17. Predicting Conversion Directly from the Residence Time Distribution

If you think you can, you can.
If you think you can’t, you can’t.
You are right either way.

—Steve LeBlanc

The answer

We now present the five models shown in Table 17-1. We shall classify each model according to the number of adjustable parameters. In this chapter we will discuss the zero adjustable parameter models and, in Chapter 18, we will discuss one and two adjustable parameter models that will be used to predict conversion.

Ways we use the RTD data to predict conversion in nonideal reactors

TABLE 17-1 MODELS FOR PREDICTING CONVERSION FROM RTD DATA

For the zero adjustable parameter models, we do not need to make any intermediate calculations; we use the E- and F-Curves directly to predict the conversion given the kinetic parameters. For the one-parameter models, we use the RTD to calculate mean residence time, t, and variance, (σ², which we can then use (1) to find the number of tanks in series necessary to accurately model a nonideal CSTR and (2) calculate the Peclet number, Pe, to find the conversion in a tubular flow reactor using the dispersion model.

For the two-parameter models, we create combinations of ideal reactors to model the nonideal reactor. We then use the RTD to calculate the model parameters such as fraction bypassed, fraction dead volume, exchange volume, and ratios of reactor volumes that then can be used along with the reaction kinetics to predict conversion.

A model is needed for reactions other than first order.

Consequently, mixing with the surrounding molecules is not important. Therefore, once the RTD is determined, we can predict the conversion that will be achieved in the real reactor provided that the specific reaction rate for the first-order reaction is known. However, for reactions other than first order, knowledge of the RTD is not sufficient to predict conversion. For reactions other than first order, the degree of mixing of molecules must be known in addition to how long each molecule spends in the reactor. Consequently, we must develop models that account for the mixing of molecules inside the reactor.

The more complex models of nonideal reactors necessary to describe reactions other than first order must contain information about micromixing in addition to that of macromixing. Macromixing produces a distribution of residence times without, specifying how molecules of different ages encounter one another in the reactor. Micromixing, on the other hand, describes how molecules of different ages encounter one another in the reactor. There are two extremes of micromixing:

(1) all molecules of the same age group remain together as they travel through the reactor and are not mixed with any other age until they exit the reactor (i.e., complete segregation);

(2) molecules of different age groups are completely mixed at the molecular level as soon as they enter the reactor (complete micromixing).

For a given state of macromixing (i.e., a given RTD), these two extremes of micromixing will give the upper and lower limits on conversion in a nonideal reactor. For single reactions with orders greater than one or less than zero, the segregation model will predict the highest conversion. For reaction orders between zero and one, the maximum mixedness model will predict the highest conversion. This concept is discussed further in Section 17.3.1.

We shall define a globule as a fluid particle containing millions of molecules all of the same age. A fluid in which the globules of a given age do not mix with other globules is called a macrofluid. A macrofluid could be visualized as non-coalescent globules where all the molecules in a given globule have the same age. A fluid in which molecules are not constrained to remain in the globule and are free to move everywhere is called a microfluid.¹ There are two extremes of mixing of the macrofluid globules—early mixing and late mixing. These two extremes of late and early mixing are shown in Figure 17-1 (a) and (b), respectively. These extremes can also be seen by comparing Figures 17-3 (a) and 17-4 (a). The extremes of late and early mixing are referred to as complete segregation and maximum mixedness, respectively.

¹ J. Villermaux, Chemical Reactor Design and Technology (Boston: Martinus Nijhoff, 1986).

In developing the segregated mixing model, we first consider a CSTR because the application of the concepts of mixing quality are most easily illustrated using this reactor type. In the segregated flow model, we visualize the flow through the reactor to consist of a continuous series of globules (Figure 17-2).

In the segregation model, globules behave as batch reactors operated for different times.

These globules retain their identity; that is, they do not interchange material with other globules in the fluid during their period of residence in the reaction environment, i.e., they remain segregated. In addition, each globule spends a different amount of time in the reactor. In essence, what we are doing is lumping all the molecules that have exactly the same residence time in the reactor into the same globule. The principles of reactor performance in the presence of completely segregated mixing were first described by Danckwerts and Zwietering.^2,3

² P. V. Danckwerts, Chem. Eng. Sci., 8, 93 (1958).

