4 th Edition Chapter 9

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1 Insert Page 547A 4 th Edition Chapter 9 In summary, if any one of the following three things had not occurred the explosion would not have happened. 1. Tripled production 2. Heat exchanger failure for 10 minutes 3. Relief valve failure. In other words, all the above had to happen to cause the explosion. If they relief had operated properly, the valve would not have prevented reaction runaway but it could have prevented the explosion. In many cases sufficient care is not taken to obtain data for the reaction at hand and to use it to properly size the valve orifice. This data can be obtained using a batch reactor call the ARSST Reactor Safety: The Use of the ARSST to Size Relief Valves The Advanced Reaction System Screening Tool (ARSST) is a calorimeter that is used routinely in industry to experiments determine activation energies, E, frequency factors, A, heats of reaction, DH Rx, and to size vent relief valves for runaway exothermic reactions [Chemical Engineering Progress 96 No.2, p.17, 2000]. The basic idea is that reactants are placed and sealed in the calorimeter which is then electrically heated as the temperature and pressure in the calorimeter are monitored. As the temperature continues to rise, the rate of reaction also increases to a point where the temperature increases more rapidly from the heat generated by the reaction (called the self heating rate, T S ) than the temperature increase by electrical heating. The temperature at which this change in relative heating rates occurs is called the onset temperature. A schematic of the calorimeter is shown in Figure E Figure 9-1 ARSST [Courtesy of Fauske & Associates.] We shall take as our system the reactants, products and inerts inside the spherical container as well as the spherical container itself, as the mass of the

2 Page 547B container may adsorb a little of the energy given off by the reaction. This system is well insulated and does not loose much heat to the surroundings. Neglecting DC P, the energy balance on the ARSST, Equation (9-12) becomes ( )(-r A V) dt dt = Q + -DH Rx = ÂN i C Pi ( )(-r A V) Ê Q ˆ Ê Á Ë ÂN i C + -DH Rx Á Pi Ë ÂN i C Pi ˆ (9-18) The total heat added, Q, is the sum electrical heat added Q E and the convective of the heat added term Q C = (UA(T a T)) Q C Q = Q E + UA T a - T ( ) Because the system is well insulated, we shall neglect there is not heat loss from the calorimeter to the surroundings to neglect the Q C and further define T Q E = E (9-19) ÂN i C Pi is called the electrical heating rate, T E. The second term, T S, in Eqn. (E9-1.1) is called the self heating rate ( )(-r A V) T S = -DH Rx (9-20) ÂN i C Pi Safety Valve CDROM LINKS Av The self heating rate, which is determined from the experiment, is what is used to calculate the vent size of the relief valve, A V, of the reactor in order to prevent runaway reactions (see CDROM). * The electrical heating rate is controlled such that the temperature rise, T E, (typically C/min) is maintained constant up to the temperature where the self heating rate becomes greater than the electrical heating rate T S > T E This temperature is called the onset temperature. A typical thermal history is shown below. * Side note. A relief valve is an instrument on the top of the reactor that releases the pressure and contents of the reactor before temperature and pressure builds up to runaway and explosive conditions. A sample calculation can be found on the Professional Reference Shelf (PRS) of the CDROM. There is a disk covering the vent in the relief valve that breaks once the reactor pressure exceeds the set pressure P S, and allows the contents to flow out through the vent. The heat of vaporization from the liquid vaporizing at exit the vent once the pressure is released will also cool the reactor contents. The self heating rate is used directly to calculate the vent size necessary to successfully release all the contents of the reactor. The necessary vent area is given by the equation. A V = m S T S in m 2 FP S ( ) where F is a reduction factor for an ideal nozzle, P S is the relief set pressure (Psia) and m S the mass of the sample kg (see PRS).

3 Page 547C Self heating rate T T onset Electrical heating rate t Figure 9-2 Typical temperature history for thermal scan with the ARSST. The self heating, T S, rate can be easily found by differentiating the temperaturetime trajectory or T S can be determined directly form the output instrumentation and software associated with the ARSST. We can re-write Equation in the form t e dt dt = T E + T S The following example uses data obtained in the senior unit operations laboratory of the University of Michigan Example 9-3 Use of the ARSST We shall use the ARSST to study the reaction between acetic anhydride and water to form acetic acid CH 3 CO) 2 O + H 2 O æ Æ 2CH 3 COOH A+ B æ Æ 2C Acetic anhydride is placed in the ARSST to form 6.7 molar solution of acetic anhydride and a 20.7 M solution of water. The sample volume is 10 ml. The electrical heating is started and the temperature and it s derivative, T S, are recorded as a function of time by the ARSST system and computer. This system and compare theory and experiment and to find the heat of reaction, DH Rx, the activation energy, E, and the frequency factor, A. The temperature time trajectory is obtained directly from the computer linked to the ARSST as is shown in Figure E Physical Properties Chemical Density (g/ml) Heat capacity (J/g.C) Mw Heat capacity (J/mol.C) Q Acetic anhydride Water Glass cell (bomb)

