As a prologue to the future, our profession is evolving to one of molecular chemical engineering. For chemical reaction engineers, computational chemistry and molecular modeling could well be our future.
Thermodynamic properties of molecular species that are used in reactor design problems can be readily estimated from thermodynamic data tabulated in standard reference sources such as Perry’s Handbook or the JANAF Tables. Thermochemical properties of molecular species not tabulated can usually be estimated using group contribution methods. Estimation of activation energies is, however, much more difficult owing to the lack of reliable information on transition-state structures, and the data required to carry out these calculations is not readily available.
Recent advances in computational chemistry and the advent of powerful, easy-to-use software tools have made it possible to estimate important reaction-rate quantities (such as activation energy) with sufficient accuracy to permit incorporation of these new methods into the reactor design process. Computational chemistry programs are based on theories and equations from quantum mechanics, which until recently, could only be solved for the simplest systems such as the hydrogen atom. With the advent of inexpensive high-speed desktop computers, the use of these programs in both engineering research and industrial practice is increasing rapidly. Molecular properties such as bond length, bond angle, net dipole moment, and electrostatic charge distribution can be calculated. Additionally, reaction energetics can be accurately determined by using quantum chemistry to estimate heats of formation of reactants, products, and also for transition-state structures.
Examples of commercially available computational chemistry programs include Spartan, developed by Wavefunction, Inc. (www.wavefun.com), and Cerius2 from Molecular Simulations, Inc. (www.accelrys.com). The Web module in Chapter 3 on molecular reaction engineering (http://www.umich.edu/~elements/6e/web_mod/quantum/index.htm) gives an example of what we can expect in the future.
There are many ways of differentiating numerical and graphical data (cf. Chapter 7). We shall confine our discussions to the technique of equal-area differentiation. In the procedure delineated here, we want to find the derivative of y with respect to x.
This method finds use in Chapter 5.
Tabulate the (yi, xi) observations as shown in Table A-1.
For each interval, calculate Δxn = xn – xn-1 and Δyn – yn – yn-1.TABLE A-1 FINDING DIFFERENTIALS FROM DISCRETE DATAxiyiΔxΔyx1y1x2 – x1y2 – y1x2y2x3 – x2y3 – y2x3y3x4y4and so on.
Calculate Δyn/Δxn as an estimate of the average slope in an interval xn-1 to xn.
Plot these values as a histogram versus xi. The value between x2 and x3, for example, is (y3 – y2)/(x3 – x2). Refer to Figure A-1.Figure A-1 Equal-area differentiation.
Next, draw in the smooth curve that best approximates the area under the histogram. That is, attempt in each interval to balance areas such as those labeled A and B, but when this approximation is not possible, balance out over several intervals (as for the areas labeled C and D). From our definitions of Δx and Δy, we know thatThe equal-area method attempts to estimate dy/dx so thatthat is, so that the area under Δy/Δx is the same as that under dy/dx, everywhere possible.
Read estimates of dy/dx from this curve at the data points x1, x2, … and complete the table.
An example illustrating the technique is given on the CRE Web site, Appendix A.
Differentiation is, at best, less accurate than integration. This method also clearly indicates bad data and allows for compensation of such data. Differentiation is only valid, however, when the data are presumed to differentiate smoothly, as in rate-data analysis and the interpretation of transient diffusion data.
Methods of solving differential equations of the type
β
can be found in such texts as Applied Differential Equations by M. R. Spiegel (Upper Saddle River, NJ: Pearson, 1958, Chapter 4; a great book even though it’s old) or in Differential Equations by F. Ayres (New York: Schaum Outline Series, McGraw-Hill, 1952). Solutions of this type are required in Chapter 15. One method of solution is to determine the characteristic roots of
which are
The solution to the differential equation is
where A1 and B1 are arbitrary constants of integration. It can be verified that Equation (A-18) can be arranged in the form
Equation (A-19) is the more useful form of the solution when it comes to evaluating the constants A and B because sinh(0) = 0 and cosh(0) = 1.0.
A.4 Numerical Evaluation of Integrals
In this section, we discuss techniques for numerically evaluating integrals for solving first-order differential equations.
Trapezoidal rule (two-point) (Figure A-2). This method is one of the simplest and most approximate, as it uses the integrand evaluated at the limits of integration to evaluate the integralwhen h = X1 = X0.Figure A-2 Trapezoidal rule illustration.
Simpson’s one-third rule (three-point) (Figure A-3). A more accurate evaluation of the integral can be found with the application of Simpson’s rule:whereMethods to solvein Chapters 2, 4, 5, 12, and in Chapter 17Figure A-3 Simpson’s three-point rule illustration.
Simpson’s three-eighths rule (four-point) (Figure A-4). An improved version of Simpson’s one-third rule can be made by applying Simpson’s three-eighths rule:whereFigure A-4 Simpson’s four-point rule illustration.
Five-point quadrature formula.where
For N = 1 points, where (N/3) is an integerwhere
For N = 1 points, where N is evenwhere
These formulas are useful in illustrating how the reaction engineering integrals and coupled ODEs (ordinary differential equation(s)) can be solved, and also when there is an ODE solver power failure or some other malfunction.
Be sure to view the actual photographs of industrial reactors on the CRE Web site so you will know them when you run into them. There are also links to view reactors on different Web sites. The CRE Web site also includes a portion of the Visual Encyclopedia of Equipment, encyclopedia.che.engin.umich.edu, “Chemical Reactors” developed by Dr. Susan Montgomery and her students at the University of Michigan. Also see Professional Reference Shelf on the CRE Web site for “Reactors for Liquid-Phase and Gas-Phase Reactions,” along with photos of industrial reactors, and Expanded Material on the CRE Web site.2
2Chem. Eng., 63(10), 211 (1956). See also AIChE Modular Instruction Series E, 5 (1984).