³ T. N. Zwietering, Chem. Eng. Sci., 11, 1 (1959).

Another way of looking at the segregation model for a continuous-flow system is the PFR shown in Figures 17-3(a) and (b). Because the fluid flows down the reactor in plug flow, each exit stream corresponds to a specific residence time in the reactor. Batches of molecules are removed from the reactor at different locations along the reactor in such a manner as to duplicate the RTD function, E(t). The molecules removed near the entrance to the reactor correspond to those molecules having short residence times in the reactor. Physically, this effluent would correspond to the molecules that channel rapidly through the reactor. The farther the molecules travel along the reactor before being removed, the longer their residence time. The points at which the various groups or batches of molecules are removed correspond to the RTD function for the reactor.

The segregation model has mixing at the latest possible point.

Little batch reactors

E(t) matches the removal of the batch reactors.

Because there is no molecular interchange between globules, each acts essentially as its own batch reactor. The reaction time in any one of these tiny batch reactors is equal to the time that the particular globule has spent in the reaction environment after exiting. The distribution of residence times among the globules is given by the RTD of the particular reactor.

Now that we have the reactor’s RTD, we will choose a model, apply the rate law and rate law parameters to predict conversion as shown in the box above. We will start with the segregation model.

To determine the mean conversion in the effluent stream, we must average the conversions of all of the various globules in the exit stream:

then

Summing over all globules, the mean conversion is

Mean conversion for the segregation model

Consequently, if we have the batch reactor equation for X (t) and measure the RTD experimentally, we can find the mean conversion in the exit stream. Thus, if we have the RTD, the reaction-rate law and parameters, then for a segregated flow situation (i.e., model), we have sufficient information to calculate the conversion. An example that may help give additional physical insight to the segregation model is given in the Chapter 17 Summary Notes on the CRE Web site (www.umich.edu/~elements/5e/index.html); click the blue button just before Section 1A.2. Segregation Model Applied to an LFR.

Segregation Model for a First-Order Reaction

Consider the following first-order reaction:

We treat the globules that spend different amounts of time in the real reactor as little batch reactors. For a batch reactor we have

For constant volume and with N_A = N_A0 (1 – X)

Solving for X(t), we have for any globule that spends a time t in the real reactor

Because different globules spend different times, we have to add up the conversion from all the globules.

Mean conversion for a first-order reaction

We will now determine the mean conversion predicted by the segregation model for an ideal PFR, a CSTR, and an LFR.

We have just shown for a first-order reaction that whether you assume complete micromixing [Equation (E17-1.6)] or complete segregation [Equation (E17-1.5)] in a CSTR, the same conversion results. This phenomenon occurs because the rate of change of conversion for a first-order reaction does not depend on the concentration of the reacting molecules [Equation (17-14)]; it does not matter what kind of molecule is next to it or colliding with it. Thus, the extent of micromixing does not affect a first-order reaction, so the segregated flow model can be used to calculate the conversion. As a result, only the RTD is necessary to calculate the conversion for a first-order reaction in any type of reactor (see Problem P17-3_C). Knowledge of neither the degree of micromixing nor the reactor flow pattern is necessary. We now proceed to calculate conversion in a real reactor using RTD data.

Important Point:

For a first-order reaction, knowledge of E(t) is sufficient.

As discussed previously, because the reaction is first order, the conversion calculated in Example 17-2 would be valid for a reactor with complete mixing, complete segregation, or any degree of mixing between the two. Although early or late mixing does not affect a first-order reaction, micromixing or complete segregation can give significantly different results for a second-order reaction system.

In many cases we can approximate the conversion for an LFR with that calculated from the PFR models

Segregation model mixing occurs at the latest possible point.

We return again to the plug-flow reactor with side entrances, only this time the fluid enters the reactor along its length (Figure 17-4). As soon as the fluid enters the reactor, it is completely mixed radially (but not longitudinally) with the other fluid already in the reactor. The entering fluid is fed into the reactor through the side entrances in such a manner that the RTD of the plug-flow reactor with side entrances is identical to the RTD of the real reactor.

