Again we consider the production of propylene glycol (C) in a CSTR with a heat exchanger in Example 12-3. Initially there is only water, C_wi = 3.45 lb-mol/ft³, at T_i = 75°F and 0.1 wt % H₂SO₄ in the 500-gallon reactor. The feed stream consists of 80 lb-mol/h of propylene oxide (A), 1000 lb-mol/h of water (B) containing 0.1 wt % H₂SO₄, and 100 lb-mol/h of methanol (M).

Plot the temperature and concentration of propylene oxide as a function of time, and a concentration vs. temperature graph for different entering temperatures and initial concentrations of A in the reactor.

The water coolant flows through the heat exchanger at a rate of 5 lb_m/s (1000 lb-mol/h). The molar densities of pure propylene oxide (A), water (B), and methanol (M) are ρ_A0 = 0.923 lb-mol/ft³, ρ_B0 = 3.45 lb-mol/ft³, and ρ_M0 = 1.54 lb-mol/ft³, respectively.

with T_a1 = 60°F, with C_PW = 18 Btu/lb-mol · °F

C_PA = 35 Btu/lb-mol · °F, C_PB = 18 Btu/lb-mol · °F,

C_PC = 46 Btu/lb-mol · °F, C_PM = 19.5 Btu/lb-mol · °F

Again, the temperature of the mixed reactant streams entering the CSTR is T₀ = 75°F.

The series reactions

are catalyzed by H₂SO₄. All reactions are first order in the reactant concentration. However Reaction (1) is exothermic and Reaction (2) is endothermic. The reaction is to be carried out in a semibatch reactor that has a heat exchanger inside with UA = 35,000 cal/h · K and a constant exchanger temperature, T_a, of 298 K. Pure A enters at a concentration of 4 mol/dm³, a volumetric flow rate of 240 dm³/h, and a temperature of 305 K. Initially there is a total of 100 dm³ in the reactor, which contains 1.0 mol/dm³ of A and 1.0 mol/dm³ of the catalyst H₂SO₄. The reaction rate is independent of the catalyst concentration. The initial temperature inside the reactor is 290 K.

Plot and analyze the species concentrations and reactor temperature as a function of time.

Additional information:

Figure E13-6.1. Aerial photograph of T2 taken December 20, 2007.

(Courtesy of Chemical Safety Board.)

T2 Laboratories manufactured a fuel additive, methylcyclopentadienyl manganese tricarbonyl (MCMT), in a 2,450-gallon, high-pressure batch reactor utilizing a three-step batch process.

Step 1a. The liquid-phase metalation reaction between methylcyclopentadiene (MCP) and sodium in a solvent of diethylene glycol dimethyl ether (diglyme) to produce sodium methylcyclopentadiene and hydrogen gas:

Hydrogen immediately comes out of the solution and is vented at the top in the gas head space.

Step 1b. At the end of Step 1a, MnCl₂ is added. The substitution reaction between sodium methylcyclopentadiene and manganese chloride produced manganese dimethylcyclopentadiene and sodium chloride:

Step 1c. At the end of Step 1b, CO is added. The carbonylation reaction between manganese dimethylcyclopentadiene and carbon monoxide produced the final product, methylcyclopentadienyl manganese tricarbonyl (MCMT):

We will only consider Step 1a as this step is the one in which the explosion occurred.

Procedure

First, solid sodium is mixed in the batch reactor with methylcyclopentadiene dimer and a solvent diethylene glycol dimethyl ether (diglyme). The batch reactor is then heated to about 422 K (300°F) with only slight reaction occurring during this heating process. On reaching 422 K the heating is turned off, as the exothermic reaction is now proceeding, and the temperature continues to increase without further heating. When the temperature reaches 455.4 K (360°F), the operator initiates cooling using the evaporation of boiling water in the reactor jacket as the heat sink (T_a = 373.15 K) (212°F).

What Happened

On December 19, 2007, when the reactor reached a temperature of 455.4 K (360°F), the process operator could not initiate the flow of cooling water to the cooling jacket shown in Figure E13-6.2. Thus, the expected cooling of the reactor was not available and the temperature in the reactor continued to rise. The pressure also increased as hydrogen continued to be produced at an increased rate, to the point that the reactor pressure control valve system on the 1-inch diameter hydrogen venting stream could no longer maintain the operating pressure at 50 psig (4.4 atm). As the temperature continued to increase further, a previously unknown exothermic reaction of the diglyme solvent that was catalyzed by sodium accelerated rapidly.

