6. Isothermal Reactor Design: Moles and Molar Flow Rates

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The mole balances are then coupled to one another using the relative rates of reaction

to arrive at Table 6-1, which gives the balance equations in terms of concentration for the four types of reactors we have been discussing. We see from Table 6-1 that we have only to specify the parameter values for the system (C_A0, υ₀, etc.) and for the rate-law parameters (e.g., k_A, α, β) to solve the coupled ordinary differential equations for either BRs, PFRs, or PBRs, or to solve the coupled algebraic equations for a CSTR.

Must write a mole balance on each species

The generic power-law rate law for species A is

Rate Law

The rate law wrt A is coupled with the equation for relative rates,

Given the rate law for species A, we use Equation (3-1) to substitute for species j, rj, in Equation (1-11), the PFR mole balance.

To relate concentrations to molar flow rates, recall Equation (4-17), with p = P/P₀

Stoichiometry

The pressure-drop equation, Equation (5-28), for isothermal operation (T = T₀) is

TABLE 6-2 ALGORITHM FOR GAS-PHASE REACTIONS

The total molar flow rate is given by the sum of the flow rates of the individual species

when species A, B, C, D, and inert I are the only ones present. Then

F_T = F_A + F_B + F_C + F_D + F_I

We now combine all the preceding information, as shown in Table 6-2.¹

¹ View the YouTube video made by the chemical reaction engineering students at the University of Alabama, entitled Find Your Rhythm. Videos can be accessed directly from the home page of the CRE Web site, www.umich.edu/~elements/5e/index.html.

A photo of a micro reactor is shown in Figure P5-21_B on page 203.

Advantages of microreactors

Figure 6-2 shows (a) a microreactor with heat exchanger and (b) a microplant with reactor, valves, and mixers. Heat, , is added or taken away by the fluid flowing perpendicular to the reaction channels, as shown in Figure 6-2(a). Production in microreactor systems can be increased simply by adding more units in parallel. For example, the catalyzed reaction

required only 32 microreaction systems in parallel to produce 2000 tons/yr of acetate!

Microreactors are also used for the production of specialty chemicals, combinatorial chemical screening, lab-on-a-chip, and chemical sensors. In modeling microreactors, we will assume they are either in plug flow for which the mole balance is

or in laminar flow, in which case we will use the segregation model discussed in Chapter 17. For the plug-flow case, the algorithm is described in Figure 6-1.

The term membrane reactor describes a number of different types of reactor configurations that contain a membrane. The membrane can either provide a barrier to certain components while being permeable to others, prevent certain components such as particulates from contacting the catalyst, or contain reactive sites and be a catalyst in itself. Like reactive distillation, the membrane reactor is another technique for driving reversible reactions to the right toward completion in order to achieve very high conversions. These high conversions can be achieved by having one of the reaction products diffuse out through a semipermeable membrane surrounding the reacting mixture. As a result, the reverse reaction will not be able to take place, and the reaction will continue to proceed to the right toward completion.

By having one of the products pass through the membrane, we drive the reaction toward completion.

Two of the main types of catalytic membrane reactors are shown in Figure 6-3. The reactor in Figure 6-3(b) is called an inert membrane reactor with catalyst pellets on the feed side (IMRCF). Here, the membrane is inert and serves as a barrier to the reactants and some of the products. The reactor in Figure 6-3(c) is a catalytic membrane reactor (CMR). The catalyst is deposited directly on the membrane, and only specific reaction products are able to exit the permeate side. As an example, consider the reversible reaction where

H₂ diffuses through the membrane, while C₆H₆ does not.

the hydrogen molecule is small enough to diffuse through the small pores of the membrane, while C₆H₁₂ and C₆H₆ cannot. Consequently, the reaction continues to proceed to the right even for a small value of the equilibrium constant.

Hydrogen, species B, flows out through the sides of the reactor as it flows down the reactor with the other products that cannot leave until they exit the reactor.

