Ideal reactors defined

The above-mentioned space-time yields were referred solely to the reaction volume, i.e. the micro channel volume. When defining this quantity via an idealized reactor geometry, taking into accoimt the construction material as well, natarally the difference in space-time yield of the micro reactors from the laboratory bubble column becomes smaller. Still, the performance of the micro reactors is more than one order of magnitude better [38], The space-time yields for the micro reactors defined in this way ranged from about 200 to 1100 mol monofluorinated product... 

The three ideal reactors form the building blocks for analysis of laboratory and commercial catalytic reactors. In practice, an actual flow reactor may be more complex than a CSTR or PFR. Such a reactor may be described by a residence time distribution function F(t) that gives the probability that a given fluid element has resided in the reactor for a time longer than t. The reactor is then defined further by specifying the origin of the observed residence time distribution function (e.g., axial dispersion in a tubular reactor or incomplete mixing in a tank reactor). 

The model defines each of these terms. Solving the set of equations provides outputs that can be validated against experimental observations and then used for predictive purposes. Mathematical models for ideal reactors that are generally useful in estimating reactor performance will be presented. Additional information on these reactors is available also in Sec. 7. 

Generally, this implies the use of ideal reactors of the plug flow or well stirred tank type with well defined residence times and residence time distributions under isothermal conditions (with some exceptions, as will be indicated). By-passing part of the catalyst by channeling in a packed bed or uneven flow distributions must be avoided. In three-phase systems (gas/liquid/solid), the even distribution of both fluid phases over the catalyst is crucial. 

In previous chapters treating ideal reactors, a parameter frequently used was the space-time or average residence time x, which was defined as being equal to V/v. It will be shown that no matter what RTD exists for a particular reactor, ideal or nonideal, this nominal holding time, x, is equal to the mean residence time.,r . 

Link types are defined to relate certain entity types of one document to entity types of another. Arbitrary many-to-many relationships are supported. For instance, it can be expressed that a combination of ideal reactor models (CSTR, PFR) and interconnecting streams as well as the aggregated connectors within a SimulationSpec document correspond to a single reactor and its ports represented in a PFD document. Link types are used for two purposes First, they provide a formal notation for a part of the organizational knowledge. Second, they constrain link templates that are defined in the next model. 

Link templates define fine-grained corresponding patterns in different documents that can be related to each other. Each link template is an instance of a link type. For example, a SimulationSpec pattern consisting of a cascade of two ideal reactors connected by a stream could be related to a PFD pattern consisting of a single reactor. This link template would be an instance of the link type used as example above. Link templates are not type but instance patterns. 

The reactor in which chemical reactions lake place is fhe mosl imporlanl piece of equipmenl in each chemical planl. A variety of reactors are used in induslry, bul all of Ihem can be assigned to cerlain basic types or a combination of fhese ideal reactors [53] (1) bafch slirred-lank reactor, (2) continuous slirred-lank reactor, and (3) lubular reactor. The ideal slirred-lank bafch reactor is characterized by complete mixing, while in the ideal tubular reactor, plug flow is assumed. In contrast to the stirred-tank batch reactor with well-defined residence time, the continuous stirred-tank reactor has a very broad residence-time distribution. In... 

Well-defined limits of macro- and micromixing can be obtained in a number of instances, and these serve to define corresponding ideal reactor types. Deviations of mixing from these limits are sometimes termed nonideal flows. Since it is difficult to define a measure for quantities such as the degree of micromixing or, indeed, to make measurements on the hydrodynamic state of the internals of a reactor system, extensive use has been made of models that describe the observable behavior in terms of external measurements. As in any other kind of modeling, these models may not be... 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

The characterization of bioreactors is not limited to the standardization of stirred tank type reactors (Dechema, 1982) It also includes ideal reactors as model types in a wider framework. The problem of defining a perfect bioreactor, including tests of pseudohomogeneity (Moser, 1983a) will be discussed later. 

Fluid mixing patterns, seen in real reactors, which are different from the mixing patterns defined for ideal reactors, are called non-ideal mixing patterns or are simply known as non-idealities. Any deviation from the ideal is consider as non-ideal. Some of the commonly observed non-ideal mixing patterns are discussed here. 

Non-ideality in a homogeneous reactor refers to any kind of deviation from the fluid mixing pattern defined for ideal reactors (ideal CSTR and ideal PFR). In reality, all the reactors are non-ideal. In order to evaluate the performance of any reactor (i.e. extent of conversion achieved in a reactor), it is necessary to diagnose the non-ideality in the reactor. 

Equations 3.315 and 3.316 define the lower and upper limits, respectively, on the fractional conversion x, achievable in a non-ideal reactor represented by tanks in series model, that is, the fractional conversion for a first-order reaction in a non-ideal reactor represented by tanks in series model is always higher than the conversion in an ideal CSTR, and lower than the conversion in an ideal PFR with space time x being the same in all the reactors. 

One of the main goals of electrochemical reactor design is to minimize the overpotential for the reactor. The cell overpotential, which expresses the deviation from ideality, is defined according to the thermodynamic convention as... 

Nonidealities defined with respect to the ideal reactors... 

The origin of Langmuir-Hinshelwood/Michaelis-Menten rate equations will be explored in Chapter 5. In the meanwhile, we will use this form of rate equation in Chapter 4, when we tackle some problems in sizing and analysis of ideal reactors. The next chapter is devoted to defining an ideal reactor and to providing the tools that are required for their sizing and analysis. 

Batch reactors often are used to develop continuous processes because of their suitabiUty and convenient use in laboratory experimentation. Industrial practice generally favors processing continuously rather than in single batches, because overall investment and operating costs usually are less. Data obtained in batch reactors, except for very rapid reactions, can be well defined and used to predict performance of larger scale, continuous-flow reactors. Almost all batch reactors are well stirred thus, ideally, compositions are uniform throughout and residence times of all contained reactants are constant. 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

The terms space time and space velocity are antiques of petroleum refining, but have some utility in this example. The space time is defined as F/2, , which is what t would be if the fluid remained at its inlet density. The space time in a tubular reactor with constant cross section is [L/m, ]. The space velocity is the inverse of the space time. The mean residence time, F, is VpjiQp) where p is the average density and pQ is a constant (because the mass flow is constant) that can be evaluated at any point in the reactor. The mean residence time ranges from the space time to two-thirds the space time in a gas-phase tubular reactor when the gas obeys the ideal gas law. 

Worz et al. stress a gain in reaction selectivity as one main chemical benefits of micro-reactor operation [110] (see also [5]). They define criteria that allow one to select particularly suitable reactions for this - fast, exothermic (endothermic), complex and especially multi-phase. They even state that by reaching regimes so far not accessible, maximum selectivity can be obtained [110], Although not explicitly said, maximum refers to the intrinsic possibilities provided by the elemental reactions of a process under conditions defined as ideal this means exhibiting isothermicity and high mass transport. 

Micro reactors are continuous-flow devices consuming small reaction volumes and allowing defined setting of reaction parameters and fast changes. Hence they are ideal tools for process screening and optimization studies to develop solution-based chemistries. 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

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