General equation heat balance chemical reactor. Heat balance equation for chemical reactors operating in isothermal, adiabatic and intermediate thermal regimes. Thermal stability of chemical reactors in the case of exo- and endothermic reactions. Reversible reaction reactor.
The heat balance equation takes into account all heat flows, entering and leaving the reactor. Such flows are: Qin – physical heat of the reaction mixture included in the elementary volume for which a balance is compiled (input flow); Qout – physical heat of reaction leaving the elementary volume (output flow); Q р – heat of chemical reaction (the sign can be positive or negative); Q t.o – heat spent on heat exchange with environment(depending on the temperature ratios in the reactor and in the environment or in the heat exchange device, this flow can also be directed into and out of the volume); Q f.pr – heat of phase transformations.
For stationary reactor operation algebraic sum of all heat flows is zero: Q in - Q out ± Q р ± Q t.o ± Q f.pr = 0 (1)
In an unsteady mode, positive or negative accumulation of heat occurs in an elementary volume:
Q in - Q out ± Q r ± Q t.o ± Q f.pr = Q nak (2)
Equations (1) and (2) are general equations for the heat balance of a chemical reactor. There are several types of thermal regimes of chemical reactions and, accordingly, specific types of heat balance equations
I. Isothermal - a mode characterized by the fact that the temperature at the inlet, inside and outlet is the same. This is possible if the release and absorption of heat as a result of a chemical reaction is compensated by heat exchange with the environment. For a stationary isothermal process with constant physical properties of the system, we can write: Q in =Q out; | Q р |=| Q t.o | .
In addition to fundamentally isothermal mixing reactors, reactors with a very low value of Q p, C A0 or x (degree of conversion) with significant thermal conductivity in the reaction mixture can approach isothermal. When modeling reactors, completely isothermal reactors include reactors of various types, mixing liquid type (Zh, Zh-Zh, Zh-T). The isothermal regime is observed on the shelf of small-sized foam and bubbling apparatus, as well as in a fluidized bed of granular material, and other apparatus.
Characteristic equation of an isothermal reactor: t cf =t k =const.
II. The adiabatic regime is characterized by a complete absence of heat exchange with the environment. In this case, all the heat of the chemical reaction is spent on heating or cooling the reaction mixture. For a stationary process |Q in -Q out |=|Q p |. The change in temperature in an adiabatic reactor ∆t is directly proportional to the degree of conversion x, the concentration of the main reagent C A0, and the thermal effect of the reaction Q p. Temperature changes are positive for exothermic reactions and negative for endothermic reactions. The heat balance equation for reaction A→B will be: G c t k ± GQ p C A 0 x=G c t k(2), from here we obtain the characteristic equation: ± GQ p C A 0 x=с (t k – t n) (2’).
The temperature change in any section along the flow axis in a plug-flow reactor is proportional to the degree of conversion: ∆t= t k – t n =±λх, where λ is the coefficient of adiabatic temperature change: λ=(Q p * C D)/c, where
C D – product concentration. The heat balance equation for an elementary section of the reactor will be: ±Q p C A dx A =cdt (3). For a fully mixed reactor, the heat balance equation is the same as (2’).
III. Intermediate(polytropic or autothermal) mode is characterized by the fact that part of the heat of reaction is spent on changing the heat content (heating or cooling) of the reaction mixture, and partly on heat exchange with the environment. This mode is most often found in TCP. This regime is described by the complete heat balance equation. With a constant weight heat capacity and steady state, the heat released (absorbed) as a result of the reaction at the degree of conversion x A will be carried away by the reaction products and transferred through the reactor wall: ±GQ p C A 0 x A =G c (t k – t n) ± k t F∆t av (4), from here the following can be found: 1) temperature change (t k – t n), degree of conversion (x A), heat transfer surface (F). This equation (4) was obtained for mixing reactor and for plug flow reactor, in which the temperature is the same along the entire length, that is, the temperature of the coolant or coolant located in the jacket is constant along the entire length of the reactor; the temperature of the reactants is the same at any point in the cross section of the reactor. Since the temperature in the reactor varies along its length, the heat balance is compiled for an elementary section of the reactor length (∆H): GQ p C A 0 x A =G c dt± k t F’(t-t arr)dH; where t is the temperature in the reactor element under consideration; t ambient – temperature in the jacket.
A comparison of the characteristics of isothermal, adiabatic and polythermal processes is shown in the figures.
Stability of reactor operation is one of the requirements placed on them. According to A.M. Lyapunov, “A system is called stable if, after applying some disturbance, it returns to its previous state when this disturbance is removed.”
The most important is the temperature (thermal) stability of chemical reactions and reactors. During exo- and endothermic reactions, automatic regulation of the temperature of the technological process occurs due to the influence of the concentration of reagents in the chemical process. In some cases, the dependence of the amount of heat released on the temperature in a complete fusion reactor at reversible exothermic reaction.
The stability of a reactor's technological regime can be determined by its sensitivity when changing one or another parameter and is called parametric sensitivity:П=dy/dx, where y is an input value - parameter (temperature, reagent consumption, concentration), x is an output value - a parameter characterizing the result of the process (degree of conversion, temperature, reaction time).
Dakhin O.Kh.Volgograd, RPK "Polytechnic", 2012. - 182 pp. Classification of reactors by design
general characteristics and purpose
Classification of reactors according to the mode of movement of the reaction mass and the type of heat exchange surface
Classification of reactors by design forms
Classification of reactors according to the phase state of the reagents and the principle of operation
General characteristics and principles of operation according to mode of operation
Batch reactors (homogeneous non-stationary reactors)
Semi-batch reactors
Continuous reactors (homogeneous stationary reactors)
Cascade of reactors
Methodology for complex calculation of chemical reactors
Reactor calculation algorithm
General provisions
Determination of chemical reaction rate, constant, degree of conversion and order
Chemical reaction rate
Simple reactions
Zero order reactions
First order reactions
Product yield
Classification of reactions
The effect of temperature on the rate of a chemical reaction
Parallel and sequential reactions
Basics mathematical modeling chemical reactors
Linear distribution functions of residence time
Experimental determination of E(τ) and F(τ) and analysis of a chemical reactor using these functions
Heat transfer in chemical reactors
Thermal effect in reactors
Classification of chemical reactors by thermal regime
Algorithm for calculating the thermal regime of chemical reactors
Thermal calculation of chemical reactors
General characteristic heat balance equation
The influence of thermal conditions on the course of chemical processes in ideal mixing and displacement reactors. Thermal calculation of a continuous isothermal reactor with full mixing
Analysis of the thermal regime of a continuous isothermal reactor
Plug flow reactor with heat exchange between reactants and product
Plug flow reactor with heat exchange surface
Thermal calculation of an adiabatic reactor with a stirrer
Analysis of the thermal regime of an adiabatic reactor
Analysis of the thermal regime of an adiabatic reactor for endothermic reactions
Thermal calculation of an isothermal batch reactor
Thermal calculation of an isothermal batch reactor for quasi-stationary mode
Example of technological and thermal calculation of a chemical reactor
Mechanism of heterogeneous catalytic reactions
Calculation of a reactor with a fixed bed of catalyst
Calculation of a fluidized bed reactor
Heat transfer in a fluidized bed reactor
Purpose, designs and main technical characteristics of devices with mixing devices
Classification of mixing processes and their main criteria
The physical essence of the mixing process with mechanical stirrers in vessels
Fluid flow in the apparatus
Suspension
Suspension conditions
The influence of stirring on chemical technology processes
Effect of stirring on mass transfer
Mass transfer between solid and liquid phases
Effect of stirring on heat transfer
Mixing apparatus and their classification
Purpose of devices and areas of their operation
Conditional pressure and temperature of the medium
Basic parameters of the devices
Selection and requirements for materials for the manufacture of chemical reactors
Basic properties of materials used in the manufacture of reactors and their structural elements
Design features of devices for mechanical mixing of liquid media
Design of the main functional elements of reactors with stirrers
High speed mixers
Hydrodynamics of high-speed mixing devices. Calculation of basic hydrodynamic parameters
Low speed mixers
Hydrodynamics of mixing in devices with low-speed mixers
Mixer drive
Sealed electric drives
Mixer shaft seals
Hydraulic valves
Lip seals
Gland seals
Mechanical seals
Reactor internals
Reflective partitions
Pressure pipe
Coils
Calculation of internal devices
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MINISTRY OF EDUCATION AND SCIENCE OF THE RF Volgograd State Technical University O.Kh. Dakhin CHEMICAL REACTORS RPK "Polytechnic" Volgograd 2012 8 1 CLASSIFICATION OF REACTORS BY DESIGN 1.1 General characteristics and purpose The same reaction can be carried out in reactors of various types. When justifying the choice of a reaction apparatus of a certain type for carrying out a particular chemical process, it is necessary to take into account the possibility of its structural design of the apparatus. A comprehensive understanding of the main reactor design types used in various industries. In accordance with this large number reactor designs, methods and ways are considered practical application chemical kinetics, hydrodynamics, heat and mass transfer, necessary for engineering design, selection of the optimal operating mode and design of the reactor. Since the main apparatus of almost any chemical production is a reactor, the cost and quality of the resulting products, the power of the unit, labor productivity, capital costs, etc. mainly depend on its operation. Due to the large differences in reactor designs, it is difficult to find scientifically based criteria for their classification . Of all the design characteristics, two can still be considered decisive: - the mode of movement of the reaction mass in the reactor; - type of heat exchange surface; - according to the structural forms of the hull. The first characteristic makes it possible to classify reaction apparatuses in accordance with known ideal types of reactors, thus establishing a connection between the kinetic laws of the processes occurring in the reactors and the design of the latter. For each of the ideal types of reactors, the design will also depend on whether a heat exchange surface is needed (external, internal) or not (Table 1). 1.2 Classification of reactors according to the mode of movement of the reaction mass and the type of heat exchange surface Table 1.1 Mode Method Heat exchange surface movement implementation Without External With reaction movement surface surface internal mass and th surface Full Mechanical Stirred Oven with Autoclave with Autoclave stirring with shelves jacketed coil Rotating Drum - - Diffusion or Reaction - - convection I chamber; - - Reactor with Reactor with Reactor with moves with moving moving moving minimum layer layering reactor furnace with shelves Mixed Convection (one of the reagents Blast furnace Pneumatic 10th Bubbling Reactor with cross Reactor with Reactor with bubbling bubbling diffusion, bubbling the rest) Full Forward flow Reactor Catalytic displacement adiabatic reactor (reagents moving from stationary minimum Counter flow - Column with - - - - Rotary Rotary - furnace transverse packing diffusion) Reaction column with trays 1.3. Classification of reactors by design forms. Table 1.2. Reactor type Con Mode Operating surface page moving heat exchange uctium phase Without Sivn reactions nar internal ion super narrowed for mass nasal mat y p s sur face 11 C Examples Tubular PV G - + - reactors Cracking gasolines, ethylene polymerization L - + - Alkniation of lower paraffins L-L - + - Hydrolysis of chlorobenzenes Column PV G-L + - + PV G-L + - - reactors Neutralization of ammonia PV for G-L + + + gas, Oxidation of nxylene NS for liquid PV G-Zh + - - Obtaining ammonium sulfate 12 Continuation of table 1. 2 Column PV G-G/T + - - reactors Ethylene-benzene dehydration - + - Oxidation of ethylene G-T + - - Limestone roasting PV PV for L-T + - - Ion exchange G-T + - - G-G/T + - - Pyrolysis of butane G-T + - - Roasting pyra F + + + Diazotization G-L + + + Chlorination of gas, PS G-G/T for the solid phase PS of ethylene derivatives F + + + Sulfonation of benzene L-T + + + Preparation of superphosphates 13 Continuation of Table 1.2 Other widely G-T + + - Oxidation of ores used G-T + - + Roasting of the reactor Zh-T Decomposition of calcium carbide with water into acetylene G-G + - + Partial oxidation of hydrocarbons into olefins and diolefins Note : PV-full displacement; PS - complete mixing; G-gas phase; Liquid-liquid Classification of reactors according to the structural forms of the vessel is not based on scientific classification criteria, but is close to factory methods of grouping reaction apparatuses (boilers, furnaces, tubes). Based on their design forms, the main types of reactors are grouped as follows: - tubular (heat exchanger type reactors); -column (including devices with a stationary or moving layer of solid phase); -reactors of the reaction chamber type (with or without mechanical stirring); - other commonly used types of reactors (eg furnaces). Below are brief information about reactors of various design forms... 