Assignments Involving BSTR Analysis
Examples from REB, The Book
Example 7.4.1 The liquid-phase reaction between A and B, equation (1), is irreversible. At the conditions of interest, the heat of reaction is constant and equal to -101.2 kJ mol-1. The rate expression is given in equation (2), where the rate coefficient exhibits Arrhenius temperature dependence with a pre-exponential factor of 5.11 x 104 L mol-1 s-1 and an activation energy of 74.8 kJ mol-1.
Two solutions, one containing only reagent A at 180 °C and one containing only reagent B at 180 °C, are charged to an adiabatic BSTR producing 1900 L of solution initially containing 2.9 mol A L-1 and 3.2 mol B L-1 at 180 °C. The solution is ideal and has a constant heat capacity of 1.23 cal g-1 K-1 and a constant density of 1.02 g cm-3. Plot the concentrations of A, B, Y, and Z, the reacting fluid temperature, and the instantaneous reaction rate for the first 2 h of reaction, and comment upon the shapes of the graphs.
\[ A + B \rightarrow Y + Z \tag{1} \]
\[ r = kC_AC_B \tag{2} \]
Example 7.4.2 A jacketed, 10 L BSTR is going to be used to process an aqueous solution of A and B. The reactor jacket is perfectly mixed with a volume of 1400 cm3, a heat transfer coefficient of 138 cal ft−2 min−1 K−1 and a heat transfer area of 1200 cm2. Cooling water at 40 °C flows into the jacket at a rate of 100 g min-1. Both the reacting fluid and the cooling water may be taken to have a density of 1 g cm−3 and a heat capacity of 1 cal g−1 K−1.
Solutions containing A, B, X, Y, and Z are ideal, and there is no heat of mixing. The reactor will be charged by mixing two separate solutions, one containing only reagent A and the other containing only reagent B, giving a 10 L charge with initial concentrations of 5 mol A L-1 and 7 mol B L-1. At the time the reactor is charged, the cooling water temperature is 40 °C. Reactions (1) and (2) will occur in the reactor. The heat of reaction (1) is −16.7 kcal mol−1, and that for reaction (2) is −14.3 kcal mol−1. The rate expression for reaction (1) is given in equation (3) where the pre-exponential factor for the rate coefficient is 9.74 x 109 L mol−1 min−1 and the activation energy is 20.1 kcal mol−1. The rate expression for reaction (2) is given in equation (4) where the pre-exponential factor for the rate coefficient is 2.38 x 1013 min−1 and the activation energy is 25.3 kcal mol−1.
What initial temperature is needed in order to convert 45% of the A in 30 min, and with that initial temperature what will the final temperature, the outlet exchange fluid temperature, and the selectivity for X over Z equal? Discuss ways to increase the selectivity.
\[ A + B \rightarrow X + Y \tag{1} \]
\[ A \rightarrow Z \tag{2} \]
\[ r_1 = k_1C_AC_B \tag{3} \]
\[ r_2 = k_2C_A \tag{4} \]
Example 7.4.3 The rate expression for liquid-phase reaction (1) is given in equation (2). The rate coefficient displays Arrhenius temperature dependence with a pre-exponential factor of 2.59 x 109 min-1 and an activation energy of 16.5 kcal mol-1. The heat of reaction (1) may be taken to be constant and equal to -22,200 cal mol-1. A solution containing only A at a concentration of 2 M and a temperature of 23 °C is going to be processed in a BSTR. The heat capacity of the solution is approximately constant and equal to 440 cal L-1 K-1, and its density is constant.
\[ A \rightarrow Z \tag{1} \]
\[ r_1 = k_1C_A \tag{2} \]
The 4.0 L BSTR has a perfectly mixed jacket with a volume of 0.5 L, a heat transfer area of 0.6 ft2, and a heat transfer coefficient of 1.13 x 104 cal ft-2 h-1 K-1. Cooling water at 20 °C can be fed to the jacket. The water may be taken to have a constant density of 1 g cm-3 and a constant heat capacity of 1 cal g-1 K-1. A heating coil with a heat transfer coefficient of 3.8 x 104 cal ft-2 h-1 K-1 and a heat transfer area of 0.23 ft2 can be submerged in and extracted from the reacting solution. Saturated steam at 120 °C can admitted to the coil.
