[Textbook cover goes here]

Figures from Chemical Reactor Analysis and Design Fundamentals

James B. Rawlings John G. Ekerdt
Department of Chemical and Biological Engineering Department of Chemical Engineering
University of Wisconsin The University of Texas
Madison, Wisconsin Austin, Texas

Copyright (C) 2007 Nob Hill Publishing

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User's Guide

Chapter 2: The Stoichiometry of Reactions

Figure 2.2 (page 52):
Estimated reaction rates from six production-rate measurements subject to measurement noise. 		Figure 2.3 (page 52):
Estimated reaction rates from 500 production-rate measurements subject to measurement noise.

Chapter 3: Review of Chemical Equilibrium

Figure 3.3 (page 75):
Gibbs energy $ G\mathaccent "0365{G}$}$ versus reaction extent $\varepsilon '$. 		Figure 3.4 (page 84):
Partial pressures of components A and C versus liquid-phase composition in a nonideal solution.
Figure 3.6 (page 95):
Gibbs energy contours for the pentane reactions as a function of the two reaction extents.

Chapter 4: The Material Balance for Chemical Reactors

Figure 4.3 (page 113):
First-order, irreversible kinetics in a batch reactor. 		Figure 4.4 (page 114):
First-order, irreversible kinetics in a batch reactor, log scale.
Figure 4.5 (page 116):
First-order, reversible kinetics in a batch reactor, $k_1=1$, $k_{-1}=0.5$, $c_{A0}=1$, $c_{B0}=0$. 		Figure 4.6 (page 118):
Second-order and first-order kinetics in a batch reactor; for first order, $k=1$, for second-order, $kc_{A0}=1$, so the rates are equal initially.
Figure 4.7 (page 121):
Reaction rate versus concentration for $n$th-order kinetics, $r=kc_A^n$, $n\geq 0$, $k=1$ for all orders. 		Figure 4.8 (page 122):
Batch reactor with $n$th-order kinetics, $r=kc_A^n$, $k_0=kc_{A0}^{n-1}=1$, $n\geq 1$.
Figure 4.9 (page 122):
Batch reactor with $n$th-order kinetics, $r=kc_A^n$, $k_0=kc_{A0}^{n-1}=1$, $n<1$. 		Figure 4.10 (page 123):
Reaction rate versus concentration for $n$th-order kinetics, $r=kc_A^n$, $n\leq 0$, $k=1$ for all orders.
Figure 4.11 (page 125):
Two first-order reactions in series in a batch reactor. 		Figure 4.12 (page 127):
Two first-order reactions in parallel in a batch reactor.
Figure 4.14 (page 131):
Reaching steady state in a CSTR. 		Figure 4.15 (page 143):
Semi-batch reactor volume for different monomer addition policies.
Figure 4.16 (page 143):
Semi-batch reactor feed flowrate for different monomer addition policies. 		Figure 4.17 (page 144):
Semi-batch reactor monomer content for different monomer addition policies.
Figure 4.18 (page 144):
Semi-batch reactor polymer content for different monomer addition policies. 		Figure 4.20 (page 153):
Benzene conversion versus reactor volume.
Figure 4.21 (page 153):
Component mole fractions versus reactor volume. 		Figure 4.22 (page 158):
Molar flowrate of ethane, ethylene and NO versus reactor volume for ethane pyrolysis example.
Figure 4.23 (page 158):
Molar flowrate of ethane versus reactor volume for inlet temperatures of 1000, 1050 and 1100 {\rm K}. 		Figure 4.27 (page 163):
Overall and per-pass conversion of A as a function of fractional recycle, $\alpha $.
Figure 4.29 (page 167):
Stochastic simulation of the first-order reactions A$\longrightarrow $B$\longrightarrow $C starting with 100 A molecules. 		Figure 4.30 (page 168):
Stochastic simulation of the first-order reactions A$\longrightarrow $B$\longrightarrow $C starting with 1000 A molecules.
Figure 4.31 (page 168):
Stochastic simulation of the first-order reactions A$\longrightarrow $B$\longrightarrow $C starting with 4000 A molecules. 		Figure 4.32 (page 170):
Species cccDNA versus time for hepatitis B virus model; deterministic and average stochastic models.
Figure 4.33 (page 170):
Species rcDNA versus time for hepatitis B virus model; deterministic and average stochastic models. 		Figure 4.34 (page 170):
Envelope versus time for hepatitis B virus model; deterministic and average stochastic models.
Figure 4.35 (page 172):
Species cccDNA versus time for hepatitis B virus model; two representative stochastic trajectories. 		Figure 4.37 (page 183):
Deterministic simulation of reaction A $+$ B $\rlh $ C compared to stochastic simulation.