14 The main content of chemical technology consists of numerous and varied processes of chemical transformation of substances. They are carried out in special apparatus - chemical reactors. The reactor is the main apparatus of a technological installation and, in terms of its importance, occupies a leading place in the production of any products from the chemical, petrochemical and food industries. Therefore, of particular importance is knowledge and mastery of methods of technological and structural calculations, selection of the optimal size of the reactor, conditions for its competent and safe operation, as well as technological repair and installation. Reactors in technological lines of petrochemical and food production usually occupy a central place, since only in them, as a result of chemical reactions, the necessary target product with specified properties is formed for further use as a finished product or processing into certain products. The rest of the equipment of the corresponding production is intended for preparing the starting components for carrying out chemical reactions in the reactor and processing or processing the finished reaction products. Each industrial chemical process is designed to economically produce a desired product from a feedstock through several successive processing steps. Figure l.l shows a diagram of a typical chemical process. The initial hydromechanical thermal (heating, materials (crushing, with - technological assistance, centrifugation, cooling, etc.) and various other processes) are subjected to special processing to a state in which they are capable, under certain conditions, of entering into a chemical reaction. 15 After this, the starting reagents are fed into the reactor to carry out the chemical reaction. With the help of certain physical processes in the reactor, optimal conditions are created for the chemical reaction. Based on kinetic dependencies, the optimal reaction time is ensured - temperature regime and reaction temperature - hydrodynamic regime and operating pressure of the reactor, the state of the reagents and their concentrations - phase, as well as the corresponding design. I – equipment for preparing initial reagents for a chemical reaction in a reactor; II – equipment for processing and processing the finished product obtained in the reactor. 1 chemical reactor; 2 – dryer; 3 – mass transfer apparatus; 4 – extruder; 5- capacity; 6 – centrifuge; 7 – filter; 8 – heat exchanger (refrigerator). Figure 1.1 – Chemical reactor in the technological scheme of petrochemical production 101; All chemical reactors consist of standard structural elements and apparatus, these are mixers, dispensers, filters, centrifuges, heat exchangers (refrigerators), dryers, etc., as well as contact devices - plates, nozzles, catalysts and mixing devices for the gas and liquid phases . Structurally, the reactor can be a simple apparatus, for example, a simple mixing tank, however, in most technological schemes of a wide variety of industries, the reactor is the main apparatus, since the chemical stage is the most important part of the process, determining its efficiency. Designing a reactor is a complex engineering task, since For a given chemical process, various types of apparatus can be used. Therefore, to design, calculate and select the optimal design, it is necessary to use patterns and data from various fields of knowledge: thermodynamics, chemical kinetics, hydrodynamics, heat transfer, mass transfer and economics. 1.4 Classification of reactors according to the phase state of the reagents and the principle of operation Chemical processes are carried out in devices of various design types, operating according to one of the following operating principles: - batch reactor; - semi-batch and semi-continuous reactor; - continuous reactor. In these reactors, the reagents can be in different phase states: gas, liquid, gas-liquid, liquid-liquid, gas-solid, liquid-solid, gas-liquid-solid. Reactions in these phases are carried out in apparatus in which mixing is carried out. movement of reagents Accordingly, in the displacement mode, the devices are either structurally designed in the form of a displacement reactor or a stirred reactor. Devices with displacement: usually continuous, and with mixing, both continuous and periodic. Periodic processes are carried out in reactors with stirring in homogeneous (L) and heterogeneous (L+G; Ll+L2; G+Tv.t; G+L+Tt) systems. Periodic processes include: -polymerization processes (L); -semi-periodic chlorination (G+L) -sulfonation (Ll+L2); -recycling (G + TV); -Ek minerals (L+Tv.t.); -hydrogenation (G + F + Tv.t.). Continuous processes are carried out in both plug-flow and mixing reactors. Continuous processes include: - thermal cracking (G); -absorption(G + F); -extraction(Ll+L2); -nitration(Ll+L2); -processes occurring in a stationary or moving suspended layer of catalyst (G+Tv.t. ); -ion exchange (F+Tv.t.). Schemes for implementing the above processes are given in Table 1.3. 103 Table 1.3 104 2 GENERAL CHARACTERISTICS AND PRINCIPLES OF OPERATION BY OPERATION MODE 2.1 Batch reactors (homogeneous non-stationary reactors) All reagents are loaded into the reactor (Figure 2.1), consisting of a vessel with a stirrer, simultaneously. Intensive mixing ensures the same concentration throughout the entire volume at any time. The process is carried out until equilibrium or the desired degree of conversion is achieved. The residence time of the components in the reaction zone is determined by the interval between the moments of loading and unloading the apparatus. Such devices, used for reactions in a liquid medium, operate in ideal (complete) mixing mode. Batch reactors are used in most cases for homogenization of processes and relatively dissolution, wide dilution, scale of chemical transformations. The decisive factors influenced by mixing are mass transfer and heat transfer. Due to mixing, the reacting components come into more complete and close contact, and the reaction accelerates, heat exchange occurs through a jacket or coil. The composition of the reaction mixture changes over time, so the reaction rate is not constant during the process. Changes in the concentration of the consumable component are presented in the diagram (Figure 2.2). It follows from the diagram that the concentration of the consumable component in the starting metals decreases over time, and the reaction products increase. periodic Full action working cycle consists of a cycle of loading operation time, reactor time of chemical reaction until a given transformation of reaction products and loading time. 105 Figure 2.1 - Diagram of a batch reactor Figure 2.2 - Diagram of changes in the concentrations of the initial component and reaction products 2.2 Semi-batch reactors The design of a semi-continuous (semi-batch) reactor is similar to a batch reactor. The difference lies in the operating principle. If all the initial reagents are loaded into the batch reactor 106 at the same time, then into the semi-continuous reactor some of the reagents are loaded at the beginning of the process, and the other is continuously fed into the apparatus during the process. It is advisable to use such reactors in case of danger of excessive temperature rise or side reactions occurring at high concentrations of one of the components. For example, in the reaction A + B - C, component A is first loaded into the apparatus, component B is supplied continuously, and the number of its moles nB is chosen so as to obtain the maximum of the target product (Figure 2.4). A diagram of changes in concentration in a semi-continuous reactor is presented in Figure 2.3. Figure 2.3 - Diagram of changes in concentration in a batch reactor 2.3 Continuous reactors (homogeneous stationary reactors) The operating principles of continuous reactors are as follows; loading of starting materials and unloading of reaction products into an apparatus with a stirrer is carried out continuously. As a result, 107 the exact residence time of the particles in the reaction zone has not been determined: apparently, only a small number of particles will be able to very quickly travel the path from the entrance to the exit of the apparatus. Most particles, due to mixing, go through a very difficult path to exit the reactor. Therefore, when calculating such reactors true time residence of the components in the reaction zone is replaced by the so-called equivalent time or average residence time of the particle in the reactor (Figure 2.4). Since the starting materials are continuously supplied and the reaction products are continuously removed, their concentrations will be constant at any point in the reaction volume and at any time; the reaction rate will also be constant over time and the volume of the apparatus. The concentration of the component upon loading is equal to c0; theoretically, it instantly decreases to the final concentration c and remains constant until the finished product is unloaded from the reactor. The diagram (Figure 2.5) shows the nature of the change in concentration and reaction rate in a continuous reactor. 108 Figure 2.4 - Diagram of a continuous reactor Figure 2.5 - Diagram of changes in concentration in a continuous reactor 2.4 Cascade of reactors The installation diagram is shown in the figure (Figure 2.6). The flow of reagents continuously flows from each reactor to the next one to further carry out the reaction. The concentrations of the starting materials change in steps. Another stepwise version of the operation of a cascade of reactors is possible, in which 109 the contents of each reactor are periodically transferred to the next one. The unloading of reaction products from the last apparatus is also periodic. Figure 2.6 - Diagram of a cascade of continuous reactors and a diagram of changes in concentrations by stages 2.5 Tubular reactors These are devices through which a flow of reagents continuously passes, which enter into chemical interaction with each other (Figure 2.7). There are reactors for homogeneous and heterogeneous processes. The flow conditions in tubular reactors are very complex. In the first approximation of mixing as mixing), it is possible to allow the movement of flows in and out without the direction of movement (longitudinal radial direction (transverse mixing). In reality, the picture is much more complicated: the presence of longitudinal and transverse mixing imposes additional influences on the flow. In the absence of longitudinal mixing, the duration the residence of the reagents in the reaction zone will be determined by the length of the apparatus and the speed of the particles, which is not the same across the cross section of the apparatus.If we consider a tubular reactor as an apparatus of ideal displacement (the so-called piston mode), then the residence time of the molecule in the reaction zone 110 is equal to the ratio of the length of the zone to the longitudinal velocity.Turbulization flows and longitudinal mixing complicate the calculation of residence time, so the concept of average residence time is introduced. At the end of the start-up period in each section of the reactor, as a result chemical interaction Constant concentrations of the consumable component are established, decreasing in the starting materials from input to output. Tubular reactors are widely used in the chemical and petrochemical industries. There are two main operating schemes for tubular reactors: flow-through (Figure 2.7) and recirculation (Figure 2.6). Figure 2.7 - Diagram of a flow-through tubular reactor and a diagram of changes in the concentrations of the initial and finished products 111 Figure 2.8 - Diagram of a reactor installation with recirculation. 1reactor; 2-separator; 3-heat exchanger; 4 - circulation pump This scheme corresponds to gas oil cracking, reforming of light products according to a single-arm scheme, as well as synthesis processes from individual components. Installations operating according to the specified scheme are widely used in industry, in particular at oil refineries. This is due to the following reasons: in most cases, without recycling it is impossible to achieve the desired degree of conversion of the reacting substances; many processes are accompanied by parallel or side reactions as a result of temperature disturbances. To avoid an increase in the yield of by-products, complete conversion of raw materials is ensured by the use of recycling. In the production of motor fuels, the reaction is often carried out with a large excess of one of the components of the raw material. For example, with an excess of isobutane, isooctane is synthesized from isobutane and isobutene; with an excess of benzene - synthesis of isopropylbenzene from benzene and propylene. In these cases, an excess amount of the component is introduced with the recirculate. The essence of the method is that the unreacted products, together with the reacted ones, enter the separation system 112 after the reactor, where they are separated from the latter and, mixed with fresh raw materials, are fed back into the reactor. 113 4 METHOD OF COMPREHENSIVE CALCULATION OF CHEMICAL REACTORS Chemical reactions occur in reactors of various types. The design and selection of the size of the apparatus for a specific chemical process (chemical reaction) depends on many factors, the phase state of the initial reagents and their physicochemical properties, heat and mass transfer processes and hydrodynamics. Moreover, all these processes occur simultaneously, which significantly complicates the design and calculation of chemical reactors. The possibility of obtaining the most optimal technological and design parameters appears when using a comprehensive calculation of the reactor. 