The BSTR is charged with 4 L of a 2 M solution of A at 23 °C. Initially there is no flow to the jacket, but it is filled with water, also at 23 °C. To start the batch process, the steam is admitted to the coil, and the coil is immersed in the solution. When the reacting fluid reaches 50 °C, the coil is extracted from the reacting fluid and cooling water flow to the jacket is started. When the reacting fluid reaches a temperature of 25 °C the cooling water flow is stopped, the reactor is drained and preparations for processing the next batch begin. The BSTR pressure is constant throughout all stages of processing. If the turnaround time for the reactor is 25 min, what coolant flow rate will maximize the net rate of production of Z? Plot the conversion of A and the reacting fluid temperature vs. reaction time corresponding to the coolant flow rate that maximizes the net rate and comment on the results.
Example 7.4.4 A BSTR will be charged with 1 atm of A and 2 atm of B at 25 °C. The reactor volume is 2 L, and it has a jacket with an area of 600 cm2 and an overall heat transfer coefficient of 0.6 cal cm-2 min-1 K-1. The temperature of the coolant in the perfectly-mixed jacket is maintained at 30°C by a temperature controller. Gas phase reactions (1) and (2) take place within the reactor; the corresponding rate expressions are given in equations (3) and (4). The rate coefficients display Arrhenius temperature dependence with pre-exponental factors of 3.34 x 109 and 1.47 x 1010 mol cm-3 min-1 atm-2 for reactions (1) and (2), respectively, and activation energies of 20.5 and 21.8 kcal mol-1. The heat of reaction (1) is constant and equal to -6,300 cal mol-1; that of reaction (2) is constant and equal to -6,900 cal mol-1. The heat capacities of A, B, D, Z and U are constant and equal to 7.4, 8.6, 10.7, 5.2 and 10.3 cal mol-1 K-1, respectively.
What reaction time will maximize the yield (moles of D per initial mole of A), and what will the yield and the conversion of A equal at that reaction time?
\[ A + B \rightarrow D + Z \tag{1} \]
\[ D + B \rightarrow U + Z \tag{2} \]
\[ r_1 = k_{0,1} \exp{\left(\frac{-E_1}{RT}\right)}P_AP_B \tag{3} \]
\[ r_2 = k_{0,2} \exp{\left(\frac{-E_2}{RT}\right)}P_DP_B \tag{4} \]
Example 7.4.5 Liquid phase reactions (1) and (2) take place in a batch stirred-tank reactor; the reaction rate expressions are given in equations (3) and (4). The rate coefficients for reactions (1) and (2) obey the Arrhenius expression. For reaction (1) the pre-exponential factor is 1.6 × 1018 gal lbmol−1 h−1, and the activation energy is 46,000 BTU lbmol−1. For reaction (2) the pre-exponential factor is 4.5 × 1018 gal lbmol−1 h−1, and the activation energy is 48,000 BTU lbmol−1. The heat capacity of the reacting liquid is constant and equal to 65 BTU ft−3 °R−1. The heat of reaction (1) is constant and equal to 45,000 BTU lbmol−1, and the heat of reaction (2) is constant and equal to 39,500 BTU lbmol−1. The 50 gal reactor initially contains only A and B at concentrations of 0.014 lbmol A gal−1 and 0.020 lbmol B gal−1. The initial temperature of the reacting fluid is 70 °F. The reactor is jacketed with an overall heat transfer coefficient of 60 BTU ft−2 °R−1 h−1 and a heat transfer area of 13 ft2. Saturated steam at 220 °F condenses in the jacket, leaving as a saturated liquid. (The heat of vaporization of steam at 220 °F is 966 BTU lbm–1.) Plot the yield of D (moles of D per initial mole of A), the temperature and the mass flow rate of water leaving the jacket as a function of the conversion of B.