The globules at the far left of Figure 17-4(a) correspond to the molecules that spend a long time in the reactor, while those at the far right correspond to the molecules that channel through the reactor and spend a very short time in the reactor. In the reactor with side entrances, mixing occurs at the earliest possible moment consistent with the RTD. This situation is termed the condition of maximum mixedness.⁷ The approach for calculating conversion for a reactor in a condition of maximum mixedness will now be developed. In a reactor with side entrances, let λ be the time it takes for the fluid to move from a particular point to the end of the reactor. In other words, λ is the life expectancy of the fluid in the reactor at that point (Figure 17-5).

⁷ T. N. Zwietering, Chem. Eng. Sci., 11, 1 (1959).

Maximum mixedness: mixing occurs at the earliest possible point.

Moving down the reactor from left to right, the life expectancy, λ, decreases and becomes zero at the exit. At the left end of the reactor, λ approaches infinity or the maximum residence time if it is other than infinite.

Consider the fluid that enters the reactor through the sides of volume ΔV in Figure 17-5. The fluid that enters here will have a life expectancy between λ and λ+Δλ. The fraction of fluid that will have this life expectancy between λ and λ+Δλ is E(λ)Δλ. The corresponding volumetric flow rate IN through the sides is [υ₀E(λ)Δλ].

Fluid balance on Δλ In + In = Out

The volumetric flow rate at λ, υ_λ, is the flow rate that entered at λ+Δλ, i.e., υ_λ+Δλ, plus what entered through the sides υ₀ E(λ)Δλ, i.e.,

υ_λ = υ_{λ + Δλ} + υ₀E(λ)Δλ

Rearranging and taking the limit as Δλ → 0

The volumetric flow rate υ at the entrance to the reactor (V = 0, λ = ∞, and X = 0) is zero (i.e., υ_λ = 0) because the fluid only enters through the sides along the length.

Integrating Equation (17-7) with limits υ_λ = 0 at λ = ∞ and υ_λ = υ_λ at λ = λ, we obtain

The volume of fluid in the reactor with a life expectancy between λ and λ + Δλ is

The rate of generation of the substance A in this volume is

We can now carry out a mole balance on substance A between λ and λ + Δλ

Mole balance

Substituting for υ_{λ + Δλ}, υ_λ, and ΔV

Dividing Equation (17-11) by υ₀ Δλ and taking the limit as Δλ → 0 gives

Taking the derivative of the term in brackets

Rearranging

We can also rewrite Equation (17-12) in terms of conversion as

or

The boundary condition is as λ → ∞, then C_A = C_A0 for Equation (17-12) [or X = 0 for Equation (17-13)]. To obtain a solution, the equation is integrated backwards numerically, starting at a very large value of λ and ending with the final conversion at λ = 0. For a given RTD and reaction orders greater than one, the maximum mixedness model gives the lower bound on conversion.

Maximum mixedness gives the lower bound on X.

Realizing

Substituting for λ in Equation (17-14)

and rearranging

One now integrates between the limit z = 0 and z = 200 to find the exit conversion at z = 200, which corresponds to λ = 0.

In fitting E(t) to a polynomial, one has to make sure that the polynomial does not become negative at large times. Another concern in the maximum mixedness calculations is that the term (1 – F(λ)) does not go to zero. Setting the maximum value of F(t) at 0.999 rather than 1.0 will eliminate this problem. It can also be circumvented by integrating the polynomial for E(t) to get F(t) and then setting the maximum value of F(t) at 0.999. If F(t) is ever greater than one when fitting a polynomial, the solution will blow up when integrating Equation (17-17) numerically.

Comparing X_seg and X_mm

For example, if the rate law is a power law model, then

From the product [(n)(n – 1)], we see

We note that in some cases X_seg is not too different from X_mm. However, when one is considering the destruction of toxic waste where X > 0.99 is desired, then even a small difference is significant!!