4.1 Algorithm for calculating a reactor To create a reactor of optimal design, initial data are required, as they say. First of all, you should know the kinetics of the target product, and about the side processes that lead to irrational consumption of raw materials and the formation of unnecessary and sometimes harmful substances (kinetics is the science of the rates of chemical reactions). Next, data is required on the heat released or absorbed during the reaction, and on the maximum possible degree of conversion of starting substances into products. Answers these questions chemical thermodynamics . Since the molecules of the starting reactants must meet each other for the reaction to occur, the reaction system must be well mixed. The efficiency of mixing depends on the viscosities of the components, the mutual solubility of the starting substances and products, flow rates, reactor geometry and various types of reagent input devices. These questions are dealt with by a science called hydrodynamics. The occurrence of a chemical reaction also affects mixing. This is studied by physicochemical hydrodynamics. Finally, 114 the temperature in the reactor should be maintained in accordance with kinetic requirements to optimize reaction rates and yield of target and by-products. The science that deals with the description of chemical reactions taking into account the processes of mass and heat transfer is called macrokinetics (macroscopic kinetics). 1. Depending on the type of chemical reaction (simple, complex, exo- and endothermic), the amount of initial reagents and material reaction products, the flows that make up the general characteristic equation of material balance are determined. 2. The basic physical properties of substances and their mixtures are determined. 3. The kinetic characteristics of the stage of chemical transformations are calculated. On the basis of which one of the main calculated values is determined - the time of the chemical reaction - r. 4. As a result of analyzing the features of this type of chemical reaction, the hardware design is selected in the form of one apparatus with a stirrer, a cascade of reactors, etc. (Selected from catalogs, normals and reference books). 5. After establishing the specific technological features of the selected design type of reactor, the general characteristic equation of the material balance is transformed into the characteristic equation of periodic, continuous, corresponding to the type of reactor: ideal mixing or ideal displacement, semi-batch operation. From the characteristic equation of this type of reactor, which expresses the relationship of all the main parameters characterizing a chemical reactor - G, p, Vr (G - productivity, p - reaction time 115 and V r - reactor volume), the main design parameter of the reactor is determined: its volume Vr and, accordingly, the surface F. 6. In reactors with a stirring device, for specific chemical processes, first of all, the type of stirrer is selected depending on the process carried out in the apparatus (catalogs, normals and reference books). Thus, the mixing device in the reactor is the main functional structural and technological element, the correct choice of which and its calculation depend on the optimal technological and thermal operating conditions of the reactor. 7. Depending on the viscosity, concentration, temperature and other physical and mechanical properties of the medium, the speed of the selected type of mixer is determined. From correct definition The number of revolutions of the mixer depends on the intensity of mixing of chemical reagents, the degree of segregation of input streams, which determines the increment of substances in a chemical reaction, as well as the processes of heat and mass transfer. At this stage of the algorithm, the number of revolutions of the mixer n is calculated, the nominal power spent on mixing is N n, the power lost in the seals is N y, the power for internal devices is N B and the total drive power of the mixer is N. 8. Thermal calculation consists of compiling a general characteristic reactor equations. After establishing all the specific features of a given reactor, the heat balance equation is transformed into the characteristic equation of the corresponding adiabatic reactor type: non-isothermal, isothermal, polytropic, autothermal. From the characteristic equation of the reactor under consideration, which expresses the relationship of all the main thermophysical parameters characterizing the thermal operating mode of the apparatus Qr, QK, Qf, 116 Q , Qф, QM (Qr is the amount of heat released or absorbed in a chemical reaction, QK is convective heat transfer, Qf - heat transfer through the surface, Q - change in the amount of heat in the volume of the reactor, Qf - the amount of heat released or absorbed in physical processes (dissolution, evaporation, adsorption, crystallization, etc.) when the thermal effect is / N f [kJ/mol]. After determining the main thermal parameters, the stability of the reactor's operation is analyzed according to the thermal regime and the optimal operating temperatures are established. 9. In the design calculation, the reactor volume Vr - and surface - F determined above are embodied in a specific geometric shape (diameter - D and the height of the apparatus - H), the diameter of the stirrer shaft is calculated - dB, the diameter of the stirrer - dm, the dimensions of fittings and pipes, sealing devices, and the basic relationships between the dimensions of the elements of the mixing device (the diameter of the stirrer - dM and the diameter of the body DM, the distance of the stirrer from the bottom apparatus and to the liquid level in the reactor, etc.). 10. Strength calculation is the final stage of the complex calculation of the reactor. It is necessary to understand that when choosing structural materials for chemical reactors and auxiliary equipment for them, the material itself does not affect the chemical process in the reactor volume, but can significantly influence heat transfer processes, especially in the case of the use of non-metallic coatings (gumming, enamel, etc.) .P. ). Also, as a result of the catalytic effect of the structural material in the near-wall region, the formation of by-products (harmful, undesirable) reaction products is possible. 117 Therefore, in those processes where the limiting stage is the heat transfer process, it is necessary to select a structural material in advance. 118 Figure 4.1 - Algorithm for calculating a chemical reactor 119 5 GENERAL PROVISIONS When technologically designing a new chemical reaction, it is necessary to establish: under what conditions is this reaction possible to occur and what is its speed under the selected conditions. The answer to the first question is given by chemical thermodynamics, to the second section of physical chemistry, chemical kinetics, which examines the course of a chemical process over time. The formation of new substances during chemical reactions occurs due to the interaction between the electrons of atoms and molecules of the reacting substances. These interactions, in turn, are determined by the probability of collisions between different atoms and molecules. Therefore, it is quite obvious that a chemical reaction is a microscopic process. In some reactions, only the target product is obtained; Other reactions also produce byproducts. There are reactions that give a continuous series of main and by-products. In the reaction A + B = C, for example, substance C is the only product. In the reaction A + B = C + D, the target product C is accompanied by some byproduct D. In carbon-containing compounds, the carbon chain has a well-defined structure, but the number of carbon atoms in the molecule can change. In general, it is necessary to keep in mind that during the reactions of inorganic substances some main and by-products are formed. At the same time for organic reactions(especially polymerization reactions) in which the distribution of substances according to their molecular weights is carried out, the distinction between main and by-products is essentially uncertain. As already indicated, a chemical reaction is a microscopic process. However, intermolar (intermolecular) 120 forces that force association or individual dissipation, not atoms (molecules) can be directly taken into account in the theory of calculation, regulation and control of chemical processes. The formation or destruction of a product must be considered solely from a macroscopic point of view. 5.1 Determination of chemical reaction rate, constant, degree of conversion and order When calculating reactors, it is necessary to know the reaction rate, its order, rate constant and degree of conversion. These calculations are based on experimental data. Kinetic equations of chemical reactions allow, in the presence of appropriate data on the reaction rate, to determine the instantaneous values of the rate constants k and the reaction duration to achieve a given degree of conversion. The average reaction rate is expressed by differential equations, which are compiled based on the theory of kinetics. These equations take into account the amount of raw materials consumed per unit of time or the amount of product produced per unit of time. 5.1.1 Rate of Chemical Reaction Critical quantitative characteristics the process of chemical transformation of substances is the rate of the chemical reaction, that is, the change in the number of moles of a component per unit volume of the reacting medium per unit time: r 1 dn , V d (5.1) where V is the volume of the reacting components, m3; n is the number of moles of any consumable (decreasing) component (this is indicated by the minus sign); - time, sec. 121 In the general case, V is a time-variable quantity. If V = const, then n = cV, where c is the concentration of the consumed component at time , then r d cV dс . d d (5.2) Based on the fact that the reactor volume VR V we obtain: r 1 dn V R d [number of moles formed/(unit reactor volume) time] In two-phase systems, based on the phase contact surface S, we have: r 1 dn S R d [number of moles formed/(unit of contact surface) time] In reactions with the solid phase: r 1 dn M d [number of moles formed/(units. mass of a solid M) time] In general, the rate of a chemical reaction can be written as: dc kc A11 c A22 ... d (5.3) This expression is called the kinetic equation of a chemical reaction. In it, k is the reaction rate constant, 1 and 2 are the reaction orders in components A 1 and A 2. The overall order of the reaction is equal to the sum of the orders of the individual reactants: 1 2 ... . 5.1.2 Simple reactions Simple reactions can be of zero, first, second and higher orders. 122 5.1.2.1 Zero-order reactions The rate of these reactions does not depend on the concentration C, and the constant Kp is constant in time: dc kc 0 k const d (5.4) 5.1.2.2 First-order reactions In this case, the reaction rate is proportional the first degree of concentration of the reactant. Let us denote by CB the concentration of the substance being formed (for example, B) at the moment τ and by CA the concentration of the substance A reacting at the same moment. Then, in differential form, the rate of change in the degree of conversion or concentration can be represented as (5.5): =− = ( 5.5) As a result of integration (5.5), we obtain dependence (5.6): =− ∫ ln where = −k τ τ ∫ (5.6) = and (5.7) is the initial concentration of the reactant A. Obviously, CA = − C And the concentration A will be is equal to: CA = = −C and the number of reacted moles: CB = − CA = (1 −) (5.8) For any component: CB = (1 −) (5.9) 5.1.3 Product yield Product yield (degree of conversion) - X (5.10) the ratio of the amount of product obtained as a result of a chemical transformation to the amount of starting material received for processing. If 123 the course of a chemical process can be quantitatively expressed by a stoichiometric equation, then the yield of the final product can be found as a percentage, as the ratio of the practically obtained amount of product to the theoretically possible one in accordance with the stoichiometric equation. 5.1.4 Classification of reactions Classification of reactions. Depending on the mechanism, reactions can be divided into simple (direct) and complex. Simple (direct) reactions proceed in one direction and involve one chemical step. Complex reactions are divided as follows: reversible reactions; parallel reactions; sequential reactions; coupled reactions, when one reaction occurs spontaneously, and the other only in the presence of the first; a combination of the listed reactions. 5.2 The influence of temperature on the rate of a chemical reaction The rate of a chemical reaction is very sensitive to changes in temperature, since the latter greatly affects the rate constant k included in the equation. The most widely used expression is the dependence of the rate constant on temperature in the form of the Arrhenius equation. Since the concentrations of reacting substances do not depend on temperature, the expression for the rate of a chemical reaction will take the form: =− = = (5.11) The constants z and E are found experimentally. Taking the logarithm of expression (5.12), we obtain the equation of a straight line in the coordinate system (1/T, Ln k). From the graphically found angle of inclination of this straight line with the horizontal axis 1/T, tan a = E/R is determined, from which, from the known gas constant R, the value of activation energy E is obtained. If the value of the rate constant k is known at a certain temperature T and value E, then from equation (5.12) it is easy to find the pre-exponential factor: z= Parameter E in the case of minimum energy (5.12) of simple reactions shows that the reacting particles have such that their collision (active) leads to the formation of new chemical compounds. Therefore, the parameter E is called the activation energy. If several reactions occur in a system, then as the temperature increases, the rate of the reaction with a larger E value will increase faster relative to the others. 5.3 Parallel and sequential reactions Parallel reactions. Let's consider reactions of type A→B A→C This scheme occurs, for example, in the chlorination of a mixture of benzene and toluene. According to formula (5.7) we have: = = () = (5.13) In this case, two cases are possible: a) = And ≠ b) from expression (5.13) we find: () = The difference and is most manifested at lower temperatures For example, if the difference in activation energy is 125 − =∆ = 2400 cal ∗ mol, and temperature T = 300; 600 and 900 °K, R=1.987≈2 cal*mol then, taking ∗ deg, we get: =e ∗ = =e ∗ = =e ∗ = , In other words, the rates of parallel reactions differ sharply at low temperatures. Therefore, typical parallel reactions, for example, chlorination and oxidation of hydrocarbons in the liquid phase, are carried out under such conditions. An increase in temperature seems to neutralize the reactivity of the reacting particles. Let now temperature ⁄ =0.001 direction − ≠ . If reactions<
может
<
, то при изменении
измениться.
