SCOTT FOGL, ER Arne in Catherine Vennema, profesorica kemijskega inženiringa Univerza v Michiganu, Ann Arbor. Ghosh, Prentice-Hall of India Private Limited, M-97, Connaught Circus, New Delhi-110001 in Printed by Syfldicate Binders, A-20, Hosiery Complex, Noida, Phase-ll Extension, Noida-201305 (N.C.R. Delhi).
9 UNSTEADY-STATE NONISOTHERMAL REACTOR DESIGN
10 CATALYSIS AND CATALYTIC REACTORS
Questions and Problems 668 Critical Journal Problems 682 CD-ROM Material 683 Supplementary Reading 684 10.8 Reaction Engineering in Microelectronics.
12 DIFFUSION AND REACTION IN POROUS CATALYSTS
14 MODELS FOR N(0NIDEAL REACTORS
Appendix B
Appendix C
NUMERICAL TECHNIQUES
IDEAL GAS CONSTANT AND CONVERSION FACTORS
927 THERMODYNAMIC RELATIONSHIPS INVOLVING
MEASUREMENT OF SLOPES ON SEMILOG PAPER 935
MOLECULAR DYNAMICS OF CHEMICAL REACTIONS 941
HOW TO USE THE CD-ROM
Appendix J
INDEX
The Goals
The algorithms presented in the reactor design text provide a framework through which one can develop confidence through reasoning rather than memorization. Tips for working with the California exam papers can be found in the Summaries and Problem Solving Thoughts on the CD-ROM.
The Applications
Chapter 4
- The Web
- What’s New
- Continuous-Flow Reactors
For example, the algebraic form of the rate law -r, for the reaction Definition of rJ. The reactor is perfectly mixed so that the concentration of the reacting species is spatially uniform.
Conversion 2
- Definition of Conversion
If NAO is the number of moles of A initially, then the total number of moles of A that have reacted after time t is [NAOX]. 2 2 Design Equations 35 The number of moles of A in the reactor after a conversion X has been achieved is.
Applications of the Design Equstions for Continuous-Flow Reactors
The rate of disappearance of A, -rA is almost always a function of the concentration of the various species present. Continuous Flow Reactors 41 each of the concentrations can be expressed as a function of the conversion X (see Chapter 3); consequently - r A can be expressed as a function of X. For this dependence, a plot of the reciprocal of the reaction rate ( - l / r A ) as a function of conversion gives a curve.
We will use this figure to illustrate how to size each of the reactors in a number of different reactor sequences. Towards the end of the reaction, when the concentration of the reactants is small (that is, the conversion is large), the reaction rate will be small. Calculate the reactor volume required to achieve 80% conversion in a PFR. (a) First use one of the integration formulas from Appendix A.4 to determine the PFR reactor volume.
We know that as we move down the reactor and more and more of the reactant is consumed, the concentration of reactant decreases, as does the rate of disappearance of A.
Conversion X
Reactors in Series
Many times the reactors are connected in series so that the output stream of one reactor is the feed stream for another reactor. That is, the conversion X is the total number of moles of A that have reacted up to that point per mole of A fed to the first reactor. However, this definition can only be used under the condition that no side streams are withdrawn and the feed stream is only to the first reactor in the series.
To demonstrate these ideas, let's look at three different schemes of reactors in series: two CSTRs, two PFRs, and a PFR connected to a CSTR. We will now use F A 0 calculated in Example 2-1 along with Figure 2-1 to size eactors for the three reactor schemes. For the first reactor in which the rate of disappearance of A -rAl at conversion is XI, the volume required to achieve the conversion is X.
In the second rfactor, the rate of disappearance of A, -rA2, is evaluated and the conversion is that of the output current of reactor 2, X 2.
CSTR 1
- If the rate of disappearance is given as a function of conversion, the following graphical techniques can be used to size a CSTR and a
- Basic Definitions
The relationship can be expressed directly from the stoichiometry of the reaction. the volumetric flow rate entering the reactor:. For many reactions it can be written as the product of a reaction rate constant k and a function of the concentrations (activi). The reaction rate constant k is not really a constant, but is only independent of the concentrations of the reaction rate constant k. species involved in the reaction.
Molecularity is the number of atoms, ions, or molecules that participate (collide) in the rate-limiting step of a reaction. We want to record the rate of disappearance of methyl bromide, - rMB, in terms of the corresponding concentrations. At a temperature of about 500°C, the reaction order is threefold with respect to acetaldehyde.
Consequently, to determine the reaction rate as a function of the conversion of X, we need to know the concentrations of the reactants as a function of the conversion. The form of the stoichiometric table for a continuous flow system (see Figure 3-2) is almost the same as for a batch system (Table 3-2), except that we replace N, with 4o and N, with < (Table 3-3). However, in gas-phase reactions, the volumetric flow rate most often changes during the course of the reaction due to a change in the total number of moles or temperature or pressure.