In analyzing membrane reactors, we only need to make a small change to the algorithm shown in Figure 6-1. We shall choose the reactor volume rather than catalyst weight as our independent variable for this example. The catalyst weight, W, and reactor volume, V, are easily related through the bulk catalyst density, ρ_b (i.e., W = ρ_bV). The mole balances on the chemical species that stay within the reactor, namely A and C, are shown in Figure 6-3(d).

The mole balance on C is carried out in an identical manner to A, and the resulting equation is

However, the mole balance on B (H₂) must be modified because hydrogen leaves through both the sides of the reactor and at the end of the reactor.

First, we shall perform mole balances on the volume element ΔV shown in Figure 6-3(d). The mole balance on hydrogen (B) is over a differential volume ΔV shown in Figure 6-3(d) and it yields

Balance on B in the catalytic bed:

Now there are two “OUT” terms for species B.

where R_B is the molar rate of B leaving through the sides of the reactor per unit volume of reactor (mol/m³·s). Dividing by ΔV and taking the limit as ΔV → 0 gives

The rate of transport of B out through the membrane R_B is the product of the molar flux of B normal to the membrane, W_B (mol/m²/s), and the surface area per unit volume of reactor, a(m²/m³). The molar flux of B, W_B in (mol/m²/s) out through the sides of the reactor is the product of the mass transfer coefficient, (m/s), and the concentration driving force across the membrane.

Here, is the overall mass transfer coefficient in m/s and C_BS is the concentration of B in the sweep gas channel (mol/m³). The overall mass transfer coefficient accounts for all resistances to transport: the tube-side resistance of the membrane, the membrane itself, and on the shell-(sweep gas) side resistance. Further elaboration of the mass transfer coefficient and its correlations can be found in the literature and in Chapter 14. In general, this coefficient can be a function of the membrane and fluid properties, the fluid velocity, and the tube diameters.

To obtain the rate of removal of B per unit volume of reactor, R_B (mol/m³/s), we need to multiply the flux through the membrane, W_B(mol/m²·s), by the membrane surface area per volume of reactor, a(m²/m³); that is

The membrane surface area per unit volume of reactor is

Letting a and assuming the concentration in the sweep gas is essentially zero (i.e., C_BS ≈ 0), we obtain

Rate of B out through the sides.

where the units of k_C are s^–1.

More detailed modeling of the transport and reaction steps in membrane reactors is beyond the scope of this text but can be found in Membrane Reactor Technology.³ The salient features, however, can be illustrated by the following example. When analyzing membrane reactors, we must use molar flow rates because expressing the molar flow rate of B in terms of conversion will not account for the amount of B that has left the reactor through the sides.

³ R. Govind and N. Itoh, eds., Membrane Reactor Technology, AIChE Symposium Series 85, no. 268 (1989). T. Sun and S. Khang, Ind. Eng. Chem. Res., 27, 1136 (1988).

According to the DOE, 10 trillion Btu/yr could be saved by using membrane reactors.

Use of Membrane Reactors to Enhance Selectivity. In addition to species leaving through the sides of the membrane reactor, species can also be fed to the reactor through the sides of the membrane. For example, for the reaction

A + B → C + D

species A will be fed only to the entrance, and species B will be fed only through the membrane as shown here.

As we will see in Chapter 8, this arrangement is often used to improve selectivity when multiple reactions take place. Here, B is usually fed uniformly through the membrane along the length of the reactor. The balance on B is

where R_B = F_B0/V_t with F_B0, representing the total molar feed rate of B through the sides and V_t the total reactor volume. The feed rate of B can be controlled by controlling the pressure drop across the reactor membrane.⁵ This arrangement will keep the concentration of A high and the concentration of B low to maximize the selectivity given by Equation (E8-2.2) for the reactions given in Section 8.6, e.g., Example 8-8.