Например,
= ∆ = −6000 кал ∗ моль
Тогда при Т= 300,600, 750 °К и том же значении R находим:
=
22
1
= 0,001e
∗
= 0,001 e
= 0,001e
∗
= 0,001 e =
15
100
= 0,001e
∗
= 0,001 4 =
5,5
100
Отсюда следует, что первая реакция (с константой скорости
при
Т = 300 ◦К) имеет преимущественное значение: ее скорость в 22 раза
больше скорости второй реакции. При Т = 750 °K скорость первой
реакции составляет только 5,5% скорости второй реакции, а при
дальнейшем повышении температуры она станет исчезающе малой.
Последовательные реакции. Такие реакции включают стадии
126
образования промежуточных продуктов. Примером может служить
реакция хлорирования бензола до монохлорбензола и последующего его
хлорирования в дихлорбензол и высшие хлорпроизводные. Рассмотрим
две последовательные реакции первого порядка
A → B→ C
127
7 ОСНОВЫ МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ
ХИМИЧЕСКИХ РЕАКТОРОВ
7.1 Линейные функции распределения времени пребывания
Ранее мы рассмотрели идеальные реакторы вытеснения и смешения.
При этом считалось, все молекулы имеют одно и то же время пребывания.
В
реальных
реакторах
движущие
частицы
имеют
разное
время
пребывания. Поэтому при вычислении степени превращения - Х,
необходимо помнить, что идеальный реактор не соответствует реальному.
Возникает вопрос о том, какая должна быть поправка к вычисленной Х.
Чтобы судить о возможности Промышленного применения различных
реакторов экспериментально определяют среднее и действительное время
пребывания и дают оценку этим данным с помощью теории вероятности.
Распределение времени пребывания в реакторе может быть количественно
охарактеризовано на основе функции плотности распределения.
E T
dF d QN / QN o
e
d
d
,
(7.1)
Функция Е(Т) для реактора смещения представляет функцию
плотности распределения времени пребывания и характеризует долю
материала, которая находится в реакторе в интервале времени между Т и
Т +dT
F T E d
0
QN
QN o
Функция Р(Т) представляет функцию,
распределения
(7.2)
Р(Т)
и
характеризует долю материала, которая находиться в реакторе время
меньше, чем Т. Или иначе Е(Т) представляет volume fraction output flow with an “age” less than T. Thus, knowing one of the distribution functions, you can get another. The following relationship exists between the average residence time T and E(T): 128 m QV E d v v 0 , (7.3) That is, knowing E(τ) you can determine Vr or τ. The function E(τ) and P(x) also have the following properties; respectively (Figures 7.1 and 7.2). Figure 7.1 - Density function of the residence time distribution E(τ) Figure 7.2 - Density function of the residence time distribution P(x) In the expressions E(τ) and F(τ) it is advisable to use the relative (dimensionless) residence time. 129 = actual residence time average residence time = ∙ (7.4) For a cascade of mixing reactors E(τ): E mm m1 e m 1 ! (7.5) For mixing reactors E(τ): F 1 e (7.6) For a cascade of mixing reactors F(τ): m F 1 e m 1 m 1 2! 2 m 1 ... m 1 ! m 1 (7.7) 7.2 Experimental determination of E(τ) and F(τ) and analysis of a chemical reactor using these functions To determine τ through E(τ) and F(τ ) the reactor is examined by introducing a tracer substance (paint, isotopes, acids, bases, etc.) and measuring the output signal as a function of time. The tracer should not undergo a chemical transformation (Figures 7.3, 7.4). To determine E(τ), a small amount of tracer is introduced in the form of a pulse, i.e. a step change in the concentration at the inlet, and the change in concentration Cm/Co-f(τ) at the outlet of the reactor is measured, this ratio changes from 0 to 1. Figure 7.3 - Experimental determination of density functions 130 distribution E(τ) and distribution F(τ) using a tracer for a single fully mixed reactor and a cascade of reactors tracer ideal reactor real reactor Figure 7.4 - Experimental determination of density functions E(τ) and distribution F(τ) using a tracer for ideal and real reactors Figure 7.5 - Analysis of the operation of a single fully mixed reactor and a cascade of reactors using the distribution density functions E(τ) and distribution F(τ) 131 Figure 7.6 - Analysis of the operation of an “ideal” reactor and a real one using experimentally certain functions E(τ) and F(τ) Figure 7.7 - Comparison of distribution functions of final reactions at different meanings m 132 The volume fraction of a substance leaving the reactor over time is determined as F() Qv C Qv0 Co, (7.8) and this is proportional to the relative concentration. The distribution functions for the most important types of chemical reactors are shown above (Figure 7.5). In practice, there are devices in which the operating conditions are very complex (for example, a rotary kiln, cracking units, etc.) that are difficult to compare with one or another type of ideal reactor. In these cases, Hoffmann-Schoenemann methods based on graphical methods are applicable. According to experimental data, the dependence C/CO - τ is plotted on the graph; from here, using the equation C/Co = 1 – X, you can immediately obtain the value of the product yield. The measured F(τ) is plotted on the same diagram and then rearranged into the dependence C/CO F(τ) (Figure 7.8). The results obtained give an accuracy of up to 10%. Figure 7.8 - Graphical method determination of the Hoffmann-Schoenemann distribution functions F(τ) 133 8 HEAT TRANSFER IN CHEMICAL REACTORS Temperature is an important dynamic parameter for chemical reactors. It increases if the heat generated by an (exothermic) reaction cannot be removed quickly enough by a coolant (convective heat transfer) or by conduction (conductive heat transfer) and radiation. Some types of chemical reactors, especially those in which the reaction occurs in the gas phase (furnace-type reactors) generate a significant amount of heat, and are characterized by thermal self-regulation. On the other hand, exothermic reactions such as polymerization can be accompanied by the release of such large amounts of heat that decomposition (destruction) of the components of the mixture occurs, consisting of starting raw materials, ... intermediates and final products. Since the rate of a reaction is an increasing function of temperature (eg Arrhenius's law), the direction of the reaction may ultimately change. Due to design flaws in the heat exchange devices of the reactor, heat exchange in it may be difficult, which naturally impairs the ability to control temperature. Side reactions also arise as a result of the presence of “stagnant zones” in the reactor; autocatalytic effect of the material of the reactor elements towards the formation of reaction by-products; as a result of improper mixing in the reactor; at the same time, “hot spots” are formed in it and an increase in the reaction rate in this area brings it closer to the conditions of an explosion. 8.1 Thermal effect in reactors Often chemical reactions are accompanied by the release or absorption of heat, that is, an exothermic or endothermic thermal effect. If the reaction proceeds exothermically, then a certain amount of heat must be removed from the reactor, and in case of an endothermic effect, it must be supplied to it. When the reaction proceeds 134 adiabatically, the temperature in the reactor changes and. therefore, the rate of reaction changes. The dependence of the chemical reaction rate - r on the temperature of the reaction mass in the reactor is determined from the Arrhenius equation K = K e (8.1) From (8.1) it follows that the chemical reaction rate - r is determined by the dependence (8.2) r = K e C C . . C, (8.2) KO is an experimental constant, R is a gas constant, E is the activation energy, it shows what minimum energy reacting particles must have for their collision to lead to the formation of new chemical compounds. If E=(10÷ 60) ∗ 10 kcal kmol, then an increase in T by 10°C gives an increase in K by (1.2-2.5) times. The dependences r = f(T) for various chemical reactions are shown in Fig. (8.1 and 8.2) Fig. 44. Dependence of speed Fig. 45. Dependence of the rate of a chemical reaction r = f(T) for: reaction r = f(T) for: a- simple irreversible reactions A B; b - heterogeneous processes, if the determining stage of the reaction is diffusion, weakly dependent on temperature; c - during combustion and chemical reactions occurring in. 135 flames; d - reversible reactions A and B; e - oxidation reactions of nitrogen oxide and hydrocarbons. To know the conditions under which a certain thermal regime of a reactor is carried out - isothermal, adiabatic or programmed - it is necessary to draw up a thermal balance of the reactor. In general form, the heat balance can be represented as follows: () τ = −(hG) + Q + W (8.3) where U is the internal energy per unit of total mass of the reaction medium; h is enthalpy per unit of total mass of the reaction medium; G - mass flow rate of reagents; Q - heat consumption; W- mechanical work per unit of time; τ - time; m is the total mass of reagents. There is a relationship between enthalpy and internal energy: h=U+ ρ dh = dP + C dT∆h dx ρ (8.4) (8.5) Here P is pressure; p - density; ∆H - thermal effect of the reaction; M- molecular mass component I; X is the degree of conversion of component I. Chemical reactions, as is known, occur either with the absorption (endothermic reactions) or with the release (exothermic reactions) of heat. In case of insufficient heat supply from the outside, the endothermic reaction dies out. If there is insufficient heat removal, the exothermic reaction is accompanied by very undesirable complications (decomposition of the product, explosion, etc.) for each reaction system there is a stationary state when an equilibrium arises between the release (or consumption) of heat and its removal (or supply). To avoid overcooling or overheating of the reactor walls, it is recommended to take ϴ = t ± 20 °C (8.7) where ϴ is the temperature at the entrance to the jacket; t is the reaction temperature in the apparatus. The amount of heat spent on heating or cooling the reaction mass and the reactor (J) is calculated by the formula Q = (m C + mj Cl)∆t () (8.8) where m, ml is the mass of the reactor and the liquid loaded into it, J/ (kg*K) The temperature differences during the heating or cooling process will be as follows: ∆t = t − t ; ∆t = t − t . Here t is the reaction temperature; t liquid after cooling; t - final temperature - the initial temperature of the liquid before heating. The mass of the reactor (kg) can be approximately determined by the formula m = 230p ∗ D, where p is the excess pressure in the reactor, MPa; D - reactor diameter, mm. The main technological and design parameters, as well as the amount of heat released or absorbed, the reaction rate and the volume of the reactor are related by the dependence (8.10) 137 q = r ∗ ∆H ∗ Vl where q is the total amount (8.10) of heat released (absorbed) as a result of chemical reactions; kcal r - reaction rate, kcal m ∗s; ∆H - thermal effect of the reaction, kcal; m ∗hour Vl is the volume of the reaction mass in the reactor. 8.2 Classification of chemical reactors by thermal regime From the point of view of thermal regimes, chemical reactions and, accordingly, reactors are classified as follows: 1. Isothermal regime is a regime of constant temperatures in the reaction zone due to heat exchange with the external environment. The reactor is isothermal. In this case, the following reactions are possible; endothermic - heat is supplied to the reaction zone; - exothermic heat is removed from the reaction zone. The isothermal regime is most easily achieved in ideal mixing apparatuses. 2. Adiabatic mode - absence of heat exchange through external and internal enclosing surfaces - adiabatic reactor. In plug-flow devices for exothermic reactions, the temperature is calculated along the length of the reactor from the product inlet to the outlet. In an endothermic reaction, the opposite picture is observed. In ideal mixing reactors, during an exothermic reaction, the temperature increases with time; during an endothermic reaction it decreases. 3. Non-isothermal and software-controlled mode. This mode is carried out in chemical reactors with insufficient heat supply or removal, which is necessary; for an isothermal reaction to occur. In this case, the temperature is regulated in accordance with the program along the length of the plug-flow reactor or 138 in time in ideal mixing reactors - the reactor is non-isothermal. 4. Autothermal regime - carried out due to the heat of reaction used to obtain the required temperature regime - the reactor is autothermal. The basis for considering reactors from a thermodynamic point of view is the heat balance equation. Therefore, if the material and structural calculation of the reactor is based on the general equation. 8.3 Algorithm for calculating the thermal regime of chemical reactors Almost all chemical reactions are accompanied by thermal effects, that is, they occur with the release or absorption of heat. This determines the design features of the device from the point of view of maintaining the required temperature conditions, i.e. optimal operating temperature of the chemical reaction in the reactor. The thermal calculation algorithm includes the following stages: - Determination of the thermal effect of the reaction and the thermal regime of the reactor. - Drawing up a general characteristic heat balance equation. - Calculation of temperature conditions in stirring and displacement reactors. - Thermal and structural calculation of the reactor heat exchange device. - Strength calculations of elements of heat exchange devices of material balance, then similarly thermal calculation is considered on the basis of the overall heat balance. 