Workshop 07: Non-isothermal reactor design

Lecture notes for chemical reaction engineering

Solutions

Solutions to these problems are uploaded at Workshop 7 solutions

Try following problems from Fogler 5e P 11-5, P 11-6, P 12-6, P 12-21

We will go through some of these problems in the workshop.

P 11-5

The elementary, irreversible gas-phase reaction

$\ce{ A -> B + C }$

is carried out adiabatically in a PFR packed with a catalyst. Pure A enters the reactor at a volumetric flow rate of 20 dm³/s, at a pressure of 10 atm, and a temperature of 450 K.

Additional information:

$C_{P_A} = 40 J/mol \cdot K$; $C_{P_B} = 25 J/mol \cdot K$; $C_{P_C} = 15 J/mol \cdot K$

$H_A^{\circ} = -70 kJ/mol$; $H_B^{\circ} = -50 kJ/mol$; $H_C^{\circ} = -40 kJ/mol$

All heats of formation are referenced to 273 K.

$$k = 0.133 \exp \left[ \frac{E}{R} \left( \frac{1}{450} - \frac{1}{T} \right) \right] \; \frac{dm^3}{kg-cat \cdot s} \; \text{with} \, E = 31.4 kJ/mol$$

1. Plot and then analyze the conversion and temperature down the plug-flow reactor until an 80% conversion (if possible) is reached. (The maximum catalyst weight that can be packed into the PFR is 50 kg.) Assume that $\Delta P = 0.0$.

2. Vary the inlet temperature and describe what you find.

3. Plot the heat that must be removed along the reactor ( Q vs. V) to maintain isothermal operation.

4. Now take the pressure drop into account in the PBR with $\rho_b = 1 kg/dm^3$. The reactor can be packed with one of two particle sizes. Choose one.

$$\alpha = 0.019/kg-cat \: \text{for particle diameter} \: D_1$$ $$\alpha = 0.0075/kg-cat \: \text{for particle diameter} \: D_2$$

5. Plot and then analyze the temperature, conversion, and pressure along the length of the reactor. Vary the parameters $\alpha$ and $P_0$ to learn the ranges of values in which they dramatically affect the conversion.

P 11-6

The irreversible endothermic vapor-phase reaction follows an elementary rate law

$\ce{ CHECOCH3 -> CH2CO + CH4 }$

$\ce{ A -> B + C }$

and is carried out adiabatically in a 500-dm³ PFR. Species A is fed to the reactor at a rate of 10 mol/min and a pressure of 2 atm. An inert stream is also fed to the reactor at 2 atm, as shown in Figure P11-6 B . The entrance temperature of both streams is 1100 K.

Additional information:

$k = \exp (34.34 - 34222/T) dm^3/mol \cdot min$ (T in degrees Kelvin); $C_{P_l} = 200 J/ mol \cdot K$

$C_{P_A} = 170 J/ mol \cdot K$; $C_{P_B} = 90 J/ mol \cdot K$; $C_{P_C} = 80 J/ mol \cdot K$; $\Delta H_{Rx}^\circ = 80000 J/ mol$

1. First derive an expression for $C_{A01}$ as a function of $C_{A0}$ and $\Phi_I$.

2. Sketch the conversion and temperature profiles for the case when no inerts are present. Using a dashed line, sketch the profiles when a moderate amount of inerts are added. Using a dotted line, sketch the profiles when a large amount of inerts are added. Qualitative sketches are fine. Describe the similarities and differences between the curves.

3. Sketch or plot and then analyze the exit conversion as a function of $\Phi_I$. Is there a ratio of the entering molar flow rates of inerts (I) to A (i.e., $\Phi_I = F_{I0}/ F_{A0}$ at which the conversion is at a maximum? Explain why there “is” or “is not” a maximum.

4. What would change in parts (b) and (c) if reactions were exothermic and reversible with $\Delta H_{Rx}^{\circ} = -80 kJ/mol$ and $K_C = 2 dm^3/mol$ at 1100 K?

5. Sketch or plot F_B for parts (c) and (d), and describe what you find.

6. Plot the heat that must be removed along the reactor ( Q vs. V) to maintain isothermal operation for pure A fed and an exothermic reaction.

P 12-6

The endothermic liquid-phase elementary reaction

$\ce { A + B -> 2 C }$

proceeds, substantially, to completion in a single steam-jacketed, continuous-stirred reactor (Table P12-6 B ). From the following data, calculate the steady-state reactor temperature:

Reactor volume: 125 gal;

Steam jacket area: 10 ft²

Jacket steam: 150 psig (365.9 $^{\circ}$F saturation temperature)

Overall heat-transfer coefficient of jacket, U: 150 $Btu/h \cdot ft^2 \cdot ^{\circ}F$

Agitator shaft horsepower: 25 hp

Heat of reaction, $\Delta H_{Rx}^{\circ} = + 20000$ Btu/lb-mol of A (independent of temperature)

P 12-21

The irreversible liquid-phase reactions

Reaction 1: $\ce{A + B -> 2 C}$ $\;\;\;\;$ $r_{1C} = k_{1C} C_A C_B$

Reaction 2: $\ce{2 B + C -> D}$ $\;\;\;\;$ $r_{2D} = k_{2D} C_B C_C$

are carried out in a PFR with heat exchange. The following temperature profiles were obtained for the reactor and the coolant stream:

The concentrations of A, B, C, and D were measured at the point down the reactor where the liquid temperature, T, reached a maximum, and they were found to be C_A = 0.1, C_B = 0.2, C_C= 0.5, and C_D= 1.5, all in mol/dm³. The product of the overall heat-transfer coefficient and the heat-exchanger area per unit volume, Ua, is 10 $cal/s \cdot dm^3 \cdot K$. The entering molar flow rate of A is 10 mol/s.

Additional information

$C_{P_A}= C_{P_B}=C_{P_C}=30 \, cal/mol/K$ $\;\;\;\;$ $C_{P_D}= 90 \, cal/mol/K$, $\;\;\;\;$ $C_{P_I}=100 \, cal/mol/K$

$\Delta H_{Rx1A}^\circ = +5000 \, cal/ molA$; $\;\;\;\;$ $k_{1C} = 0.043 (dm^3/mol \cdot s)$ at 400 K

$\Delta H_{Rx2B}^\circ = +5000 \, cal/ molB$; $\;\;\;\;$ $k_{2D} = 0.4 (dm^3/mol \cdot s) \exp 5000 K \left[ \frac{1}{500} - \frac{1}{T}\right]$

1. What is the activation energy for Reaction (1)?