⁵ The velocity of B through the membrane, U_B, is given by Darcy’s law

U_B = K(P_s – P_r)

where K is the membrane permeability, P_s is the shell-side pressure, and P_r the reactorside pressure

where, as before, a is the membrane surface area per unit volume, C_B0 is the entering concentration of B, and V_t is the total reactor volume.

An unsteady-state analysis can be used to determine the startup time for a CSTR (Figure 6-4(a)) and this analysis is given in the Expanded Material for Chapter 6 on the CRE Web site. Here, we show the time to steady state for a first-order reaction is approximately

For most first-order systems, the time to reach steady state is 3 to 4 space times.

There are two basic types of semibatch operations. In one type, one of the reactants in the reaction

A + B → C + D

(e.g., B) is slowly fed to a reactor containing the other reactant (e.g., A), which has already been charged to a reactor such as that shown in Figure 6-4(b). This type of reactor is generally used when unwanted side reactions occur at high concentrations of B (see Section 8.1) or when the reaction is highly exothermic (Chapter 11). In some reactions, the reactant B is a gas and is bubbled continuously through liquid reactant A. Examples of reactions used in this type of semibatch reactor operation include ammonolysis, chlorination, and hydrolysis. The other type of semibatch reactor is reactive distillation and is shown schematically in Figure 6-4(c). Here, reactants A and B are charged simultaneously and one of the products vaporizes and is withdrawn continuously. Removal of one of the products in this manner (e.g., C) shifts the equilibrium toward the right, increasing the final conversion above that which would be achieved had C not been removed. In addition, removal of one of the products further concentrates the reactant, thereby producing an increased rate of reaction and decreased processing time. This type of reaction operation is called reactive distillation. Examples of reactions carried out in this type of reactor include acetylation reactions and esterification reactions in which water is removed.

with the rate law

and the other reaction produces an undesired product U

with the rate law

The instantaneous selectivity S_D/U is the ratio of these two rates

We want S_D/U as large as possible.

and guides us in how to produce the most amount of our desired product and the least amount of our undesired product (see Section 8.1). We see from the instantaneous selectivity that we can increase the formation of D and decrease the formation of U by keeping the concentration of A high and the concentration of B low. This result can be achieved through the use of the semibatch reactor, which is charged with pure A and to which B is fed slowly to A in the vat.

A + B → C

in which reactant B is slowly added to a well-mixed vat containing reactant A. A mole balance on species A yields

Mole balance on species A

Three variables can be used to formulate and solve semibatch reactor problems: the concentrations, C_j, the number of moles, N_j, and the conversion, X.

We shall use concentration as our preferred variable, leaving the analysis of semibatch reactors using the number of moles, N_j, and conversion X to the CRE Web site Summary Notes and Professional Reference Shelf for Chapter 6.

Recalling that the number of moles of A, N_A, is just the product of the concentration of A, C_A, and the volume, V, [i.e., (N_A = C_AV)], we can rewrite Equation (6-16) as

We note that since the reactor is being filled, the volume, V, varies with time. The reactor volume at any time t can be found from an overall mass balance of all species. The mass flow rate into the reactor, , is just the product of the liquid density, ρ₀, and volumetric flow rate υ₀. The mass of liquid inside the reactor, m, is just the product of the liquid density ρ and the volume of liquid V in the reactor, i.e., m = ρV. There is no mass flow out and no generation of mass.

