Heat steady-state tubular flow

Steady-State Tubular Flow with Heat Loss... 

In particular cases simplified reactor models can be obtained neglecting the insignificant terms in the governing microscopic equations (without averaging in space) [9]. For axisymmetrical tubular reactors, the species mass and heat balances are written in cylindrical coordinates. Himelblau and Bischoff [9] give a list of simplified models that might be used to describe tubular reactors with steady-state turbulent flow. A representative model, with radially variable velocity profile, and axial- and radial dispersion coefficients, is given below ... 

All chemical reactions are accompanied by some heat effects so that the temperature will tend to change, a serious result in view of the sensitivity of most reaction rates to temperature. Factors of equipment size, controllability, and possibly unfavorable product distribution of complex reactions often necessitate provision of means of heat transfer to keep the temperature within bounds. In practical operation of nonflow or tubular flow reactors, truly isothermal conditions are not feasible even if they were desirable. Individual continuous stirred tanks, however, do maintain substantially uniform temperatures at steady state when the mixing is intense enough the level is determined by the heat of reaction as well as the rate of heat transfer provided. 

In many tubular reactors cooling or heating occurs as the process fluid flows through the reactor. This produces a major difference between an adiabatic and a nonadiabatic tubular reactor. In an adiabatic reactor, with an exothermic irreversible reaction, the maximum steady-state temperature occurs at the end of the reactor. In a cooled reactor, the maximum steady-state temperature usually occurs at some axial position part way down the reactor. Thus the temperature does not change monotonically with length. 

Conclusions. In tubular multiphase reactors with an exothermic reaction where one phase with a high throughput serves to carry the heat of reaction out of the reactor, a sudden flow reduction in this phase (whether accompanied by a similar reduction in the other phases or not) can lead to a considerable transient temperature rise, well above the new steady state temperature. The maximum excess temperature depends in a complex way upon the rate of the flow reduction, the flow rates in the different phases, the heat capacities and the reaction rates of the system. 

This last item is important because it leads to an easy way to accommodate the molar contraction of the gas as the reaction proceeds. The program calculates steady-state profiles of each of these down the length of the tubular reactor, given the reaction kinetics models, a description of the reactor and catalyst geometries, and suitable inlet gas flow-rate, pressure and composition information. Reactor performance is calculated from the flow-rate and composition data at the reactor outlet. Other data, such as the calculated pressure drop across the reactor and the heat of reaction recovered as steam, are used in economic calculations. The methods of Dixon and Cresswell (7) are recommended for heat-transfer calculations. 

The second issue for cooled tubular reactors is how to introduce the coolant. One option is to provide a large flowrate of nearly constant temperature, as in a recirculation loop for a jacketed CSTR. Another option is to use a moderate coolant flowrate in countercurrent operation as in a regular heat exchanger. A third choice is to introduce the coolant cocurrently with the reacting fluids (Borio et al., 1989). This option has some definite benefits for control as shown by Bucala et al. (1992). One of the reasons cocurrent flow is advantageous is that it does not introduce thermal feedback through the coolant. It is always good to avoid positive feedback since it creates nonmonotonic exit temperature responses and the possibility for open-loop unstable steady states. 

Tubular reactors do not necessarily operate under isothermal conditions in industry, be it for reasons of chemical equilibrium or of selectivity, of profit optimization, or simply because it is not economically or technically feasible. It then becomes necessary to consider also the energy equation, that is, a heat balance on a differential volume element of the reactor. For reasons of analogy with the derivation of Eq. 9.1-1 assume that convection is the only mechanism of heat transfer. Moreover, this convection is considered to occur by plug flow and the temperature is completely uniform in a cross section. If heat is exchanged through the wall the entire temperature difference with the wall is located in a very thin film close to the wall. The energy equation then becomes, in the steady state ... 

Tubular flow reactors are characterized by a continuous and decreasing concen-tiadon of reactants in the direction of flow. This is in contrast to the discontinuous characteristic of the CSTR reactor. Most of these units consist of one or several pipes or tubes in parallel. Either horizontal or vertical orientation is common. The reactants are charged continuously at one end, and the products are removed continuously at the other end. The unit almost always operates in a steady-state mode. This greatly simplifies design and predictive calculations. It is a unit that is amendable to automatic control and to experimental work. When heat transfer is required, a jacketed tube or a construction similar to that of a shell-and-tube heat exchanger is employed. In the latter case the reactants may be on either the tube or shell side. 

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