In this chapter, and on the CRE Web site, we’ve introduced each of the major types of industrial reactors: batch, stirred tank, tubular, and fixed bed (packed bed). Many variations and modifications of these commercial reactors (e.g., semibatch, fluidized bed) are in current use and these reactors will be discussed in Chapters 6 and 10, respectively. For further elaboration, refer to the detailed discussion of industrial reactors given by Walas.3
3 S. M. Walas, Reaction Kinetics for Chemical Engineers, New York: McGraw-Hill, 1959, Chap. 11.
The CRE Web site describes industrial reactors, along with typical feed and operating conditions. In addition, two solved example problems for Chapter 1 can be found on the CRE Web site, http://www.umich.edu/~elements/6e.
1.6 And Now… A Word from Our Sponsor–Safety 1 (AWFOS–S1 Safety)
A note to students: In this sixth edition of Elements of Chemical Reaction Engineering, I am including a section at the end of each chapter to bring a greater awareness to process safety. A critical aspect of process safety is “anticipating” what could go wrong in a chemical process and ensuring it won’t go wrong. Equipment and processes involving exothermic chemical reactions are some of the most at risk in a chemical plant. Consequently, each chapter will end with a segment “And Now… A Word From Our Sponsor–Safety” (AWFOS–S). In addition, to highlight process safety across the chemical engineering curriculum, a Web site (http://umich.edu/~safeche/) has been developed that features a safety module specific to every core chemical engineering lecture course plus lab safety. In this chapter, we define process safety along with a very brief discussion on why it is important to study process safety.
1.6.1 What Is Chemical Process Safety?
Chemical process safety is a blend of engineering and management practices focused on preventing accidents, namely explosions, fires, and toxic releases that result in loss of life and property.
Industrial disasters such as UCIL Bhopal, T2 Laboratories, BP Texas City, and Flixborough have collectively killed and injured thousands of people and caused billions of dollars in damage to chemical plants and nearby communities. Accidents such as these occur because chemical engineering processes are some of the most potentially dangerous due to extreme operating conditions and the use of explosive, reactive, and flammable materials. What surprises people is that most of these chemical engineering accidents, such as those listed in the Chemical Safety Board Videos on the companion Web site (http://umich.edu/~safeche/) were preventable. They were the result of poor engineering decisions, made by people who lacked fundamental understanding of basic chemical engineering concepts and chemical engineering safety. Thus, knowing the fundamentals of chemical engineering and process safety may save your life and the lives of innocent people, and prevent the loss of millions of dollars of material and equipment.
Engineers have an ethical and professional obligation to work only in areas for which they are competent and qualified. The best way to prevent future industrial disasters is to understand how to effectively and safely design, operate, and troubleshoot chemical processes. To prepare a prevention plan, we must take the time and effort to understand chemical processes and chemical process safety. To help achieve this understanding, the last section of every chapter has a tutorial, AWFOS–S, that can help you prevent accidents.
A comparison of process safety and personal safety is very succinctly given on the Web site (http://www.energysafetycanada.com/files/pdf/Personal_vs_Process_Safety_v3.pdf).
Closure. The goal of this text is to weave the fundamentals of chemical reaction engineering into a structure or algorithm that is easy to use and apply to a variety of problems. We have just finished the first building block of this algorithm: mole balances.
This algorithm and its corresponding building blocks will be developed and discussed in the following chapters:
With this algorithm, one can approach and solve chemical reaction engineering problems through logic rather than memorization.
A Word of Caution: The falling CRE Tower. As we proceed through the next five chapters, we will see how these building blocks form a tower. Now, if one cuts corners when studying this material, the building blocks become cylinders and as a result the tower becomes unstable and all of the understanding of CRE falls apart. See http://www.umich.edu/~elements/6e/01chap/assets/player/KeynoteDHTMLPlayer.html#3.
Summary
Each chapter summary gives the key points of the chapter that need to be remembered and carried into succeeding chapters.
A mole balance on species j, which enters, leaves, reacts, and accumulates in a system volume V, isIf, and only if, the contents of the reactor are well mixed will the mole balance (Equation (S1-1)) on species A give
The kinetic rate law for rj is
The rate of formation of species j per unit volume (e.g., mol/s·dm3)
Solely a function of the properties of reacting materials and reaction conditions (e.g., concentration [activities], temperature, pressure, catalyst, or solvent [if any]) and does not depend on reactor type
An intensive quantity (i.e., it does not depend on the total amount)
An algebraic equation, not a differential equation (e.g., −rA = kCA or )
For homogeneous catalytic systems, typical units of –rj may be gram moles per second per liter; for heterogeneous systems, typical units of may be gram moles per second per gram of catalyst. By convention, –rA is the rate of disappearance of species A and rA is the rate of formation of species A.
Mole balances on species A in four common reactors are shown in Table S1-1.TABLE S1-1 SUMMARY OF REACTOR MOLE BALANCES ReactorCommentMole Balance Differential FormAlgebraic FormIntegral FormBRNo spatial variationsCSTRNo spatial variations, steady state——PFRSteady statePBRSteady stateFluidized CSTRSteady state——
Photograph by Radoslaw Lecyk/Shutterstock (http://www.umich.edu/~elements/6e/web_mod/la_basin/index.htm) Living Example Problem: http://www.umich.edu/~elements/6e/01chap/live.html
Interactive Computer Games (http://www.umich.edu/~elements/6e/icm/index.html) A. Quiz Show I (http://www.umich.edu/~elements/6e/icm/kinchal1.html)
This game could help prepare you for the AIChE student chapter Jeopardy Competition held each year at the Annual AIChE meeting.
