91Ó°ÊÓ

Cumene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C}_{3} \mathrm{H}_{7}\right)\) is produced by reacting benzene with propylene \(\left[\Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=-39,520 \mathrm{Btu}\right]\) A liquid feed containing 75 mole \(\%\) propylene and \(25 \%\) n-butane and a second liquid stream containing essentially pure benzene are fed to the reactor. Fresh benzene and recycled benzene, both at \(77^{\circ} \mathrm{F},\) are mixed in a 1: 3 ratio \((1 \text { mole fresh feed } / 3\) moles recycle) and passed through a heat exchanger, where they are heated by the reactor effluent before being fed to the reactor. The reactor effluent enters the exchanger at \(400^{\circ} \mathrm{F}\) and leaves at \(200^{\circ} \mathrm{F}\). The pressure in the reactor is sufficient to maintain the effluent stream as a liquid. After being cooled in the heat exchanger, the reactor effluent is fed to a distillation column (T1). All of the butane and unreacted propylene are removed as overhead product from the column, and the cumene and unreacted benzene are removed as bottoms product and fed to a second distillation column (T2) where they are scparated. The benzenc leaving the top of the sccond column is the recycle that is mixed with the fresh benzene feed. Of the propylene fed to the process, \(20 \%\) does not react and leaves in the overhead product from the first distillation column. The production rate of cumene is \(1200 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}\). (a) Calculate the mass flow rates of the streams fed to the reactor, the molar flow rate and composition of the reactor effluent, and the molar flow rate and composition of the overhead product from the first distillation column, T1. (b) 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: \(C_{p}\left[\operatorname{Btu} /\left(\operatorname{lb}_{m} \cdot F\right)\right]=0.57\) for propylene, 0.55 for butane, 0.45 for benzene, and 0.40 for cumene. (c) Most people unfamiliar with the chemical process industry imagine that chemical engineers are people who deal mainly with chemical reactions carried out on a large scale. In fact, in most industrial processes, a visitor to the plant would have trouble finding the reactor in a maze of towers and tanks and pipes that were added to the process design to improve the profitability of the process. Briefly explain how the heat exchanger, the two distillation columns, and the recycle stream in the cumene process serve that function.

Step by step solution

01

Calculate the mass flow rates

First, it's necessary to determine the mass flow rate of cumene production (given in the problem as 1200 lb_m/h) and use this information and the unreacted propylene percentage to find the total propylene added to the process. The mass flow rate of propylene in the feed (unreacted propylene + reacted propylene) can then be used to calculate the mass flow rates of the feed streams.

02

Calculate the molar flow rates and compositions

Next, the molar flow rates and the composition of the reactor effluent should be determined. Knowing the mass flow rates from step 1, and the fact that all butane and unreacted propylene are removed as overhead product, these can be figured out. Likewise, the molar flow rate and composition of the overhead product from the first distillation column (T1) can be determined.

03

Calculate the reactor's feed temperature

Given the heat capacities of the compounds involved and the temperatures of the entering and exiting reactor effluent, an energy balance can be used to find out the temperature of the benzene stream fed to the reactor.

04

Calculate the required rate of heat addition/removal

The required rate of heat addition or removal from the reactor can be determined using the previously calculated temperature, the heat capacity of cumene and the heat produced during the reaction.

05

Explain the roles of different components in the process

Finally, the roles of the heat exchanger, the two distillation columns, and the recycle stream in the cumene process should be briefly explained in terms of their contribution to overall process efficiency/profitability. The heat exchanger allows for heat transfer from the hot reactor effluent to the entering mixed feed, enhancing energy efficiency. The two distillation columns enable separation of different components of the end product. Recycle of unreacted benzene contributes to resource conservation. Each component plays an essential role in improving overall process profitability.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cumene Production Process

Cumene, also known as isopropylbenzene, is a critical chemical used as a precursor for producing phenol and acetone, with widespread applications in the plastics and synthetic fibers industry.

In the cumene production process, the reaction between benzene and propylene is a fundamental step. This reaction is exothermic, releasing heat, which is a factor to consider in reactor design and operation. The process commences with the mixing of a benzene feed with a propylene and n-butane mixture. Once the reaction occurs in the reactor, the products and unreacted materials are passed on to a distillation column.

Stream Separation and Optimization

The first distillation column, known as T1, separates unreacted propylene and by-product butane from cumene and benzene. Following the separation, the cumene is extracted as needed, whereas unreacted benzene is routed to a second distillation column, T2, for further purification and recycling. Recycling unreacted benzene is a crucial step in enhancing the economic efficiency of the process by reducing waste and raw material costs.

The careful control of temperature and pressure throughout the process is essential to achieve the desired reaction and separation outcomes, making the cumene production process a classic example of chemistry's synergy with chemical engineering principles.

Chemical Reactor Design

Chemical reactor design is a cornerstone of process engineering that combines principles of thermodynamics, kinetics, mass transfer, and fluid mechanics to optimize chemical reactions.

Efficiency and Control

In the cumene production process, the reactor must be designed to handle the exothermic reaction between benzene and propylene efficiently, maintaining the desired product quality and yield. The reactor should facilitate the adequate mixing of reactants, efficient heat removal or addition, and sufficient residence time for the reaction to go to completion. Moreover, the design should ensure safe operation under the necessary temperature and pressure conditions.

For cumene production, the reactor not only needs to support the chemical reaction but also work in tandem with the energy recovery systems such as heat exchangers, reflective of the process's energy-conscious approach. The heat exchange between the reactor's effluent and the feed stream conserves energy, minimizing external heat requirements and maximizing the efficiency of the overall process. The reactor's pressure is maintained to ensure that the effluent remains a liquid, highlighting the importance of phase equilibria in reactor design.

Distillation Column Operation

Distillation is a purification technique that separates components in a mixture based on differences in boiling points, and it plays a vital role in the cumene production process through the operation of two distillation columns, T1 and T2.

Column Functionality

The operational control of these columns is paramount. The first distillation column, T1, must effectively separate lighter unreacted propylene and butane from the heavier cumene and benzene. Temperature control, reflux ratio, and internal column conditions such as the number of trays or the type of packing material significantly impact separation efficiency.

After T1, the bottoms product containing cumene and benzene is sent to the second column, T2, where further separation is necessary to recover and recycle the benzene. Controlling the separation in T2 is equally critical since it influences the purity of cumene product and the recycling efficiency of benzene.

The ability to manage energy consumption through heat integration and the careful selection of optimal operating conditions for both columns is fundamental for the profitability and environmental footprint of the cumene production process.

By understanding and applying these core concepts, students will not only be able to tackle textbook exercises but also appreciate the practical and economic aspects intertwining in chemical engineering operations.