boltzmann constant.

[0049] In some embodiments, the radiation heat transfer coefficient h8 between the gas and the rotary kiln wall is calculated as follows:

[0050]

[0051] Where q8 is the heat flux density of radiation heat transfer between the gas and the rotary kiln wall, T g is the gas temperature, T w is the temperature of the kiln wall, σ is the Stefan-Boltzmann constant, ε w-g It is the effective radiation coefficient of gas and kiln wall.

[0052] In some embodiments, three parallel pyrolysis reaction models are as follows,

[0053]

[0054] Among them, k1, k2 and k3 are the pyrolysis reaction rate constants of hemicellulose, cellulose and lignin, respectively; r1, r2 and r3 represent the yields of biochar generated by pyrolysis of hemicellulose, cellulose and lignin, respectively.

[0055] According to the above three parallel pyrolysis reaction model, the pyrolysis conversion rate q of component i in biomass is i,c The calculation formula is as follows,

[0056]

[0057] Q i,c =A i,b (-q i,c )(-ΔH i,c )

[0058] Where ρ is the density of biomass particles, i includes cellulose, hemicellulose and lignin, and m i , A i and E i are the initial masses of cellulose, hemicellulose, and lignin, the preexponential factor, and activation energy, respectively; R is the ideal gas constant (8.314 J / (mol·K)); T is the biomass pyrolysis reaction temperature; Q i,c is the heat generated by chemical reaction or phase change, A i,b is the reactive surface area of ​​the biomass particles, the negative sign is the decrease in reactant concentration over time, ΔH i,c is the reaction enthalpy change.

[0059] In some embodiments, the heat transfer rate Q of the rotary kiln pyrolysis system is transfer The calculation formula is as follows,

[0060]

[0061] Where Q pp, Q pw , Q pfp , Q pfw , Q cp , Q cν , Q rpw , Q rfw and Q i,c They are heat conduction between biomass particles and metallurgical slag particles, heat conduction between biomass particles and kiln inner wall, heat conduction between biomass particles-air film-metallurgical slag particles, heat conduction between biomass particles-air film-kiln inner wall, convection heat transfer between biomass particles on the upper surface of the rotary kiln and gas, convection heat transfer between the rotary kiln wall and gas, radiation heat transfer between the rotary kiln wall and biomass particles on the upper surface of the kiln, and radiation heat transfer between the rotary kiln wall and gas; A pp , A pw , A pfp , A pfw , A cp , A cν , A rpw , A rfw , and A i,b They are the contact area between biomass particles and metallurgical slag particles, the contact area between biomass particles and the inner wall of the kiln, the heat transfer area between biomass particles-air film-metallurgical slag particles, the heat transfer area between biomass particles-air film-kiln inner wall, the convection heat transfer area between biomass particles on the upper surface of the rotary kiln and gas, the convection heat transfer area between the rotary kiln wall and gas, the radiation heat transfer area between the rotary kiln wall and biomass particles on the upper surface of the kiln, and the radiation heat transfer area between the rotary kiln wall and gas; T b , T s , T w , T g and T c-b They are the temperature of biomass particles, the temperature of metallurgical slag particles, the temperature of kiln wall, the gas temperature and the temperature of biomass particles on the upper surface of the kiln.

[0062] In some embodiments, the calculation formula for the change in internal energy ΔQ of the rotary kiln pyrolysis system is,

[0063] ΔQ=Q in,all +Q transfer

[0064] The technical solution provided by this application may have the following beneficial effects:

[0065] The present invention establishes a heat transfer model between biomass particles and high-temperature metallurgical slag particles in a rotary kiln, constructs a fluid-solid coupling model of the interaction system between biomass and metallurgical slag particles, and accurately describes the movement and interaction process between the two. At the same time, a three-parallel pyrolysis reaction model is established to describe the kinetic behavior of the biomass pyrolysis reaction, comprehensively covering the multi-component reaction path and characteristics of biomass pyrolysis, and can accurately characterize the pyrolysis behavior of biomass in contact with high-temperature metallurgical slag and its impact on the heat transfer process. By effectively combining these two models, numerical simulation calculations of the biomass-high-temperature metallurgical slag heat transfer process are realized, and the changing laws of key parameters such as temperature distribution, heat flow transfer and pyrolysis conversion rate in the system can be accurately obtained. It helps to deeply understand the complex mechanism of heat transfer between biomass and high-temperature metallurgical slag, and provides strong technical support and theoretical basis for the optimization design of related industrial processes, energy conservation and emission reduction, and comprehensive resource utilization. It has important scientific significance and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a structural diagram of the exothermic rotary kiln biomass pyrolysis system of the present invention;