9 THERMAL CALCULATION OF CHEMICAL REACTORS 9.1 General characteristic heat balance equation The thermal balance of a chemical reactor is compiled on the basis of the 139 law of conservation of energy, according to which in a closed system the sum of all types of energy is constant. In this case, all heat supplied to the reactor and released (absorbed) as a result of a chemical reaction or physical transformation must be taken into account; the heat contributed by each component, both entering and leaving the reactor, as well as heat exchange with the environment. Consider Q - convective heat transfer Q = (ϑ ∙ ρ ∙ C ∙ t in) − (ϑ ∙ ρ ∙ C ∙ t) (9.1) where: ϑ - flow rate of reagents, ρ - density, C - specific heat capacity, t in and 0t - respectively, the temperatures at the outlet and inlet of the reactor. In the presence of several flows of chemical reagents (n flows) Q =∑ Q ϑ ∙ρ ∙C ∙t (9.2) - the amount of heat released or absorbed in a chemical reaction, which, according to the definition of the thermal effect of a chemical reaction ±∆H, has the form Q = (± r) ∙ V(±∆H) (9.3) Q - heat transfer through the heat exchange surface Q = ±K ∙ F ∙ ∆T) (9.4) where K is the heat transfer coefficient, and the sign depends on the direction of the process (+) heating, (- ) cooling. - change in the amount of heat in the volume of the reactor = Where r.st, r.st f ∙ Av.st + l ∙ Avg ∙ =∑ (∙ Av) ∙ (9.5) , Av.st, Avg mass and heat capacity of the reactor material and reaction mass. It is necessary to take into account the amount of heat spent on heating the metal parts of the reactor, especially for batch reactors, since it is commensurate with the amount of heat spent on heating the reaction medium itself due to the significant mass of the metal of the apparatus. - the amount of heat released during stirring. This heat must be taken into account due to the fact that the power supplied by the stirrer is dissipated in the volume of liquid by viscous friction, which leads to its heating. This value can be expressed through the power factor, the rotation speed of the mixer - n and the diameter of the mixer = ∙ ∙ , ∙ (9.6) This value is quite significant only when mixing highly viscous media. For low-viscosity media it is insignificant and can be ignored in practical calculations. f - the amount of heat released or absorbed in physical processes (dissolution, crystallization, ∙∆ condensation, absorption, etc.), when the thermal effect f = (±∆ f) evaporation, kcal f [kmol] ∙ Av ∙ (9.7 ) After summing up all the considered components of the reactor heat balance, the general heat balance equation for any type of apparatus can be presented as + + + + + f =0 (9.8) or ∑ (∙ Av) + ϑ ∙ Cp ∙ tk − ∆Tcp + ± ∆ ∑n i=1 ϑi ∙ ρi ∙ Cpi ∙ t0i + (±r) ∙ V f ∙ Av ∙ + ∙ ∙ 3∙ ±∆Hr ± K ∙ F ∙ 5 (9.9) As a rule, all material and thermal calculations are reduced to tables. Depending on the type of reactor (batch, semi-continuous, (isothermal, or continuous) adiabatic, and or polytropic temperature regime). The general heat balance equation (9.8 and 9.9) is simplified and converted into 141 characteristic equations for a specific reactor, which is the basis for calculating the temperature regime of the reactor. 9.1 The influence of thermal conditions on the course of chemical processes in ideal mixing and displacement reactors. Thermal calculation of a continuous isothermal reactor with full mixing. At steady state, the heat balance equation (9. 9) for a reactor with complete mixing and a heat exchange surface. (Fig.9.1) and (Fig.9.2) can be written as follows Figure 9.1 – Scheme of operation of a continuous isothermal reactor with complete mixing and a heat exchange surface from a thermodynamic point of view. 142 Fig.9.2 Temperature profile in a continuous isothermal reactor. 0 = −G ∙ (h − h) + K ∙ F ∙ (T ,) (9.10) where h is the enthalpy of the inlet flow; h is the enthalpy of the outlet flow; K - heat transfer coefficient; F - heat exchange surface; T is the average reaction temperature; T, - average coolant temperature. The value of h −h can be obtained by integrating equation (9.5). Therefore, at constant pressure we have: h − h = ∫T,H, [ ∙ dT ∙ (∆h) ∙ dx ] (9.11) Substituting (9.11) and (9.12) we get: 0 = −∫ () − [(∆ h) 143 ∙x + ∙ (T − T,) (9.12) By solving this equation together with the characteristic equation of an isothermal reactor, we can calculate the effect of the amount of supply heat on the temperature in the reactor. In the case when the enthalpy of the reaction mixture varies slightly with temperature and composition, equation (9.12) can be written in the form: x (∆h) = ∙ (T − T) + ∙ (T − T,) (9.13) Expression on the left part of this equation is the free enthalpy per unit mass of the reaction medium; it is proportional to the molar enthalpy of the system, the degree of conversion and, presumably, the rate of reaction. 9.2 Analysis of the thermal regime of a continuous isothermal reactor The right side of equation (9.13) represents the total heat absorbed during the reaction per unit mass. The first expression is the heat absorbed by the flow, and the second is the heat transferred by the thermal agent. For an exothermic reaction, equation (9.13) is graphically depicted in Fig. 8.5 in the form of a functional dependence released as a result of the exothermic reaction Qr(QS) on the temperature in the reactor Tr °C. The point of intersection of the straight lines corresponding to the absorbed heat with the general curve satisfies equation (9.20) and temperatures that ensure a steady-state reaction. The total heat of reaction =− ∙ (∆h) (9.14) is presented in the diagram of curve 1 and at low temperatures is practically zero. As the temperature increases, the reaction rate increases rapidly. If the reaction is not reversible, the increase in rate occurs continuously until the reagents are completely consumed, can be represented graphically by straight lines 2, 3 and 4 for three different 144 cases. If the heat transfer coefficient and coolant temperature remain constant values, then this dependence in all cases will be depicted as a straight line. Figure 9.3 Temperature characteristics of an autothermal reactor. Absorbed heat = ∙ (T − T) + ∙ (T − T,) (9.15) Straight 3 intersects curve / at point A, which for the case under consideration corresponds to the maximum temperature in the reactor. A slight increase in temperature increases the speed, and therefore the total heat, but cooling lowers the temperature to normal, and therefore the process will be steady-state. This is possible because at temperatures close to the TA limit, the total heat is less than the heat that can be transferred. Point A is in the region of low degrees of conversion. 145 Fig. 9.4 Possible changes autothermal reactor temperatures. Straight 2 intersects with curve / at three points, of which B and D correspond to stable operation conditions, and point C corresponds to unstable operation. At point C, the total amount of heat increases faster than the transferred heat, and an increase in temperature will bring the reaction system to a state corresponding to point D. On the contrary, a decrease in temperature will direct the reaction system to point B. Point D most corresponds to the optimal mode of operation of the reactor and is located at areas of high degrees of conversion. Line 4 does not intersect with curve 7, which means it is necessary to work with cooling at a low temperature or at a high heat transfer coefficient. However, very low coolant temperatures can weaken the reaction, so it is necessary to maintain good control of temperatures that affect coolant flow, thereby reducing temperature losses. To do this, it is necessary: - to have a control system that would ensure the necessary heat transfer by lowering the temperature of the coolant in the jacket or by increasing its flow rate; - apply a control system, which, in the event of unstable operation of the reactor, increases the power consumption of reagents, which reduces the contact time and, therefore, reduces the drop in x and Q. (in Fig. 6, curve 1 moves to the right with increasing power consumption, taking the shape of curve 2, parallel to curve 1, but with a smaller slope than straight line 3, which corresponds to the condition of stable operation); - use a control system that, in case of unstable operation or in the case of dilution of reagents, would increase the slope of straight line 3 so that heat losses from the system are greater in comparison with the total heat. When the reagent is diluted, straight line 3 will take the position of straight line 4 (the reactor operates stably). From the above it follows that for certain cases of unstable operation of exothermic reactors, it is possible to use regulation and control systems that ensure the stability of the reactor. The intersection points in Fig. jo correspond to the operating conditions of an isothermal reactor. In the case of an exothermic reaction, which occurs at high temperature, the total heat of the reaction is used to heat the reactants. Thus, no additional heat is required to maintain the reaction. To avoid crossing the working fluid zone, an average temperature difference of ∆tcp = 15 + 20 °C is provided. If at any moment of the reaction the surface of the heat exchanger F is not enough to remove (supply) heat, coils or remote heat exchangers (refrigerators) are additionally installed in the apparatus. To maintain the required thermal operating conditions of a continuous apparatus, the coolant (water) flow rate is calculated as = (ϴ ϴ), (9.16) where QF is the heat flow through the heat transfer surface; ST - heat capacity of the coolant, J/kg∙K; ϴ and ϴ are, respectively, the temperature of the coolants at the inlet and outlet of the reactor jacket. Temperature ϴ to avoid overcooling of the reactor walls must be taken ϴ = (tp-20) °C. 9.3 Plug-flow reactor with heat exchange between reactants and product A plug-flow adiabatic reactor, in which the exothermic reaction occurs, can be combined with a heat exchanger, where heat exchange occurs between the reactant and the product. Rice. 9.5. Rice. 9.5 Temperature change in a reactor with complete displacement - 1, connected to a heat exchanger (autothermal system) - 2. Tn - initial temperature of the initial components entering 148 heat exchanger 2; T is the temperature of the heated initial component entering the reactor; Tp is the temperature of the reaction products in the reactor and at its outlet; Tk is the final temperature of the finished product of the heat exchanger. The autothermal reactor-heat exchanger system acts as a recirculating reactor. Figure 9.5 shows the temperature change in such a system along the length of the reactor. 9.4 Reactor with complete displacement and heat exchange surface Heat balance compiled for an infinitesimal volume element in stationary mode (Fig. 9.6) = ∙ ℎ+ (9.17) At constant pressure we have: ℎ= ∙ + (∆h) dx (9.18) Heat , transmitted through the surface of the reactor with diameter D: = ∙ ∙ ∙ (T − T,) ∙ dz (9.19) Introducing this value into expression (9.17), we obtain the equation 0= ∙ ∙ dT + ∙ (∆h) ∙ dx + ∙ ∙ ∙ (T − T ,) ∙ dz (9.20) which must be solved together with the differential equation of the plug-flow reactor: 0 = −G ∙ dx + r ∙ π ∙ D ∙ dz (9.21) Fig. 9.6 To derive the thermal balance of a reactor with complete displacement and a heat transfer surface. 149 Simultaneous solution of the last two equations makes it possible to depict the profile of temperature and degree of conversion along the length of the reactor. 9.5 Thermal calculation of an adiabatic reactor with a stirrer Exothermic reactions. Let us consider an exothermic direct first-order reaction of type A→B, which occurs continuously (Fig. 9.7). As the process progresses, heat QR is released in the apparatus in the reactor. The flows entering and exiting the apparatus bring in and carry away heat. There is no other heat exchange with the external environment (cooling of the reactor walls, heat losses). Fig.-52. Adiabatic reactor with stirrer. Let's introduce the following notation: QVBX - food, m3 sek-1; γ - specific gravity, kgf/m3; 150 s = const - heat capacity of the reacting medium, kcal/kgf∙deg; C is the concentration of the target component, kmol∙m3 and T temperature, °C. In and out indices refer to the values of the flows entering and exiting the reactor. At the degree of conversion Xq, the number of reacted moles will be Swx Xq, and the heat released during the thermal effect of the reaction q - kcal∙kmol will be: = in kcal∙sec-1 ∙ Swx ∙ (9.22) The change in heat in the reaction mass due to the temperature difference at stationary mode is equal to: pot = ∙ ∙ ∙ out − ∙ ∙ ∙ 9.23) in Let us take the temperature in the reaction zone T = TA equal to the temperature at the outlet of the reactor. In a steady state, QR = Qpot and ∙ ∙ = Allowing for simplifications: out = in ∙ ∙ out = ∙ in out − in ∙ ∙ ∙ kmol∙sec-1 and = (9.24) in ∙ in = ∙ from equation (9.24) we obtain: ∙ ∙ = ∙ ∙(∙ = ∙ (outout − − inin (9.25))) (9.26) From equation (9.22) it follows: = ∙ in ∙ = sweat ∙ in ∙ = ∙ in ∙ (out − in) ( 9.27) 9.6 Analysis of the thermal regime of an adiabatic reactor In Fig. Figure 9.8 shows the dependence of the degree of conversion U on T for direct irreversible first-order exothermic reactions of type A → B. The values of T and U are obtained from expressions (9.22) and (9.26). Since the U values are expressed as a function of QR and Qpot, this graph gives the dependence QR=ƒ(T). The dependence QR=ƒ(T) is characterized by the MN curve. 151 Fig. 9.8 Graph of the degree of conversion versus temperature for a direct exothermic reaction occurring in an adiabatic mode. At low temperatures, QR increases very slowly - the first section ML in the graph. However, with an increase in the reaction rate associated with an increase in T, the heat release QR sharply increases according to a curvilinear law (section I-III) and then in section IV remains almost constant. The amount of heat Qpot removed by the flow of substance is proportional, according to formula (9.26), to the first power of the temperature difference at the outlet and inlet; on the Qpot graph be depicted as a series of parallel straight lines A, B, E, C, R, D with an angular coefficient of 152 tan = ∙с Ce ∙ (9.26) Straight lines Qpot AND 5-shaped curve MN (QR) have one, two or three intersection points depending on the temperature difference T-TE Boundary positions of the straight lines correspond to two points of tangency Ps and P2 Depending on Tgr2 and Tgr1 - boundary values T. The intersection points of the straight lines and the curve correspond to the equality QR = Qpot, subject to material balance. In position A (TE< Тгр2)
существует только одна точка пересечения V в нижней части кривой. Здесь
разность температур Т- ТЕ степень превращения U крайне малы.
