Heat transfer, reactors overall coefficients

A fundamental aspect in the reactor design is the contribution of different thermal resistances in achieving a highly efficient heat transfer. The overall heat coefficient U is given by the relation ... 

To reduce the pressure drop, a batch reactor with a half-pipe jacket of length L and flowrate W can be partitioned into a two-zone jacket, each with a length L/2 and each supplied with W jacket flowrate. This doubles the jacket flow at a lower pressure drop in each zone. The flow in each zone can then be increased to increase the outside and overall heat transfer coefficients, which is similar to those of the single-zone jacket. 

A stirred reactor contains a batch of 700 kg reactants of specific heat 3.8 kJ/kg K initially at 290 K, which is heated by dry saturated steam at 170 kN/m2 fed to a helical coil. During the heating period the steam supply rate is constant at 0.1 kg/s and condensate leaves at the temperature of the steam. If heat losses arc neglected, calculate the true temperature of the reactants when a thermometer immersed in the material reads 360 K. The bulb of the thermometer is approximately cylindrical and is 100 mm long by 10 mm diameter with a water equivalent of 15 g, and the overall heat transfer coefficient to the thermometer is 300 W/m2 K. What would a thermometer with a similar bulb of half the length and half the heat capacity indicate under these conditions ... 

U = overall heat transfer coefficient V = reactor volume = number average DP Xyf = weight average DP... 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

As is common in most polymer reactor design problems, heat transfer is one of the major process concerns. For example, if the heat transfer is primarily through the wall of a jacketed reactor, the overall heat transfer coefficient is a function of both the agitator configuration and the degree of swelling of the particles. 

The polymerizations were conducted in a 20-liter stainless steel reactor with a pitched-blade turbine agitator and four side-wall baffles. The monomer was polymerized at the same temperature, initiator and monomer concentration in two different inert diluents. The data (Figure 6) illustrate the substantial lowering of the overall heat transfer coefficient for the system with the more highly swollen particles. 

The heat transfer term envisions convection to an external surface, and U is an overall heat transfer coefficient. The heat transfer area could be the reactor jacket, coils inside the reactor, cooled baffles, or an external heat exchanger. Other forms of heat transfer or heat generation can be added to this term e.g, mechanical power input from an agitator or radiative heat transfer. The reactor is adiabatic when 7 = 0. 

Figure 12.8 Temperature profile along the reactor at steady state for different 1. Table 12.7 Overall heat transfer coefficient for all experiments (with reaction).

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

The desired product is P, while S is an unwanted by-product. The reaction is carried out in a solution for which the physical properties are independent of temperature and composition. Both reactions are of first-order kinetics with the parameters given in Table 5.3-2 the specific heat of the reaction mixture, c, is 4 kJ kg K , and the density, p, is 1000 kg m . The initial concentration of /I is cao = 1 mol litre and the initial temperature is To = 295 K. The coolant temperature is 345 K for the first period of 1 h, and then it is decreased to 295 K for the subsequent period of 0.5 h. Figs. 5.3-13 and 5.3-14 show temperature and conversion curves for the 63 and 6,300 litres batch reactors, which are typical sizes of pilot and full-scale plants. The overall heat-transfer coefficient was assumed to be 500 W m K. The two reactors behaved very different. The yield of P in a large-scale reactor is significantly lower than that in a pilot scale 1.2 mol % and 38.5 mol %, respectively. Because conversions were commensurate in both reactors, the selectivity of the process in the large reactor was also much lower. 

Fig. 3.2 shows the case of a jacketed, stirred-tank reactor, in which either heating by steam or cooling medium can be applied to the jacket. Here V is volume, Cp is specific heat capacity, p is density, Q is the rate of heat transfer, U is the overall heat transfer coefficient, A is the area for heat transfer, T is temperature, H is enthalpy of vapour, h is liquid enthalpy, F is volumetric flow... 

The rate at which heat is transferred to a system can be expressed in terms of an overall heat transfer coefficient U, the area through which the heat exchange occurs and on which U is based, and the difference between the temperature of the heat source (or sink) Tm9 and that of the reactor contents T. 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3. Determine the volume required to produce 2 million lb of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 hr annually with 97% conversion of the A fed to the reactor. The feed enters at 163 C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperature of 160 °C. The overall heat transfer coefficient based on the... 

However, the energy balance equation appropriate for use in this illustration differs from that employed in the previous case because thermal losses through the reactor walls must be accounted for. It will be of the same general form as equation 12.7.48, but with the wall heat transfer coefficient replaced by an overall heat... 

A process fluid is available to cool the reactor. If it is used, the wall temperature of the reactor is constant at 4 10 K, and the overall heat transfer coefficient ((/) is 125 W m-2 K-1. 

It is important to calculate U accurately to determine the required heat transfer area for a reactor. Typical expressions to calculate overall heat transfer coefficients for agitated vessels are presented in [174,180] and generally in standard chemical engineering texts and reference books. 

The overall heat transfer coefficient calculated using the joint parameter estimation and data reconciliation approach is shown in Fig. 9. It is evident from this figure that the overall heat transfer coefficient remains fairly constant throughout the whole operating cycle of the pyrolysis reactor. Near the end of the cycle, the heat transfer coefficient drops to a comparably low value, signifying that the reactor needs to be regenerated. 

In the second example, that of an industrial pyrolysis reactor, simplified material and energy balances were used to analyze the performance of the process. In this example, linear and nonlinear reconciliation techniques were used. A strategy for joint parameter estimation and data reconciliation was implemented for the evaluation of the overall heat transfer coefficient. The usefulness of sequential processing of the information for identifying inconsistencies in the operation of the furnace was further demonstrated. 

The heat transfer area between the reactor and jacket is 140 The overall heat transfer coefficient is 70 Btu/h °F ft. Mass of the metal walls can be negleaed. Heal losses are negligible. 

We used the wall temperature in the boundary condition, and this may be different from the coolant temperature T. There may be temperature variations across the wall as well as through the coolant. These are described through the overall heat transfer coefficient U, but in practice all these effects must be considered for a detailed description of the wall-cooled tubular reactor. 

There are several possible mechanisms for the heat exchange between a reacting medium and a heat carrier radiation, conduction and forced or natural convection. Here we shall consider convection only. Other mechanisms are considered in the chapter on heat accumulation. The heat exchanged with a heat carrier (q ) across the reactor wall by forced convection is proportional to the heat exchange area (A) and to the driving force, that is, the temperature difference between the reaction medium and the heat carrier. The proportionality coefficient is the overall heat transfer coefficient (U) ... 

Industrial reactors are thermally insulated for safety reasons (hot surfaces) and for economical reasons (heat losses). Nevertheless, at higher temperatures, heat losses may become important. Their calculation may become tedious, since heat losses are often due to a combination of losses by radiation and by natural convection. If an estimation is required, a simplified expression using a global overall heat transfer coefficient (a) may be useful ... 

A reaction A—>P is to be performed in a batch reactor. The reaction follows first-order kinetics and at 50 °C, the conversion reaches 99% in 60 seconds (the rate constant is k = 0.077 s 1. The charge will be 5 m3 in a reactor with a heat exchange area of 15 m2 and an overall heat transfer coefficient of 500 Wm 2 K 1. The maximum temperature difference with the cooling system is 50 K. 

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