Chapter 5: Chemical Kinetics

Figure 5.1 (page 196):
Morse potential for \formula {H_2} and HF. 		Figure 5.3 (page 198):
Contour representation of the potential-energy surface.
Figure 5.4 (page 199):
Reaction-coordinate diagram. 		Figure 5.5 (page 208):
Comparison of measured and calculated rate constant versus temperature for oxirane decomposition.
Figure 5.6 (page 210):
Full model solution for $k_1=1, k_{-1}=0.5, k_2=k_{-2}=1$. 		Figure 5.7 (page 211):
Full model solution for $k_1=1, k_{-1}=0.5, k_2=k_{-2}=10$.
Figure 5.8 (page 212):
Concentrations of B and C versus time for full model with increasing $k_2$ with $K_2=k_2/k_{-2}=1$. 		Figure 5.9 (page 214):
Comparison of equilibrium assumption to full model for $k_1=1, k_{-1}=0.5, k_2=k_{-2}=10$.
Figure 5.10 (page 221):
Normalized concentration of C versus dimensionless time for the series reaction A $\rightarrow $ B $\rightarrow $ C. 		Figure 5.11 (page 224):
Fractional error in the QSSA concentration of C for the series reaction A $\rightarrow $ B $\rightarrow $ C.
Figure 5.12 (page 225):
Fractional error in the QSSA concentration of C versus dimensionless time for the series-parallel reaction, $ {A}\rlh {B}\rightarrow {C}$. 		Figure 5.13 (page 234):
Molar flowrates of \formula {C_2H_6}, \formula {C_2H_4} and \formula {CH_4} corresponding to the exact solution.
Figure 5.14 (page 237):
Fractional error in the QSSA molar flowrate of \formula {C_2H_4} versus reactor volume. 		Figure 5.15 (page 238):
Comparison of the molar flowrates of \formula {C_2H_6} and \formula {C_2H_4} for the exact solution (solid lines) and the simplified kinetic scheme (dashed lines).
Figure 5.18 (page 244):
Fractional coverage versus adsorbate concentration for different values of the adsorption constant, $K$. 		Figure 5.19 (page 246):
Langmuir isotherm for CO uptake on Ru.
Figure 5.20 (page 246):
Linear form of Langmuir isotherm for CO uptake on Ru. 		Figure 5.23 (page 252):
Dimensionless \formula {CO_2} production rate versus dimensionless gas-phase \formula {CO} and \formula {O_2} concentrations.
Figure 5.24 (page 253):
Dimensionless \formula {CO_2} production rate versus a single dimensionless gas-phase concentration. 		Figure 5.25 (page 264):
Adsorbed oxygen concentration versus gas-phase oxygen concentration.