Overall mass balance

For a constant-density system, ρ₀ = ρ, and

with the initial condition V = V₀ at t = 0, integrating for the case of constant volumetric flow rate υ₀ yields

Semibatch reactor volume as a function of time

Substituting Equation (6-19) into the right-hand side of Equation (6-17) and rearranging gives us

The balance on A, seen in Equation (6-17), can be rewritten as

Mole balance on A

A mole balance on B that is fed to the reactor at a rate F_B0 is

Rearranging gives

Substituting for N_B in terms of concentration and reactor volume (N_B = C_BV), differentiating, and then using Equation (6-19) to substitute for (dV/dt), and F_B0 = C_B0 υ₀, the mole balance on B given in Equation (6-23) becomes

Rearranging gives

Mole balance on B

Similarly, for species C we have

Combining Equations (6-24) and (6-25) and rearranging we obtain

Mole balance on C

Following the same procedure for species D

Mole balance on D

At time t = 0, the initial concentrations of B, C, and D in the vat are zero, C_Bi = C_Ci = C_Di = 0. The concentration of B in the feed is C_B0. If the reaction order is other than zero- or first-order, or if the reaction is nonisothermal, we must use numerical techniques to determine the concentrations and conversion as a function of time. Equations (6-21), (6-23), (6-26), and (6-27) are easily solved with an ODE solver.

Equilibrium Conversion. For reversible reactions carried out in a semibatch reactor, the maximum attainable conversion (i.e., the equilibrium conversion) will change as the reaction proceeds because more reactant is continuously added to the reactor. This addition shifts the equilibrium continually to the right toward more product.

An outline of what is given on the CRE Web site follows:

At Equilibrium

Using the number of moles in terms of conversion

Substituting

Solving for X_e

One notes the equilibrium conversion, X_e, changes with time. Further discussion on this point and calculation of the equilibrium conversion can be found in Professional Reference Shelf R6.1, in the example problem on the CRE Web site.

When using measures other than conversion for reactor design, the mole balances are written for each species in the reacting mixture:

Mole balances on each and every species

The mole balances are then coupled through their relative rates of reaction. If

Rate Law

for aA + bB → cC + dD, then

Relative Rates

Concentration can also be expressed in terms of the number of moles (batch) and in terms of molar flow rates).

Stoichiometry

2. For membrane reactors, the mole balances for the reaction

when reactant A and product C do not diffuse out the membrane

Mole Balance

with

Tansport Law

and k_c is the overall mass transfer coefficient.

3. For semibatch reactors, reactant B is fed continuously to a vat initially containing only A

Mole Balances

The Polymath solutions to the above equations are given on the CRE Web site in the Chapter 6 Summary Notes under “Link” PBR ODE Solver.

1. Start-Up of a CSTR

2. Puzzle Problem “What’s Wrong with this Solution?”

3. Additional Homework Problems

• Learning Resources

1. Summary Notes

2. Modules and Games

A. Wetlands Web Module

B. Tic-Tac Interactive Game

• Living Example Problems

Example 6-1 Gas-Phase Reaction in Microreactor—Molar Flow Rate

Example 6-2 Membrane Reactor

Example 6-3 Isothermal Semibatch Reactor

• Professional Reference Shelf

R6.1. Unsteady CSTRs and Semibatch Reactors

R6.1A Startup of a CSTR

R6.1B Semibatch Reactor Balances in Terms of Number of Moles

R6.1C Semibatch Reactor Balance in Terms of Conversion

R6.1D Equilibrium Conv ersion

R6.2. The Practical Side

A number of practical guidelines for operating chemical reactors are given.

R6.3. Aerosol Reactors

Aerosol reactors are used to synthesize nano-size particles. Owing to their size, shape, and high specific surface area, nanoparticles can be used in a number of applications such as pigments in cosmetics, membranes, photocatalytic reactors, catalysts and ceramics, and catalytic reactors.

We use the production of aluminum particles as an example of an aerosol plug-flow reactor (APFR) operation. A stream of argon gas saturated with Al vapor is cooled.

Aerosol reactor and temperature profile.

As the gas is cooled, it becomes supersaturated, leading to the nucleation of particles. This nucleation is a result of molecules colliding and agglomerating until a critical nucleus size is reached and a particle is formed. As these particles move down the reactor, the supersaturated gas molecules condense on the particles, causing them to grow in size and then to flocculate. In the development on the CRE Web site in the Web Modules category, we will model the formation and growth of aluminum nanoparticles in an AFPR.

