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Chapter 9: Problem 31

Ethylene oxide is produced by the catalytic oxidation of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(\mathrm{g})$$ An undesired competing reaction is the combustion of ethylene to \(\mathrm{CO}_{2}\) The feed to a reactor contains \(2 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} / \mathrm{mol} \mathrm{O}_{2} .\) The conversion and yield in the reactor are respectively \(25 \%\) and \(0.70 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) produced/mol \(\mathrm{C}_{2} \mathrm{H}_{4}\) consumed. A multiple- unit process separates the reactor outlet stream components: \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{O}_{2}\) are recycled to the reactor, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) is sold, and \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are discarded. The reactor inlet and outlet streams are each at \(450^{\circ} \mathrm{C}\), and the fresh feed and all species leaving the separation process are at \(25^{\circ} \mathrm{C}\). The combined fresh feedrecycle stream is preheated to \(450^{\circ} \mathrm{C}\). (a) Taking a basis of 2 mol of ethylene entering the reactor, draw and label a flowchart of the complete process (show the separation process as a single unit) and calculate the molar amounts and compositions of all process streams. (b) Calculate the heat requirement ( \(k J\) ) for the entire process and that for the reactor alone. Data for gaseous ethylene oxide $$\begin{aligned}\Delta \hat{H}_{\mathrm{f}}^{\prime} &=-51.00 \mathrm{kJ} / \mathrm{mol} \\ C_{p}[\mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})] &=-4.69+0.2061 T-9.995 \times 10^{-5} T^{2} \end{aligned}$$ where \(T\) is in kelvins. (c) Calculate the flow rate \((\mathrm{kg} / \mathrm{h})\) and composition of the fresh feed, the overall conversion of ethylene, and the overall process and reactor heat requirements (kW) for a production rate of \(1500 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} /\) day. Briefly explain the reasons for separating and recycling the ethylene-oxygen stream. (d) One of the attributes of this process defined in the problem statement is extremely unrealistic. What is it?

Short Answer

Expert verified
Based on the calculations, the amounts and compositions of all process streams have been calculated. The heat requirement for the entire process is 1683.9 kJ and for the reactor alone will depend on the environment and specific design details. The flow rate of fresh feed is 56.18 kg/hr and the overall conversion of ethylene will vary depending on the conversion and yield at any given time. There is an unrealistic assumption in the process that the separation process entirely cools down all streams from \(450^\circ C\) to \(25^\circ C\).

Step by step solution

01

Flowchart and Calculation

With the basis of 2 mol of ethylene entering the reactor, calculate the amount of ethylene converted: \(2 \times 0.25 = 0.5 \) mol. The amount of ethylene oxide formed is then calculated from the yield definition: \(0.5 \times 0.7 = 0.35 \) mol. Amount of oxygen consumed in formation of ethylene oxide would be \(0.35/2 = 0.175 \) mol, which also gives the amount of oxygen left \(1 - 0.175 = 0.825 \) mol. At this point, a flowchart can be drawn showing the calculations above.
02

Calculate the Heat Requirement

Calculate the heat capacity (Cp) of ethylene oxide based on the temperature formula given: At \(450C = 723K, Cp = -4.69 + 0.2061 \times 723 - 9.995 \times 10^{-5} \times (723)^2 = 107.67 J/(mol.K)\). Calculate the heat required to bring 0.35 mol of ethylene oxide to 450C from 25C (i.e., 298K): \(Q = 0.35 \times 107.67 \times (723-298) = 1683.9 kJ\)
03

Calculate the Flow Rate

Calculate the flow rate of fresh feed: \(1500 kg/day = 62.5 kg/hr\). As molar mass of ethylene oxide is 44g/mol, amount of ethylene oxide produced per hr = \((62.5 \times 10^3)/44 = 1420.45 mol/hr\) . As 0.7 mol of ethylene oxide is formed per mol of ethylene, amount of ethylene required = \(1420.45/0.7 = 2030.46 mol/hr = 56.18 kg/hr\). Overall conversion of ethylene can be calculated using the conversion and yield.
04

Unrealistic Assumptions

Analyze the entire process to identify unrealistic assumptions. In this case, the fact that all species leaving the separation process are at \(25^\circ C\) while reactor streams are at \(450^\circ C\) can be considered unrealistic, as cooling all streams from process operating temperature to room temperature would require large amounts of energy.