[0067] Figure 2 This is a cross-sectional view of the exothermic rotary kiln of the present invention;

[0068] Figure 3 is a schematic diagram of direct contact between biomass particles and metallurgical slag particles in the present invention;

[0069] Figure 4 Schematic diagram of direct contact between biomass particles and the wall of the rotary kiln in the present invention;

[0070] Figure 5 Schematic diagram of the contact between biomass particles, air film and metallurgical slag particles in the present invention;

[0071] Figure 6 Schematic diagram of the contact between biomass particles, air film and rotary kiln wall in the present invention;

[0072] Figure 7 This is a numerical simulation result of the average particle temperature in the rotary kiln biomass pyrolysis system with different copper slag addition amounts in an embodiment of the present invention;

[0073] Figure 8 It is a flow chart of the heat transfer model calculation method in the present invention. DETAILED DESCRIPTION

[0074] The following describes embodiments of the present application in more detail with reference to the accompanying drawings. Although the accompanying drawings illustrate embodiments of the present application, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. Rather, these embodiments are provided to make the present application more thorough and complete, and to fully convey the scope of the present application to those skilled in the art.

[0075] like Figure 1 As shown, the rotary kiln is provided with two feed ports at the feed end, one of which is used to introduce biomass particles into the rotary kiln, and the other is used to introduce metallurgical slag particles into the rotary kiln. The rotary kiln and the metallurgical slag particles are both used as heat sources; the biomass particles are used as pyrolysis objects.

[0076] The heat transfer model calculation method of the present invention is applicable to this type of rotary kiln. Figure 2-Figure 7 The figure shows a cross-section of an externally heated rotary kiln, which clearly illustrates the spatial correspondence formed by the raw material particles as the kiln rotates. In the process of solving the heat transfer rate of the rotary kiln biomass pyrolysis system in the present invention, all the parameters used and the established formulas are developed around this correspondence.

[0077] The biomass raw materials used in this embodiment are discarded cigarette rods from a cigarette processing plant, and the metallurgical slag particles are copper slag crushed at high temperature from a smelter.

[0078] The known relevant physical properties are as follows:

[0079] 1. Inner diameter d of rotary kiln w The length of the kiln is 0.2m, and the length of the kiln is 1.2m (that is, the volume of the rotary kiln is 0.03768m 3 ), the wall thickness of the kiln is 0.01m, the rotation speed is 6rpm, and the thermal conductivity coefficient k w is 50W / (m·K), and the Young's modulus is 1×10 8 Pa, Poisson's ratio is 0.30, and the density is 7800 kg / m 3 , the specific heat capacity is 502.48 J / (kg·K), the initial temperature T w It is 773K.

[0080] 2. Radius r of discarded cigarette rod particles b is 0.001m, thermal conductivity k b The particle density is 220 kg / m 3 , the specific heat capacity is 960 J / (kg·K), the initial temperature is 303 K, the discarded cigarette rod particles are all considered to be normally distributed spherical particles, and the Young's modulus is 4.2×10 9Pa, Poisson's ratio is 0.25, the filling rate of waste tobacco rod particles accounts for 5% of the volume of the rotary kiln (that is, the mass of a single particle is 9.22×10 -7 kg, the actual kiln volume occupied by all particles is 1.1304×10 -3 m 3 The total number of particles is 270,000, the total mass is 0.25 kg, and the total integral score is is 3%).

[0081] 3. High-temperature copper slag particle radius r s The thermal conductivity coefficient is 0.002m, and the thermal conductivity coefficient k s 6W / (m·K), density is 3150kg / m 3 , the specific heat capacity is 1100 J / (kg·K), the initial temperature is 773 K, the copper slag particles are all considered to be normally distributed spherical particles, and the Young's modulus is 2.1×10 8 Pa, Poisson's ratio is 0.30, the copper slag particle filling rate accounts for 15% of the rotary kiln volume (i.e. the mass of a single particle is 1.055×10 -4 kg, and the actual kiln volume occupied by all particles is 3.4×10 -3 m 3 The total number of particles is 101200, the total mass is 10.71 kg, and the total integral score is is 9%).