Questions, Simulations, and Problems
I wish I had an answer for that, because I’m getting tired of answering that question.
—Yogi Berra, New York Yankees Sports Illustrated, June 11, 1984
The subscript to each of the problem numbers indicates the level of difficulty, that is, A, least difficult; B, moderate difficulty; C, fairly difficult; D, (double black diamond), most difficult. A = • B = ▪ C = ♦ D = ♦♦ For example, P1-5B means “1” is the Chapter number, “5” is the problem number, “B” is the problem difficulty, in this case B means moderate difficulty.
Before solving the problems, state or sketch qualitatively the expected results or trends.
Questions
Q1-1AQBRQuestions Before Reading. Research has shown (J. Exp. Psychol. Learn. Mem. Cogn., 40, 106–114 (2014)) that if you ask a question of the material before reading the material you will have greater retention. Consequently, the first question of every chapter will have such a question on that chapter’s material. For Chapter 1, the question is “Is the generation term, G, the only term in the mole balance that varies for each type of reactor?”
Q1-2A Go to Chapter 1 Evaluation on the Web site. Click on i>Clicker Questions (http://www.umich.edu/~elements/6e/01chap/iclicker_ch1_q1.html) and view at least five i>clicker questions. Choose one that could be used as is, or a variation thereof, to be included on the next exam. You also could consider the opposite case: explaining why the question should not be on the next exam. In either case, explain your reasoning.
The first step to knowledge is to know that we are ignorant.
—Socrates (470–399 B.C.)
The Wide, Wild World of Chemical Reaction Engineering
Chemical kinetics is the study of chemical reaction rates and reaction mechanisms. The study of chemical reaction engineering (CRE) combines the study of chemical kinetics with the reactors in which the reactions occur. Chemical kinetics and reactor design are at the heart of producing almost all industrial chemicals, such as the manufacture of phthalic anhydride shown in Figure 1-1. It is primarily a knowledge of chemical kinetics and reactor design that distinguishes the chemical engineer from other engineers. The selection of a reaction system that operates in the safest and most efficient manner can be the key to the economic success or failure of a chemical plant. For example, if a reaction system produces a large amount of undesirable product, subsequent purification and separation of the desired product could make the entire process economically unfeasible.
How is a chemical engineer different from other engineers?
Figure 1-1 Manufacture of phthalic anhydride.
The chemical reaction engineering (CRE) principles learned here can also be applied in many areas, such as waste water treatment, microelectronics, nanoparticles fabrication, and pharmacokinetics of living systems, in addition to the more traditional areas of the manufacture of chemicals and pharmaceuticals. Some of the examples that illustrate the wide application of CRE principles in this book are shown in Figure 1-2. These examples, which can be found either in the text or as Web modules (www.umich.edu/~elements/6e/index.html), include modeling smog in the Los Angeles (L.A.) basin (Chapter 1 Web module), the digestive system of a hippopotamus (Chapter 2 Web module), molecular CRE (Chapter 3 Web module), use of wetlands to degrade toxic chemicals (Chapter 6 on the CRE Web site); pharmacokinetics of cobra bites (Chapter 8 Web module); free-radical scavengers used in the design of motor oils (Chapter 9); enzyme kinetics (Chapter 9) and drug delivery pharmacokinetics (Chapter 9 on the CRE Web site). Also shown in Figure 1-2 are the manufacture of ethylene glycol (antifreeze), where three of the most common types of industrial reactors are used (Chapters 5 and 6). Other examples shown are heat effects, runaway reactions, and plant safety (Chapters 11–13); and increasing the octane number of gasoline and the manufacture of computer chips (Chapter 10).
Figure 1-2 The wide world of CRE applications.
Overview. This chapter develops the first building block of chemical reaction engineering, mole balances, which will be used continually throughout the text. After completing this chapter, you will be able to:
Describe and define the rate of reaction
Derive the general mole balance equation
Apply the general mole balance equation to the four most common types of industrial reactors
Before entering into discussions of the conditions that affect chemical reaction rates mechanisms and reactor design, it is necessary to account for the various chemical species entering, leaving, reacting, and accumulating in a system. This accounting process is achieved through overall mole balances on individual species in the reacting system. In this chapter, we develop a general mole balance that can be applied to any species (usually a chemical compound) entering, leaving, reacting, and accumulating within the reaction system volume. After defining the rate of reaction, –rA, we show how the general mole balance equation (GMBE) may be used to develop a preliminary form of the design equations of the most common industrial reactors (http://encyclopedia.che.engin.umich.edu/Pages/Reactors/menu.html).
Batch Reactor (BR)
Continuous-Stirred Tank Reactor (CSTR)
Plug-Flow Reactor (PFR)
Packed-Bed Reactor (PBR)
In developing these equations, the assumptions pertaining to the modeling of each type of reactor are delineated. Finally, a brief summary and series of short review questions and problems are given at the end of the chapter.
1.1 The Rate of Reaction, –rA
Identify
– Kind
– Number
– Configuration
The rate of reaction tells us how fast the number of moles of one chemical species are being consumed to form another chemical species. The term chemical species refers to any chemical component or element with a given identity. The identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms. For example, the species para-xylene is made up of a
fixed number of specific atoms in a definite molecular arrangement or configuration. The structure shown illustrates the kind, number, and configuration of atoms on a molecular level. Even though two chemical compounds have exactly the same kind and number of atoms of each element, they could still be different species because of different configurations. For example, 2-butene has four carbon atoms and eight hydrogen atoms; however, the atoms in this compound can form two different arrangements.