\[ A + B \rightarrow D + Z \tag{1} \]
\[ D + B \rightarrow U + Z \tag{2} \]
\[ r_1 = k_1C_AC_B \tag{3} \]
\[ r_2=k_2C_DC_B \tag{4} \]
Learning Activities from REB, The Course
Learning Activity 14 Liquid phase reaction (1) takes place in an adiabatic batch reactor with a volume of 1200 L. The reactor initially contains 2500 mol of A and 5000 moles of B at a temperature of 300K. The reaction is allowed to proceed until half of the A has been consumed. The rate expression is given in equation (2) where the pre-exponential factor equals 6 x 105 min–1 and the activation energy is 42 kJ mol–1. If the heat capacities of A, B and Z are constant and equal to 180, 70 and 225 J mol–1 K–1, respectively, and the heat of reaction at 298 K is equal to –16.5 kJ mol–1, how long will the reaction run? Plot the concentrations of A, B, and Z, the reacting fluid temperature, and the instantaneous reaction rate over the duration of the process. Compare the shapes of the graphs to those from Example 7.4.1 and explain the reasons for the differences.
\[ A + B \rightarrow Z \tag{1} \]
\[ r_1 = k_1C_A \tag{2} \]
Learning Activity 14 Calculations
Learning Activity 15 A batch stirred tank reactor is being used for the production of Z according to reaction (1). Reactants A and B are available in separate 3 M solutions at 50 °C. To avoid undesirable side reactions, the reacting fluid must remain at or below 90 °C at all times. To facilitate doing so, the reactor has a cooling jacket with an area of 66 cm2, a volume of 40 cm3 and a heat transfer coefficient of 35 BTU ft–2 h–1 °F–1. Cooling water is available at 40 °C. Turnaround time for the reactor is 30 min.
The heat capacity of all solutions containing A, B, Y and/or Z is essentially constant and equal to that of the solvent, 0.35 cal g–1 K–1, and the density of all solutions is constant and equal to 0.93 g cm–3. The rate expression for reaction (1) is given in equation (2) where the pre-exponential factor equals 1.24 x 1013 cm3 mol–1 s–1 and the activation energy equals 20 kcal mol–1. The heat of reaction (1) may be assumed to be constant and equal to -80 kJ mol–1. The cooling water density and heat capacity may be assumed to equal 1 g cm–3 and 1 cal g–1 K–1, respectively.
At the start of each batch, the reactor contains 250 cm3 of the solution containing A and the jacket is full of water at 40 °C. To begin processing, 250 cm3 of the solution containing B is instantaneously added, and cooling water flow is initiated. Processing ends when the conversion reaches 90%. Calculate the coolant flow rate at which the maximum reacting fluid temperature equals 90 °C. Then plot the net rate of production of Z as a function of reaction time when that cooling rate is used.
\[ A + B \rightarrow Y + Z \tag{1} \]
\[ r_1 = k_1C_AC_B \tag{2} \]
Learning Activity 15 Calculations
Learning Activity 16 A 10 L laboratory BSTR with two separate heat exchange coils is being used to study the endothermic conversion of A to Z, equation (1). Two perfectly mixed coils each can be submerged in the reacting fluid or removed from it. In the heating coil with a heat transfer coefficient, \(U_1\), of 76 cal h–1 cm–2 K–1 and a heat transfer area, \(A_1\), of 600 cm2, saturated steam at 110 °C condenses. In the cooling coil (\(U_2\) = 91 cal h–1 cm–2 K–1 and \(A_2\) = 375 cm2) the temperature of the exchange fluid is maintained at 30 °C by a temperature controller.
\[ A \rightarrow Z \tag{1} \]
The reaction is first order in reagent A, equation (2), with a pre-exponential factor of 2.85 x 1015 h–1, an activation energy of 25 kcal mol–1, and a heat of reaction of 20 kcal mol–1. The reacting solution is aqueous, and the heat capacity and density equal those of water. When the reactor is charged, only reagent A is present at a concentration of 5 M and a temperature of 25 °C.
\[ r_1 = k_1C_A \tag{2} \]
To start the process, suppose that the heating coil is submerged in the reacting fluid for 1 h. The heating coil is then extracted and simultaneously the cooling coil is submerged. When the reacting fluid temperature reaches 35 °C, processing ends. The turnaround time is 0.5 h. Calculate the processing time, final conversion and net rate of production of Z, and plot the reacting fluid temperature and the conversion as functions of the processing time.