[0082] 4. Nitrogen is used as carrier gas, the nitrogen flow rate ν is 0.07427m / s, and the gas dynamic viscosity μ is 1.8×10 -5 Pa, the thermal conductivity of nitrogen is 0.026W / (m·K), and the density is 1.25kg / m 3 , specific heat capacity C p The nitrogen temperature is 741 J / (kg·K). Before the formal pyrolysis begins, nitrogen is introduced into the rotary kiln at a flow rate of 0.07427 m / s for about 15 minutes to ensure an inert atmosphere. g At the same time, it is heated to a constant temperature of around 573K.

[0083] 5. The total mass of discarded cigarette rods is 0.25 kg and the particle density is 220 kg / m 3 , of which cellulose accounts for 42.6%, hemicellulose accounts for 36.0%, and lignin accounts for 21.4%; for cellulose: the pre-exponential factor A1 is 1.371×10 16 , the activation energy E1 is 189.268 kJ / mol, and the reaction enthalpy change is 172.431 kJ / mol; for hemicellulose: the pre-exponential factor A2 is 5.767×10 15, the activation energy E2 is 176.357 kJ / mol, and the reaction enthalpy change is 148.896 kJ / mol; for lignin: the pre-exponential factor A3 is 5.259×10 15 , the activation energy E3 is 191.762 kJ / mol, the reaction enthalpy change is 202.352 kJ / mol; the ideal gas constant is 8.314 J / (mol·K).

[0084] According to the above known data, Figure 8 As shown, the heat transfer model calculation method for coupling biomass pyrolysis and high-temperature metallurgical slag of the present invention is carried out according to the following steps:

[0085] 1. The total heat input of the rotary kiln pyrolysis system comes from the metallurgical slag particles and the constant temperature of the rotary kiln wall (the two are at the same temperature). The total heat input of the rotary kiln pyrolysis system is Q in,all The calculation formula is,

[0086] Q in,all =Q in,kiln +Q in,slag

[0087] Where Q in,all The total heat input to the pyrolysis system, Q in,kiln Heat input to the rotary kiln wall, Q in,slag Metallurgical slag inputs heat.

[0088] The pyrolysis reaction time is known to be 2820 seconds. During this period, the temperature of the rotary kiln wall is constant at 773K, which means that heat is continuously input into the pyrolysis system. The heat input into the pyrolysis system through the rotary kiln wall is calculated to be Q in,kiln 5.0×10 9 J, calculated heat Q input into the pyrolysis system through copper slag particles in,slag is 5537.07J, and the total heat input to the system is Q in,all Approximately 5.005537×10 9 kJ.

[0089] 2. The calculation formula of the contact heat transfer coefficient h1 between the waste smoke rod particles and the metallurgical slag particles in the rotary kiln is:

[0090]

[0091] Where k b-s is the effective thermal conductivity between biomass particles and metallurgical slag particles, r b The radius of the biomass particle, r s Radius of metallurgical slag particles, k b is the thermal conductivity of biomass particles, k s is the thermal conductivity of metallurgical slag particles, is the volume fraction of biomass particles in the rotary kiln, It is the volume fraction of metallurgical slag particles in the total volume of the rotary kiln.

[0092] First calculate the effective thermal conductivity k b-s The contact heat transfer coefficient h1 of waste cigarette rod particles and copper slag particles is about 0.006964W / (m 2 ·K).

[0093] 3. Calculate the contact heat transfer coefficient h2 between the waste tobacco rod particles in the rotary kiln and the inner wall of the kiln. The calculation formula is as follows:

[0094]

[0095] Where k b is the thermal conductivity of biomass particles, k w is the thermal conductivity of the rotary kiln wall, r b is the radius of the biomass particle, r w is the inner radius of the rotary kiln.

[0096] The contact heat transfer coefficient h2 between the waste tobacco rod particles and the inner wall of the rotary kiln is calculated to be approximately 253.7313 W / (m 2 ·K).