Important point

In this section we have addressed the case where all we have is the RTD and no other knowledge about the flow pattern exists. Perhaps the flow pattern cannot be assumed because of a lack of information or other possible causes. Perhaps we wish to know the extent of possible error from assuming an incorrect flow pattern. We have shown how to obtain the conversion, using only the RTD, for two limiting mixing situations: the earliest possible mixing consistent with the RTD, or maximum mixedness, and mixing only at the reactor exit, or complete segregation. Calculating conversions for these two cases gives bounds on the conversions that might be expected for different flow paths consistent with the observed RTD.

The concentrations of the individual species, C_A (t) and C_B (t), in the different globules are determined from batch reactor calculations. For a constant-volume batch reactor, where q reactions are taking place, the coupled mole balance equations are

These equations are solved simultaneously with

to give the exit concentration. The RTDs, E (t), in Equations (17-25) and (17-26) are determined from experimental measurements and then fit to a polynomials.

After substitution for the rate laws for each reaction (e.g., r_1A = k₁C_A), these equations are solved numerically by starting at a very large value of λ, say , and integrating backwards to λ = 0 to yield the exit concentrations C_A, C_B, ... .

We will now show how different RTDs with the same mean residence time can produce different product distributions for multiple reactions.

Calculations similar to those in Example 17-6 are given in an example on the CRE Web site for the series reaction

Living Example CD17-RTD (LEP), parts (a) through (h), explores the above series reaction and also multiple reactors with different residence time distributions (e.g., asymmetric, bimodal).

2. The dimensionless residence time is

and is equal to the number space times. Then

3. The internal-age distribution, [I (α) dα], gives the fraction of material inside the reactor that has been inside between a time α and a time (α + dα).

4. Segregation model: The conversion is

and for multiple reactions

5. Maximum mixedness: Conversion can be calculated by solving the following equations

and for multiple reactions

from λ = λ_max to λ = 0. To use an ODE solver, let z = λ_max – λ.

1. The Intensity Function, Λ(t)

2. Heat Effects

3. Example LEP 17-4 and Problem 17-5 with Heat Effects

4. Problem 17-16_B

• Learning Resources

1. Summary Notes

2. Solved Problems

A. Example Web17-1 Calculate the exit concentrations for the series reaction

B. Example Web17-2 Determination of the effect of variance on the exit concentrations for the series reaction

• Living Example Problems

1. Living Example 17-2 Mean Conversion, X_seg, in a Real Reactor

2. Living Example 17-3 Second-Order Reaction in a PFR

3. Living Example 17-4 Conversion Boundary, X_seg and X_mm, for a Nonideal Reactor

4. Living Example 17-5 Using Software to Make Maximum Mixedness Model Calculations

5. Living Example 17-6 (a) RTD and Complex Reactions (a) Segregation Model with Asymmetric E(t)

6. Living Example 17-6 (b) RTD and Complex Reactions (b) Maximum Mixedness with a Bimodal E(t)

7. Living Example Web17-1 (a) RTD Calculations for Reactions in a Series in a PFR

8. Living Example Web17-1 (b) RTD Calculations for Reactions in a Series in a CSTR

9. Living Example Web17-1 (c) RTD Calculations for a Series Reaction Segregation Model with Asymmetric RTD

10. Living Example Web17-1 (d) RTD Calculations for a Series Reaction Segregation Model with Bimodal Distribution

11. Living Example Web17-1 (e) RTD Calculations for a Series Reaction Maximum Mixedness Model with Asymmetric RTD

12. Living Example Web17-1 (f) RTD Calculations for a Series Reaction Maximum Mixedness Model with Bimodal Distribution

13. Living Example Web17-1 (g) RTD Calculations for a Series Reaction Segregation Model with Bimodal Distribution (Multiple Reactions)

14. Living Example Web17-1 (h) RTD Calculations for a Series Reaction Maximum Mixedness Model with Asymmetric RTD (Multiple Reactions)

• Professional Reference Shelf

R17.1. Comparing X_seg with X_mm

The derivation of equations using the second derivative criteria

is carried out.