Figure E13-6.2. Reactor

This reaction produced even more hydrogen, causing the pressure to rise even faster, eventually causing the ruptured disk to break, which was set at 28.2 atm absolute (400 psig), in the 4-inch diameter relief line of H₂. Even with the relief line open, the rate of production of H₂ was now for greater than the rate of venting, causing the pressure to continue to increase to the point that it ruptured the reactor vessel initiating a horrific explosion. The T2 plant was completely leveled and four personnel lives were lost. Surrounding businesses were heavily damaged and additional injuries were sustained.

Before continuing with this example it might be helpful to view the 9 minute Chemical Safety Board (CSB) video, which you can access directly from the Chapter 13 Summary Notes on the Web site, or you can read the supporting reports [http://www.chemsafety.gov/videoroom/detail.aspx?VID=32]. You can also search the Web for “T2 explosion video.”

Simplified Model

Let A = methycylcopentadiene, B = sodium, S = Solvent (diglyme), and D = H₂. This runaway reaction can be approximately modeled with two reactions. These reactions are

(1) A + B → C + 1/2 D (gas)

(2) S → 3 D (gas) + miscellaneous liquid and solid products

In reaction (1), A and B react to form products. Reaction (2) represents the decomposition of the liquid-phase solvent S catalyzed by the presence of B, but this reaction only begins to proceed once a temperature of approximately 470 K is reached.

The rate laws, along with the specific reaction rate constants at the initial temperature of 422 K, are:

–r_1A = k_1AC_AC_B

A_1A = 5.73 × 10² dm³ mol^–1 hr^–1 with E_1A = 128,000 J/mol K

–r_2S = k_2S*C_S

A_2S = 9.41 × 10¹⁶ hr^–1 with E_2S = 800,000 J/mol K

The heats of reaction are constant.

ΔH_Rx1A = 45,400 J/mol

ΔH_Rx2S = 3.2 × 10⁵ J/mol

The sum of products of the moles of each species and their corresponding heat capacities (cf. Equation 13-18) is essentially constant at

ΣN_jC_Pj = 1.26 × 10⁷ J/K

Assumptions

Assume that the liquid volume, V₀, in the reactor remains constant at 4,000 dm³ and that the vapor space, V_H, above the reactor occupies 5,000 dm³. Any gas, H₂ (i.e., D), that is formed by reactions (1) and (2) immediately appears as an input stream F_D to the head space volume. The dissolved H₂ and the vapor pressures for the liquid components in the reactor can be neglected. The initial absolute pressure within the reactor is 4.4 atm (50 psig). During normal operation, H₂ generated obeys the ideal gas law. The pressure control system on the H₂ vent stream maintains the pressure, P, at 4.40 atm up to a flow of 11,400 mol/hr. The reactor vessel will fail when the pressure exceeds 45 atm or the temperature exceeds 600 K.

Additional Information

UA = 2.77 × 10⁶ J hr^–1 K^–1. The concentrations in the reactor at the end of the reactor heating at 422 K are C_A0 = 4.3 mol/dm³, C_B0 = 5.1 mol/dm³, C_I0 = 0.088, and C_S0 = 3 mol/dm³. The sensible heat of the two gas venting streams may be neglected.

Problem Statement

Plot and analyze the reactor temperature and head space pressure as a function of time along with the reactant concentrations for the scenario where the reactor cooling fails to work (UA = 0). In Problem P13-2(f) you will be asked to redo the problem when the cooling water comes as expected whenever the reactor temperature exceeds 455 K.

P13-1_C

Prepare a list of safety considerations for designing and operating chemical reactors. See the August 1985 issue of Chemical Engineering Progress.

P13-2_B

Review the example problems in this chapter and use a software package such as Polymath or MATLAB to carry out a parameter sensitivity analysis to answer the following “What if...” questions.

What if...

a. Example 13-1. (1) How would your answer change if the heat of the mixing had been neglected? (2) How much time would it take to achieve 90% conversion if the reaction were started on a very cold day where the initial temperature was 20°F? (Methanol won’t freeze at this temperature.) (3) Now, consider that a heat exchanger is added such that for propylene oxide C_A0 = 1 lb-mol/ft³, V = 1.2 ft³ (then neglecting ΔC_P, ΣN_iC_Pi = 403 Btu/°R), UA = 0.22 Btu/°R/s, and T_a = 498 K. Plot and analyze the trajectories X, T, Q_g, and Q_r as a function of time.

b. Example 13-2. Explore the ONCB explosion described in Example 13-2.