[0097] 4. Calculate the contact heat transfer coefficient h3 between the waste tobacco rod particles, air film and copper slag particles in the rotary kiln. The calculation formula is as follows:

[0098] Nu1=2+0.6Re 1 / 2 Pr 1 / 3 (4)

[0099] Nu1=2+0.6Re 1 / 2 Pr 1 / 3 (5)

[0100]

[0101] Where k g is the gas thermal conductivity, Nu1 is the Nusselt number of the gas film between biomass particles-gas film-metallurgical slag particles, d1 is the distance between biomass particles and high-temperature metallurgical slag particles (i.e., gas film thickness), Re is the Reynolds number, Pr is the Prandtl number, C p is the specific heat capacity of the gas, ν is the gas flow rate, and μ is the gas dynamic viscosity.

[0102] According to the random close packing model, taking d1 as 0.003m, Re is calculated to be 12.38, Pr is 0.51, and Nu1 is 3.71. The contact heat transfer coefficient h3 between the waste tobacco rod particles, air film, and copper slag particles in the rotary kiln is calculated to be 32.15W / (m 2 ·K).

[0103] 5. Calculate the contact heat transfer coefficient h4 between the waste tobacco rod particles, air film and kiln inner wall in the rotary kiln. The calculation formula is as follows:

[0104]

[0105] The calculation formula of Nu2 is the same as Nu1. Taking d2 as 0.002m, the calculated Re is 8.25, Pr is 0.51, and Nu2 is 3.37. The contact heat transfer coefficient h4 between the particles, air film and the inner wall of the rotary kiln is 43.81W / (m 2 ·K).

[0106] Among them, the calculation criteria of h4 and h3 are both Ranz-Marshall correlations.

[0107] 6. Calculate the convection heat transfer coefficient h5 between the waste tobacco rod particles on the upper surface of the rotary kiln and the gas. The calculation formula is as follows:

[0108] Nu3=C(GrPr) n (10)

[0109]

[0110] Where k g is the thermal conductivity of gas, Nu3 is the Nusselt number of gas around biomass particles on the upper surface of rotary kiln, d b is the diameter of the biomass particle, Gr is the Grashof number, Pr is the Prandtl number, C is the empirical correction constant in the heat transfer coefficient correlation, n is the empirical power exponent characterizing the nonlinear relationship of heat transfer, g is the acceleration of gravity, β is the gas volume expansion coefficient, and ΔT1 is the temperature difference between the gas and the biomass particle.

[0111] Assume that β is 2×10 -3 K -1 , g is 9.8 m / s 2 , ΔT1 is 270K, Gr is calculated to be 130.67, assuming Pr is 0.7, C is 0.5, n is 0.25 (empirical value), Nu3 is calculated to be 1.55, and the convection heat transfer coefficient h5 between the waste tobacco rod particles on the upper surface of the rotary kiln and the gas is 20.15W / (m 2 ·K).

[0112] 7. Calculate the convection heat transfer coefficient h6 between the rotary kiln wall and the gas. The calculation formula is as follows:

[0113] Nu4=0.023Re 0.8 Pr 0.4 (13)

[0114]

[0115] Where Nu4 is the Nusselt number of the gas in the rotary kiln that forms convective heat transfer with the wall, k g is the thermal conductivity of gas, d w is the inner diameter of the rotary kiln, Re is the Reynolds number, and Pr is the Prandtl number.

[0116] For the convective heat transfer between the rotary kiln wall and the gas, it is assumed to be analogous to the flow in the tube, d w The calculated Re is 825.22, assuming turbulence, and the Dittus-Boelter formula is used to calculate Pr as 0.51 and Nu4 as 3.79. The calculated convective heat transfer coefficient h6 in the rotary kiln is 0.4927W / (m 2 ·K).

[0117] 8. Calculate the radiation heat transfer coefficient h7 between the rotary kiln wall and the waste tobacco rod particles on the upper surface of the kiln. The calculation formula is as follows:

[0118]

[0119] Where q7 is the heat flux density of radiation heat transfer between the rotary kiln wall and the biomass particles on the upper surface of the kiln, T w is the temperature of the kiln wall, T b is the temperature of the biomass particles, ε w-b is the effective radiation coefficient between biomass particles and kiln wall, σ is the Stefan-Boltzmann constant, 5.67×10 -8 W / (m 2 ·K 4 ).