(a) Living Example 17-2. How does the conversion predicted from the segregation model, X_seg, compare with the conversion predicted by the CSTR, PFR, and LFR models for the same mean residence time, t_m?

(b) Living Example 17-3. (1) Vary k by a factor of 5–10 or so above and below the nominal value given in the problem statement of 4.93 × 10^–3 dm³/mol/s. When do X_PFR and X_LFR come close together and when do they become farther apart? (2) Use the E(t) and F(t) in Examples 16-1 and 16-2 to predict conversion, and compare in parts (a), (b), and (c).

(c) Living Example 17-4. (1) Vary the parameter kC_A0, whose nominal value is

by a factor of 10 above and below the value nominal of 0.08 s^–1 and describe when X_seg and X_mm come closer together and when they become farther apart. (2) How do X_mm and X_seg compare with X_PFR, X_CSTR, and X_LFR for the same mean residence time? (3) How would your results change if T = 350 K with E = 10 kcal/mol? How would your answer change if the reaction was pseudo first order with kC_A0 = 4 × 10^–3/s?

(d) Living Example 17-5. (1) Vary the parameters kC_A0, above and below the nominal value 0.08 s^–1, by a factor of 10 and describe when X_seg and X_mm come closer together and when they become farther apart. (2) How do X_mm and X_seg compare with X_PFR, X_CSTR, and X_LFR for the same t_m? (3) How would your results change if the reaction was pseudo first order with k₁ = C_A0k = 0.08 min^–1? (4) If the reaction was third order with ? (5) If the reaction was half order with ? Describe any trends.

(e) Living Example 17-6. Download the Living Example Problem from the CRE Web site. (1) If the activation energies in cal/mol are E₁ = 5,000, E₂ = 1,000, and E₃ = 9,000, how would the selectivities and conversion of A change as the temperature was raised or lowered around 350 K? (2) If you were asked to compare the results from Example 17-6 for the asymmetric and bimodal distributions in Tables E17-6.2 and E17-6.4, what similarities and differences do you observe? What generalizations can you make?

P17-2_B An irreversible first-order reaction takes place in a long cylindrical reactor. There is no change in volume, temperature, or viscosity. The use of the simplifying assumption that there is plug flow in the tube leads to an estimated degree of conversion of 86.5%. What would be the actually attained degree of conversion if the real state of flow is laminar, with negligible diffusion? (Ans.: X_PFR = 0.85 and _laminar = 0.782)

P17-3_C Show that for a first-order reaction

the exit concentration maximum mixedness equation

is the same as the exit concentration given by the segregation model

Hint: Verify

is a solution to Equation (P17-3.1).

P17-4_C The first-order reaction

with k = 0.8 min^–1 is carried out in a real reactor with the following RTD function:

Mathematically, this hemi circle is described by the equations for 2τ ≥ t ≥ 0 then (hemi circle)

For t > 2τ, then E(t) = 0.

(a) What is the mean residence time?

(b) What is the variance?

(c) What is the conversion predicted by the segregation model? (Ans.: X_seg = 0.72)

(d) What is the conversion predicted by the maximum mixedness model? (Ans.: X_mm = 0.445)

P17-5_B A step tracer input was used on a real reactor with the following results:

For t ≤ 10 min, then C_T = 0.

For 10 ≤ t ≤ 30 min, then C_T = 10 g/dm³.

For t ≥ 30 min, then C_T = 40 g/dm³.

The second-order reaction A → B with k = 0.1 dm³/mol • min is to be carried out in the real reactor with an entering concentration of A of 1.25 mol/dm³ at a volumetric flow rate of 10 dm³/min. Here, k is given at 325 K.

(a) What is the mean residence time t_m?

(b) What is the variance σ²?

(c) What conversions do you expect from an ideal PFR and an ideal CSTR in a real reactor with t_m?

(d) What is the conversion predicted by

(1) the segregation model?

(2) the maximum mixedness model?

(e) What conversion is predicted by an ideal laminar flow reactor?

P17-6_B The following E(t) curves were obtained from a tracer test on two tubular reactors in which dispersion is believed to occur.

