Adiabatic operations tubular reactors

Many tubular reactors are operated adiabatically because of the problems in providing heat transfer. Figure 1.11a shows a complete gas-phase reaction process with a high-temperature tubular reactor that is cooled by generating steam. Figure 1.11 b shows a fuel-fired furnace being used as a tubular reactor. 

There is also a wider variety of reactor and system types for tubular reactors. Many operate adiabatically, while others are heated or cooled. Multiple tubular reactors in series with intermediate heating or cooling are quite common. The most common industrial use of tubular reactors is in systems where a solid catalyst is required. The catalyst is installed in beds or inside tubes in the shell of the reactor vessel, and the process reacting fluid (gas or liquid) flows through the fixed catalyst. 

Assuming constant thermodynamic properties, determine the length of a 2-in inner-diameter (ID) tubular reactor that operates adiabatically and provides 93% conversion of B. The heat of reaction is AHr -48,000 Btu/lbmo and the mixture heat capacity is Cp = 110 Btu/lbmo °R. 

Adiabatic plug flow reactors operate under the condition that there is no heat input to the reactor (i.e., Q = 0). The heat released in the reaction is retained in the reaction mixture so that the temperature rise along the reactor parallels the extent of the conversion. Adiabatic operation is important in heterogeneous tubular reactors. 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

The summation involves the effluent molal flow rates. This equation and equation 10.4.2 must be solved simultaneously in order to determine the tubular reactor size and to determine the manner in which the heat transfer requirements are to be met. For either isothermal or adiabatic operation one of the three terms in equation 10.4.7 will drop out, and the analysis will be much simpler than in the general case. In the illustrations which follow two examples are treated in detail to indicate the types of situations that one may encounter in practice and to indicate in more detail the nature of the design calculations. 

ILLUSTRATION 10.4 DETERMINATION OF THE VOLUME REQUIREMENTS FOR ADIABATIC OPERATION OF A TUBULAR REACTOR WITH EXOTHERMIC REACTION... 

The process in question involved the reaction of two materials, A and B, to produce a product C. The reaction was noncatalytic, homogeneous, and in the gas phase. It took place in a tubular reactor which could not be considered either adiabatic or isothermal. The reactor was divided into four sections, the first three of which were cooled while the fourth was adiabatic. Coking of the reactor tube introduced a time variant in the system, requiring adjustment of operating conditions and eventual shutdown for cleaning. 

We shall consider, in turn, the various problems which have to be faced when designing isothermal, adiabatic and other non-isothermal tubular reactors, and we shall also briefly discuss fluidised bed reactors. Problems of instability arise when inappropriate operating conditions are chosen and when reactors are started up. A detailed discussion of this latter topic is outside the scope of this chapter but, since reactor instability is undesirable, we shall briefly inspect the problems involved. 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

A tubular reactor is to be designed in such a way that it can be stopped safely. The reaction mass is thermally instable and a decomposition reaction with a high energetic potential may be triggered if heat accumulation conditions occur. The time to maximum rate under adiabatic conditions of the decomposition is 24 hours at 200 °C. The activation energy of the decomposition is 100 kj mol-1. The operating temperature of the reactor is 120 °C. Determine the maximum diameter of the reactor tubes, resulting in a stable temperature profile, in case the reactor is suddenly stopped at 120 °C. 

It is useful to initially examine the tubular reactor as an isolated unit so that some insight can be gained about the effects of various design and operating parameters on its inherent behavior. The equations describing the steady-state operation of a tubular reactor are presented and illustrated for a specific numerical example. Both adiabatic and nonadiabatic tubular reactors are considered. 

A theoretical and experimental study of multiplicity and transient axial profiles in adiabatic and non-adiabatic fixed bed tubular reactors has been performed. A classification of possible adiabatic operation is presented and is extended to the nonadiabatic case. The catalytic oxidation of CO occurring on a Pt/alumina catalyst has been used as a model reaction. Unlike the adiabatic operation the speed of the propagating temperature wave in a nonadiabatic bed depends on its axial position. For certain inlet CO concentration multiplicity of temperature fronts have been observed. For a downstream moving wave large fluctuation of the wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions erratic behavior of temperature profiles in the reactor has been observed. 

The multi-mode model for a tubular reactor, even in its simplest form (steady state, Pet 1), is an index-infinity differential algebraic system. The local equation of the multi-mode model, which captures the reaction-diffusion phenomena at the local scale, is algebraic in nature, and produces multiple solutions in the presence of autocatalysis, which, in turn, generates multiplicity in the solution of the global evolution equation. We illustrate this feature of the multi-mode models by considering the example of an adiabatic (a = 0) tubular reactor under steady-state operation. We consider the simple case of a non-isothermal first order reaction... 