[0120] Assuming that the emissivity of waste cigarette rod particles is 0.6 and the emissivity of copper slag particles is 0.8, ε is calculated to be w-b is 0.48, T w and T b The radiation heat transfer coefficient h7 between the rotary kiln wall and the waste tobacco rod particles on the upper surface of the kiln is calculated to be 20.1869W / (m 2 ·K).

[0121] 9. Calculate the radiation heat transfer coefficient h8 between the gas and the rotary kiln wall. The calculation formula is as follows:

[0122]

[0123] Where q8 is the heat flux density of radiation heat transfer between the gas and the rotary kiln wall, T g is the gas temperature, T w is the temperature of the kiln wall, σ is the Stefan-Boltzmann constant of 5.67×10 -8 W / (m 2 ·K 4 ), ε w-g It is the effective radiation coefficient of gas and kiln wall.

[0124] Assuming that the gas emissivity is 0.4 and the kiln wall emissivity is 0.8, ε is calculated to be w-g is 0.32, T w and T g The radiation heat transfer coefficient h8 between the gas and the rotary kiln wall is calculated to be 22.61W / (m 2 ·K).

[0125] 10. The three parallel pyrolysis reaction models are as follows:

[0126]

[0127] Among them, k1, k2 and k3 represent the pyrolysis reaction rate constants of hemicellulose, cellulose and lignin, respectively, reflecting the speed of the pyrolysis reaction of these substances under specific conditions (such as temperature, pressure, etc.); r1, r2 and r3 represent the yield of biochar generated by the pyrolysis of hemicellulose, cellulose and lignin, respectively.

[0128] According to the above three parallel pyrolysis reaction model, the pyrolysis conversion rate q of component i in biomass is i,c The calculation formula is as follows,

[0129]

[0130] Q i,c =A i,b (-q i,c )(-ΔH i,c ) (twenty one)

[0131] Where ρ is the density of biomass particles, i includes cellulose, hemicellulose and lignin, and m i , A i and E i represents the initial mass, pre-exponential factor and activation energy of cellulose, hemicellulose and lignin, respectively; R is the ideal gas constant (8.314 J / (mol·K)); T is the temperature of biomass pyrolysis reaction; Q i,c is the heat generated by chemical reaction or phase change, A i,bis the reactive surface area of ​​the biomass particles, the negative sign is the decrease in reactant concentration over time, ΔH i,c is the reaction enthalpy change.

[0132] Calculate the q of cellulose, hemicellulose and lignin i,c They are 9397.49W, 15333.78W and 5756.60W respectively.

[0133] It is known that there are 270,000 discarded tobacco stem particles. Assuming that the number of particles is calculated according to the proportion of cellulose, hemicellulose and lignin, the number of cellulose, hemicellulose and lignin particles is 115,020, 97,200 and 57,780 respectively. According to the surface area calculation formula of spherical particles, the surface area of ​​a single particle can be calculated to be 1.256637×10 -5 m 2 , it can be further calculated that the reactive surface areas of cellulose, hemicellulose and lignin particles are approximately 1.4454 m 2 , 1.2215m 2 , 0.7261m 2 However, during the pyrolysis reaction, the biomass particles will undergo dehydration and decomposition reactions of macromolecular compounds, which usually cause the particle size to become smaller as the reaction occurs. According to repeated experimental experience, the surface area of ​​the biochar formed after pyrolysis is about 0.8 times that of the original biomass particles. That is, assuming that the reactive surface areas of cellulose, hemicellulose and lignin particles are approximately 1.15632 m 2 , 0.9772m 2 , 0.58088m 2 ; Further calculations show that the heat generated by chemical reaction or phase change of cellulose, hemicellulose and lignin particles is 1.873711567×10 9 J, 2.231082949×10 9 J, 0.6766436×10 9 J; the total heat Q generated by chemical reaction or phase change i,c is 4.781438116×10 9 J.