In each of the following questions and problems, rather than just drawing a box around your answer, write a sentence or two describing how you solved the problem, the assumptions you made, the reasonableness of your answer, what you learned, and any other facts that you want to include. You may wish to refer to W. Strunk and E. B. White, The Elements of Style, 4th ed. (New York: Macmillan, 2000) and Joseph M. Williams, Style: Ten Lessons in Clarity & Grace, 6th ed. (Glenview, IL: Scott, Foresman, 1999) to enhance the quality of your sentences. See the preface for additional generic parts (x), (y), and (z) to the home problems.

Before solving the problems, state or sketch qualitatively the expected results or trends.

(a) Example 6-1. Download the Living Example Problem 6-1 from the CRE Web site. (1) What would be the conversion if the pressure were doubled and the temperature were decreased by 20°C? (2) Compare Figure E6-1.1 profiles with those for a reversible reaction with K_C = 0.02 mol/dm³ and describe the differences in the profiles. (3) How would your profiles change for the case of an irreversible reaction with pressure drop when α_p = 99 × 10³ dm^–3 for each tube?

(b) Example 6-2. Download the Living Example Problem 6-2 from the CRE Web site. You might find it easiest to answer most of the following questions using Wolfram. (1) Starting with all values of K_C, k, C_T0, and k_C in the middle range (K_C = 0.25, k = 2.1, C_T0 = 0.52, and k_C = 1.06), vary each parameter individually and describe what you find. Note and explain any maximum or minimum values of your plots down the length (i.e., volume = 500dm³) of your reactor. Hint: Go to the extremes of the range. (2) Repeat (1) but set K_C at its maximum value and then vary k and k_C, and describe what you find. (3) Use Polymath to find the parameter values at which R_B is a maximum and the concentrations/flow rates are at the maximum. (4) Vary ratios of parameters such as (k/k_C) and (k τC_A0/K_C) [Note: τ = 400 min] and write a paragraph describing what you find. What ratio of parameters has the greatest effect on the conversion X = (F_A0–F_A0)/F_A0? (5) Write a summary paragraph of all the trends and your results. (6) Make up a question/problem on membrane reactors with a solution in which Wolfram must be used to obtain the answer. Hint: See Preface Table P-4, page xxviii. Also comment on what types of questions would you ask when using Wolfram.

(c) Example 6-3. Download the Living Example Problem 6-3 from the CRE Web site. The temperature is to be lowered by 35°C so that the reaction-rate constant is now one-tenth its original value. (1) If the concentration of B is to be maintained at 0.01 mol/dm³ or below, what is the maximum feed rate of B?(2) How would your answer change if the concentration of A were tripled? (3) Redo this problem when the reaction is reversible with K_C = 0.1 and compare with the irreversible case. (Only a couple of changes in the Polymath program are necessary.)

(d) Web Module on Wetlands on the CRE Web site. Download the Polymath program and vary a number of parameters such as rainfall, evaporation rate, atrazine concentration, and liquid flow rate, and write a paragraph describing what you find. This topic is a hot Ch.E. research area.

(e) Web Module on Aerosol Reactors on the CRE Web site. Download the Polymath program and (1) vary the parameters, such as cooling rate and flow rate, and describe their effect on each of the regimes: nucleation, growth, and flocculation. Write a paragraph describing what you find. (2) It is proposed to replace the carrier gas by helium.

(i)   Compare your plots (He versus Ar) of the number of Al particles as a function of time. Explain the shape of the plots.

(ii)  How does the final value of d_p compare with that when the carrier gas was argon? Explain.

(iii) Compare the time at which the rate of nucleation reaches a peak in the two cases (carrier gas = Ar and He). Discuss the comparison.

Data for a He molecule: mass = 6.64×10^–27 kg, volume = 1.33×10^–29 m³, surface area = 2.72 × 10^–19m², bulk density = 0.164 kg/m³, at normal temperature (25°C) and pressure (1 atm).