Chapter 6: The Energy Balance for Chemical Reactors

Figure 6.5 (page 293):
Conversion of A versus reactor temperature. 		Figure 6.6 (page 296):
Steady-state conversion versus residence time for different values of the heat of reaction.
Figure 6.7 (page 296):
Steady-state temperature versus residence time for different values of the heat of reaction. 		Figure 6.8 (page 298):
Steady-state conversion versus residence time for $\Delta H_R = -3 \times 10^5$ kJ/kmol; ignition and extinction points.
Figure 6.9 (page 298):
Steady-state temperature versus residence time for $\Delta H_R = -3 \times 10^5$ kJ/kmol; ignition and extinction points. 		Figure 6.10 (page 299):
Steady-state temperature versus residence time for $\Delta H_R = -3 \times 10^5$ kJ/kmol.
Figure 6.11 (page 301):
Rates of heat generation and removal for $\tau =1.79$ min. 		Figure 6.12 (page 302):
Rates of heat generation and removal for $\tau =15$ min.
Figure 6.13 (page 302):
Rates of heat generation and removal for $\tau =30.9$ min. 		Figure 6.14 (page 307):
Eigenvalues of Jacobian matrix vs. reactor temperature.
Figure 6.15 (page 307):
Eigenvalues of Jacobian matrix vs. reactor conversion. 		Figure 6.19 (page 310):
Steady-state conversion versus residence time.
Figure 6.20 (page 310):
Steady-state temperature versus residence time. 		Figure 6.21 (page 311):
Steady-state conversion vs. residence time --- log scale.
Figure 6.22 (page 311):
Steady-state temperature vs. residence time --- log scale. 		Figure 6.23 (page 312):
Eigenvalues of the Jacobian matrix versus reactor conversion in the region of steady-state multiplicity.
Figure 6.24 (page 312):
Eigenvalues of the Jacobian matrix versus reactor conversion in the region of steady-state multiplicity. 		Figure 6.25 (page 313):
Real and imaginary parts of the eigenvalues of the Jacobian matrix near points C--F.
Figure 6.26 (page 314):
Conversion and temperature vs. time for $\tau =35$ min. 		Figure 6.27 (page 315):
Phase portrait of conversion versus temperature for feed initial condition; $\tau =35$ min.
Figure 6.28 (page 315):
Phase portrait of conversion versus temperature for several initial conditions; $\tau =35$ min. 		Figure 6.29 (page 317):
Conversion and temperature vs. time for $\tau =30$ min.
Figure 6.30 (page 317):
Conversion and temperature vs. time for $\tau =72.3$ min. 		Figure 6.31 (page 318):
Phase portrait of conversion versus temperature at showing stable and unstable limit cycles.
Figure 6.36 (page 329):
Molar flow of o-xylene versus reactor length for different feed temperatures. 		Figure 6.37 (page 329):
Reactor temperature versus length for different feed temperatures.
Figure 6.39 (page 333):
Coolant temperature at reactor outlet versus temperature at reactor inlet; three steady-state solutions. 		Figure 6.40 (page 334):
Reactor and coolant temperature profiles versus reactor length.
Figure 6.41 (page 334):
Ammonia mole fraction versus reactor length. 		Figure 6.42 (page 352):
Coolant temperature at reactor outlet versus temperature at reactor inlet.

Chapter 7: Fixed-Bed Catalytic Reactors

Figure 7.3 (page 371):
Hyperbolic trigonometric functions sinh, cosh, tanh. 		Figure 7.4 (page 372):
Dimensionless concentration versus dimensionless radial position for different values of the Thiele modulus.
Figure 7.5 (page 374):
Effectiveness factor versus Thiele modulus for a first-order reaction in a sphere. 		Figure 7.6 (page 374):
Effectiveness factor versus Thiele modulus for a first-order reaction in a sphere (log-log scale).
Figure 7.8 (page 379):
Effectiveness factor versus Thiele modulus for the sphere, cylinder and slab. 		Figure 7.9 (page 381):
Effectiveness factor versus Thiele modulus in a spherical pellet; reaction orders greater than unity.
Figure 7.10 (page 381):
Effectiveness factor versus Thiele modulus in a spherical pellet; reaction orders less than unity. 		Figure 7.11 (page 382):
Dimensionless concentration versus radius for zero-order reaction in a spherical pellet.
Figure 7.13 (page 387):
Effectiveness factor versus an inappropriate Thiele modulus in a slab; Hougen-Watson kinetics. 		Figure 7.14 (page 387):
Effectiveness factor versus appropriate Thiele modulus in a slab; Hougen-Watson kinetics.
Figure 7.16 (page 389):
Dimensionless concentration versus radius for different values of the Biot number; first-order reaction in a spherical pellet with $\Phi =1$. 		Figure 7.17 (page 390):
Effectiveness factor versus Thiele modulus for different values of the Biot number; first-order reaction in a spherical pellet.
Figure 7.18 (page 391):
Asymptotic behavior of the effectiveness factor versus Thiele modulus; first-order reaction in spherical pellet. 		Figure 7.19 (page 397):
Effectiveness factor versus normalized Thiele modulus for a first-order reaction in nonisothermal spherical pellet.
Figure 7.20 (page 399):
Dimensionless concentration versus radius for the nonisothermal spherical pellet: lower (A), unstable middle (B), and upper (C) steady states. 		Figure 7.21 (page 400):
Dimensionless temperature versus radius for the nonisothermal spherical pellet: lower (A), unstable middle (B), and upper (C) steady states.
Figure 7.22 (page 402):
Concentration profiles of reactants; fluid concentration of O$_2$ ($\scriptstyle \times $), CO ($\scriptstyle +$), C$_3$H$_6$ ($\scriptstyle \ast $). 		Figure 7.23 (page 402):
Concentration profiles of reactants (log scale); fluid concentration of O$_2$ ($\scriptstyle \times $), CO ($\scriptstyle +$), C$_3$H$_6$ ($\scriptstyle \ast $).
Figure 7.24 (page 404):
Concentration profiles of products. 		Figure 7.26 (page 411):
Molar flow of A versus reactor volume for second-order, isothermal reaction in a fixed-bed reactor.
Figure 7.27 (page 414):
Molar concentrations versus reactor volume. 		Figure 7.28 (page 414):
Dimensionless equilibrium constant and Thiele modulus versus reactor volume.
Figure 7.29 (page 416):
Fluid molar concentrations versus reactor volume. 		Figure 7.30 (page 416):
Fluid temperature and pressure versus reactor volume.
Figure 7.32 (page 417):
Pellet CO profiles at several reactor positions. 		Figure 7.34 (page 432):
Effectiveness factor versus Thiele modulus for different values of the Biot number; second-order reaction in a cylindrical pellet.