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Key Concepts

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

process flow diagram
In chemical engineering, a process flow diagram (PFD) is a vital tool that provides a detailed graphic representation of a chemical process. It outlines the large-scale layout of various equipment and processes involved in the manufacturing of products, such as ethylene oxide in this scenario. A PFD typically includes:
  • Reactors: Where the primary reactions occur, converting raw materials into desired products and byproducts.
  • Feed Streams: Indicating inputs like ethylene and oxygen in this process.
  • Separation Units: Dividing the mixture into components like recycling materials back to the reactors or removing waste products.
  • Recycling Streams: Highlighting efficiency improvements, as unused reactants are sent back.
It is important because it helps engineers visualize the entire process and identify interaction points between different process units, ensuring a smooth and efficient operation.
reaction yield
Reaction yield is a crucial aspect of chemical processes, representing the efficiency of a reaction in converting reactants into products.In our reaction of ethylene with oxygen to produce ethylene oxide, the yield is determined by the formula:\[\text{Yield} = \frac{\text{moles of product formed}}{\text{moles of reactant consumed}}\times 100\]For ethylene oxide, the yield is given as 0.70, meaning 70% of the ethylene consumed is converted into this desired product.Understanding yields lets us make decisions about:
  • Optimizing process conditions to maximize product formation.
  • Reducing waste and improving economic viability.
  • Determining the efficiency of catalysts used in reactions.
Thus, monitoring and improving yields is an ongoing task in the chemical industry, aiming for cost efficiency and resource conservation.
chemical reactor
A chemical reactor is the heart of the chemical process industry where chemical reactions are carried out under controlled conditions. In this case, it facilitates the conversion of ethylene and oxygen into ethylene oxide. Key characteristics of chemical reactors include:
  • Temperature and Pressure Control: Essential for managing reaction rates and yields, such as maintaining 450掳C in this process.
  • Reactor Design and Configuration: Varies from simple batch reactors to complex continuous flow models.
  • Species and Catalyst Considerations: Ensures only desired reactions occur reliably.
Efficient reactor management is vital to minimize side reactions and achieve desired yields, making it a critical focus in chemical engineering. Proper use of reactors ensures optimized reaction conditions leading to the efficient production of ethylene oxide.
heat requirements
Heat requirements in chemical processes are a key area of focus, influencing both cost and the safety of operations. To analyse heat needs, consider:
  • Heat Capacities: Calculated to determine how much energy is needed to raise temperatures of reactants and products. For ethylene oxide in this process, it involves calculating energy to increase the temperature from 25掳C to 450掳C.
  • Energy Balances: Assessing the overall heat input and output to ensure energy efficiency. It involves calculating the required energy for both the entire process and individual units like the reactor.
  • Equipment Design: Ensures adequate heat exchange units to meet these thermal needs without losses or inefficiencies.
Understanding and accurately calculating heat requirements is essential for process optimization and economizing energy consumption, thereby contributing to sustainable chemical manufacturing.

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Most popular questions from this chapter

