Chapter 11: Nonisothermal Reactor Design: The Steady State Energy Balance and Adiabatic PFR Applications

Adiabatic Liquid Phase in A CSTR

Given T
Find X and V
Also given k, E, C_PA=C_PB, \(\Delta H_{Rx}\), C_Ao, and v_o

Diagram of a Continuous Stirred Tank Reactor (CSTR). The input stream enters from the top, labeled with initial temperature T₀, molar flow rate Fₐ₀, volumetric flow rate V₀, and concentration Cₐ₀. The output stream exits from the side of the reactor, labeled with temperature T and conversion X.

Solution

Mole Balance: \( V = \frac{F_{Ao} X}{-r_A} \)

Rate Law: \( -r_A = k C_A \)

\( k = A e^{-E/RT} \)

Stoichiometry: \( C_A = C_{Ao} (1 - X) \)

Combine: \( V = \frac{C_{Ao} v_o X}{k C_{Ao} (1 - X)} \Rightarrow \tau = \frac{1}{k (1 - X)} \)

Energy Balance: \( T = T_0 - \frac{-\Delta H_{rx} X}{C_{pA}} \)

Given \( T \)

1) Calculate \( X = \frac{C_{pA} (T - T_0)}{\Delta H_{rx}} \)

2) Calculate \( k = A e^{-E/RT} = k_1(T_1) \exp\left( \frac{E}{R} \left( \frac{1}{T_1} - \frac{1}{T} \right) \right) \)

3) Calculate \( \tau = \frac{1}{k (1 - X)} \)

4) Calculate \( V = v_o \tau \)

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