Learning Activity 16 Calculations
Learning Activity 17 The rate of gas phase reaction (1) is given by the rate expression, equation (2). The pre-exponential factor, \(k_{01}\), is equal to 265 L mol-1 min-1, and the activation energy, \(E_1\), is equal to 73 kJ mol-1. The standard heat of reaction (1) at 298 K is equal to -165 kJ mol-1. The heat capacities of A, Y and Z are given by equations (3) through (5), where the temperature must be substituted in K, and the resulting heat capacity will have units of J mol-1 K-1.
If the reaction takes place in a constant volume, adiabatic batch reactor that is initially charged with pure A at 1000 Torr and 1225 K, how long will it take for the temperature to increase by 10 K and at that point what percentage of the original A will have been converted? How long will it take for the temperature to increase by 100 K and at that point what percentage of the original A will have been converted?
\[ 2A \rightarrow 2Y + Z \tag{1} \]
\[ r_1 = k_1C_A^2 \tag{2} \]
\[ \hat{C}_{p,A}= 28 + 0.05T \tag{3} \]
\[ \hat{C}_{p,Y}= 26 + 0.01T \tag{4} \]
\[ \hat{C}_{p,Z}= 30 + 0.005T \tag{5} \]
Learning Activity 17 Calculations
Learning Activity 18 Liquid-phase reaction (1) is exothermic with a heat of reaction equal to –16.6 kcal mol–1. If a solution containing only A at a concentration of 2 M and a temperature of 20 °C reacts adiabatically in a BSTR, the temperature increases to 110 °C. The reaction is first order in the concentration of A as shown in equation (2). The pre-exponential factor is 2.5 x 108 L mol–1 min–1, and the activation energy is 14.3 kcal mol–1.
\[ A \rightarrow Z \tag{1} \]
\[ r_1 = k_1C_A \tag{2} \]
Adiabatic operation has undesirable side effects, making isothermal operation preferable. To do so, using a 0.4 L BSTR with a 0.1 L shell has been proposed. The heat transfer area is 32.5 cm2, and the heat transfer coefficient is 0.2 cal min–1 cm–2 K–1. Chilled water at 10 °C would initially fill the shell and be fed to it. The water can be taken to have a density of 1 g cm–3 and a heat capacity of 1 cal g–1 K–1. The reactor temperature will not be close to isothermal if a fixed coolant flow rate is used. Consequently it has been proposed to set the cooling water flow rate to 217 g min–1 initially and to linearly decrease it by 212 g min–1 over the duration of the 60 min reaction time.
Assuming the reacting fluid density to equal 879 g L–1 and its heat capacity to equal 0.42 cal g–1 K–1, plot the conversion, reacting fluid temperature, and cooling water temperature over the course of the reaction and comment on how closely the operation approaches being isothermal.
Practice Assignments from REB, The Course
Practice Assignment 14 Acid A is to be neutralized using base B, reaction (1), by mixing a 4 M solution of the base with a 10 M solution of the acid. The neutralization reaction is irreversible with a heat of reaction equal to -44 kcal mol-1. The reaction is first order in both acid and base with a pre-exponential factor of 8.11 x 1012 L mol-1 s-1 and an activation energy of 17.7 kcal mol-1. A jacketed, perfectly mixed, 25 L batch reactor will be charged with 4 L of the 10 M solution of A at 20 °C, while cooling water at 20 °C flows at 1.0 kg min-1 to the perfectly mixed, 0.5 L jacket. To start the reaction, 10 L of the 4 M solution of B at 20 °C will then added all at once. The heat transfer area is 0.6 ft2 and the heat transfer coefficient is 1.13 x 104 cal ft-2 h-1 K-1. The cooling water and the solutions of A and B may be taken to have a constant density of 1 g cm-3 and a constant heat capacity of 1 cal g-1 K-1. The pressure in the reactor will be constant and equal to 1 atm. Plot the acid concentration, the reactor temperature, and the exchange fluid temperature as functions of time after the addition of the base solution.
\[ A + B \rightarrow S + H_2O \tag{1} \]
Practice Assignment 14 Solution
Practice Assignment 14 Calculations
Practice Assignment 15 A jacketed, 50 gal BSTR is being considered for the conversion of A to Z, reaction (1). The reactor would be filled with a 60 °F solution containing reagent A at a concentration of 0.02 lbmol gal–1. Saturated steam at 212 °F would condense in the jacket to provide heat. The conversion must reach 90% in 50 min.