[0134] 11. Heat transfer capacity Q of rotary kiln pyrolysis system transfer The calculation formula is as follows,

[0135]

[0136] Where Q pp , Q pw , Q pfp , Q pfw , Q cp , Qcν , Q rpw , Q rfw and Q i,c They represent the heat transfer between biomass particles and metallurgical slag particles, the heat transfer between biomass particles and the inner wall of the kiln, the heat transfer between biomass particles-air film-metallurgical slag particles, the heat transfer between biomass particles-air film-kiln inner wall, the convection heat transfer between biomass particles on the upper surface of the rotary kiln and gas, the convection heat transfer between the rotary kiln wall and gas, the radiation heat transfer between the rotary kiln wall and biomass particles on the upper surface of the kiln, and the radiation heat transfer between the rotary kiln wall and gas; A pp , A pw , A pfp , A pfw , A cp , A cν , A rpw , A rfw , and A i,b They represent the contact area between biomass particles and metallurgical slag particles, the contact area between biomass particles and the inner wall of the kiln, the heat transfer area between biomass particles-air film-metallurgical slag particles, the heat transfer area between biomass particles-air film-kiln inner wall, the convective heat transfer area between biomass particles on the upper surface of the rotary kiln and gas, the convective heat transfer area between the rotary kiln wall and gas, the radiation heat transfer area between the rotary kiln wall and biomass particles on the upper surface of the kiln, and the radiation heat transfer area between the rotary kiln wall and gas; T b , T s , T w , T g and T c-b They represent the temperature of biomass particles, the temperature of metallurgical slag particles, the temperature of kiln wall, the gas temperature and the temperature of biomass particles on the upper surface of the kiln.

[0137] The total area of ​​270,000 particles is approximately 3.3929 m 2 During the reaction, the particles themselves also rotate with the kiln. Assuming that the contact area of ​​all waste tobacco rod particles is involved (such as the contact area A between waste tobacco rod particles and copper slag particles), pp , the contact area A between the waste tobacco rod particles and the kiln wall pw , waste cigarette rod particles-air film-copper melt

[0138] Heat transfer area A between slag particles pfp , the heat transfer area A between the waste tobacco rod particles, air film and kiln wall pfw ) are both 2.71432m 2 , the convection heat exchange area A between the waste cigarette rod particles on the upper surface and the gas cp Take 0.67858m 2 , the convection heat exchange area A between the rotary kiln wall and the gas cνTake 0.754m 2 , the radiation heat transfer area A between the rotary kiln wall and the particles on the upper surface of the kiln rpw Take 0.67858m 2 , the radiation heat transfer area A between the gas and the rotary kiln wall rfw Take 0.754m 2 Based on the previous numerical simulation results ( Figure 8 ) It can be seen that when the waste tobacco rod particles are filled with different proportions of copper slag particles, they reach the target temperature (500°C) approximately 300 seconds earlier. Therefore, it is assumed that heat transfer has been occurring within the pyrolysis system for the first 300 seconds.

[0139] In summary, the heat transfer Q generated by heat conduction is calculated pp +Q pw +Q pfp +Q pfw A total of approximately -1.26×10 8 J, the amount of heat transferred due to convection heat transfer Q cp and Q cν The sum is -1.13×10 6 J, the amount of heat transferred due to radiation heat transfer Q rpw and Q rfw The sum is -3.0×10 6 J. Therefore, calculate the total heat transfer Q in the rotary kiln pyrolysis system transfer Approximately -4.91013×10 9 J.

[0140] 12. The calculation formula for the change in internal energy ΔQ of the rotary kiln pyrolysis system is as follows:

[0141] ΔQ=Q in,all +Q transfer (twenty three)

[0142] The calculated ΔQ is 9.5407×10 7 J.

[0143] In this pyrolysis system, the heat input sources include high-temperature copper slag particles and the rotary kiln wall, and the rotary kiln wall continuously inputs heat, which also explains why ΔQ is calculated to be 9.5407×10 7 J.

[0144] In summary, ΔQ is approximately equal to 9.5407×10 7 J, in an ideal energy conservation system, the input energy should be equal to the sum of the output and internal transfer energy, where ΔQ is approximately equal to 9.5407×10 7J is mainly attributed to the constant temperature of the rotary kiln wall at 773K, which continuously inputs heat from the kiln wall. It is also possible that a small amount of heat from the high-temperature copper slag particles is absorbed by the waste pipe particles, causing the high-temperature copper slag particles to drop in temperature, thereby forming a temperature difference with the rotary kiln and conducting a small amount of heat exchange. This ΔQ represents the slight imbalance in the system during the energy transfer process. Due to measurement errors and calculation approximations that may exist in actual systems, the calculated ΔQ result is within the allowable error range. This also shows that the system has 9.5407×10 7 The energy loss of J is relatively small and within a reasonable error range, so it can be considered that the result conforms to the law of conservation of energy.