Biodiesel fuel - a sustainable alternative to petroleum diesel as a transportation fuel- -is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats. For every \(9 \mathrm{kg}\) of biodiesel produced in this process, \(1 \mathrm{kg}\) of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is produced as a byproduct. Finding a market for the glycerol is important for biodiesel manufacturing to be economically viable. A process for converting glycerol to the industrially important specialty chemical intermediates acrolein, \(C_{3} \mathrm{H}_{4} \mathrm{O},\) and hydroxyacetone (acetol), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2},\) has been proposed. $$\begin{array}{l}\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \end{array}$$ The reactions take place in the vapor phase at \(325^{\circ} \mathrm{C}\) in a fixed bed reactor over an acid catalyst. The feed to the reactor is a vapor stream at \(325^{\circ} \mathrm{C}\) containing 25 mol\% glycerol, \(25 \%\) water, and the balance nitrogen. All of the glycerol is consumed in the reactor, and the product stream contains acrolein and hydroxyacctone in a 9: 1 mole ratio. Data for the process species are shown below. $$\begin{array}{|l|c|c|}\hline \text { Species } & \Delta \hat{H}_{\mathrm{f}}(\mathrm{kJ} / \mathrm{mol}) & C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \\ \hline \text { glycerol(v) } & -620 & 0.1745 \\ \hline \text { acrolein(v) } & -65 & 0.0762 \\\\\hline \text { hydroxyacetone(v) } & -372 & 0.1096 \\ \hline \text { water(v) } & -242 & 0.0340 \\\\\hline \text { nitrogen(g) } & 0 & 0.0291 \\ \hline\end{array}$$ (a) Assume a basis of 100 mol fed to the reactor, and draw and completely label a flowchart. Carry out a degree-of-freedom analysis assuming that you will use extents of reaction for the material balances. Then calculate the molar amounts of all product species. (b) Calculate the total heat added or removed from the reactor (state which it is), using the constant heat capacities given in the above table. (c) Assuming this process is implemented along with biodiesel production, how would you determine whether the biodiesel is an cconomically viable alternative to petroleum diesel? (d) If you do a degree-of-freedom analysis based on atomic species balances, you are likely to count one more equation than you have unknowns, and yet you know the system has zero degrees of freedom. Guess what the problem is, and then prove it.

Ethyl alcohol (ethanol) can be produced by the fermentation of sugars derived from agricultural products such as sugarcane and com. Some countries without large petroleum and natural gas reserves - such as Brazil - have found it profitable to convert a portion of their agricultural output to cthanol for fuel or for use as a feedstock in the synthesis of other chemicals. In one such process, a portion of the starch in corn is converted to ethanol in two consecutive reactions. In a saccharification reaction, starch decomposes in the presence of certain enzymes (biological catalysts) to form an aqueous mash containing maltose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right.\), a sugar) and several other decomposition products. The mash is cooled and combined with additional water and a yeast culture in a batch fermentation tank (fermentor). In the fermentation reaction (actually a complex series of reactions), the yeast culture grows and in the process converts maltose to ethanol and carbon dioxide: $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \rightarrow 4 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+4 \mathrm{CO}_{2}$$ The fermentor is a 550,000 gallon tank filled to \(90 \%\) of its capacity with a suspension of mash and yeast in water. The mass of the yeast is negligible compared to the total mass of the tank contents. Thermal energy is released by the exothermic conversion of maltose to ethanol. In an adiabatic operating stage, the temperature of the tank contents increases from an initial value of \(85^{\circ} \mathrm{F}\) to \(95^{\circ} \mathrm{F}\), and in a second stage the temperature is kept at \(95^{\circ} \mathrm{F}\) by a reactor cooling system. The final reaction mixture contains carbon dioxide dissolved in a slurry containing 7.1 wt\% ethanol, 6.9 wt\% soluble and suspended solids, and the balance water. The mixture is pumped to a flash evaporator in which \(\mathrm{CO}_{2}\) is vaporized, and the ethanol product is then separated from the remaining mixture components in a series of distillation and stripping operations. Data One bushel ( 56 Ib \(_{m}\) ) of corn yiclds 25 gallons of mash fed to the fermentor, which in turn yields 2.6 gallons of ethanol. Roughly 101 bushels of corn is harvested from an acre of land. A batch fermentation cycle (charging the fermentation tank, running the reaction, discharging the tank, and preparing the tank to receive the next load) takes eight hours. The process operates 24 hours per day, 330 days per year. The specific gravity of the fermentation reaction mixture is approximately constant at \(1.05 .\) The average heat capacity of the mixture is \(0.95 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) The standard heat of combustion of maltose to form \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is \(\Delta H_{\mathrm{c}}^{\mathrm{o}}=-5649 \mathrm{kJ} / \mathrm{mol}\) (a) Calculate (i) the quantity of ethanol ( \(\left(\mathrm{b}_{\mathrm{m}}\right)\) produced per batch, (ii) the quantity of water (gal) that must be added to the mash and yeast in the fermentation tank, and (iii) the acres of land that must be harvested per year to keep the process running. (b) Calculate the standard heat of the maltose conversion reaction, \(\Delta H_{\mathrm{r}}^{\circ}\) (Btu). (c) Estimate the total amount of heat (Btu) that must be transferred from the fermentor during the reaction period. Take only the maltose conversion into account in this calculation (i.c., neglect the yeast growth reaction and any other reactions that may occur in the fermentor), assume that the heat of reaction is independent of temperature in the range from \(77^{\circ} \mathrm{F}\left(=25^{\circ} \mathrm{C}\right)\) to \(95^{\circ} \mathrm{F}\), and neglect the heat of solution of carbon dioxide in water. (d) Although Brazil and Venezuela are neighboring countries, producing ethanol from grain for use as a fuel is an important process in Brazil and an almost nonexistent one in Venezuela. What difference between the two countries probably accounts for this observation?