The heat capacity of the reacting fluid is 1 BTU lbm–1, and its density is 8.5 lbm gal–1. The heat of reaction (1) is –5150 BTU lbmol–1. The rate coefficient exhibits Arrhenius temperature dependence with a pre-exponential factor of 4630 gal lbmol–1 min–1 and an activation energy of 6580 BTU lbmol–1.
If the heat transfer coefficient is 37.3 BTU h–1 ft–2 °R–1, what heat transfer area is needed, and how long will the conversion take?
\[ A \rightarrow Z \tag{1} \]
\[ r_1 = k_1C_A^2 \tag{2} \]
Practice Assignment 15 Solution
Practice Assignment 15 Calculations
Practice Assignment 16 In the Class 16 Learning Activity a BSTR operating protocol with a heating stage and a cooling stage was analyzed, The reaction was endothermic, and the conversion was found to depend mostly on the duration of the heating stage. The net rate was also calculated.
It can be useful to plot the net rate as a function of the conversion for systems like this. On the same graph, plot the net rate of production for the system from the Class 16 Learning activity as a function of conversion for turnaround times of 0.25, 0.5, and 0.75 h. Discuss the shape of the graphs and the trends associated with turnaround time.
Practice Assignment 16 Solution
Practice Assignment 16 Calculations
Practice Assignment 17 Irreversible gas phase reaction (1) is exothermic with a heat of reaction equal to –12.9 kcal mol–1. The rate expression is presented in equation (2), where the pre-exponential factor equals 1.75 x 109 L0.5 mol–0.5 s–1 and the activation energy is 35.7 kcal mol–1. The heat capacities of A, B, Y, and Z are 37, 34, 36, and 38 cal mol–1 K–1, respectively. If an adiabatic 5.0 L BSTR is charged with equal molar amounts of A and B at 400 °C and 1 atm, how long will it take to convert 50% of reagent A and what will the temperature equal?
\[ A + B \rightarrow Y + Z \tag{1} \]
\[ r_1 = k_1C_A\sqrt{C_B} \tag{2} \]
Practice Assignment 17 Solution
Practice Assignment 17 Calculations
Practice Assignment 18 An 11.5 L BSTR is charged with a 3.6 M liquid solution of reagent A at 35 °C. The reactor has a jacket with a volume of 1.4 L, a heat transfer area of 0.012 m2, and a heat transfer coefficient of 1485 cal m–2 min–1 K–1. Saturated steam at 1 atm (373.15 K) condenses in the jacket and exits as saturated water. The heat of vaporization of water at 1 atm and 373.15 K is 540 cal g–1. Reaction (1) takes place within the BSTR; the rate expression is given in equation (2) where the forward and reverse rate display Arrhenius temperature dependence with \(k_{0,f}\) = 6.297 x 105 L mol–1 min–1, \(E_f\) = 12.65 kcal mol–1, \(k_{0,r}\) = 5.148 x 1018 L mol–1 min–1, and \(E_r\) = 30.95 kcal mol–1. The heat of reaction (1) is –18.3 kcal mol–1. The reacting fluid density, 1.0 g L–1, and heat capacity, 1.0 cal g–1 K–1, are constant. Plot the conversion, reacting fluid temperature, and condensate mass flow rates during the first 2 h of operation.
\[ A \rightarrow Y + Z \tag{1} \]
\[ r_1 = k_{1,f}C_A^2 - k_{1,r}C_YC_Z \tag{2} \]
Additional Assignments for Extra Practice
Additional assignments will be added as they become available.
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