4 Page 547D Total volume 10 ml with Water g Acetic anhydride g 1.0 g 180 T f Temperature ( o C) T on Time (min) Figure E9-3.1 Temperature time trajectory for hydrolysis of acetic anhydride Solution Because we are taking our system as the contents inside the bomb as well as the bomb itself, the term ÂN i C Pi needs to be modified to account for the heat absorbed by the bomb calorimeter that hold the reactants. Thus, we include terms for the mass of the calorimeter, m b, and heat capacity of the calorimeter, C Pb, in the sum ÂN i C Pi, i.e., ÂN i C Pi = N A C PA + N B C PB + N C C PC + N I C PI + m b C Pb For this reaction we neglect DC P and m b C Pb to obtain ÂN i C Pi = N A0 ÂQ i C Pi We now apply our algorithm to analyzing the ARSST for the reaction A+ B æ Æ 2C (E9-3.1) (E9-3.1)

5 Page 547E Mole Balance TABLE E9-3.1 BALANCE EQUATIONS dn A dt Rate Law r A = - k C A C B = r A V (E9-3.2) -E RT k = Ae (E9-3.4) Stoichiometry V = V 0 (E9-3.3) C A = C A0 ( 1- X) (E9-3.5) C B = C A0 ( Q B - X) (E9-3.6) C C = 2C A0 X For Q B = 3, as a first approximation we take C B ª C A0 Q B = C B0 (E9-3.7) (Note: In Problem P9-10 C we do not assume C B0 is constant) r A = - k C B0 C A = kc A Combine k = k C B0 (E9-3.8) Energy Balance dc A dt = -kc A (E9-3.9) dt dt = T E + T S (E9-3.10) Q T E E = N A0 ÂQ i C Pi (9-19) Recalling N i = VC i we can substitute Equations E9-3.5 through E9-3.6 into Equation (E9-3.1 and then neglect DC P to obtain N A0 ÂQ i C Pi = N A0 C PA + N B0 C PB + DC P N A0 X + N I C PI + m b = N A0 ( C PA + Q B C PB ) Neglect C Pb (E9-3.12) Usually N I = 0, DC P = 0 and m b C Pb is negligible with respect to the other terms. The self heating rate is ( )(-r A V) T S = -DH Rx N A0 ÂQ i C Pi ( ) ( ) C B0 Ae -E RT C A V = -DH Rx (9-20) N A0 ÂQ i C Pi

6 Page 547F Calculating the Heat of Reaction The heat of reaction for adiabatic operation can be found from the adiabatic temperature rise for complete conversion X=1. the onset temperature is taken as the part at which the self heating rate is greater than the electrical heating rate to be 55 C. From Figure E9-3.1 we see the maximum temperature is 165 C. Recalling Equation (8-49) with DC P = 0 For X = 1, T = T f X = ÂQ i C P T- T 0 o -DH Rx ( ) o ( ) -DH Rx = ( C PA + Q B C PB )( T f - T 0 ) ( ) = 415 ÂQ i C Pi = ( 75.4) Determining the Activation Energy J molk Ê J ˆ = Á 415 ( ) C = 45,600 J mol Ë mol C DH R = -45,650 J mol A temperature-time trajectory for the hydrolysis of acetic anhydride similar to the one shown in Figure 9-2 was recorded as shown in Figure E The self heating rate T S is shown as a function of temperature in Figure E The ARSST software will differentiate the data directly to give T S or dt/dt can be found from T versus t using any of the differentiational techniques in Chapter 5. One notes that the self heating rate goes to zero as a result of the reactants being consumed. The electrical heating rate, T E, is either shut off, or becomes negligible wrt T S after the onset temperature T ON is reached. We now take the log of the self heating rate, T S, c.f. Equation (E9.3-13). dt Ê T S = -DH Rx VC B0 Á Ë N A0 ÂQ i C Pi ˆ Ae-E RT C A ln T ( S = ln -DH Rx )C B0 V + ln A+ ln C A - E N A0 ÂQ i C Pi RT (E9.3-13) (E9.3-14) After the onset temperature is reached a plot, T S vs. ( 1 T) neglecting changes in ln C A (i.e., use initial value) we can obtain the activation energy from the slope of a plot of ln ( dt dt)as a function of ( 1 T) neglecting changes in ln C A. The slope of the line will be ( E/R) as shown in Figure E9-3.1.

