Calculate the temperature of the benzene stream fed to the reactor and the required rate of heat addition to or removal from the reactor. Use the following approximate heat capacities in your calculations: Cp[Btu/(lbm °F)] = 0.57 for propylene, 0.55 for butane, 0.45 for benzene, and 0.40 for cumene. ### Cumene Production Process**Chemical Reaction**:Cumene (\(C_6H_5C_3H_7\)) is produced by reacting benzene with propylene. The reaction has an enthalpy change (\(\Delta H_r^o\)) of -39,520 Btu.**Process Flow Diagram**:The process involves several key components, including a reactor, heat exchanger, and distillation columns. Here's a detailed explanation:- **Reactor**: The starting point where the chemical reaction occurs.- **Heat Exchanger**: This device heats the benzene and propylene mixture before entering the reactor. The reactor effluent at 350.0°F is cooled to 200.0°F in the exchanger.- **Distillation Columns (T1 and T2)**: These columns separate various components after the reaction. - **T1**: The effluent is fed into this column, where butane and unreacted propylene are removed overhead. - **T2**: The bottoms product from T1, containing cumene and unreacted benzene, is fed into this second column for further separation.- **Recycling**: The unreacted benzene is recycled back into the system. Specifically, 20.0% of the propylene is not reacted and is removed as an overhead product.**Chemical Feed**:- **Propylene and Butane**: The liquid feed consists of 85.0 mole% propylene and 15.0% n-butane, maintained at 77°F.- **Benzene**: Both fresh and recycled benzene are at 77°F and mixed in a 1:2.5 mole ratio (fresh:recycle) before entering the heat exchanger.**Production Rate**:The system produces cumene at a rate of 1200.0 lb\(_m\)/h.This overview provides a conceptual understanding of cumene production, emphasizing heat exchange, separation processes, and recycling within the system. ## Tutorial: Calculating Mass Flow Rates and CompositionsThis section aims to guide you through calculating the mass flow rates of streams fed to a reactor, as well as the molar flow rates and composition of both the reactor effluent and the overhead product from the first distillation column, labeled T1.### Reactor FeedYou will need to determine the following mass flow rates:- **Propylene fed to reactor:** Enter the flow rate in lb\(_m\)/h.- **Butane fed to reactor:** Enter the flow rate in lb\(_m\)/h.- **Benzene fed to reactor:** Enter the flow rate in lb\(_m\)/h.### Reactor EffluentNext, calculate and input the compositions and total molar flow rate of the reactor effluent:- **Total Molar Flow Rate:** Enter the flow rate in lb-mol/h.- **Composition of Butane (\(x_{butane}\)):** Enter the molar fraction.- **Composition of Propylene (\(x_{propylene}\)):** Enter the molar fraction.- **Composition of Benzene (\(x_{benzene}\)):** Enter the molar fraction.- **Composition of Cumene (\(x_{cumene}\)):** Enter the molar fraction.### Overhead from T1Finally, determine the overhead product variables from the first distillation column T1:- **Total Molar Flow Rate:** Enter the flow rate in lb-mol/h.- **Composition of Butane (\(x_{butane}\)):** Enter the molar fraction.- **Composition of Propylene (\(x_{propylene}\)):** Enter the molar fraction.These calculations are essential for understanding the efficiency and product distribution in chemical processes. Make sure you have all necessary data before proceeding with the calculations.

The basis of the given process is taken as 1200 lbm/h of the cumene (C) produced. Convert it into…

Answered: Calculate the temperature of the…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

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Calculate the temperature of the benzene stream fed to the reactor and the required rate of heat addition to or removal from the reactor. Use the following approximate heat capacities in your calculations: C_p[Btu/(lb_m °F)] = 0.57 for propylene, 0.55 for butane, 0.45 for benzene, and 0.40 for cumene.

### Cumene Production Process

**Chemical Reaction**:
Cumene (\(C_6H_5C_3H_7\)) is produced by reacting benzene with propylene. The reaction has an enthalpy change (\(\Delta H_r^o\)) of -39,520 Btu.

**Process Flow Diagram**:
The process involves several key components, including a reactor, heat exchanger, and distillation columns. Here's a detailed explanation:

- **Reactor**: The starting point where the chemical reaction occurs.
- **Heat Exchanger**: This device heats the benzene and propylene mixture before entering the reactor. The reactor effluent at 350.0°F is cooled to 200.0°F in the exchanger.
- **Distillation Columns (T1 and T2)**: These columns separate various components after the reaction.

- **T1**: The effluent is fed into this column, where butane and unreacted propylene are removed overhead.
- **T2**: The bottoms product from T1, containing cumene and unreacted benzene, is fed into this second column for further separation.

- **Recycling**: The unreacted benzene is recycled back into the system. Specifically, 20.0% of the propylene is not reacted and is removed as an overhead product.

**Chemical Feed**:
- **Propylene and Butane**: The liquid feed consists of 85.0 mole% propylene and 15.0% n-butane, maintained at 77°F.
- **Benzene**: Both fresh and recycled benzene are at 77°F and mixed in a 1:2.5 mole ratio (fresh:recycle) before entering the heat exchanger.

**Production Rate**:
The system produces cumene at a rate of 1200.0 lb\(_m\)/h.

This overview provides a conceptual understanding of cumene production, emphasizing heat exchange, separation processes, and recycling within the system.

## Tutorial: Calculating Mass Flow Rates and Compositions

This section aims to guide you through calculating the mass flow rates of streams fed to a reactor, as well as the molar flow rates and composition of both the reactor effluent and the overhead product from the first distillation column, labeled T1.

### Reactor Feed

You will need to determine the following mass flow rates:

- **Propylene fed to reactor:** Enter the flow rate in lb\(_m\)/h.
- **Butane fed to reactor:** Enter the flow rate in lb\(_m\)/h.
- **Benzene fed to reactor:** Enter the flow rate in lb\(_m\)/h.

### Reactor Effluent

Next, calculate and input the compositions and total molar flow rate of the reactor effluent:

- **Total Molar Flow Rate:** Enter the flow rate in lb-mol/h.
- **Composition of Butane (\(x_{butane}\)):** Enter the molar fraction.
- **Composition of Propylene (\(x_{propylene}\)):** Enter the molar fraction.
- **Composition of Benzene (\(x_{benzene}\)):** Enter the molar fraction.
- **Composition of Cumene (\(x_{cumene}\)):** Enter the molar fraction.

### Overhead from T1

Finally, determine the overhead product variables from the first distillation column T1:

- **Total Molar Flow Rate:** Enter the flow rate in lb-mol/h.
- **Composition of Butane (\(x_{butane}\)):** Enter the molar fraction.
- **Composition of Propylene (\(x_{propylene}\)):** Enter the molar fraction.

These calculations are essential for understanding the efficiency and product distribution in chemical processes. Make sure you have all necessary data before proceeding with the calculations.

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