Continuous flow reactors steady state

The three main types of immobilized enzyme reactors used are batch (Fig. 9.1), plug-flow (Fig. 9.2), and continuous-stirred (Fig. 9.3). In both batch and plug-flow reactors, non-steady-state reaction conditions prevail, while in continuous-stirred reactors, steady-state reaction conditions are prevalent. 

In a continuous-stirred reactor, steady-state reaction conditions prevail. Therefore, the model used is different from the one used for batch and plug-flow reactors. For the case of a continuous-stirred reactor, the reaction velocity (u) equals the product of the flow rate (Q) through a reactor... 

Semibatch or semiflow processes are among the most difficult to analyze from the viewpoint of reactor design because one must deal with an open system under nonsteady-state conditions. Hence the differential equations governing energy and mass conservation are more complex than they would be for the same reaction carried out batchwise or in a continuous flow reactor operating at steady state. 

Equation 10.1.1 represents a very general formulation of the first law of thermodynamics, which can be readily reduced to a variety of simple forms for specific applications under either steady-state or transient operating conditions. For steady-state applications the time derivative of the system energy is zero. This condition is that of greatest interest in the design of continuous flow reactors. Thus, at steady state,... 

For the vast majority of situations of interest in the design of industrial scale chemical reactors, equation 10.1.4 provides an adequate approximation to the true situation for continuous flow reactors operating at steady state. Since... 

In order to minimize the complications arising from a change in the total moles within the catalyst particles, they restricted their studies to feeds containing less than 17% ethylene. They used continuous flow reactors operating at steady state to obtain the data reported on page 530. The pressure was one atmosphere. Two forms of catalyst were used in their studies. 

Other methods involve the use of continuous-flow reactors, and in certain cases, the rate is measured directly rather than indirectly. One advantage of a flow method is that a steady-state can usually be established, and this is an advantage for relatively fast reactions, and for continuous monitoring of properties. A disadvantage is that it may require relatively large quantities of materials. Furthermore, the flow rate must be accurately measured, and the flow pattern properly characterized. 

If the same reactions occur in a continuous-flow reactor with complete back-mixing then, at steady-state conditions... 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

So far in dealing with tubular reactors we have considered a spatial coordinate as the variable, i.e. an element of volume SV, situated at a distance z from the reactor inlet (Fig. 1.14), although z has not appeared explicitly in the equations. For a continuous flow reactor operating in a steady state, the spatial coordinate is indeed the most satisfactory variable to describe the situation, because the compositions do not vary with time, but only with position in the reactor. 

Various laboratory reactors have been described in the literature [3, 11-13]. The most simple one is the packed bed tubular reactor where an amount of catalyst is held between plugs of quartz wool or wire mesh screens which the reactants pass through, preferably in plug flow . For low conversions this reactor is operated in the differential mode, for high conversions over the catalyst bed in the integral mode. By recirculation of the reactor exit flow one can approach a well mixed reactor system, the continuous flow stirred tank reactor (CSTR). This can be done either externally or internally [11, 12]. Without inlet and outlet feed, this reactor becomes a batch reactor, where the composition changes as a function of time (transient operation), in contrast with the steady state operation of the continuous flow reactors. 

Figure 10. Effect of influent cation concentration on steady state substrate concentration for continuous flow reactor...

However this "definition" is wrong It is simply a mole balance that is only valid for a constant volume batch system. Equation (1-1) will not apply to any continuous-flow reactor operated at steady state, such as the tank tCSTR) reactor where the concentration does not vary from day to day (i.c.. the concentration is not a function of time). For amplification on this point, see the section "Is Sodium Hydroxide Reacting " in the Summary Notes for Chapter 1 on the CD-ROM or on the web. 

Continuous flow reactors are almost always operated at steady state. We will consider three types the continuous stirred tank reactor (CSTR). the plug flow reactor (PFR). and the packed bed reactor (PBR). Detailed descriptions of these reactors can be found in both the Professional Reference Shelf (PRS) for Chapter 1 and in the Visual Encyclopedia of Equipinent on the CD-ROM,... 

An important special case of these equations is their application to the steady-state operation of a continuous-flow reactor. At steady-state the contents of the reactor do not change with time, so that dC /dt = 0 mvddU jdt = dH/dt = 0, and the design equations reduce to... 

PCE was oxidized in a fixed-bed continuous flow reactor. The reactor was a 6-mm-o.d. Pyrex glass tube operated in the down flow mode. A reactant mainly containing air with 30 10,000 ppm of PCE was fed into the reactor charging 60/80 mesh size catalyst at a flow rate of 600 ml/min to avoid mass transfer resistance. The reaction temperatures were maintained at 350 °C under atmospheric pressure as a typical reactor condition [9]. The feed and product streams of the reactor were analyzed by on-line H.P. 5890A gas chromatography (GC) with TCD and FID detectors. The steady-state conversion of PCE was calculated based upon the difference between inlet and outlet concentrations of PCE. It has also been examined that more than 90% of PCE is converted to CO and CO2 by carbon balance. More detailed experimental procedures are described elsewhere [2]. 

Process residence time has a major impact on the time required to bring a continuous process to steady state and thus making on speciflcation product. For plug flow type processes such as tubular reactors, changes to the process take on the order of one residence time to make good product. However, for CSTRs, at least 3-4 residence times is needed during a transition before the system is at steady state. Thus, a CSTR with 5 min residence time can come to steady state in 15-20 min, whereas a CSTR with a 2 h residence time would take 6-8 h. In either case, the amount of intermediate waste material would equal several reactor turnovers [95]. 

The approach to be followed in the determination of rates or detailed kinetics of the reaction in a liquid phase between a component of a gas and a component of the liquid is, in principle, the same as that outlined in Chapter 2 for gas-phase reactions on a solid catalyst. In general the experiments are carried out in flow reactors of the integral type. The data may be analyzed by the integral or the differential method of kinetic analysis. The continuity equations for the components, which contain the rate equations, of course depend on the type of reactor used in the experimental study. These continuity equations will be discussed in detail in the appropriate chapters, in particular Chapter 14 on multiphase flow reactors. Consider for the time being, by way of example, a tubular type of reactor with the gas and liquid in a perfectly ordered flow, called plug flow. The steady-state continuity equation for the component A of the gas, written in terms of partial pressure over a volume element dV and neglecting any variation in the total molar flow rate of the gas is as follows ... 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

The copolymer equation represents the composition ratio of the copolymer produced at the given instant and is rewritten in Fig. 3.46. The final correlation between composition ratio, F1/F2, and the feed ratio, x = fi/f2 = [Mi]/[M2], can be reorganized, as also given in Fig. 3.46. For a reaction in a continuous flow reactor in steady state, one can thus predict the composition of the copolymer from the monomer feed ratio. In a batch reaction, in contrast, the composition changes continuously. 

In a completely mixed continuous flow reactor, the composition is thought to be uniform throughout the reactor, and is the same as in the exist stream (cf. Fig. 3.30). Applying the law of conservation of mass (cf. Equ. 2.3) to a CSTR yields Equ. 3.90 for the steady state. The dilution rate D is reciprocal to the mean residence time of a fluid (7). 

The analysis in Section 6.2 demonstrated that both the steady-state conversion and the optimum conversion in open chemical reaction systems (continuous-flow reactors) are always lower than the equilibrium conversion in closed chemical systems (batch reactors). 

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