Chapter 8: Mixing in Chemical Reactors

Figure 8.5 (page 446):
CSTR residence-time distribution. 		Figure 8.8 (page 449):
RTD $p(\theta )$ versus $\theta $ for $n$ CSTRs in series, $\tau =2$.
Figure 8.9 (page 450):
$P(\theta )$ versus $\theta $ for $n$ CSTRs in series, $\tau =2$. 		Figure 8.10 (page 453):
$P(\theta )$ versus $\theta $ for plug flow with dispersion number $D$, $\tau =2$.
Figure 8.11 (page 453):
Residence-time distribution $p(\theta )$ versus $\theta $ for plug flow with dispersion number $D$, $\tau =2$. 		Figure 8.12 (page 456):
Start-up of the tubular reactor; $c_A(t,z)$ versus $z$ for various times, $0\leq t\leq 2.5$ min, $\Delta t=0.25$ min.
Figure 8.14 (page 458):
Comparison of the effluent concentrations for the two cases shown in Figure 8.13 . 		Figure 8.19 (page 467):
Dimensionless effluent concentration versus dimensionless rate constant for second-order reaction.
Figure 8.22 (page 472):
Total concentration of A in the reactor effluent versus particle size. 		Figure 8.23 (page 472):
Particle concentrations of A and B versus particle age for three different-sized particles.
Figure 8.29 (page 479):
Reaction rate versus concentration of limiting reactant; rate expression is neither convex nor concave. 		Figure 8.30 (page 480):
Inverse of reaction rate versus concentration; optimal sequence to achieve 95\% conversion is PFR--CSTR--PFR.
Figure 8.31 (page 481):
RTD for the optimal reactor configuration. 		Figure 8.33 (page 487):
Conversion of reactant for single, ideal CSTR, and as a function of internal flowrate in a 2-CSTR mixing model.
Figure 8.34 (page 487):
Yield of desired product C for single, ideal CSTR, and as a function of internal flowrate, $\rho =Q_r/Q_2$, in a 2-CSTR mixing model. 		Figure 8.35 (page 488):
Step response for single, ideal CSTR, and 2-CSTR mixing model with $\rho =0,1$.
Figure 8.36 (page 491):
Conversion of reactant A versus reactor length for different dispersion numbers. 		Figure 8.37 (page 491):
Yield of desired product B versus reactor length for different dispersion numbers.
Figure 8.39 (page 496):
Tracer concentrations in the feed and effluent streams versus time. 		Figure 8.41 (page 500):
Effluent concentration versus time after unit step change in the first reactor.