1. Explain what you would do to prevent an explosion of this type from ever occurring again while still operating at the triple production specified by management.
2. Show that no explosion would have occurred if the cooling was not shut off for the 9.04-kmol charge of ONCB or if the cooling was shut off for 10 min after 45 min of operation for the 3.17-kmol ONCB charge.
3. Show that if the cooling had been shut off for 10 min after 12 h of operation, no explosion would have occurred for the 9.04-kmol charge.
   

   

4. Develop a set of guidelines as to when the reaction should be quenched should the cooling fail. Perhaps safe operation could be discussed using a plot of the time after the reaction began at which the cooling failed, t₀, versus the length of the cooling failure period, t_f, for the different charges of ONCB. Parameter values used in this example predict that the reactor will explode at midnight.
5. What parameter values would predict the time the reactor would explode at the actual time of 18 min after midnight? Find a set of parameter values that would cause the explosion to occur at exactly 12:18 A.M. For example, include heat capacities of metal reactor and/or make a new estimate of UA.
6. Finally, what if a 1/2-in. rupture disk rated at 800 psi had been installed and did indeed rupture at 800 psi (270°C)? Would the explosion still have occurred? (Note: The mass flow rate varies with the cross-sectional area of the disk. Consequently, for the conditions of the reaction, the maximum mass flow rate out of the 1/2-in. disk can be found by comparing it with the mass flow rate of 830 kg/min of the 2-in. disk.

c. Example 13-3. Load the Living Example Problem. (1) At what times will the number of moles of C (N_C = C_CV) and the concentration of species C reach a maximum? Are they different, if so, why? What would the X versus t and T versus t trajectories look like if the coolant rate is increased by a factor of 10. Why is the reaction time (252s) so short? Should a semibatch reactor be used for this reaction?

d. Example 13-4. Load the Living Example Problem for Startup of a CSTR, for an entering temperature of 70°F, an initial reactor temperature of 160°F, and an initial concentration of propylene oxide of 0.1 M. Try other combinations of T₀, T_i, and C_Ai, and report your results in terms of temperature–time trajectories and temperature–concentration phase planes. Find a set of conditions above which the practical stability limit will be reached or exceeded and those conditions below which it will not.

e. Example 13-5. Load the Living Example Problem. (1) Plot and analyze N_A = C_AV and N_B = C_BV for long times (e.g., t = 15h). What do you observe? (2) Can you show that for long times N_A ≅ C_A0V₀/k_1A and N_B ≅ C_A0V₀/2/k_2B? (3) What do you think is happening to this semibatch reactor if it has no lid and a maximum volume of 1,000 dm³ at long times? (4) If B is the deserved product, how would you maximize N_B?

f. Example 13-6. T2 Laboratory Explosion.

1. View the Chemical Safety Board (CSB) video online and read the supporting reports (http://www.chemsafety.gov/videoroom/detail.aspx?VID=32). Also search Web for “T2 explosion video.”
2. (a) What did you learn from watching the video? (b) Suggest how this reactor system should be modified and/or operated in order to eliminate any possibility of an explosion. (c) Would you use backup cooling and, if so, how? (d) How could you learn if a second reaction could be set in at a higher temperature? [Hint: See PRS R13.1 The Complete ARSST.]
3. Load the Living Example Polymath E13-6. Plot C_A, C_B, C_C, P, and t as a function of time. Vary UA between 0.0 and 2.77×10⁶ J/h/K to find the lowest value of UA that you observe a runaway. Describe the trends as you approach runaway. Did it occur over a very narrow range of UA values? [Hint: The problem becomes very stiff near the explosion condition when T > 600 K or P > 45 atm. If the temperature or pressure reaches these values, set all derivatives (concentration changes, temperature change, and pressure change) and reaction rates equal to zero so that the numerical solution will complete the analysis and hold all variables at the explosion point of the reactor.]
4. Now let’s consider the actual operation in more detail. The reactor contents are heated from 300 K to 422 K at a rate of = 4 K/minute. At 422 K, the reaction rate is sufficient such that heating is turned off. The reactor temperature continued to rise because the reaction is exothermic, and, when the temperature reached 455 K, the cooling water turned on and cooling was initiated. Model this situation for the case when UA = 2.77×10⁶ J/h/K and when UA = 0.
5. What is the maximum time in minutes that the cooling can be lost (UA = 0) starting at the time when the reactor temperature reaches 455 K so that the reactor will not reach the explosion point? The conditions are those of part (1).
6. Vary the parameters and operating conditions and describe what you find.

