Reactor problems

The early attempts at NMP of S in emulsion used TEMPO and related nitroxides and needed to be carried out at high temperatures (100-130 °C) necessitating a pressure reactor. Problems with colloidal stability and molecular weight control and limiting conversions were reported.215 217... 

Major reactor problems in batch-mass reactors are ... 

Major Suspension Reactor Problems. The critical problems in defining or optimizing a suspension reactor can be divided into three areas. In approximate order of importance, these are ... 

In a formal sense, Equation (2.38) applies to all batch reactor problems. So does Equation (2.42) combined with Equation (2.40). These equations are perfectly general when the reactor volume is well mixed and the various components are quickly charged. They do not require the assumption of constant reactor volume. If the volume does vary, ancillary, algebraic equations are needed as discussed in Section 2.6.1. The usual case is a thermodynamically imposed volume change. Then, an equation of state is needed to calculate the density. 

None of the above efforts considered depropagation effects in combination with the optimal reactor problem. When a polymerization is carried out at high temperature to reach a fmal monomer concentration which is low, the thermodynamic (depropagation) effects may become more important than the kinetic ones. 

Consider Equations (6-10) that represent the CVD reactor problem. This is a boundary value problem in which the dependent variables are velocities (u,V,W), temperature T, and mass fractions Y. The mathematical software is a stand-alone boundary value solver whose first application was to compute the structure of premixed flames.Subsequently, we have applied it to the simulation of well stirred reactors,and now chemical vapor deposition reactors. The user interface to the mathematical software requires that, given an estimate of the dependent variable vector, the user can return the residuals of the governing equations. That is, for arbitrary values of velocity, temperature, and mass fraction, by how much do the left hand sides of Equations (6-10) differ from zero ... 

For a general introduction to some of the techniques employed to solve difference equations of the types encountered in chemical engineering, consult the text by Lapidus (116). Detailed numerical examples of one method of numerical solution to the two-dimensional reactor problem are contained in the texts of Smith (117) and Jensen and Jeffreys (118). 

The following reactor problems illustrate some process calculations that involve material and/or... 

A transfer function may not be always analytically invertable, but it has nevertheless value in that the moments of an RTD may be derived from it, notably the variance.. One or two of the moments often are adequate characterizations of an RTD curve and enable useful deductions about the behavior of a vessel as a chemical reactor. Problem P5.02.01 covers the basic theory and P5.02.07 is another application. Figure 5.3 is of a simple process flow diagram, individual transfer functions, and the overall transfer function. 

Flow-reactor problems are just as simple as batch-reactor problems. In fact, they are the same mathematical problem even though the reactor configuration and operation are totally different. 

Here we review some of the correlations of convective mass transfer. We will find that many reactors are controlled by mass transfer processes so this topic is essential in describing many chemical reactors. This discussion will necessarily be very brief and qualitative, and we win summarize material that most students have encountered in previous courses in mass transfer. Our goal is to write down some of the simple correlations so we can work examples. The assumptions in and validity of particular expressions should of course be checked if one is interested in serious estimations for particular reactor problems. We will only consider here the mass transfer correlations for gases because for liquids the correlations are more comphcated and cannot be easily generalized. 

Thus far we have considered only two flow patterns the completely mixed reactor and the completely unmixed reactor. This is because only for these flow patterns can we completely ignore the fluid flow configurations in the reactor. In this chapter we will begin to see how reactors that have more complex flow patterns should be treated. We will not attempt to describe the fluid mechanics completely. Rather, we will hint at how one would go about solving more realistic chemical reactor problems and examine the errors we have been making by using the completely mixed and unmixed approximations. 

We have in fact had to make many approximations to obtain even these complicated expressions, and it is evident that numerical solutions to most multiphase chemical reactor problems can only be obtained after considerable computations and approximations. 

If the SCR is placed downstream of an ESP or TSS, the design can take advantage of a cleaner flue gas. This would allow for smaller catalyst volumes using finer pitch catalyst and thus smaller SCR reactors. Problems occur when the ESP or TSS collection efficiency no longer removes the particulates from the flue gas. Not only does the SCR catalyst bed foul, requiring increased run frequency on the soot blowers, the stack opacity will also increase. 

Baron, Manning, and Johnstone (B4) have discussed the experimental aspects of the tubular-reactor problem, and an analysis of the results is made by means of the solution to the differential equations for mass... 

In Section 16.4 the perfectly stirred reactor problem is derived, without considering surface reaction at the channel walls. Reformulate the problem to include the possibility of elementary heterogeneous chemistry at the reactor walls. 

Aurora, simulates zero-dimensional perfectly stirred reactor problems, including heterogeneous chemistry at the walls. 

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. 

Batch processes present challenging control problems due to the time-varying nature of operation. Chylla and Haase [4] present a detailed example of a batch reactor problem in the polymer products industry. This reactor has an overall heat transfer coefficient that decreases from batch to batch due to fouling of the heat transfer surface inside the reactor. Bonvin [5] discusses a number of important topics in batch processing, including safety, product quality, and scale-up. He notes that the frequent repetition of batch runs enables the results from previous runs to be used to optimize the operation of subsequent ones. 

While introducing a heat carrier solves the reactor problem, it unfortunately creates some other concerns. First, we increase the size of the separation section since we have to separate the products from a large amount of heat carrier. Second, we make the plant thermally inefficient by significantly increasing the plant s energy load due to repeated heating and cooling of the heat carrier. To solve the efficiency problem we... 

For practical purposes the concentration distribution inside particles is not needed. For chemical reactor problems the overall conversion rate (per unit reactor volume or per unit of catalyst mass) and its dependence on conditions in the reactor are of interest. These questions are considered in detail in Chapters 6 and 7. 

Solution of a reactor problem in the mass transfer limit requires an estimation of the appropriate mass transfer coefficient. Fortunately, mass transfer correlations have been developed to aid the determination of mass transfer coefficients. For example, the Sherwood number, Sh, relates the mass transfer coefficient of a species A to its diffusivity and the radius of a catalyst particle, Rp ... 

Three examples are given here to demonstrate various capabilities of DDAPLUS. In the first example, DDAPLUS is used to solve a system of ordinary differential equations for the concentrations in an isothermal batch reactor.In the second example, the same state equations are to be integrated to a given time limit, or until one of the state variables reaches a given limit. The last example demonstrates the use of DDAPLUS to solve a differential-algebraic reactor problem with constraints of electroneutrality and ionization equilibria. 

There are three variables that can be used to formulate and solve semibatch reactor problems the concentration, Cj, the number of moles, iVj, and the conversion, X. 

Writing the Semibatcb Reactor Equations in Terms of the Number of Moles. We can also solve ffimibatch reactor problems by leaving the mole bal ance equations in terms of the number of moles of each species (i.e.,... 

By using these formulas and the standard pressure drop algorithm, one can solve a variety of spherical reactor problems. Note that Equations (4-38) and... 

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