As a consequence of the different configurations, these two isomers display different chemical and physical properties. Therefore, we consider them as two different species, even though each has the same number of atoms of each element.
When has a chemical reaction taken place?
We say that a chemical reaction has taken place when a detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms. In this classical approach to chemical change, it is assumed that the total mass is neither created nor destroyed when a chemical reaction occurs. The mass referred to is the total collective mass of all the different species in the system. However, when considering the individual species involved in a particular reaction, we do speak of the rate of disappearance of mass of a particular species. The rate of disappearance of a species, say species A, is the number of A molecules that lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reaction. In order for a particular species to “appear” in the system, some prescribed fraction of another species must lose its chemical identity.
Definition of Rate of Reaction
There are three basic ways a species may lose its chemical identity: decomposition, combination, and isomerization. In decomposition, the molecule loses its identity by being broken down into smaller molecules, atoms, or atom fragments. For example, if benzene and propylene are formed from a cumene molecule,
A species can lose its identity by
Decomposition
Combination
Isomerization
the cumene molecule has lost its identity (i.e., disappeared) by breaking its bonds to form these molecules. A second way that a molecule may lose its chemical identity is through combination with another molecule or atom. In the above reaction, the propylene molecule would lose its chemical identity if the reaction were carried out in the reverse direction, so that it combined with benzene to form cumene. The third way a species may lose its chemical identity is through isomerization, such as the reaction
Here, although the molecule neither adds other molecules to itself nor breaks into smaller molecules, it still loses its identity through a change in configuration.
To summarize this point, we say that a given number of molecules (i.e., moles) of a particular chemical species have reacted or disappeared when the molecules have lost their chemical identity.
The rate at which a given chemical reaction proceeds can be expressed in different ways by referring it to different chemical species in the reaction. To illustrate, consider the reaction of chlorobenzene with chloral in the presence of fuming sulfuric acid to produce the banned insecticide DDT (dichlorodiphenyl trichloroethane).
CCl3CHO + 2C6H5Cl → (C6H4Cl)2CHCCl3 + H2O
Letting the symbol A represent chloral, B be chlorobenzene, C be DDT, and D be H2O, we obtain
A + 2B → C + D
What is –rA?
The rate of reaction, –rA, is the number of moles of A (e.g., chloral) reacting (disappearing) per unit time per unit volume (mol/dm3·s).
The numerical value of the rate of disappearance of reactant A, –rA, is a positive number.
Example 1–1 Rates of Disappearance and Formation
Chloral is being consumed at a rate of 10 moles per second per m3 when reacting with chlorobenzene to form DDT and water in the reaction described above. In symbol form, the reaction is written as
A + 2B → C + D
Write the rates of disappearance and formation (i.e., generation; mol/m3·s) for each species in this reaction when the rate of reaction of chloral [A] (–rA) is 10 mol/m3·s.
Rate of disappearance of A = –rA = 10 mol/m3·sRate of formation of A = rA = –10 mol/m3·s
(b) Chlorobenzene[B]:
For every mole of chloral that disappears, two moles of chlorobenzene [B] also disappear.Rate of disappearance of B = –rB = –2rA = 20 mol/m3·sRate of formation of B = rB = –20 mol/m3·s
(c) DDT[C]:
For every mole of chloral that disappears, one mole of DDT [C] appears. rC = –rARate of disappearance of C = –rC = –10 mol/m3·sRate of formation of C = rC = –rA = –(–10 mol/m3·s) = 10 mol/m3·s
(d) Water[D]:
Same relationship to chloral as the relationship to DDTRate of formation of D = rD = 10 mol/m3·sRate of disappearance of D = –rD = –10 mol/m3·s
Analysis: The purpose of this example is to better understand the convention for the rate of reaction. The symbol rj is the rate of formation (generation) of species j. If species j is a reactant, the numerical value of rj will be a negative number. If species j is a product, then rj will be a positive number. The rate of reaction, –rA, is the rate of disappearance of reactant A and must be a positive number. A mnemonic relationship to help remember how to obtain relative rates of reaction of A to B, and so on, is given by Equation (3-1) on page 77.
In Equation (3-1) in Chapter 3, we will delineate the prescribed relationship between the rate of formation of one species, rj (e.g., DDT [C]), and the rate of disappearance of another species, – ri (e.g., chlorobenzene [B]), in a chemical reaction.
Be sure to view the actual photographs of industrial reactors on the CRE Web site so you will know them when you run into them. There are also links to view reactors on different Web sites. The CRE Web site also includes a portion of the Visual Encyclopedia of Equipment, encyclopedia.che.engin.umich.edu, “Chemical Reactors” developed by Dr. Susan Montgomery and her students at the University of Michigan. Also see Professional Reference Shelf on the CRE Web site for “Reactors for Liquid-Phase and Gas-Phase Reactions,” along with photos of industrial reactors, and Expanded Material on the CRE Web site.2
2Chem. Eng., 63(10), 211 (1956). See also AIChE Modular Instruction Series E, 5 (1984).
In this chapter, and on the CRE Web site, we’ve introduced each of the major types of industrial reactors: batch, stirred tank, tubular, and fixed bed (packed bed). Many variations and modifications of these commercial reactors (e.g., semibatch, fluidized bed) are in current use and these reactors will be discussed in Chapters 6 and 10, respectively. For further elaboration, refer to the detailed discussion of industrial reactors given by Walas.3
3 S. M. Walas, Reaction Kinetics for Chemical Engineers, New York: McGraw-Hill, 1959, Chap. 11.
The CRE Web site describes industrial reactors, along with typical feed and operating conditions. In addition, two solved example problems for Chapter 1 can be found on the CRE Web site, http://www.umich.edu/~elements/6e.