A second-order reaction

is to be carried out in this reactor. There is no dispersion occurring either upstream or downstream of the reactor, but there is dispersion inside the reactor.

(a) What is the final time t₁ (in minutes) for the reactor shown in Figure P17-6_B (a)? In Figure P17-6_B (b)?

(b) What is the mean residence time, t_m, and variance, (σ², for the reactor shown in Figure P17-6_B (a)? In Figure P17-6_B (b)?

(c) What is the fraction of the fluid that spends 7 minutes or longer in Figure P17-6_B (a)? In Figure P17-6_B (b)?

(d) Find the conversion predicted by the segregation model for reactor A.

(e) Find the conversion predicted by the maximum mixedness model for reactor B.

(f) Repeat (d) and (e) for reactor B.

P17-7_B The third-order liquid-phase reaction with an entering concentration of 2M

was carried out in a reactor that has the following RTD:

(a) For isothermal operation, what is the conversion predicted by

1) a CSTR, a PFR, an LFR, and the segregation model, X_seg?

Hint: Find t_m (i.e., t) from the data and then use it with E(t) for each of the ideal reactors.

2) the maximum mixedness model, X_mm? Plot X vs. z (or λ) and explain why the curve looks the way it does.

(b) Now calculate the exit concentrations of A, B, and C for the reaction

using (1) the segregation model, and (2) the maximum mixedness model.

P17-8_A Consider again the nonideal reactor characterized by the RTD data in Example 17-5, where E(t) and F(t) are given as polynomials. The irreversible gas-phase nonelementary reaction

is first order in A and second order in B, and is to be carried out isothermally. Calculate the conversion for:

(a) A PFR, a laminar flow reactor with complete segregation, and a CSTR all at the same t_m.

(b) The cases of complete segregation and maximum mixedness.

Additional information (obtained at the Jofostan Central Research Laboratory in Riça, Jofostan):

C_A0 = C_B0 = 0.0313 mol/dm³, V = 1000 dm³,

υ₀ = 10 dm³/s, k = 175 dm⁶/mol² · s at 320 K.

P17-9_A Consider an ideal PFR, CSTR, and LFR.

(a) Evaluate the first moment about the mean for a PFR, a CSTR, and an LFR.

(b) Calculate the conversion in each of these ideal reactors for a second-order liquid-phase reaction with Da = 1.0 (τ = 2 min and kC_A0 = 0.5 min^–1).

P17-10_B For the catalytic reaction

the rate law can be written as

Which will predict the highest conversion, the maximum mixedness model or the segregation model? Hint: Specify the different ranges of the conversion where one model will dominate over the other.

P17-11_B Use the RTD data in Example 16-1 and 16-2 to predict X_PFR, X_CSTR, X_LFR, X_seg and X_mm for the following elementary gas phase reactions

(a) A → B       k = 0.1 min^–1

(b) A → 2B    k = 0.1 min^–1

(c) 2A → B    k = 0.1 min^–1 m³/kmol   C_A0 = 1.0 kmol/m³

(d) 3A → B   k = 0.1 m⁶/kmol²min

Repeat (a) through (d) for the RTD given by

(e) P16-3_B

(f) P16-4_B

(g) P16-5_B

P17-12_C The second-order, elementary liquid-phase reaction

is carried out in a nonideal CSTR. At 300 K the specific reaction rate is k_1A = 0.5 dm³/mol · min. In a tracer test, the tracer concentration rose linearly up to 1 mg/dm³ at 1.0 minutes and then decreased linearly to zero at exactly 2.0 minutes. Pure A enters the reactor at a temperature of 300 K.

(a) Calculate the conversion predicted by the segregation and maximum mixedness models.

(b) Now consider that a second elementary reaction also takes place

Compare the selectivities predicted by the segregation and maximum mixedness models.

P17-13_B The reaction and corresponding rate data discussed in Example 8-8 are to be carried out in a nonideal reactor where RTD is given by the data (i.e. E(t) and F(t)) in Example 16-2.

Determine the exit selectivities

(a) Using the segregation model.