Точка V соответствует минимальной температуре аппарата и
характеризует устойчивый ход процесса и способность к авторегулировке.
При повышении температуры в реакторе (ТА возрастает) количество
выводимого с потоком тепла по уравнению (9.3 Г) возрастает, становится
больше количества выделяемого тепла QR вследствие чего температура в
аппарате может снизиться до нормальной. То же произойдет и в случае
понижения температуры в зоне реакции, но только в обратном
направлении
В рассматриваемом случае (А) реакция идет крайне медленно и
легко затухает. С возрастанием ТЕ до Тгр1 прямая (положение В) касается
кривой в точке Р1. Здесь наступает предел самопроизвольному затуханию
реакции. Дальнейшее повышение температуры ТЕ < Тгр1, и дает три точки
пересечения (I, II и III). При ТЕ= Tгр1 (положение С) прямая отвода тепла
касается кривой тепловыделения в точке Р2.
В области между положениями В и С точки пересечения с нижней
(7) и верхней (III) ветвями кривой термохимически устойчивы. Средняя
точка II характеризует неустойчивое состояние.
В области ТЕ >Tgr1, the heat removal straight line (position D) intersects the upper part of the curve at one point IV. Here, at a relatively high 153 initial temperature, a fairly high degree of U conversion is achieved. The reaction develops spontaneously and the possibility of “spontaneous combustion” occurs. The position of straight line C characterizes the beginning of the spontaneous reaction (touch point P2). At point II the equality QR = Qpot is observed, and it indicates the critical temperature. With a slight increase in temperature QR>Qpot, and the intersection point moves to position III. On the contrary, with a slight decrease in temperature QR Topic 6. CHEMICAL REACTORS Modern chemical reactor
-
1)
2)
heat exchangers; 3)
mixing devices, 1.
2.
High product yield F φ-
R, X. 3.
productivity
(raw materials) and high degree of transformation
X A(reagent): in schemes with open loop preference is given to high degree of conversion X A reagents; in closed systems preference is given to high productivity.
Factors influencing the design of the rector 1.
Physical properties and state of aggregation of reagents and products. 2.
Required mixing intensity. 3
. Thermal effect of XP and the required heat transfer intensity. 4
. Temperature and pressure are process parameters. 5.
Aggressiveness, toxicity of the reaction mass. 6
. Explosion and fire hazards of production. For industry, an important task is to obtain a certain amount of product in a certain period of time, i.e. it is necessary to calculate the residence time of the reactants in the reactor to achieve a given degree of conversion. To do this, the kinetic model of this reaction must be known. Mathematical modeling is used to approximately calculate the residence time. A mathematical model is a system of equations that relates certain most important process parameters. A physical model is a drawing, a sample that displays the most essential aspects of an object. To obtain simpler dependencies during mathematical modeling, some parameters are neglected. Let's consider chemical reactors operating in isothermal mode. Since in such reactors there is no driving force of heat exchange inside their volume (∆T = 0), the heat balance equation can initially be excluded from the mathematical model of the reactor and it (mathematical model) is reduced to a material balance equation that takes into account the chemical reaction, mass transfer and transfer impulse. To further simplify the mathematical model, we can separate REACTORS WITH AN IDEAL FLOW STRUCTURE into a separate group perfect mixing
And perfect displacement
.
Assumptions about the ideal flow structure make it possible to exclude a number of operators from the general material balance equation and thereby significantly simplify calculations based on this equation. MODELS OF IDEAL REACTORS Residence time of the reagent in RIS and RPS Let's expand the brackets: The equation allows (if the kinetics of the process is known) to calculate the time required to achieve the required degree of conversion. For reaction P
-th order : from here Where P - reaction order. At n = 0: At n = 1: Depends only on the degree of transformation X A and does not depend on the initial concentration At n = 2: According to the RIS model, the following is calculated: 1)
reactors with stirrers with not very high viscosity η of the medium and not very large volume υ of the reactor; 2) flow-circulating devices
-
with high circulation rates; 3
) reactors with "fluidized bed" 1.
P. Plug flow reactor (PPR) In RIS, all volume parameters are constant. All characteristics (concentration With A, degree of conversion X A, temperature T and etc.) change smoothly throughout the reactor volume, therefore, a material balance cannot be compiled for the entire volume of the reactor. Rice. 2. Dependency graphs: A) C A =f (τ or H)b) w= f (τ or H) V) X A = f (τ or H) An infinitesimal reactor volume dV is selected and a material balance is drawn up for it. These infinitesimal volumes are then integrated over the entire volume of the reactor. Let it be simple irreversible reaction flows in the reactor without changing volume υ: Where , S A - initial and current concentrations, respectively; υ - volumetric flow Where V- reactor volume (m3); dV is the elementary volume of the reactor (m 3). Let's sum it up: (Coming) elementary volume RIV-N To obtain the equation math. balance of the entire reactor, we integrate the resulting equation after separating the variables (over the volume of the entire reactor): Where w A we find, knowing the kinetics of the process. The characteristic equation of RIV-N allows, knowing the kinetics of the process (to find w A), determine timeτ
residence of reagents in the reactor proportion of achieving the specified degree of conversion X A, and then the dimensions of the reactor. For reaction nth
order : Where P - reaction order. At n=0: At n=1: Depends only on the degree of conversion of X A and does not depend on the initial concentration; At n=2: In some production reactors conversion degree X A is so insignificant that the model can be used for calculation RIV- This tubular contact devices
with catalyst in pipes or annulus (“shell and tube”), serving for heterogeneous gas-phase reactions. Model repression also used in design liquid phase tubular reactors
with a large ratio of pipe length to its diameter. Under the same conditions for carrying out the same reaction, in order to achieve an equal conversion depth, the average residence time of the reactants in a flow-through ideal mixing reactor is longer than in a plug-flow reactor. In the RIS, the concentrations at all points are equal to the final concentration, and in the RIV, the concentrations of the reagents at 2 neighboring points are different. The reaction rate, according to the ZDM, is proportional to the concentration of the reagents. Therefore, in RIV it is always higher than in RIS. Those. Less residence time is required to achieve the same conversion depth. III. Reactor cascade (RIS) In these cases, it is more appropriate to install a number of series-connected reactors (sections) - reactor cascade
.
The reaction mixture passes through all sections. One can consider as an example of such a model not only a system of sequentially located individual apparatuses, but also a flow reactor, one way or another divided internally into sections, in each of which the reaction mixture is mixed. For example, a disc bubble column is close to this type of apparatus. Driving force ∆С: ΔС RIS< ΔС Каскад РИС < ΔС РИВ In a single RIS-N, the concentration of the key reagent A changes abruptly to CA (final), this suggests that the reaction rate in RIS-N is significantly reduced. Due to the fact that each reactor in the cascade has a small volume, the abrupt change in concentration is much less than in a single large-volume RIS-N, therefore the process speed in each stage of the cascade is much higher. The RIS-N reactor cascade, therefore, is approaching RIV-N (the RIV reactor turns out to be more profitable than RIS, because driving force in it, equal to (concentration gradient) ΔC = C equal - C work, greater than in FIGURE). Average driving force ΔС RIS<ΔС Каскад РИС < ΔС РИВ When a chemical reaction occurs, the highest speed of the process is achieved in RIV-N due to the higher driving force of the process. RIV-N has the highest productivity. The performance of the RIS-N cascade is less than the performance of RIV-N, but greater than the performance of a single RIS-N. The greater the number of reactors in the cascade, the smaller the jump in concentrations, the greater the driving force of the process, the greater the speed of the process and, accordingly, the higher its productivity. Calculation of the number of cascade stages Calculation of a cascade of ideal mixing reactors usually comes down to determining the number of sections of a given volume required to achieve a certain conversion depth. Distinguish analytical And numerical methods cascade calculation. The application of the analytical method is possible if the material balance equations can be solved analytically with respect to concentration With i. This can be done, for example, if the occurring reactions are described by kinetic equations of the first or second order. To calculate the number of cascade stages required to achieve the required degree of conversion of the reagent, 2 methods are used: 1) algebraic; 2) graphic. Example Second order reaction given 2A →R, or 2A→ R+ S, kinetic equation w A = 2.5 (k = 2.5), final degree of conversion X A =0.8, A) RIV-N; b) RIS-N; c) RIS-N cascade, where all sections of the cascade have the same volume (V 1 = V 2 =... = Vn), selected in such a way that the average stay in each of them is equal to Rice. 4 – Dependence of the reaction rate on the concentration of the day of calculating the number of sections of a cascade of ideal mixing reactors. From Figure 4 we see that to achieve the specified degree of conversion, four sections are needed. Turns out, chyu at the exit from 4th section the degree of transformation is even higher than that specified by the condition, but in three sections the degree of transformation is not is achieved). Thus, the total average residence time of reagents in a cascade of ideal mixing reactors is For calculation cascade RIS-N analytical method
compose for each stage of the cascade the equation material balance: IV. Batch reactor (RPR) Concentration distribution S A reagent at any degree of mixing of reagents is similar to RIV: However performance RIV above: specified in the RPD degree of conversionX A achieved in time τ chem. reactions +τ auxiliary operations (Loading and unloading) therefore the performance of the RPD is lower: Since τ RIV< τ РПД =>P RIV >P RPD, so usually: For small-tonnage
industries (e.g. pharmaceuticals) are used RPD; For large-tonnage –
give maximum performance RIV-N. Polythermic Reactors characterized by partial removal of heat of reaction or supply of heat from outside in accordance with a given program for changing the temperature T° along the height of the reactor ("software controlled reactors"). Example: Mixing reactors RICE- periodic action. When studying and quantitatively assessing processes in a reactor, temperature calculation formulas are used to derive heat balances.