1.6 And Now… A Word from Our Sponsor–Safety 1 (AWFOS–S1 Safety)
A note to students: In this sixth edition of Elements of Chemical Reaction Engineering, I am including a section at the end of each chapter to bring a greater awareness to process safety. A critical aspect of process safety is “anticipating” what could go wrong in a chemical process and ensuring it won’t go wrong. Equipment and processes involving exothermic chemical reactions are some of the most at risk in a chemical plant. Consequently, each chapter will end with a segment “And Now… A Word From Our Sponsor–Safety” (AWFOS–S). In addition, to highlight process safety across the chemical engineering curriculum, a Web site (http://umich.edu/~safeche/) has been developed that features a safety module specific to every core chemical engineering lecture course plus lab safety. In this chapter, we define process safety along with a very brief discussion on why it is important to study process safety.
1.6.1 What Is Chemical Process Safety?
Chemical process safety is a blend of engineering and management practices focused on preventing accidents, namely explosions, fires, and toxic releases that result in loss of life and property.
Industrial disasters such as UCIL Bhopal, T2 Laboratories, BP Texas City, and Flixborough have collectively killed and injured thousands of people and caused billions of dollars in damage to chemical plants and nearby communities. Accidents such as these occur because chemical engineering processes are some of the most potentially dangerous due to extreme operating conditions and the use of explosive, reactive, and flammable materials. What surprises people is that most of these chemical engineering accidents, such as those listed in the Chemical Safety Board Videos on the companion Web site (http://umich.edu/~safeche/) were preventable. They were the result of poor engineering decisions, made by people who lacked fundamental understanding of basic chemical engineering concepts and chemical engineering safety. Thus, knowing the fundamentals of chemical engineering and process safety may save your life and the lives of innocent people, and prevent the loss of millions of dollars of material and equipment.
Engineers have an ethical and professional obligation to work only in areas for which they are competent and qualified. The best way to prevent future industrial disasters is to understand how to effectively and safely design, operate, and troubleshoot chemical processes. To prepare a prevention plan, we must take the time and effort to understand chemical processes and chemical process safety. To help achieve this understanding, the last section of every chapter has a tutorial, AWFOS–S, that can help you prevent accidents.
A comparison of process safety and personal safety is very succinctly given on the Web site (http://www.energysafetycanada.com/files/pdf/Personal_vs_Process_Safety_v3.pdf).
Closure. The goal of this text is to weave the fundamentals of chemical reaction engineering into a structure or algorithm that is easy to use and apply to a variety of problems. We have just finished the first building block of this algorithm: mole balances.
This algorithm and its corresponding building blocks will be developed and discussed in the following chapters:
With this algorithm, one can approach and solve chemical reaction engineering problems through logic rather than memorization.
A Word of Caution: The falling CRE Tower. As we proceed through the next five chapters, we will see how these building blocks form a tower. Now, if one cuts corners when studying this material, the building blocks become cylinders and as a result the tower becomes unstable and all of the understanding of CRE falls apart. See http://www.umich.edu/~elements/6e/01chap/assets/player/KeynoteDHTMLPlayer.html#3.
To perform a mole balance on any system, the system boundaries must first be specified. The volume enclosed by these boundaries is referred to as the system volume. We shall perform a mole balance on species j in a system volume, where species j represents the particular chemical species of interest, such as water or NaOH (Figure 1-3).
Figure 1-3 Mole balance on species j in a system volume, V.
A mole balance on species j at any instant in time, t, yields the following equation:
Mole balance
Accumulation: In this equation, Nj represents the number of moles of species j in the system at time t and is the rate of accumulation of species j within the system volume.
Generation: If all the system variables (e.g., temperature, catalytic activity, and concentration of the chemical species) are spatially uniform throughout the system volume, the rate of generation of species j, Gj (moles/time) is just the product of the reaction volume, V, and the rate of formation of species j, rj.
Now suppose that the rate of formation of species j for the reaction varies with position in the system volume. That is, it has a value rj1 at location 1, which is surrounded by a small volume, ΔV1, within which the rate is uniform; similarly, the reaction rate has a value at location 2 and an associated volume, rj2, and so on (Figure 1-4).
Figure 1-4 Dividing up the system volume, V.
The rate of generation, ΔGj1, in terms of rj1 and subvolume ΔV1, is
ΔGj1 = rj1 ΔV1
Similar expressions can be written for ΔGj2 and the other system subvolumes, ΔVi. The total rate of generation within the system volume is the sum of all the rates of generation in each of the subvolumes. If the total system volume is divided into M subvolumes, the total rate of generation is
By taking the appropriate limits (i.e., let M → ∞ and ΔV → 0) and making use of the definition of an integral, we can rewrite the foregoing equation in the form
From this equation, we see that rj will be an indirect function of position, since the properties of the reacting materials and reaction conditions (e.g., concentration, temperature) can have different values at different locations in the reactor volume.
We now replace Gj in Equation (1-3), that is,
by its integral form to yield a form of the general mole balance equation for any chemical species j that is entering, leaving, reacting, and/or accumulating within any system volume V.
This is a basic equation for chemical reaction engineering.
From this general mole balance equation, we can develop the design equations for the various types of industrial reactors: batch, semibatch, and continuous-flow. Upon evaluation of these equations, we can determine the time (batch), reactor volume or catalyst weight (continuous-flow) necessary to convert a specified amount of the reactants into products.
