Reactor performance models

For proper design and simulation of HDT reactors, kinetic and reactor modeling are aspects that need to be deeply studied however, this is not a trivial task due to the numerous physical and chemical processes that occur simultaneously in the reactor phase equilibrium, mass transfer of reactants and products between the gas-liquid-solid phases, diffusion inside the catalyst particle, a complex reaction network, and catalyst deactivation. Ideally, the contribution of all these events must be coupled into a robust reactor performance model. The level of sophistication of the model is generally defined based upon the pursued objectives and prediction capability [4]. 

A detailed literature review on esterification of carboxylic acids with different alcohols has been made. The type of catalysts used, their activity, selectivity, kinetic modeling and reaction engineering aspects have been discussed. A general review of the esterification of carboxylic acid with alcohol in presence of mineral acid or heterogeneous acid catalyst have been presented. Critical analyses of reaction engineering aspects such as external and intraparticle mass transfer effects and reactor performance models have been presented and scope and objective of the present thesis outlined. 

Juraidan, M., Al-Shamali, M., Qabazard, H., Kam, E.K.T. 2006. A refined hydroprocessing multicatalyst deactivation and reactor performance models pilot-plant accelerated test applications. Energy Fuels 20 1354—1364. 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

In using a spreadsheet for process modeling, the engineer usually finds it preferable to use constant physical properties, to express reactor performance as a constant "conversion per pass," and to use constant relative volatiHties for distillation calculations such simplifications do not affect observed trends in parametric studies and permit the user quickly to obtain useful insights into the process being modeled (74,75). 

The predictions checked in the pilot-plant reactor were reasonable. Later, when the production unit was improved and operators learned how to control the large-scale reactor, performance prediction was also very good. The highest recognition came from production personnel, who believed more in the model than in their instruments. When production performance did not agree with model predictions, they started to check their instruments, rather than questioning the model. 

The basic problem of design was solved mathematically before any reliable kinetic model was available. As mentioned at start, the existence of solutions—that is, the integration method for reactor performance calculation—gave the first motivation to generate better experimental kinetic results and the models derived from them. 

Water at room temperature is flowing through a 1.0-in i.d. tubular reactor at Re= 1000. What is the minimum tube length needed for the axial dispersion model to provide a reasonable estimate of reactor performance What is the Peclet number at this minimum tube length Why would anyone build such a reactor ... 

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

In Fig. 1, a comparison can be observed for the prediction by the honeycomb reactor model developed with the parameters directly obtained from the kinetic study over the packed-bed flow reactor [6] and from the extruded honeycomb reactor for the 10 and 100 CPSI honeycomb reactors. The model with both parameters well describes the performance of both reactors although the parameters estimated from the honeycomb reactor more closely predict the experiment data than the parameters estimated from the kinetic study over the packed-bed reactor. The model with the parameters from the packed-bed reactor predicts slightly higher conversion of NO and lower emission of NHj as the reaction temperature decreases. The discrepancy also varies with respect to the reactor space velocity. 

In the following, tiie performance of a UASB reactor with the same size of a pilot plant [7] is evaluated according to the reactor simulation model incorporated with the Monod kinetic paramet for fire hypothetical influait coirqxwiticHi for the three VFA componaits as indicated in Table 2. 

When a number of competing reactions are involved in a process, and/or when the desired product is obtained at an intermediate stage of a reaction, it is important to keep the residence-time distribution in a reactor as narrow as possible. Usually, a broadening of the residence-time distribution results in a decrease in selectivity for the desired product. Hence, in addition to the pressure drop, the width of the residence-time distribution is an important figure characterizing the performance of a reactor. In order to estimate the axial dispersion in the fixed-bed reactor, the model of Doraiswamy and Sharma was used [117]. This model proposes a relationship between the dispersive Peclet number ... 

The cyclohexene hydrogenation is a well-studied process especially in conventional trickle-bed reactors (see original citations in [11,12]) and thus serves well as a model reaction. In particular, flow-pattern maps were derived and kinetics were determined. In addition, mass transfer can be analysed quantitatively for new reactor concepts and processing conditions, as overall mass transfer coefficients were determined and energy dissipations are known. In lieu of benchmarking micro-reactor performance to that of conventional equipment such as trickle-bed reactors, such a knowledge base facilitates proper, reliable and detailed comparison. 

The homogeneously catalyzed oxidation of butyraldehyde to butyric acid is a well-characterized gas/Hquid reaction for which kinetic data are available. It thus serves as a model reaction to evaluate mass transfer and reactor performance in general for new gas/liquid micro reactors to be tested. This reaction was particularly used to validate a reactor model for a micro reactor [9, 10]. 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

As with continuous processes, the heart of a batch chemical process is its reactor. Idealized reactor models were considered in Chapter 5. In an ideal-batch reactor, all fluid elements have the same residence time. There is thus an analogy between ideal-batch reactors and plug-flow reactors. There are four major factors that effect batch reactor performance ... 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop assume that the residence time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used... 

Illustration 11.6 indicates how the longitudinal dispersion model may be used to predict reactor performance. 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

ILLUSTRATION 11.7 USE OF THE CASCADE OF STIRRED TANK REACTORS MODEL TO PREDICT REACTOR PERFORMANCE... 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

The units of rv are moles converted/(volume-time), and rv is identical with the rates employed in homogeneous reactor design. Consequently, the design equations developed earlier for homogeneous reactors can be employed in these terms to obtain estimates of fixed bed reactor performance. Two-dimensional, pseudo homogeneous models can also be developed to allow for radial dispersion of mass and energy. 

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