g. PRS R13.2 Example CD13-5. Load the Living Example Problem for Falling Off the Upper Steady State. Try varying the entering temperature, T₀, between 80 and 68°F and plot the steady-state conversion as a function of T₀. Vary the coolant rate between 10,000 and 400 mol/h. Plot conversion and reactor temperature as a function of coolant rate.

h. PRS R13.3 Example CD13-2. Load the Living Example Problem. Vary the gain, k_C, between 0.1 and 500 for the integral controller of the CSTR. Is there a lower value of k_C that will cause the reactor to fall to the lower steady state or an upper value to cause it to become unstable? What would happen if T₀ were to fall to 65°F or 60°F?

i. PRS R13.3 Example CD13-3. Load the Living Example Problem. Learn the effects of the parameters k_C and τ_I. Which combination of parameter values generates the least and greatest oscillations in temperature? Which values of k_C and τ_I return the reaction to steady state the quickest?

j. SAChE. Go to the SAChE Web site www.sache.org. On the left-hand menu, select “SaChe Products”. Select “All” tab and go to the module entitled: “Safety, Health and the Environment (S, H & E).” The problems are for KINETICS (i.e., CRE). There are some example problems marked K and explanations in each of the above S, H & E selections. Solutions to the problems are in a different section of the site. Specifically look at: Loss of Cooling Water (K-1), Runaway Reactions (HT-1), Design of Relief Values (D-2), Temperature Control and Runaway (K-4) and (K-5), and Runaway and the Critical Temperature Region (K-7). Go through the K problems and write a paragraph on what you have learned. Your instructor or department chair should have the user name and password to enter the SAChE Web site in order to obtain the module with the problems.

P13-3_B

The following is an excerpt from The Morning News, Wilmington, Delaware (August 3, 1977): “Investigators sift through the debris from blast in quest for the cause [that destroyed the new nitrous oxide plant]. A company spokesman said it appears more likely that the [fatal] blast was caused by another gas—ammonium nitrate—used to produce nitrous oxide.” An 83% (wt) ammonium nitrate and 17% water solution is fed at 200°F to the CSTR operated at a temperature of about 520°F. Molten ammonium nitrate decomposes directly to produce gaseous nitrous oxide and steam. It is believed that pressure fluctuations were observed in the system and, as a result, the molten ammonium nitrate feed to the reactor may have been shut off approximately 4 min prior to the explosion. Can you explain the cause of the blast? If the feed rate to the reactor just before shutoff was 310 lb_m of solution per hour, what was the exact temperature in the reactor just prior to shutdown? Use the data to calculate the exact time it took to explode after the feed was shut off for the reactor. How would you start up or shut down and control such a reaction?

Assume that at the time the feed to the CSTR stopped, there was 500 lb_m of ammonium nitrate in the reactor at a temperature of 520°F. The conversion in the reactor is virtually complete at about 99.99%. Additional data for this problem are given in Problem 12-4_C. How would your answer change if 100 lb_m of solution were in the reactor? 310 lb_m? 800 lb_m? What if T₀ = 100°F? 500°F?

P13-4_B

The liquid-phase reaction in Problem P11-3_B is to be carried out in a semibatch reactor. There are 500 mol of A initially in the reactor at 25°C. Species B is fed to the reactor at 50°C and a rate of 10 mol/min. The feed to the reactor is stopped after 500 mol of B has been fed.

a. Plot and analyze the temperature Q_r, Q_g and conversion as a function of time when the reaction is carried out adiabatically. Calculate to t = 2 h.

b. Plot and analyze the conversion as a function of time when a heat exchanger (UA = 100 cal/min · K) is placed in the reactor and the ambient temperature is constant at 50°C. Calculate to t = 3 h.

c. Repeat part (b) for the case where the reverse reaction cannot be neglected.

New parameter values:

k = 0.01 (dm³/mol · min) at 300 K with E = 10 kcal/mol

V₀ = 50 dm³, υ₀ = 1 dm³/min, C_A0 = C_B0 = 10 mol/dm³

For the reverse reaction: k_r = 0.1 min^–1 at 300 K with E_r = 16 kcal/mol

P13-5_B

You are operating a batch reactor and the reaction is first-order, liquid-phase, and exothermic. An inert coolant is added to the reaction mixture to control the temperature. The temperature is kept constant by varying the flow rate of the coolant (see Figure P13-5_B).