1.3 Batch Reactors (BRs)
When is a batch reactor used?
A batch reactor is used for small-scale operation, for testing new processes that have not been fully developed, for the manufacture of expensive products, and for processes that are difficult to convert to continuous operations. The reactor can be charged (i.e., filled) through the holes at the top (see Figure 1-5(a)). The batch reactor has the advantage of high conversions that can be obtained by leaving the reactant in the reactor for long periods of time, but it also has the disadvantages of high labor costs per batch, the variability of products from batch to batch, and the difficulty of large-scale production (see Industrial Reactor Photos in Professional Reference Shelf [PRS] (http://www.umich.edu/~elements/6e/01chap/prof-reactors.html) on the CRE Web sites, www.umich.edu/~elements/6e/index.html). Also see http://encyclopedia.che.engin.umich.edu/Pages/Reactors/menu.html.
Figure 1-5(a) Simple homogeneous batch reactor (BR). [Excerpted by special permission from Chem. Eng., 63(10), 211 (Oct. 1956). Copyright 1956 by McGraw-Hill, Inc., New York, NY 10020.]Figure 1-5(b) Batch reactor mixing patterns. Further descriptions and photos of the batch reactors can be found in both the Visual Encyclopedia of Equipment and in the Professional Reference Shelf on the CRE Web site.
Also see http://encyclopedia.che.engin.umich.edu/Pages/Reactors/Batch/Batch.html.
A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out: Fj0 = Fj = 0. The resulting general mole balance on species j is
If the reaction mixture is perfectly mixed (Figure 1-5(b)) so that there is no variation in the rate of reaction throughout the reactor volume, we can take rj out of the integral, integrate, and write the differential form of the mole balance, that is,
Perfect mixing
Let’s consider the isomerization of species A in a batch reactor
As the reaction proceeds, the number of moles of A decreases and the number of moles of B increases, as shown in Figure 1-6.
Figure 1-6 Mole-time trajectories.
We might ask what time, t1, is necessary to reduce the initial number of moles from NA0 to a final desired number NA1. Applying Equation (1-5) to the isomerization
rearranging,
and integrating with limits that at t = 0, then NA = NA0, and at t = t1, then NA = NA1, we obtain
This equation is the integral form of the mole balance on a batch reactor. It gives the time, t1, necessary to reduce the number of moles from NA0 to NA1 and also to form NB1 moles of B.
1.4 Continuous-Flow Reactors
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 physical descriptions of these reactors can be found in both the Professional Reference Shelf (PRS), (http://www.umich.edu/~elements/6e/01chap/prof.html) of Chapter 1 and in the Visual Encyclopedia of Equipment, http://encyclopedia.che.engin.umich.edu/Pages/Reactors/CSTR/CSTR.html, and on the CRE Web site.
The rate of reaction tells us how fast the number of moles of one chemical species are being consumed to form another chemical species. The term chemical species refers to any chemical component or element with a given identity. The identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms. For example, the species para-xylene is made up of a
fixed number of specific atoms in a definite molecular arrangement or configuration. The structure shown illustrates the kind, number, and configuration of atoms on a molecular level. Even though two chemical compounds have exactly the same kind and number of atoms of each element, they could still be different species because of different configurations. For example, 2-butene has four carbon atoms and eight hydrogen atoms; however, the atoms in this compound can form two different arrangements.
As a consequence of the different configurations, these two isomers display different chemical and physical properties. Therefore, we consider them as two different species, even though each has the same number of atoms of each element.
When has a chemical reaction taken place?
We say that a chemical reaction has taken place when a detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms. In this classical approach to chemical change, it is assumed that the total mass is neither created nor destroyed when a chemical reaction occurs. The mass referred to is the total collective mass of all the different species in the system. However, when considering the individual species involved in a particular reaction, we do speak of the rate of disappearance of mass of a particular species. The rate of disappearance of a species, say species A, is the number of A molecules that lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reaction. In order for a particular species to “appear” in the system, some prescribed fraction of another species must lose its chemical identity.
Definition of Rate of Reaction
There are three basic ways a species may lose its chemical identity: decomposition, combination, and isomerization. In decomposition, the molecule loses its identity by being broken down into smaller molecules, atoms, or atom fragments. For example, if benzene and propylene are formed from a cumene molecule,
A species can lose its identity by
Decomposition
Combination
Isomerization
the cumene molecule has lost its identity (i.e., disappeared) by breaking its bonds to form these molecules. A second way that a molecule may lose its chemical identity is through combination with another molecule or atom. In the above reaction, the propylene molecule would lose its chemical identity if the reaction were carried out in the reverse direction, so that it combined with benzene to form cumene. The third way a species may lose its chemical identity is through isomerization, such as the reaction
Here, although the molecule neither adds other molecules to itself nor breaks into smaller molecules, it still loses its identity through a change in configuration.
To summarize this point, we say that a given number of molecules (i.e., moles) of a particular chemical species have reacted or disappeared when the molecules have lost their chemical identity.
The rate at which a given chemical reaction proceeds can be expressed in different ways by referring it to different chemical species in the reaction. To illustrate, consider the reaction of chlorobenzene with chloral in the presence of fuming sulfuric acid to produce the banned insecticide DDT (dichlorodiphenyl trichloroethane).
CCl3CHO + 2C6H5Cl → (C6H4Cl)2CHCCl3 + H2O
Letting the symbol A represent chloral, B be chlorobenzene, C be DDT, and D be H2O, we obtain
A + 2B → C + D
What is –rA?