Heat balance based on law of conservation of energy
E: The heat input in a given production reaction must be equal to its consumption in the same operation: Q in. =Q consumption Heat balances are compiled according to the material balance of the process and the thermal effects of chemical reactions, as well as physical transformations occurring in the reactor, taking into account the supply of heat from the outside, as well as the removal of heat with the reaction products and through the walls of the reactor. I. Adiabatic reactor (usually RIV) According to the ideal model, in an adiabatic reactor there is no heat exchange with the environment. In real conditions, approaching the absence of heat transfer is achieved due to good insulation of the reactor walls from the environment (double walls, insulating material) Temperature change T 0 in an adiabatic reactor ΔT° = T° con. - T° start proportionally - degree of conversion
reagent X A - concentrations
main reagent ,
- thermal effect Q r reactions and inversely proportional - average heat capacity
reaction mixture. For exothermic
reactions ΔH< 0 ΔT° = T° кон. - T° нач >
O (+ sign) For endothermic
reactions ΔH >
0 ΔT° = T° end. - T° start< О (знак-) Application Using the RIV adiabatic reactor model, contact devices with catalyst filter layer. This model is also applicable for calculating chamber reactors for homogeneous reactions, for direct-flow absorbents with an insulating lining (lining), in which gas moves towards the sprayed liquid. Adiabatic RIV-N are suitable for carrying out exothermic reactions. If heat is not supplied from outside, then the process proceeds in autothermal mode (due to the heat of the chemical reaction itself). Endothermic reactions are also carried out in adiabatic mode, but in this case the reaction mass is supplied along with steam. II. Isothermal reactor Analysis adiabatic equations
ΔT° = T° end. - T° start = shows that to isothermal reactors
reactors may be approaching small
meanings: Q x.r. - specific thermal effect
(per unit of substance); -
- initial concentration of the reagent;
-
X A- degree of transformation
at large
values - - thermal conductivity
reaction mixture. Application Practically isothermal reactors: For processing low concentrated(↓ C A) gases ( → 0),
And Reactors in which exo-
And endo thermal effects are practically are balanced (q x.p →0). Those. an isothermal regime is observed in the case when the thermal effect of the main process is compensated by thermal effects of side reactions or physical processes (evaporation, dissolution) equal in magnitude but opposite in sign When modeling to completely isothermal reactors include liquid reactors
- (F - F) - emulsion - (F - T) - suspension With mechanical, pneumatic and jet-circulation mixing devices. Isothermal regime is observed on the shelves foamy
And bubbling apparatus
not large in size, in some contact devices with stationary catalyst.
The regime may be close to isothermal aAdsorption
And aAbsorptive
devices in which the heat generated during adsorption or asorption is spent on the evaporation of water or other solvent. Isothermal mode can be achieved through heat exchange devices by supplying or removing heat from the reactor. The heat removal for an exothermic reaction is proportional to how much should be released. The tip for endo is to be absorbed. APPLICATIONS Polythermal mode observed in reactors in which thermal effect
Qx. p. The main chemical reaction is only partially compensated by the thermal effects of side reactions or physical processes that are opposite in sign to the main process. Such reactors include many shaft and blast furnaces. Ways to implement it Optimal temperature conditions – this is a temperature regime that provides an economically feasible maximum productivity of the P for the target product (at the maximum possible speed w r process), while it is necessary to achieve high conversion - for simple reactions and high selectivity - for complex reactions. The solution to the practical problem of carrying out a process in an industrial reactor in accordance with the optimal temperature regime depends on many factors and, above all, on the thermal effect and reaction kinetics. Analyzing this reaction rate equation, we conclude that an increase in the reaction rate will lead to: Temperature increase; Reduced conversion rate. To compensate for the reduction in speed w r reactions with increasing degree of conversion Ha it is advisable to increase the temperature T°. That's why exothermic(ΔН<0) simple(A→R) irreversible
(→)
it is advisable to carry out reactions in adiabatic RIV
(no heat exchange with the environment - reactors operating without supplying or removing heat Q to the environment through the walls of the reactor. That. all heat released or absorbed during the reaction is accumulated (absorbed) by the reaction mixture) In this case, it is possible to ensure high speed
w r reactions and high performance
P reactor without use extraneous heat sources
Q. The temperature increases with increasing conversion, therefore, the rate constant also increases, which means the speed of the process also increases. The best organization of the process is achieved if the heat Q products leaving the reactor serves to heat the reactants as they enter the reactor. Reactions endothermic
(ΔH>0) simple(A→R) irreversible
(→)
it is unprofitable to carry out in adiabatic RIM, but it is more expedient to carry out it in reactors with heat supply Q, maintaining a certain temperature T0, the maximum possible for structural and technological reasons (isothermal, polythermal). (with increasing conversion, the temperature decreases, which means both the rate constant and the speed itself decrease). Endothermic processes are still carried out in the adiabatic RIV-N, but the supply of raw materials is carried out together with steam. Simple reversible reactions (↔
)
T 0 => w r For speed w r reactions are also influenced by the sign thermal effect
Q r(or enthalpy ΔH): 1) If the direct reaction is endothermic ΔН>0 ( heat absorption) then increase temperature T 0 will also have a beneficial effect on the situation chemical equilibrium
↔
(will shift it's to the side direct reaction
→).
Therefore, such reactions are carried out in reactors with heat supply in the same way as irreversible (→) endothermic
(ΔH
>0) reactions. 2) If the direct reaction is exothermic (ΔH<
0) (with heat release) then the KINETICS and THERMODYNAMICS of the process come into conflict: an increase temperature T 0 will adversely affect the situation chemical equilibrium ↔
(will move it to the side reverse reaction ←).
Therefore, the following mode is used: - at the beginning of the process
when product concentration With R still small temperature is increased T 0 until, Byespeed process w r will not become high enough; - at the end of the process -
the temperature is gradually reduced T 0 ↓ By lines optimal temperatures (LOT) so that the speed of the process w r remained as high as possible under the given conditions. This regime is not feasible either in an adiabatic or an isothermal reactor. An approximation to this mode is the REV, located inside the heat exchange tube, inside which the cooling agent passes. Another way is to carry out the process in a multi-section reactor, in which each section operates in adiabatic mode, but there is cooling between sections. For endothermic (reversible and irreversible) reactions, it is advisable to carry out the chemical process in reactors with heat supply, and it is desirable to ensure a fairly uniform temperature distribution throughout the reactor volume. A common type of apparatus for carrying out endothermic reactions are tubular reactors, similar in design to shell-and-tube heat exchangers. In these devices, the tube space represents the reactor itself, in which the reagents move in a displacement mode, and a coolant, for example flue gases, passes through the intertube space. A tubular reactor for carrying out catalytic reactions, heated by flue gases, is used, in particular, for steam reforming of natural gas. A retort furnace for the synthesis of butadiene from ethyl alcohol, wherein Furnace Rice. Tubular reactor gases for endothermic instead of pipes, the catalyst is placed in retorts - narrow channels with rectangular cross-section. In such reactors, the cross-sectional width of the channels through which the reaction mixture moves must be small in order to obtain a fairly uniform temperature distribution across the cross-section. Since in real reactors the hydrodynamic regime deviates from the ideal displacement regime, in which conditions are equalized in any cross section, the temperature in the center of the channel differs from the temperature at the wall. In large-diameter pipes, the temperature at the pipe axis is significantly lower than the temperature at the wall. Consequently, the reaction rate in that part of the reaction flow that moves close to the pipe axis is lower than the average speed in the apparatus. When carrying out catalytic processes, it is possible to apply the catalyst only to the inner surface of the pipes, which will ensure approximately the same temperature throughout the reactor. Homogeneous endothermic reactions can also be carried out in reactors with intensive mixing and a heat exchange surface, since in this case a uniform temperature distribution throughout the reactor will be ensured. Exothermic reactions are carried out, as a rule, either under adiabatic conditions or in apparatus with heat removal. When irreversible exothermic reactions occur, an increase in temperature clearly only leads to an increase in the rate of the process. To reduce energy costs, it is advantageous to carry out such reactions in an autothermal mode, when the required temperature is provided solely by the released heat of a chemical reaction without supplying energy from the outside. There are two temperature limits (lower and upper), between which it is advisable to carry out the process. The lower limit is the temperature at which the rate of the exothermic reaction (and, consequently, the rate of heat release) is sufficient to ensure an autothermal regime. Below this heat, the rate of heat release is less than the rate of heat removal with the reaction flow leaving the reactor, and the temperature in the flow adiabatic apparatus will drop. The upper temperature limit is associated with side processes (side chemical reactions or side physical phenomena), as well as with the heat resistance of structural materials. For example, when carrying out heterogeneous processes of firing granular solid material, an increase in temperature above a certain limit value leads to sintering of solid particles, and, consequently, to an increase in the time of their complete transformation and a decrease in reactor productivity. Often the temperature increase is limited by the strength of structural materials and the inappropriateness of using expensive heat-resistant materials. When carrying out exothermic processes of microbiological synthesis, the temperature increase is limited by the viability of microorganisms. Therefore, it is advisable to carry out such processes in reactors with heat removal, and in order to avoid local overheating, it is better to use reactors in which the hydrodynamic regime approaches ideal mixing. Intensive mixing in such processes not only ensures uniform temperature distribution, but also intensifies the stages of oxygen mass transfer from the gas phase to the liquid phase. Reversible exothermic reactions must be carried out in accordance with the optimal temperature line, i.e., lowering the temperature in the apparatus as the degree of conversion of the reagents increases. This mode is not feasible in either adiabatic or isothermal reactors: in an adiabatic mode, an increase in the degree of conversion is accompanied by the release of heat and heating, rather than cooling, of the reaction mixture; in isothermal mode, the temperature remains constant and does not change with increasing degree of conversion. It is extremely difficult to carry out the process strictly along the line of optimal temperatures. This could be done in a reactor with a heat exchange surface operating in a displacement mode, provided that the amount of heat removed through the reactor wall will differ by various areas apparatus. The reagents should be heated to a high temperature before starting the reaction, and heat removal should be provided immediately after they enter the apparatus. If the reactor is divided along the length into several sections, then in order to ensure movement along the line of optimal temperatures, in each of them the amount of heat removed must be slightly greater than the amount of heat released during the reaction. It should be borne in mind that as the degree of conversion increases, the reaction rate decreases and, consequently, the rate of heat release decreases. Therefore, in the sections of the reactor where the reaction is completed, less heat needs to be removed than in the initial sections. Topic 6. CHEMICAL REACTORS Any CTP is impossible without a chemical reactor, in which both chemical and physical processes take place. CHEMICAL REACTORS (from the Latin re - prefix meaning reverse action, and actor - putting into action, acting), industrial devices for carrying out chemical reactions. The design and operating mode of a chemical reactor are determined by the type of reaction, the phase state of the reagents, the nature of the process over time (periodic, continuous, with varying catalyst activity), the mode of movement of the reaction medium (periodic, semi-flowing, with recycle), the thermal operating mode (adiabatic, isothermal , with heat exchange), type of heat exchange, type of coolant. Modern chemical reactor
-
This is a complex device that has special devices, for example: 1)
loading and unloading devices (pumps); 2)
heat exchangers; 3)
mixing devices, intended to obtain the target product, equipped complex system instrumentation and control equipment. Requirements for industrial reactors 1.