(f) The Work Self-Tests on the Web. Write a question for this problem that involves critical thinking and explain why it involves critical thinking. See examples on the CRE Web site, Summary Notes for Chapter 6.

P6-2_B Download the Interactive Computer Games (ICG) from the CRE Web site. Play the game and then record your performance number, which indicates your mastery of the material. Your instructor has the key to decode your performance number. Knowledge of all sections is necessary to pit your wit against the computer adversary in playing a game of Tic-Tac-Toe.

Performance number: _________________________

P6-3_C The second-order liquid phase reaction

is carried out in a batch reactor at 35°C. The specific reaction-rate constant is 0.0445 dm³/mol/min. Reactor 1 is charged with 1,000 dm³, where the concentration of each reactant after mixing is 2M.

(a) What is the conversion after 10, 50, and 100 minutes?

Now, consider the case when, after filling reactor 1, the drain at the bottom of reactor 1 is left open and it drains into reactor 2, mounted below it, at a volumetric rate of 10 dm³/min.

(b) What will be the conversion and concentration of each species in reactor 1 after 10, 50, and 80 minutes in the reactor that is being drained? (Ans.: At t = 10 min then X = 0.47)

(c) What is the conversion and concentration of each species in reactor 2 that is filling up with the liquid from reactor 1 after 10 and after 50 minutes? (Ans.: At t = 50 min then X = 0.82)

(d) At the end of 50 minutes, the contents of the two reactors are added together. What is the overall conversion after mixing?

(e) Apply one or more of the six ideas in Preface Table P-4, page xxviii, to this problem.

P6-4_B The elementary gas-phase reaction

(CH₃)₃COOC(CH₃)₃ → C₂H₆ + 2CH₃COCH₃

A → B + 2C

is carried out isothermally at 400 K in a flow reactor with no pressure drop. The specific reaction rate at 50°C is 10^–4 min^–1 (from pericosity data) and the activation energy is 85 kJ/mol. Pure di-tert-butyl peroxide enters the reactor at 10 atm and 127°C and a molar flow rate of 2.5 mol/min, i.e., F_A = 2.5 mol/min.

(a) Use the algorithm for molar flow rates to formulate and solve the problem. Plot F_A, F_B, F_C, and then X as a function of plug-flow reactor volume and space time to achieve 90% conversion.

(b) Calculate the plug-flow volume and space time for a CSTR for 90% conversion.

P6-5_B For the reaction and data in P6-4_B, we now consider the case when the reaction is reversible with K_C = 0.025 dm⁶/mol² and the reaction is carried out at 300 K in a membrane reactor where C₂H₆ is diffusing out. The membrane transport coefficient is k_C = 0.08 s^–1.

(a) What is the equilibrium conversion and what is the exit conversion in a conventional PFR? (Ans.: X_eq = 0.52, X = 0.47)

(b) Plot and analyze the conversion and molar flow rates in the membrane reactor as a function of reactor volume up to the point where 80% conversion of di-tert-butyl peroxide is achieved. Note any maxima in the flow rates.

(c) Apply one or more of the six ideas in Preface Table P-4, page xxviii, to this problem.

P6-6_C (Membrane reactor) The first-order, gas-phase, reversible reaction

is taking place in a membrane reactor. Pure A enters the reactor, and B diffuses out through the membrane. Unfortunately, a small amount of the reactant A also diffuses through the membrane.

(a) Plot and analyze the flow rates of A, B, and C and the conversion X down the reactor, as well as the flow rates of A and B through the membrane.

(b) Next, compare the conversion profiles in a conventional PFR with those of a membrane reactor from part (a). What generalizations can you make?

(c) Would the conversion of A be greater or smaller if C were diffusing out instead of B?

(d) Discuss qualitatively how your curves would change if the temperature were increased significantly or decreased significantly for an exothermic reaction. Repeat the discussion for an endothermic reaction.