The rate of reaction, –rA, is the number of moles of A (e.g., chloral) reacting (disappearing) per unit time per unit volume (mol/dm3·s).
The numerical value of the rate of disappearance of reactant A, –rA, is a positive number.
Example 1–1 Rates of Disappearance and Formation
Chloral is being consumed at a rate of 10 moles per second per m3 when reacting with chlorobenzene to form DDT and water in the reaction described above. In symbol form, the reaction is written as
A + 2B → C + D
Write the rates of disappearance and formation (i.e., generation; mol/m3·s) for each species in this reaction when the rate of reaction of chloral [A] (–rA) is 10 mol/m3·s.
NFPA Diamond
DDT See Section 2.7
Solution
(a) Chloral[A]:
Rate of disappearance of A = –rA = 10 mol/m3·sRate of formation of A = rA = –10 mol/m3·s
(b) Chlorobenzene[B]:
For every mole of chloral that disappears, two moles of chlorobenzene [B] also disappear.Rate of disappearance of B = –rB = –2rA = 20 mol/m3·sRate of formation of B = rB = –20 mol/m3·s
(c) DDT[C]:
For every mole of chloral that disappears, one mole of DDT [C] appears. rC = –rARate of disappearance of C = –rC = –10 mol/m3·sRate of formation of C = rC = –rA = –(–10 mol/m3·s) = 10 mol/m3·s
(d) Water[D]:
Same relationship to chloral as the relationship to DDTRate of formation of D = rD = 10 mol/m3·sRate of disappearance of D = –rD = –10 mol/m3·s
Analysis: The purpose of this example is to better understand the convention for the rate of reaction. The symbol rj is the rate of formation (generation) of species j. If species j is a reactant, the numerical value of rj will be a negative number. If species j is a product, then rj will be a positive number. The rate of reaction, –rA, is the rate of disappearance of reactant A and must be a positive number. A mnemonic relationship to help remember how to obtain relative rates of reaction of A to B, and so on, is given by Equation (3-1) on page 77.
In Equation (3-1) in Chapter 3, we will delineate the prescribed relationship between the rate of formation of one species, rj (e.g., DDT [C]), and the rate of disappearance of another species, – ri (e.g., chlorobenzene [B]), in a chemical reaction.
Heterogeneous reactions involve more than one phase. In heterogeneous reaction systems, the rate of reaction is usually expressed in measures other than volume, such as reaction surface area or catalyst weight. For a gas–solid catalytic reaction, the gas molecules must interact with the solid catalyst surface for the reaction to take place, as described in Chapter 10.
What is ?
The dimensions of this heterogeneous reaction rate, (prime), are the number of moles of A reacting per unit time per unit mass of catalyst (e.g., mol/s·g catalyst).
Definition of rj
Most of the introductory discussions on chemical reaction engineering in this book focus on homogeneous systems, in which case we simply say that rj is the rate of formation of species j per unit volume. It is the number of moles of species j generated per unit volume per unit time.
We can say four things about the reaction rate rj: rj is
The rate law does not depend on the type of reactor used!!
The rate of formation of speciesj(mole/time/volume)
An algebraic equation
Independent of the type of reactor (e.g., batch or continuous flow) in which the reaction is carried out
Solely a function of the properties of the reacting materials and reaction conditions (e.g., species concentration, temperature, pressure, or type of catalyst, if any) at a point in the system
The man who has ceased to learn ought not to be allowed to wander around loose in these dangerous days.
—M. M. Coady
A. Who Is the Intended Audience?
This book was written with today’s students in mind. It provides instantaneous access to information; does not waste time on extraneous details; cuts right to the point; uses more bullets to make information easier to access; and includes new, novel problems on chemical reaction engineering (e.g., solar energy).1 The interaction between the text and Web site (http://www.umich.edu/~elements/6e/) breaks new ground and provides one of the most comprehensive active learning resources available. With the advent of sliders in both Wolfram and Python, students can explore the reactions and the reactor in which they occur, by carrying out simulation experiments and then writing a set of conclusions to describe what they found.
This book and interactive Web site are intended for use as both an undergraduate-level and a graduate-level text in chemical reaction engineering. The undergraduate course/courses usually focus on Chapters 1–13; the graduate course material includes topics such as diffusion limitations, effectiveness factors (discussed in Chapters 14 and 15), nonideal reactors, and residence time distribution (discussed in Chapters 16–18) along with the additional material and Professional Reference Shelf (PRS) on the Web site.
This edition emphasizes chemical reactor safety by ending each chapter with a safety lesson called And Now… A Word From Our Sponsor-Safety (AWFOS–S). These lessons can also be found on the Web site at http://umich.edu/~safeche/.
B. What Are the Goals of This Book?
B.1 To Have Fun Learning Chemical Reaction Engineering (CRE)
Chemical reaction engineering (CRE) is a great subject that is fun to learn and is the heart of chemical engineering. I have tried to provide a little Michigan humor as we go. Take a look at the humorous YouTube videos (e.g., “Black Widow” or “Chemical Engineering Gone Wrong”) that illustrate certain principles in the text. These videos were made by chemical engineering students at the universities of Alabama and Michigan. In addition, I have found that students enjoy the Interactive Computer Games (ICGs) that, along with the videos, are linked from the CRE homepage (http://www.umich.edu/~elements/6e/index.html).
B.2 To Develop a Fundamental Understanding of Reaction Engineering
The second goal of this book is to help the reader clearly understand the fundamentals of CRE. This goal is achieved by presenting a structure that allows the reader to solve reaction engineering problems through reasoning rather than through memorization and recall of numerous equations and the restrictions and conditions under which each equation applies (http://www.umich.edu/~elements/6e/toc/Preface-Complete.pdf.