MAX productivity and work intensity. 2.
High product yield F and the highest selectivity of the process φ-
this is ensured by the optimal operating mode of the reactor (T, R, C), high degree of conversion X. 3.
Optimal energy consumption for mass transfer in a reactor There is a contradiction between the requirement for high productivity
(raw materials) and high degree of transformation
X A(reagent): in schemes with open loop preference is given to high degree of conversion X A reagents; in closed systems preference is given to high productivity.
When producing a high-quality product, the reactor must ensure its minimum cost. Classification of chemical reactors 1)
By design features: Rice. 1 – Main types of chemicals. reactors: a – flow-through capacitive reactor with a stirrer and heat exchange jacket; b – multilayer catalytic reactor with intermediate and heat exchange elements; c – column reactor with packing for a two-phase process; d – tubular reactor; I-starting substances; P – reaction products; T – coolant; K – catalyst; N – nozzle; TE – heat exchange elements. It is a tubular apparatus in which the ratio of the pipe length L to its diameter d is quite large. The reactor is continuously fed with reagents, which are converted into products as they move along the length of the reactor. The hydrodynamic regime in RIV is characterized by the fact that any particle of the flow moves only in one direction along the length of the reactor, there is no longitudinal mixing, and there is also no mixing along the cross section of the reactor. It is assumed that the distribution of substances over this cross section is uniform, i.e., the values of the parameters of the reaction mixture over the cross section are the same. Each element of the volume of the reaction mass dV does not mix with either previous or subsequent volumes, and behaves like a piston in a cylinder. This mode is called piston or full displacement. The composition of each volume element changes sequentially due to the occurrence of a chemical reaction. Changes in the concentration of the reagent CA and the degree of conversion of XA along the length of the reactor. To compile a mathematical description of the RIV, they proceed from differential equation material balance. Since in RIM the reaction mixture moves only in one direction (along the length L), then A choosing the direction of the flow in the reactor as the direction of the X axis, where W – linear speed movement of the mixture. Since each volume element does not mix with either the previous or the subsequent one, there is neither longitudinal nor radial diffusion, and molecular diffusion is small, then Then This material balance equation is a mathematical description of the flow of reagents in the reactor in an unsteady mode (when the parameters change not only along the length of the reactor, but are also not constant in time - the period of start-up or shutdown). The term is characterized by the change in concentration A over time for a given point in the reactor. The stationary mode is characterized by the fact that the parameters at each point of the reaction volume do not change with time and . Then . But the speed A Integrating this equation within the limits of the change in the degree of conversion from 0 to X A we get From the data obtained it is clear that the equation for RIV is the same as for RIS – P. Continuous ideal mixing reactor RIS – N It is an apparatus into which reagents are continuously fed and reaction products are continuously removed, while the reagents are continuously mixed using a stirrer. The initial mixture entering such a reactor is instantly mixed with the reaction mass already in the reactor, where the concentration of the initial reagent is lower than in the incoming mixture. To derive the characteristic equation, let's create a material balance equation. The number of moles of the initial substance A supplied with the flow, where V 0 is the volumetric feed rate, CA, 0 is the concentration of A in the flow. The number of moles removed from the reactor is , where V is the volumetric velocity, CA is the concentration in the flow. The number of moles of substance A consumed as a result of a chemical transformation is Where V p is the filled volume in the reactor. The accumulation of reagent A is equal to the change in its quantity in the reaction space over the time period dτ. Let's combine all parts of the balance sheet General design equation for a fully stirred reactor.
Except for periods of shutdown and startup, a continuous reactor operates in a steady state. The design equation in this case is reduced to the form If the reaction is carried out in the liquid phase, then the change in volume is small and V 0 = V k = V. Then C A,0 – C A = τ ω A, where is the conditional residence time. Material balance is the equality of the inflow and outflow of a substance in a reactor or in a process. The theoretical basis for compiling material balances is the law of conservation of matter by M.I. Lomonosov. Let's draw up a material balance for a reactor in which a simple irreversible reaction A → C occurs. The mass of the reagent entering the reactor per unit time is equal to the mass of reagent A consumed in the reactor per unit time. m And income = m Expense Reagent A is spent on a chemical reaction, part of the reagent leaves the reactor, part remains unchanged in the reaction volume (accumulates). m A consumption = m A chemical solution + m A drain + m A storage m A income = m A chemical r. + m A drain + m A storage m A income - m A drain = m A chemical. + m A accumulated Let us denote m A arrival -m A drain =m A convection. is the mass of reagent A transported by convection (flow of the reaction mass). Then m A accumulated. =m A convection. -m A chem.r. The mass of reactant A, which remains unchanged in the reaction flow, is equal to the difference between the mass of substance A carried by the convective flow and the mass of substance A spent on the chemical reaction. This is the equation material balance in general form. When the concentration of a reagent is not constant at different points in the reactor volume or over time, it is impossible to compile a material balance in general form for the entire reactor volume. In this case, a material balance is drawn up for the elementary volume of the reactor. The basis of this material balance is the convective transport equation (see Amelin et al. pp. 71-73). where CA is the concentration of reagent A in the reaction mixture; x,y,z – spatial coordinates; W x , W y , W z – flow velocity components; D – diffusion coefficient; r A – rate of chemical reaction. Member Member Member The term r A shows the change in the concentration of reagent A in an elementary volume due to a chemical reaction. It corresponds to the m A chemical term. in the general material balance equation. The resulting differential equation is very difficult to solve. Depending on the type of reactor and its operating mode, it can be transformed and simplified. Previously, we reviewed the basic models of chemical processes and their mathematical description. Let us complicate the model of the chemical technological process by taking into account hydrodynamic processes, that is, methods of directed movement of the flow of the reaction mixture in the reactor. Any reactor used in chemical production. To a greater or lesser approximation, it can be described by one of the following models: batch ideal mixing reactor RIS-P; continuous ideal mixing reactor RIS-N; continuous plug flow reactor RIV-N; cascade of continuous ideal mixing reactors K-RIV-N (cell model). For each model it is shown characteristic equation, which expresses the dependence of the residence time of the reagents in the reactor o, the initial concentration of the reagent, the conversion value and the rate of the chemical reaction. τ = f (C A 0 , α A , r A) This equation is mathematical description of the reactor model. It makes it possible, by specifying C A0 (composition of the initial mixture) and r A (type of chemical reaction, temperature, pressure, catalyst, etc.), to calculate the residence time of the reagents in the reactor required to achieve a given conversion (α A), and therefore , and the volume of the reactor, its overall dimensions and productivity. By comparing the obtained values for reactors of different types, you can choose the most optimal option for carrying out a given chemical reaction. The basis for deriving the characteristic equation is the material balance of the reactor, compiled one by one of the components of the reaction mixture. Ideal Mixing Batch Reactor
RIS-P is an apparatus with a stirrer into which the starting reagents are periodically loaded and the products are also periodically unloaded. The initial equation for obtaining the characteristic equation is the material balance equation in differential form: Since, due to intense mixing, all parameters are the same throughout the entire volume of the reactor, at any time the derivative of any order of concentration along the x, y, z axes is zero. Then At V reaction mixture = const C A = C A 0 (1-α A). If a simple irreversible reaction of “n” order occurs in the reactor, then When n = 0 n=1 For n ≠ 0 and 1, τ is determined by the method of graphic integration. To do this, build a graphical dependence calculate the area under the curve between the initial and final values of the degree of conversion.Tgr1 to achieve “self-ignition” (position D). Once the reaction has started, it is possible to reduce the inlet temperature to TE without much change in the reaction rate< Тгрl и работать в интервале
температур примерно до Тф2. Однако, если ТЕ уменьшится хотя бы один
раз до ТЕ < Тгр2, может про изойти затухание реакции и степень
превращения значительно уменьшится.
При обратимой экзотермической реакции первого порядка типа А и
В, протекающей в адиабатическом режиме, кривая тепловыделения QR
имеет вид, показанный на рис 9.8. Это является следствием смещения
равновесия при высоких температурах. Линия теплоотвода TQ может
касаться
или
пересекать
линию
тепловыделения
в
двух
точках.
Практически целесообразно работать в таких условиях, чтобы точка II
пересечения Q и QR была как можно выше.
9.7 Анализ теплового режима адиабатического реактора для
эндотермических реакций
Соотношение
(8.26)
между
степенью
превращения
U
и
температурами справедливо также и для эндотермических процессов с
154
учетом того, что q и ТА
- ТЕ отрицательны. Как видно из рис.9.9; прямые
теплоотвода имеют одну точку пересечения с кривой тепловыделения. Ее
положение определяется только температурой у входа в реактор,
скоростью перемещения потоков и тепловым эффектом реакции. Она
характеризует
температуру
реакции
и
степени
превращения
в
установившемся состоянии.
Рис. 9.9 График соотношения тепловыделения и теплоотвода при
обратимой экзотермической, реакции протекающей в адиабатическом
режиме
Рис. 9.10 График зависимости степени превращения от температуры при
эндотермической реакции.
155
9.8 Тепловой расчет изотермического реактора периодическою
действия
Конструктивно изотермический реактор периодического действия
аналогичен реактору непрерывного действия (Рис. 9.11)
Рис. 9.11 Схема изотермического реактора периодического действия
На рис.9.12 представлены температурные характеристики изотермического
реактора периодического действия.
156
Рис. 9.12 Температурные характеристики изотермического реактора
периодического действия.
9.9 Тепловой расчет изотермического реактора периодического
действия для квазистационарного режима
Рассмотрим реакцию 0го порядка, kinetic equation which has the form − =K=K ∙e (9.29) Heat generated per unit time due to the thermal effect ∆ =∆ ∙ ∙K ∙e (9.30) Heat that is removed with the cooling medium due to heat transfer ∆ = 157 ∙ ∙(− ) (9.31) Abscissas of the intersection points I and III of a given operating temperature TI and TIII Fig. 9.12 The limiting position of the heat removal lines T0 - II will be tangent to QR. When the heat removal line T0 - II is placed below this limit value, the heat removal is insufficient and an isothermal process is impossible. With increasing heat removal, two intersection points I and III are obtained. At any T< Т1 линия теплоотвода ниже линии тепловыделения
(QT
←Characteristic equation FIG-N.
,
- process speed per unit volume
-
Math equation balance
-
Characteristic equation RIV-N.
,
If, according to the process conditions, it is the RIS design that is required, then large-volume reactors are required to achieve high conversion rates in a short period of time.
. . Determine how long it will take to carry out the reaction in:
.
IN RPD certain quantities of reagents are loaded at a time and are kept in it until those until the desired degree of conversion is achieved. After this, the reactor is unloaded.
given degree of conversionX A is achieved in RIV in less time τ:
Analyzing this reaction rate equation, we conclude that increase speed
w r reactions will lead to an increase temperatures:
And 
,
,
,
characterizes the change in the concentration of reagent A over time in an elementary volume and corresponds to m A accumulation. in the general material balance equation.
reflects the change in the concentration of the reagent due to its transfer in a direction coinciding with the direction of the general flow.
reflects the change in the concentration of reagent A in the elementary volume as a result of its transfer by diffusion. Together, these terms characterize the total transport of matter in a moving medium by convection and diffusion; in general, the material balance equation corresponds to the term m A convec. .Lecture No. 12 Hydrodynamic models of reactors. Derivation of characteristic equations.
In such a reactor, such intense mixing is created that at each moment of time the concentration of reagents is the same throughout the entire volume of the reactor and changes only over time, as the chemical reaction proceeds.
-
characteristic equation RIS-P
,
.