Additional information:

k = 10 min^–1

K_C = 0.01 mol²/dm⁶

k_CA = 1 min^–1

k_CB = 40 min^–1

F_A0 = 100 mol/min

υ₀ = 100 dm³/min

V_reactor = 20 dm³

P6-7_B Fuel Cells Rationale. With the focus on alternative clean-energy sources, we are moving toward an increased use of fuel cells to operate appliances ranging from computers to automobiles. For example, the hydrogen/oxygen fuel cell produces clean energy as the products are water and electricity, which may lead to a hydrogen-based economy instead of a petroleum-based economy.

A large component in the processing train for fuel cells is the water-gas shift membrane reactor. (M. Gummala, N. Gupla, B. Olsomer, and Z. Dardas, Paper 103c, 2003, AIChE National Meeting, New Orleans, LA.)

Here, CO and water are fed to the membrane reactor containing the catalyst. Hydrogen can diffuse out the sides of the membrane, while CO, H₂O, and CO₂ cannot. Based on the following information, plot the concentrations and molar flow rates of each of the reacting species down the length of the membrane reactor. Assume the following: The volumetric feed is 10 dm³/min at 10 atm, and the equimolar feed of CO and water vapor with C_T0 = 0.4 mol/dm³.

The equilibrium constant is K_e = 1.44, with k = 1.37 dm⁶/mol kg-cat · min, and the mass transfer coefficient k_H2 = 0.1 dm³/kg-cat · min (Hint: First calculate the entering molar flow rate of CO and then relate F_A and X.)

(a) What is the membrane reactor volume necessary to achieve 85% conversion of CO?

(b) Sophia wants you to compare the MR with a conventional PFR. What will you tell her?

(c) For that same membrane reactor volume, Nicolas wants to know what would be the conversion of CO if the feed rate were doubled?

P6-8_C The production of ethylene glycol from ethylene chlorohydrin and sodium bicarbonate

CH₂OHCH₂Cl + NaHCO₃ → (CH₂OH)₂ + NaCl + CO₂^↑

is carried out in a semibatch reactor. A 1.5-molar solution of ethylene chlorohydrin is fed at a rate of 0.1 mole/minute to 1500 dm³ of a 0.75-molar solution of sodium bicarbonate. The reaction is elementary and carried out isothermally at 30°C where the specific reaction rate is 5.1 dm³/mol/h. Higher temperatures produce unwanted side reactions. The reactor can hold a maximum of 2500 dm³ of liquid. Assume constant density.

(a) Plot and analyze the conversion, reaction rate, concentration of reactants and products, and number of moles of glycol formed as a function of time.

(b) Suppose you could vary the flow rate between 0.01 and 200 mol/min. What flow rate and holding time would you choose to make the greatest number of moles of ethylene glycol in 24 hours, keeping in mind the downtimes for cleaning, filling, etc., shown in Table 5-3?

(c) Suppose the ethylene chlorohydrin is fed at a rate of 0.15 mol/min until the reactor is full and then shut in. Plot the conversion as a function of time.

(d) Discuss what you learned from this problem and what you believe to be the point of this problem.

P6-9_C The following elementary reaction is to be carried out in the liquid phase

The initial concentrations are 0.2 M in NaOH and 0.25 M in CH₃COOC₂H₅ with k = 5.2 × 10^–5 dm³/mol-s at 20°C with E = 42,810 J/mol. Design a set of operating conditions (e.g., υ₀, T, . . .) to produce 200 mol/day of ethanol in a semibatch reactor and not operate above 37°C and below a concentration of NaOH of 0.02 molar.⁶ The semibatch reactor you have available is 1.5 m in diameter and 2.5 m tall. The reactor down time is (t_c + t_e + t_f) = 3h.

⁶ Manual of Chemical Engineering Laboratory, University of Nancy, Nancy, France, 1994 ([email protected]; www.sysbio.del/AICHE).