B.3 To Enhance Thinking Skills
A third goal of this text is to enhance critical thinking skills and creative thinking skills. How does the book help enhance your critical and creative thinking skills? We discuss ways to achieve this enhancement in Table P-2, Critical Thinking Questions; Table P-3, Critical Thinking Actions; and Table P-4, Practicing Creative Thinking, in the complete preface on the CRE Web site (http://www.umich.edu/~elements/6e/toc/Preface-Complete.pdf) and also from the Problem Solving Web site (http://umich.edu/~scps/).
C. What Is the Structure of CRE?
C.1 What Are the Concepts That Form the Foundation of CRE?
The strategy behind the presentation of material is to build continually on a few basic ideas in CRE to solve a wide variety of problems. The building blocks of CRE and the primary algorithm allow us to solve isothermal CRE problems through logic rather than memorization. We start with the Mole Balance Building Block (Chapter 1) and then place the other blocks one at a time on top of the others until we reach the Evaluate Block (Chapter 5), by which time we can solve a multitude of isothermal CRE problems. As we study each block, we need to make sure we understand everything in that block and be sure not to cut corners by leaving anything out so we don’t wind up with a stack of cylindrical blocks. An animation of what happens to such a stack is shown at the end of Lecture 1 notes (http://www.umich.edu/%7Eelements/6e/lectures/umich.html).
For nonisothermal reactions, we replace the “Combine” building block in Figure I-1 with the “Energy Balance” building block because nonisothermal reactions almost always require a computer-generated solution. Consequently, we don’t need the “Combine” block because the computer combines everything for us. From these pillars and building blocks, we construct our CRE algorithm:
C.2 What Is the Sequence of Topics in Which This Book Can Be Used?
The selection and order of topics and chapters are shown in Figure P-3 in the Complete Preface/Introduction on the Web site (http://www.umich.edu/~elements/6e/toc/Preface-Complete.pdf). There are notes in the margins, which are meant to serve two purposes. First, they act as guides or commentary as one reads through the material. Second, they identify key equations and relationships that are used to solve CRE problems.
Margin Notes
D. What Are the Components of the CRE Web Site?
The interactive companion Web site material has been significantly updated and is a novel, and integral part of this book. The main purposes of the Web site are to serve as an interactive part of the text with enrichment resources. The home page for the CRE Web site (http://www.umich.edu/~elements/6e/index.html) is shown in Figure I-2. For discussion of how to use the Web site and text interactively, see Appendix I.
Figure I-2 Screen shot of the book’s companion Web site (http://www.umich.edu/~elements/6e/index.html).
The objectives of the Web site are fourfold:
To facilitate the interactive learning of CRE by using the companion Web site and Wolfram and Python sliders to explore Living Example Problems to gain a deep understanding of the reaction and the reactors in which they take place.
To provide additional technical material in the extended material and in the Professional Reference Shelf.
To provide tutorial information and self-assessment exercises such as the i>clicker questions.
To make the learning of CRE fun through the use of interactive games, LEP simulations, and computer experiments, which allow one to use Inquiry-Based Learning (IBL) to explore the concepts of CRE.
D.1 How to Use the Web Site
I would like to expand a bit on a couple of things that we use extensively, namely the useful links. These items can be accessed by clicking on the Chapter number on the Home Page. After clicking on Chapter 1 shown in Figure I-3, one will arrive at
The important point I want to make here is the list of all resources shown in Figures I-3 and I-4. In addition to listing the objectives for this chapter, you will find all the major hot buttons, such as
Figure I-4 Useful links.
The Living Example Problems (LEPs), including COMSOL, have all numerical Example Problems programmed and ready for use with the click of a button. The Extra Help includes interactive notes, screen casts, and techniques that facilitate learning and studying. The Additional Material and Professional Reference Shelf provide expanded derivations and material that is relevant to CRE, but did not make the final cut owing to limitations of the thickness of the book; that is, students can’t concentrate about CRE if their backpacks are so heavy they are suffering from carrying them. The Self Tests and i>Clicker Questions help readers gauge their level of understanding.
D.2 Living Example Problems (LEPs)
What are LEPs? LEPs are Living Example Problems that are really simulations that can be used to carry out experiments on the reactor and the reactions occurring inside the reactor. Here, rather than being stuck with the parameter values the author gives, the LEPs allow you to change the value of a parameter and see its effect on the reactor’s operation. LEPs have been unique to this book since their invention and inclusion in the Third Edition of this title, published in 1999. However, Wolfram and Python have allowed us to take LEPs to a new level, resulting in a minor paradigm shift. The LEPs use simulation software, which can be downloaded directly onto one’s own computer in order to “play with” the key variables and assumptions. Using the LEPs to explore the problem and asking “What if…?” questions provide students with the opportunity to practice critical and creative thinking skills. To guide students in using these simulations, questions for each chapter are given on the Web site (e.g., http://www.umich.edu/~elements/6e/12chap/obj.html).2 In this edition, there are more than 80 interactive simulations (LEPs) provided on the Web site. It is the author’s strong belief that using the LEP sliders will develop an intuitive feel for Chemical Reaction Engineering (CRE).
Figure A-1 Equal-area differentiation.
Figure A-2 Trapezoidal rule illustration.
Figure A-3 Simpson’s three-point rule illustration.
Figure A-4 Simpson’s four-point rule illustration.
BRNo spatial variations
CSTRNo spatial variations, steady state——
PFRSteady state
PBRSteady state
Fluidized CSTRSteady state——