Chapter 9: Parameter Estimation for Reactor Models

Figure 9.4 (page 521):
Univariate normal with zero mean and unit variance. 		Figure 9.5 (page 522):
Multivariate normal for $n_p=2$.
Figure 9.7 (page 526):
Measured rate constant at several temperatures. 		Figure 9.8 (page 527):
Transformed data set, $\qopname o{ln}k$ versus $1/T$.
Figure 9.9 (page 528):
Several replicate data sets, $\qopname o{ln}k$ versus $1/T$. 		Figure 9.10 (page 529):
Distribution of estimated parameters.
Figure 9.11 (page 530):
Reducing parameter correlation by centering the data. 		Figure 9.12 (page 532):
Values of $\chi ^2$ and $F$ versus the number of data points when estimating 2 and 5 parameters.
Figure 9.13 (page 533):
Parameter estimates with only 10 data points. 		Figure 9.14 (page 534):
Confidence intervals with known (solid line) and unknown (dashed line) error variance.
Figure 9.15 (page 537):
Model fit to a single adsorption experiment. 		Figure 9.16 (page 538):
Model fit to all adsorption experiments.
Figure 9.18 (page 541):
Effect of next measurement temperature on parameter confidence intervals. 		Figure 9.19 (page 543):
Uncertainty in activation energy $E$ and rate constant $\qopname o{ln}k_m$ versus next measurement temperature.
Figure 9.20 (page 544):
Uncertainty in activation energy $E$ and rate constant $\qopname o{ln}k_m$ versus number of replicated experiments. 		Figure 9.21 (page 549):
Experimental measurement and best parameter fit for $n$th-order kinetic model, $r=k c_A^n$.
Figure 9.22 (page 550):
Monte Carlo evaluation of confidence intervals. 		Figure 9.23 (page 554):
Species cccDNA versus time for hepatitis B virus model; initial guess and estimated parameters fit to data.
Figure 9.24 (page 554):
Species rcDNA versus time for hepatitis B virus model; initial guess and estimated parameters fit to data. 		Figure 9.25 (page 554):
Envelope versus time for hepatitis B virus model; initial guess and estimated parameters fit to data.
Figure 9.26 (page 557):
Species cccDNA versus time for hepatitis B virus model. 		Figure 9.27 (page 557):
Species rcDNA versus time for hepatitis B virus model.
Figure 9.28 (page 557):
Envelope versus time for hepatitis B virus model. 		Figure 9.31 (page 563):
Base addition rate and LC measurement versus time.
Figure 9.32 (page 564):
Comparison of data to model with optimal parameters. 		Figure 9.33 (page 565):
Concentrations of species A, C and D versus time.
Figure 9.34 (page 566):
Concentration of species B versus time. 		Figure 9.35 (page 568):
Predictions of LC measurement for reduced model.
Figure 9.36 (page 569):
Fit of LC measurement versus time for reduced model; early time measurements have been added. 		Figure 9.37 (page 569):
Parameter estimates and confidence intervals for reduced model with redesigned experiment.
Figure 9.38 (page 574):
Batch reactor data for Exercise {9.3 }. 		Figure 9.39 (page 575):
Batch-reactor data for Exercise {9.4 }; 3 runs with different measurement error variance.
Figure 9.40 (page 579):
Batch-reactor data for Exercise {9.11 }. 		Figure 9.41 (page 579):
A second experiment for Exercise {9.11 }.
Figure 9.42 (page 580):
Batch-reactor data for Exercise {9.12 }. 		Figure 9.43 (page 580):
A second experiment for Exercise {9.12 }.

Appendix A: Computational Methods

Figure A.1 (page 587):
Estimated reaction rates from 2000 production-rate measurements subject to measurement noise. 		Figure A.2 (page 591):
Gibbs energy contours for the pentane reactions as a function of the two reaction extents.
Figure A.3 (page 598):
Solution to first-order differential equation $dc_A/dt=-kc_A$, and sensitivities $S_1=\partial c_A/\partial k$ and $S_2=\partial c_A/\partial c_{A0}$. 		Figure A.5 (page 602):
Dimensionless concentration versus dimensionless radial position for different numbers of collocation points.
Figure A.6 (page 603):
Relative error in the effectiveness factor versus number of collocation points. 		Figure A.7 (page 605):
Molar flow of A versus reactor volume for second-order, isothermal reaction in a fixed-bed reactor; two approximations and exact solution.
Figure A.8 (page 605):
Magnified view of Figure {A.7 }. 		Figure A.9 (page 607):
Dimensionless concentration versus radius for the nonisothermal spherical pellet: lower (A), unstable middle (B), and upper (C) steady states.