P6-10_B Go to Professor Herz’s Reactor Lab Web site at www.reactorlab.net. From the menu at the top of the page, select Download and then click on the English version link. Provide the required information and then download, install, and open the software. Select Division D2, Lab L2 and there the labeled PFR of The Reactor Lab concerning a packed-bed reactor (labeled PFR) in which a gas with the physical properties of airflows over spherical catalyst pellets. Perform experiments here to get a feeling for how pressure drop varies with input parameters such as reactor diameter, pellet diameter, gas-flow rate, and temperature. In order to get significant pressure drop, you may need to change some of the input values substantially from those shown when you enter the lab. If you get a notice that you can’t get the desired flow, then you need to increase the inlet pressure.

P6-11_B Pure butanol is to be fed into a semibatch reactor containing pure ethyl acetate to produce butyl acetate and ethanol. The reaction

is elementary and reversible. The reaction is carried out isothermally at 300 K. At this temperature, the equilibrium constant is 1.08 and the specific reaction rate is 9 × 10^–5 dm³/mol·s. Initially, there is 200 dm³ of ethyl acetate in the vat, and butanol is fed at a volumetric rate of 0.05 dm³/s. The feed and initial concentrations of butanol and ethyl acetate are 10.93 mol/dm³ and 7.72 mol/dm³, respectively.

(a) Plot and analyze the equilibrium conversion of ethyl acetate as a function of time.

(b) Plot and analyze the conversion of ethyl acetate, the rate of reaction, and the concentration of butanol as a function of time.

(c) Rework part (b), assuming that ethanol evaporates (reactive distillation) as soon as it forms. (This is a graduate level question.)

(d) Use Polymath or some other ODE solver to learn the sensitivity of conversion to various combinations of parameters (e.g., vary F_B0, N_A0, υ₀).

(e) Apply one or more of the six ideas in Preface Table P-4, page xxviii, to this problem.

(f) Write a question that requires critical thinking and then explain why your question requires critical thinking. (Hint: See Preface Section I.)

P6-12_C Use the reaction data in P6-11_B and the molar flow rate algorithm to carry out the following problems:

(a) Calculate the CSTR reactor volume to achieve 80% of the equilibrium conversion for an equal molar feed and for a volumetric feed of 0.05 dm³/s.

(b) Safety. Now consider the case where we want to shut down the reactor by feeding water at a volumetric rate of 0.05 dm³/s. How long will it take to reduce the rate to 1% of the rate in the CSTR under the conditions of part (a)?

P6-13_C An isothermal reversible reaction is carried out in an aqueous solution. The reaction is firstorder in both directions. The forward rate constant is 0.4 h^–1 and the equilibrium constant is 4.0. The feed to the plant contains 100 kg/m³ of A and enters at the rate of 12 m³/h. Reactor effluents pass to a separator, where B is completely recovered. The reactor is a stirred tank of volume 60 m³. A fraction, f1, of the unreacted effluent is recycled as a solution containing 100 kg/m³ of A and the remainder is discarded. Product B is worth $2 per kilogram and operating costs are $50 per cubic meter of solution entering the separator. What value offmaximizes the operational profit of the plant? What fraction A fed to the plant is converted at the optimum? Source: H. S. Shankar, IIT Mumbai.

KEILLOR, GARRISON and TIM RUSSELL, Dusty and Lefty: The Lives of the Cowboys (Audio CD). St. Paul, MN: Highbridge Audio, 2006.

FROMENT, G. F., and K. B. BISCHOFF, Chemical Reactor Analysis and Design, 2nd ed. New York: Wiley, 1990.

Recent information on reactor design can usually be found in the following journals: Chemical Engineering Science, Chemical Engineering Communications, Industrial and Engineering Chemistry Research, Canadian Journal of Chemical Engineering, Jofostan Journal of Chemical Engineering, AIChE Journal, and Chemical Engineering Progress.