Also consult the cumnt chemistry literature for the appropriate algebraic form of the rate law for a given reaction. For example, check the Journal of Physical
- Design Structure for Isothermal Reactors
In this chapter we bring together all the material in the previous three chapters to arrive at a logical structure for the design of different types of reactors. We begin by studying a liquid phase batch reactor to determine the specific reaction rate constant needed for the design of a CSTR. After illustrating the design of a CSTR from batch reaction rate data, we carry out the design of a tubular reactor for a gas-phase pyrolysis reaction.
The following procedure is presented as a path one should follow in the design of isothermal (and in some cases non-isothermal) reactors. By combining the information in levels 4 and 5, one can express the response rate as a function of conversion and arrive at level 6. The design equation is then evaluated in the appropriate manner (Le., analytically using a table of integrals, or numerically using an ODE solver).
In the 2nd step we select the rate law (eiztre'e), and in the 3rd step we determine whether the reaction is a gas or liquid phase (cheese or dessen).
Analytically (Ap- 2) Graphically (Ch. 2)
- Scale-up of Liquid-Phase Batch
- Batch Operation
In sbme cases, the reaction time calculated from equation (4-5) may be only a small fraction of the total cycle time, ie. Since the reaction will proceed isothermally, the specific reaction rate will only need to be determined at the reaction temperature of the CSTR. Since water is usually present in excess, its concentration can be considered constant during the course of the reaction.
The Damkohler number is the ratio of the reaction rate A to the convective transport rate A at the reactor inlet. The conversion for these n steel reactors in series would be Conversion as a. a function of the number of tanks in series. -1 1) A plot of the conversion as a function of the number of reactors in series for a first-order reaction is shown in Figure 4-4 for various values of Damkohler.
For a second-order liquid-phase reaction carried out in a CSTR, the result is a combination of a rate law and a design equation.
Design equation
- Tubular Reactors
Assuming no dispersion and no radial gradients in temperature, velocity, or concentration, we can model the flow in the reactor as plug flow. In the absence of pressure drop or heat exchange the integral form of the JEow outlet design equation is used. A plot of conversion along the length of the reactor is shown for four different reactions and values of E in Figure 4-7 to illustrate volume effects.
We see from this figure that for identical rate law parameters, the reaction with a decrease in total mol (i.e. c = -0.5) pi has the highest conversion for a fixed reactor length. Similarly, reactants that produce an increase in total moles upon reaction (e.g., E = 2) will spend less time in the reactor than reactants of reactions for which E is zero or negative. Ethylene ranks fourth in the United States in terms of total pounds of chemicals produced each year, and is the largest organic chemical produced each year.
Sixty-five percent of the ethylene produced is used in the manufacture of manufactured plastics, 20%.
Parameter evaiuation
- Pressure Drop in Reactors
- Flow Through a Packed Bed
As a result, the effect of pressure drop on the reaction rate can be completely neglected when sizing liquid-phase chemical reactors. However, in gas-phase reactions, the concentration of reactants is proportional to the overall pressure, and as a result, proper consideration of the effects of pressure drop on the reaction system can in many cases be a key factor in the success or failure of reactor operation. We now focus on considering the pressure drop in the power law.
Note from Equation (4-20) that the larger the pressure drop @e., the smaller P) due to frictional losses, the smaller the reaction rate. We now need to relate the pressure drop to the catalyst weight to determine the conversion as a function of catalyst weight. The e q u a ~ o n most commonly used to calculate pressure drop in a packed porous bed is the Ergun equation:2.
We now proceed (Example 4-6) by combining pressure drop with packed bed reaction for the case where we will include EX 4 1 in the Ergun equation but not in the velocity law to obtain an analytical solution.
Rate law
Rather than deriving everything starting with the etry, and pressure drop equations, we will use the 4-6 Combining Equationc (E4 6.1) and (E4-6.8) g I . The reason for this is that the numerical solution accounts for the fact that the pressure drop will be less because E is negative. For gas-phase reactions with orders greater than zero, this decrease in pressure will cause the reaction rate to be less than in the case of no pressure drop.
One type of reactor that minimizes pressure drop and is also inexpensive to manufacture is the spherical reactor shown in Figure 4-8. Since the cross-sectional area of the reactor near the inlet and outlet is small, the presence of catalyst there would cause a significant pressure drop. Various spherical reactor problems can be solved using these formulas and the standard pressure drop algorithm.
Compare the pressure drop and conversion when this reaction is performed in a tubular packed bed of 2.4 m in diameter and 25 m in length with that of a spherical packed bed of 6 m in diameter.