7 Page 547G Figure E9-3.2 Self heating curve for the hydrolysis of acetic anhydride 1000 Heating rate (K/min) y = 6.10E+10e -7.75E+03x R 2 = 9.96E-01 T onset /Temperature (1/K) Figure E9-3.3 Arhenius plot of self heating rate for of acetic anhydride. From the slope of the plot we find the activation to be E = -R Slope = E =15.4 kcal mol cal mol K -7,750K ( )

8 Page 547H Calculating the Frequency Factor, A We will now make an approximate calculation to determine the frequency factor. The intricate details of a more accurate calculation are given in the Professional Reference Shelf where the conversion obtained during the electrical heating phase is taken into account. Neglecting the conversion during heating C A =C A0, Equation (E9-3.13) can be arranged in the form È N A = T A0 ÂQ i C Pi S onset Í e E RT onset Î -DH Rx C A0 C B0 V (E9-3.15) At the onset, Ton = 55 C, at 10 minutes the self heat rate can be estimated from the slope of T vs. t to be 5.2K/min. Evaluating the parameters. Ê N A0 ÂQ i C Pi = 6.7 mol ˆ È Á Ë dm dm 3 Î = 28 J K We now calculate the frequency factor to be A = 5.2K min ( ) Í 415 J mol C È Í 28 J K È Í 15,400 cal mol Ê Á 45,650 J ˆ Ê Á 6.7 mol ˆ Ê Ë mol Ë dm 3 Á 20.2 mol expí Í ˆ Í Ë dm dm 3 Î cal mol Î A = dm 3 mol min ( )( 330K) Now that we have the activation energy, E, and the Arrhenius factor A, we can use Polymath to simulate the equations in Table E9-1.1 and compare with the experimental results. The Polymath program is shown in Table E9-1.2, and the corresponding output is shown in Figure E9-1.3.

9 Page 547I TABLE E9-1.2 POLYMATH PROGRAM ODE Report (RKF45) Differential equations as entered by the user [1] d(ca)/d(t) = ra [2] d(t)/d(t) = Tedot+Tsdot Explicit equations as entered by the user [1] CB0 = 20.2 [2] V = 0.01 [3] SUMNA0THEiCpi = 28 [4] dhrx = [5] A = 3.734e7 [6] E = [7] R = [8] Tedot = if (T>55+273) then 0 else 2 [9] ra = -A*exp(-E/R/T)*CA*CB0 [10] Tsdot = (-dhrx)*(-ra*v)/sumna0theicpi Comments [1] d(ca)/d(t) = ra Mole balance on Acetic Anhydride [2] d(t)/d(t) = Tedot+Tsdot Energy Balance [3] ra = -A*exp(-E/R/T)*CA*CB0 Rate of the reaction-mol/l.min [4] V = 0.01 Volume of the reactive solution-l [5] SUMNA0THEiCpi = 28 J/mol.C [6] dhrx = Heat of reaction-j/mol [7] A = 3.734e7 rate constant- 1/min [8] E = cal/mol [9] R = cal/mol.k [10] Tedot = if (T>55+273) then 0 else 2 (ok/min) After the onset point, electrical heating is only to compensate for heat loss [11] Tsdot = (-dhrx)*(-ra*v)/sumna0theicpi Self-heating rate (ok/min)

10 Page 547J Figure E9-3.4 Temperature time trajectory for hydrolysis of acetic anhydride As one can see there is excellent agreement between the simulation and the experiment. The decrease in temperature at 13.5 minutes in the experimental data is a result of a small heat loss to the surroundings which was not accounted for in the simulation. The CDROM describes how to size the vent size form this data. When using the ARSST in the laboratory to actually size relief valve, one should follow the procedure in the Professional Reference Shelf, which accounts for the conversion during the electrical heating and also taking the onset temperature at a point where T S >> T E. Also see the Fauske web site:

ChE 344 Winter 2013 Final Exam + Solution. Open Course Textbook Only Closed everything else (i.e., Notes, In-Class Problems and Home Problems

ChE 344 Winter 2013 Final Exam + Solution. Open Course Textbook Only Closed everything else (i.e., Notes, In-Class Problems and Home Problems ChE 344 Winter 03 Final Exam + Solution Thursday, May, 03 Open Course Textbook Only Closed everything else (i.e., Notes, In-Class Problems and Home Problems Name Honor Code (Please sign in the space provided