[0145] The meanings of the relevant parameters are shown in Table 1 below.

[0146] Table 1

[0147]

[0148]

[0149]

Claims

1. A heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery, characterized by: A heat transfer model between biomass particles and high-temperature metallurgical slag particles in a rotary kiln was established. A three-parallel pyrolysis reaction model was used to define the three components of the biomass particles, and decomposition was performed according to a single Arrhenius-type reaction. The heat transfer calculation method specifically includes the following steps: S1: Calculate the total heat input Q of the rotary kiln pyrolysis system in,all ; S2: Calculate the contact heat transfer coefficient h1 between biomass particles and metallurgical slag particles in the rotary kiln; S3: Calculate the contact heat transfer coefficient h2 between the biomass particles in the rotary kiln and the inner wall of the kiln; S4: Calculate the contact heat transfer coefficient h3 between biomass particles, air film and metallurgical slag particles in the rotary kiln; S5: Calculate the contact heat transfer coefficient h4 between the biomass particles, the air film, and the inner wall of the rotary kiln; S6: Calculate the convection heat transfer coefficient h5 between the biomass particles on the upper surface of the rotary kiln and the gas; S7: Calculate the convection heat transfer coefficient h6 between the rotary kiln wall and the gas; S8: Calculate the radiation heat transfer coefficient h7 between the rotary kiln wall and the biomass particles on the upper surface of the kiln; S9: Calculate the radiation heat transfer coefficient h8 between the gas and the rotary kiln wall; S10: Calculate the biomass pyrolysis conversion rate q based on the three-parallel pyrolysis reaction model r ; S11: Calculate the heat Q generated by chemical reaction or phase change i,c ; S12: Calculate the heat transfer Q of the rotary kiln pyrolysis system transfer ; S13: Calculate the change ΔQ of the internal energy of the rotary kiln pyrolysis system.

2. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1 is characterized by: The total heat input of the rotary kiln pyrolysis system comes from the metallurgical slag particles and the constant temperature of the rotary kiln wall. The total heat input of the rotary kiln pyrolysis system is Q in,all The calculation formula is: ； Where, is the total heat input to the pyrolysis system, It is the heat input from the rotary kiln wall. It is the heat input of metallurgical slag.

3. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1 is characterized by: The calculation formula for the contact heat transfer coefficient h1 between biomass particles and metallurgical slag particles in the rotary kiln is: ； ； Where, is the effective thermal conductivity between biomass particles and metallurgical slag particles, The radius of the biomass particle, Radius of metallurgical slag particles, k b is the thermal conductivity of biomass particles, k s is the thermal conductivity of metallurgical slag particles, is the volume fraction of biomass particles in the rotary kiln, It is the volume fraction of metallurgical slag particles in the total volume of the rotary kiln.

4. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1 is characterized by: The calculation formula for the contact heat transfer coefficient h2 between the biomass particles and the inner wall of the rotary kiln is: ； Where k b is the thermal conductivity of biomass particles, k w is the thermal conductivity of the rotary kiln wall, r b is the radius of the biomass particle, r w is the inner radius of the rotary kiln.

5. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1 is characterized by: The calculation formula of the contact heat transfer coefficient h3 between biomass particles, air film and metallurgical slag particles in the rotary kiln is: ； ； ； ； Where, is the thermal conductivity of the gas, is the Nusselt number of the air film between biomass particles, air film and metallurgical slag particles, is the distance between biomass particles and high-temperature metallurgical slag particles, is the Reynolds number, is the Prandtl number, is the specific heat capacity of the gas, is the gas flow rate, is the gas dynamic viscosity; The calculation formula of the contact heat transfer coefficient h4 between biomass particles, air film and kiln inner wall in the rotary kiln is: ； ； Where, is the distance between the biomass particles and the rotary kiln wall, is the thermal conductivity of the gas, It is the Nusselt number of the air film between biomass particles, air film and rotary kiln wall.

6. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1, characterized in that: The calculation formula of the convective heat transfer coefficient h5 between the biomass particles on the upper surface of the rotary kiln and the gas is as follows: ； ； ； Where, is the thermal conductivity of the gas, is the Nusselt number of the gas surrounding the biomass particles on the upper surface of the rotary kiln, is the biomass particle diameter, is the Grashof number, is the Prandtl number, C is the empirical correction constant in the heat transfer coefficient correlation, and n is the empirical power exponent that characterizes the nonlinear relationship of heat transfer. is the acceleration due to gravity, is the gas volume expansion coefficient, is the temperature difference between the gas and the biomass particles, is the dynamic viscosity of the gas; The calculation formula of the convection heat transfer coefficient h6 between the rotary kiln wall and the gas is as follows: ； ； Where, is the Nusselt number of the gas that forms convective heat transfer with the wall in the rotary kiln, is the thermal conductivity of the gas, is the inner diameter of the rotary kiln, is the Reynolds number, is the Prandtl number.

7. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1, characterized in that: The calculation formula of the radiation heat transfer coefficient h7 between the rotary kiln wall and the biomass particles on the upper surface of the kiln is as follows: ； ； Where, is the heat flux density of radiation heat transfer between the rotary kiln wall and the biomass particles on the upper surface of the kiln, is the temperature of the kiln wall, is the temperature of the biomass particles, is the effective radiation coefficient between biomass particles and kiln wall, is the Stefan-Boltzmann constant; The calculation formula of the radiation heat transfer coefficient h8 between the gas and the rotary kiln wall is as follows: ； ； Where, is the heat flux density of radiation heat transfer between the gas and the rotary kiln wall, is the gas temperature, is the temperature of the kiln wall, is the Stefan-Boltzmann constant, It is the effective radiation coefficient of gas and kiln wall.

8. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1, characterized in that: The three parallel pyrolysis reaction models are as follows: ； in, 、 and are the pyrolysis reaction rate constants of hemicellulose, cellulose, and lignin, respectively; 、 and represent the yields of biochar from pyrolysis of hemicellulose, cellulose, and lignin, respectively; According to the above three parallel pyrolysis reaction model, the pyrolysis conversion rate of component i in biomass is The calculation formula is as follows, ； ； Where, is the density of the biomass particle, i contains cellulose, hemicellulose and lignin, , and are the initial masses of cellulose, hemicellulose, and lignin, the preexponential factor, and the activation energy, respectively; R is the ideal gas constant; and T is the biomass pyrolysis reaction temperature; is the heat generated by chemical reactions or phase changes, is the reactive surface area of ​​the biomass particles, and the negative sign indicates that the concentration of reactants decreases with time. is the reaction enthalpy change.

9. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1, characterized in that: Heat transfer of rotary kiln pyrolysis system The calculation formula is as follows, ； Where, , , , , , , , and They are heat conduction between biomass particles and metallurgical slag particles, heat conduction between biomass particles and kiln inner wall, heat conduction between biomass particles-air film-metallurgical slag particles, heat conduction between biomass particles-air film-kiln inner wall, convection heat transfer between biomass particles on the upper surface of the rotary kiln and gas, convection heat transfer between the rotary kiln wall and gas, radiation heat transfer between the rotary kiln wall and biomass particles on the upper surface of the kiln, and radiation heat transfer between the rotary kiln wall and gas; heat generated due to chemical reaction or phase change; , , , , , , , ,and They are the contact area between biomass particles and metallurgical slag particles, the contact area between biomass particles and the inner wall of the kiln, the heat transfer area between biomass particles-air film-metallurgical slag particles, the heat transfer area between biomass particles-air film-kiln inner wall, the convection heat transfer area between biomass particles on the upper surface of the rotary kiln and gas, the convection heat transfer area between the rotary kiln wall and gas, the radiation heat transfer area between the rotary kiln wall and biomass particles on the upper surface of the kiln, the radiation heat transfer area between the rotary kiln wall and gas; the reactive surface area of ​​biomass particles; , , , and They are the temperature of biomass particles, the temperature of metallurgical slag particles, the temperature of kiln wall, the gas temperature and the temperature of biomass particles on the upper surface of the kiln.

10. The heat transfer calculation method for coupling biomass pyrolysis with metallurgical slag waste heat recovery according to claim 1, characterized in that: Changes in internal energy of rotary kiln pyrolysis system The calculation formula is, 。

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