(b) Using the maximum mixedness model.

(c) Compare the selectivities in parts (a) and (b) with those that would be found in an ideal PFR and ideal CSTR in which the space time is equal to the mean residence time.

P17-14_B The reactions described in Example 8-12 are to be carried out in the reactor whose RTD is described in Example 17-4 with C_A0 = C_B0 = 0.05 mol/dm³.

(a) Determine the exit selectivities using the segregation model.

(b) Determine the exit selectivities using the maximum mixedness model.

(c) Compare the selectivities in parts (a) and (b) with those that would be found in an ideal PFR and ideal CSTR in which the space time is equal to the mean residence time.

(d) What would your answers to parts (a) through (c) be if the RTD curve rose from zero at t = 0 to a maximum of 50 mg/dm³ after 10 min, and then fell linearly to zero at the end of 20 min?

P17-15_B Using the data in problem P16-11_B,

(a) Plot the internal age distribution I (t) as a function of time.

(b) What is the mean internal age α_m ?

(c) The activity of a “fluidized” CSTR is maintained constant by feeding fresh catalyst and removing spent catalyst at a constant rate. Using the preceding RTD data, what is the mean catalytic activity if the catalyst decays according to the rate law

with

k_D = 0.1 s^–1?

(d) What conversion would be achieved in an ideal PFR for a second-order reaction with kC_A0 = 0.1 min^–1 and C_A0 = 1 mol/dm³?

(e) Repeat (d) for a laminar flow reactor.

(f) Repeat (d) for an ideal CSTR.

(g) What would be the conversion for a second-order reaction with kC_A0 = 0.1 min^-1 and C_A0 = 1 mol/dm³ using the segregation model?

(h) What would be the conversion for a second-order reaction with kC_A0 = 0.1 min^-1 and C_A0 = 1 mol/dm³ using the maximum mixedness model?

P17-16_B The relative tracer concentrations obtained from pulse tracer tests on a commercial packed-bed desulfurization reactor are shown in Figure P17-15_B. After studying the RTD, what problems are occurring with the reactor during the period of poor operation (thin line)? The bed was repacked and the pulse tracer test again carried out with the results shown in Figure P17-15_B (thick line). Calculate the conversion that could be achieved in the commercial desulfurization reactor during poor operation and during good operation (Figure P17-15_B) for the following reactions:

(a) A first-order isomerization with a specific reaction rate of 0.1 h^–1

(b) A first-order isomerization with a specific reaction rate of 2.0 h^–1

(c) What do you conclude upon comparing the four conversions in parts (a) and (b)?

From Additional Home Problem CDP17-I_B [3rd ed. P13-5]

Application Pending for a Problem Hall of Fame

CURL, R. L., and M. L. MCMILLIN, “Accuracies in residence time measurements,” AIChE J., 12, 819–822 (1966).

LEVENSPIEL, O., Chemical Reaction Engineering, 3rd ed. New York: Wiley, 1999, Chaps. 11–16.

2. An excellent discussion of segregation can be found in

DOUGLAS, J. M., “The effect of mixing on reactor design,” AIChE Symp. Ser., 48, vol. 60, p. 1 (1964).

3. Also see

DUDUKOVIC, M., and R. FELDER, in CHEMI Modules on Chemical Reaction Engineering, vol. 4, ed. B. Crynes and H. S. Fogler. New York: AIChE, 1985.

NAUMAN, E. B., “Residence time distributions and micromixing,” Chem. Eng. Commun., 8, 53 (1981).

NAUMAN, E. B., and B. A. BUFFHAM, Mixing in Continuous Flow Systems. New York: Wiley, 1983.

ROBINSON, B. A., and J. W. TESTER, “Characterization of flow maldistribution using inlet-outlet tracer techniques: an application of internal residence time distributions,” Chem. Eng. Sci., 41 (3), 469–483 (1986).

VILLERMAUX, J., “Mixing in chemical reactors,” in Chemical Reaction Engineering—Plenary Lectures, ACS Symposium Series 226. Washington, DC: American Chemical Society, 1982.