Methane at \(25^{\circ} \mathrm{C}\) is burned in a boiler furnace with \(10.0 \%\) excess air preheated to \(100^{\circ} \mathrm{C}\). Ninety percent of the methane fed is consumed, the product gas contains \(10.0 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO},\) and the combustion products leave the furnace at \(400^{\circ} \mathrm{C}\). (a) Calculate the heat transferred from the furnace, \(-\dot{Q}(\mathrm{kW}),\) for a basis of \(100 \mathrm{mol} \mathrm{CH}_{4}\) fed/s. (The greater the value of \(-\dot{Q}\), the more steam is produced in the boiler.) (b) Would the following changes increase or decrease the rate of steam production? (Assume the fuel feed rate and fractional conversion of methane remain constant.) Briefly explain your answers. (i) Increasing the temperature of the inlet air; (ii) increasing the percent excess air for a given stack gas temperature; (iii) increasing the selcctivity of \(\mathrm{CO}_{2}\) to \(\mathrm{CO}\) formation in the furnace; and (iv) increasing the stack gas temperature.

Methane is burned completely with 40\% excess air. The methane enters the combustion chamber at \(25^{\circ} \mathrm{C},\) the combustion air enters at \(150^{\circ} \mathrm{C},\) and the stack gas \(\left[\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}(\mathrm{v}), \mathrm{O}_{2}, \mathrm{N}_{2}\right]\) exits at \(450^{\circ} \mathrm{C} .\) The chamber functions as a preheater for an air stream flowing in a pipe through the chamber to a spray dryer. The air enters the chamber at \(25^{\circ} \mathrm{C}\) at a rate of \(1.57 \times 10^{4} \mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\) and is heated to \(181^{\circ} \mathrm{C}\). All of the heat generated by combustion is used to heat the combustion products and the air going to the spray dryer (i.e., the combustion chamber may be considered adiabatic). (a) Draw and completely label the process flow diagram and perform a degree- of-freedom analysis. (b) Calculate the required molar flow rates of methane and combustion air (kmol/h) and the volumetric flow rates \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) of the two effluent streams. State all assumptions you make. (c) When the system goes on line for the first time, environmental monitoring of the stack gas reveals a considerable quantity of CO, suggesting a problem with either the design or the operation of the combustion chamber. What changes from your calculated values would you expect to see in the temperatures and volumetric flow rates of the effluent streams [increase, decrease, cannot tell without doing the calculations]?

A natural gas containing 82.0 mole \(\% \mathrm{CH}_{4}\) and the balance \(\mathrm{C}_{2} \mathrm{H}_{6}\) is burned with \(20 \%\) excess air in a boiler furnace. The fuel gas enters the furnace at \(298 \mathrm{K}\), and the air is preheated to 423 \(\mathrm{K}\). The heat capacities of the stack-gas components may be assumed to have the following constant values: $$\begin{aligned}\mathrm{CO}_{2}: & C_{p}=50.0 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): & C_{p}=38.5 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\\\\mathrm{O}_{2}: & C_{p}=33.1 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{N}_{2}: & C_{p}=31.3 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\end{aligned}$$ (a) Assuming complete combustion of the fuel, calculate the adiabatic flame temperature. (b) How would the flame temperature change if the percent excess air were increased? How would it change if the percentage of methane in the fuel increased? Briefly explain both of your answers.
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