This set of equations describes the behaviour of multiple, first order reactions in a tubular reactor using the relative conversion to desired product Xp and to undesired product Xx, the dimensionless temperature T and the dimensionless reactor length Z. The is characterized by the ratio of the reaction heats H in addition to kR, TR, y and p. The operating and design are determined by PC, the dimensionless cooling medium temperature Da, the dimensionless residence time in the reactor U, the dimensionless cooling capacity per unit of reactor volume and ATacp the dimensionless adiabatic temperature rise for the desired reaction, which, of course, depends on the initial concentration of the reactant A. 

In this section we apply the general energy balance [Equation (8-22)] to the CSTR and to the tubular reactor operated at steady state. We then present example problems showing how the mole and energy balances are combined to size reactors operating adiabatically. 

Tubular reactors are commonly used in laboratory, pilot plant, and commercial-scale operations. Because of their versatility, they are used for heterogeneous reactions as well as homogeneous reactions. They can be run with cocurrent or counter-current flow patterns. They can be run in isothermal or adiabatic modes and can be used alone, in series, or in parallel. Tubular reactors can be empty, packed with inert materials for mixing, or packed with catalyst for improved reactions. It is often the process that will dictate the design of the reactor, as discussed in this entry. 

As we observed earlier, the adiabatic reactor is not so much a type, more a way of operation. We shall therefore refer to both stirred tank reactors and to tubular ones, and this chapter forms a suitable bridge between the two. We shall introduce the simplest model of the tubular reactor, but this is so elementary that the anticipation of the following chapter will cause no difficulty. 

We may first divide tubular reactors into those designed for homogeneous reactions, and therefore basically just an empty tube, and those designed for a heterogeneously catalyzed reaction, and hence to be packed with a catalyst. Both types can of course be operated adiabatically, and it was the simplest model of these that we discussed in the last chapter. If the temperature of the reactor is to be controlled this is through the wall, and the associated problems of heat transfer now arise. These include transfer at the wall and subsequent radial diffusion across the flowing reactants. In the empty tubular reactor there may be considerable variations in flow rate across the tube. For example, in the slow laminar flow the fluid... 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

Reactors (both flow and batch) may also be insulated from the surroundings so that their operation approaches adiabatic conditions. If the heat of reaction is significant, there will be a change in temperature with time (batch reactor) or position (flow reactor). In the flow reactor this temperature variation will be limited to the direction of flow i.e., there will be no radial variation in a tubular-flow reactor. We shall see in Chap. 13 that the design procedures are considerably simpler for adiabatic operation. 

Even adiabatic operation results in the formation of considerable amounts of the undesirable dichloropropane. This occurs in the first part of the reactor, where the temperature of the flowing mixture is low. This is an illustration of the discussion at the beginning of the chapter with respect to Fig. 5-la and b. The conditions correspond to the low-conversion range of Fig. 5-lb before the maximum rate is reached. A tubular-flow reactor is less desirable for these conditions than a stirred-tank unit. The same reaction system is illustrated in Example 5-3 for a stirred-tank unit. 

Recent developments in shift catalyst formulations allow the combination of high temperature and low temperature shift reactors in a single medium temperature step. The medium temperature shift catalyst is a copper-based catalyst that operates in the range of 260-280°C (500-540 F). Carbon monoxide conversion is improved, resulting in an overall savings on feed and fuel of 0.3% to 0.8% [2]. The medium temperature shift reactor has been commercially proven with isothermal tubular reactors, however, the use of an adiabatic reactor with intercooling is also possible. 

This problem requires an analysis of coupled thermal energy and mass transport in a differential tubular reactor. In other words, the mass and energy balances should be expressed as coupled ordinary differential equations (ODEs). Since 3 mol of reactants produces 1 mol of product, the total number of moles is not conserved. Hence, this problem corresponds to a variable-volume gas-phase flow reactor and it is important to use reactor volume as the independent variable. Don t introduce average residence time because the gas-phase volumetric flow rate is not constant. If heat transfer across the wall of the reactor is neglected in the thermal energy balance for adiabatic operation, it... 

Nitrogen and hydrogen produce ammonia in a gas-phase adiabatic tubular reactor operating at 5 atm total pressure. A stoichiometric feed of N2 and H2 enters the reactor. The reversible elementary chemical reaction is... 

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