Figure . Figure P13-5_B Semi-batch reactor with inert coolant stream.

a. Calculate the flow rate of the coolant 2 h after the start of the reaction. [Ans.: F_C = 3.157 lb/s.]

b. It is proposed that rather than feeding a coolant to the reactor, a solvent be added that can be easily boiled off, even at moderate temperatures. The solvent has a heat of vaporization of 1000 Btu/lb and initially there are 25 lb-mol of A placed in the tank. The initial volume of solvent and reactant is 300 ft³. Determine the solvent evaporation rate as a function of time. What is the rate at the end of 2 h?

Additional information:

Temperature of reaction: 100°F

Value of k at 100°F: 1.2 × 10^–4 s^–1

Temperature of coolant: 80°F

Heat capacity of all components: 0.5 Btu/lb· °F

Density of all components: 50 lb/ft³

: –25,000 Btu/lb-mol

Initially:

Vessel contains only A (no B or C present)

C_A0: 0.5 lb-mol/ft³

Initial volume: 50 ft³

P13-6_B

The reaction

is carried out adiabatically in a constant-volume batch reactor. The rate law is

Plot and analyze the conversion, temperature, and concentrations of the reacting species as a function of time.

Additional information:

Initial Temperature = 100°C

P13-7_B

The biomass reaction

is carried out in a 25 dm³ batch chemostat with a heat exchanger.

The initial concentration of cells and substrate are 0.1 and 300 g/dm³, respectively. The temperature dependence of the growth rate follows that given by Aiba et al., Equation (9-61).⁵

9-61

a. For adiabatic operation and an initial temperature of 278 K, plot T, I′, r_g, –r_S, C_C, and C_S as a function of time up to 300 hours. Discuss the trends.

b. Repeat (a) and increase the initial temperature in 10°C increments up to 330 K and describe what you find. Plot the concentration of cells at 24 hours as a function of inlet temperature.

c. What heat exchange area should be added to maximize the total number of cells at the end of 24 hours? For an initial temperature of 310 K and a constant coolant temperature of 290 K, what would be the cell concentration after 24 hours?

Additional information:

Y_C/S = 0.8 g cell/g substrate

K_M = 5.0 g/dm³

μ_1max = 0.5 h^–1 (note μ = μ_max at 310 K and C_S → ∞)

C_PS = Heat capacity of substrate solution including all cells

C_PS = 5 J/g/K

= 100 kg/h

ρ = density of solution including cells = 1000 kg/m³

= –20,000 J/g cells

C_PC = Heat capacity of cooling water = 4.2 J/g/K

U = 50,000 J/h/K/m²

P13-8_B

The elementary irreversible liquid-phase reaction

is to be carried out in a semibatch reactor in which B is fed to A. The volume of A in the reactor is 10 dm³, the initial concentration of A in the reactor is 5 mol/dm³, and the initial temperature in the reactor is 27°C. Species B is fed at a temperature of 52°C and a concentration of 4 M. It is desired to obtain at least 80% conversion of A in as short a time as possible, but at the same time the temperature of the reactor must not rise above 130°C. You should try to make approximately 120 mol of C in a 24-hour day, allowing for 30 minutes to empty and fill the reactor between each batch. The coolant flow rate through the reactor is 2000 mol/min. There is a heat exchanger in the reactor.

a. What volumetric feed rate (dm³/min) do you recommend?

b. How would your answer or strategy change if the maximum coolant rate dropped to 200 mol/min? To 20 mol/min?

Additional information:

P13-9_B

The reaction in Problem P11-3_A is to be carried out in a 10-dm³ batch reactor. Plot and analyze the temperature and the concentrations of A, B, and C as a function of time for the following cases:

a. Adiabatic operation.

b. Values of UA of 10,000, 40,000, and 100,000 J/min · K.

c. Use UA = 40,000 J/min · K and different initial reactor temperatures.

P13-10_B

The reactions on the DVD-ROM in Problem CD12GA2 are to be carried out in a semibatch reactor. How would you carry out this reaction (i.e., T₀, υ₀, T_i)? The molar concentrations of pure A and pure B are 5 and 4 mol/dm³ respectively. Plot and analyze the concentrations, temperatures, and the overall selectivity as a function of time for the conditions you chose.