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Chapter 9: Problem 33

Ethylbenzene is converted to styrene in the catalytic dehydrogenation reaction $$\mathrm{C}_{8} \mathrm{H}_{10}(\mathrm{g}) \rightarrow \mathrm{C}_{8} \mathrm{H}_{8}(\mathrm{g})+\mathrm{H}_{2}: \quad \Delta H_{\mathrm{r}}^{\circ}\left(600^{\circ} \mathrm{C}\right)=+124.5 \mathrm{kJ}$$ A flowchart of a simplified version of the commercial process is shown here. Fresh and recycled liquid ethylbenzene combine and are heated from \(25^{\circ} \mathrm{C}\) to \(500^{\circ} \mathrm{C} \mathrm{C}\) ? and the heated ethylbenzene is mixed adiabatically with steam at \(700^{\circ} \mathrm{C}\) ? to produce the feed to the reactor at \(600^{\circ} \mathrm{C}\) (The steam suppresses undesired side reactions and removes carbon deposited on the catalyst surface.) A once-through conversion of \(35 \%\) is achieved in the reactor ? and the products emerge at \(560^{\circ} \mathrm{C}\).The product stream is cooled to \(25^{\circ} \mathrm{C}\) ? condensing essentially all of the water, ethylbenzene, and styrene and allowing hydrogen to pass out as a recoverable by-product of the process. The water and hydrocarbon liquids are immiscible and are separated in a settling tank decanter ? The water is vaporized and heated ? to produce the steam that mixes with the cthylbenzene feed to the reactor. The hydrocarbon stream leaving the decanter is fed to a distillation tower ? (actually, a seriesof towers), which separates the mixture into essentially pure styrene and ethylbenzene, each at \(25^{\circ} \mathrm{C}\) after cooling and condensation steps have been carried out. The ethylbenzene is recycled to the reactor preheater, and the styrene is taken off as a product. (a) On a basis of \(100 \mathrm{kg} / \mathrm{h}\) styrene produced, calculate the required fresh ethylbenzene feed rate, the flow rate of recycled ethylbenzene, and the circulation rate of water, all in mol/h. (Assume \(P=1\) atm.) (b) Calculate the required rates of heat input or withdrawal in \(\mathrm{kJ} / \mathrm{h}\) for the ethylbenzene preheater ? steam generator ? ind reactor ? (c) Suggest possible ways to improve the energy economy of this process.

Short Answer

Expert verified
The fresh ethylbenzene feed rate is approximately equal to 962 mol/h. The recycled ethylbenzene is about 65% of the fresh feed which is about 622 mol/h. Due to insufficient given data, the water circulation rate can not be determined. The heat requirements for each component may vary significantly based on different factors including specific heats and temperature differences. Energy economy can be improved by heat recovery and optimized operating conditions.

Step by step solution

01

Calculation of Ethylbenzene Feed Rates

First, the molar mass of styrene \( C_{8}H_{8} \) is computed which is roughly 104 g/mol. On a basis of 100 kg/h styrene (which is equivalent to \( \frac{100,000}{104} \) mol/h), the stoichiometry of the reaction is used to calculate the fresh ethylbenzene feed rate. Since one mol of styrene requires one mol of ethylbenzene (from the balanced chemical reaction), the required fresh ethylbenzene feed rate is the same as the flow rate of styrene.
02

Calculation of Recycled Ethylbenzene and Water Circulation Rates

The once-through conversion of the reactor is given as 35 %, this implies that 65 % of the fed ethlybenzene is unreacted and is recycled back to the reactor. Therefore, the recycled ethylbenzene rate is 65% of the fresh feed rate. With regards to water, it is used to suppress side reactions and clean the catalyst surface. From the problem, there are no explicit relationships given for water use, thus, without additional data provided or assumptions, the water circulation rate can't be determined.
03

Heat Calculations

The heat calculations depend on the reaction enthalpy, the specific heats of the substances involved and the temperature difference. The heat for the ethylbenzene preheater is calculated using \( q=mc\Delta T \), where m is the mass flow rate of ethylbenzene, c is the specific heat of ethylbenzene, and \( \Delta T \) is the change in temperature. For the reactor, it can be assumed as an adiabatic process. Therefore, the heat is calculated by multiplying the enthalpy change of reaction by the mol flow rate of ethylbenzene. For the heat of the steam generator, the specific heat of water and the change in temperature are used.
04

Suggestions for Energy Economy

Energy saving could be achieved through different methods. One way could be to use a heat exchanger to recover the heat from the hot product stream from the reactor which otherwise is discarded. This reduces the necessary heat load to the preheater. Another way could be to optimize the operation conditions to maximize the conversion rate in the reactor so as to minimize the recycling of ethylbenzene and hence save energy.

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Key Concepts

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

Catalytic Dehydrogenation
In chemical process design, catalytic dehydrogenation plays a crucial role, especially in industries-focused on producing aromatics like styrene. Ethylbenzene is converted to styrene in the presence of a catalyst in a reaction characterized by the release of hydrogen. This dehydrogenation process is endothermic, meaning it requires the input of energy to proceed.

A catalyst is vital as it speeds up the reaction without being consumed. In this process, steam is used not only for heat but also to clean the catalyst surface, removing carbon deposits and reducing unwanted side reactions. This helps in achieving higher yields of styrene while maintaining the efficiency of the catalyst.

Further, managing the heat within the process is critical due to the reaction's energy demands. Careful temperature regulation ensures the optimal functioning of the catalyst and the desired conversion efficiency. Therefore, understanding catalytic dehydrogenation within the context of chemical reaction engineering is essential for designing efficient and effective chemical processes.
Energy Efficiency in Chemical Processes
Energy efficiency is a significant consideration in chemical processes, especially those involving reactions like the dehydrogenation of ethylbenzene to produce styrene. There are several methods to improve energy efficiency in such processes.

One effective strategy is the utilization of heat exchangers, which can recover heat from the reactor's hot product stream and use it to preheat incoming reactants. This recycling of heat reduces the total energy input required, leading to lower operational costs and diminished environmental impact.

Another approach is optimizing reactor conditions to increase conversion rates. This minimizes the recycle of unreacted feed, thereby decreasing energy consumption associated with reheating these recycled materials. Fine-tuning temperatures, pressures, and flow rates to their optimal values can enhance overall process efficiency.
  • Using renewable energy sources for process heating
  • Implementing advanced control systems for real-time energy monitoring
  • Regular maintenance and cleaning of heat transfer surfaces
Each of these can contribute to a more energy-efficient and sustainable chemical process.
Chemical Reaction Engineering
Chemical reaction engineering focuses on understanding how chemical reactions can be controlled, optimized, and scaled up from the laboratory to industrial production levels. It plays a vital role in designing reactors and processes such as the dehydrogenation of ethylbenzene. In this particular process, engineers must balance numerous factors to optimize yield and efficiency.

Factors considered include the kinetics of the reaction, which determines how quickly reactants are converted to products. Engineers utilize reaction rate equations to model and predict conversion rates under various conditions. Also, the reactor design needs consideration鈥攚hether to use a continuous stirred-tank reactor (CSTR) or a packed bed reactor depends on factors like reaction kinetics and heat management needs.

Moreover, attention to scale-up is critical. A reaction efficient in a lab setting might behave differently under the larger scales of industrial production, necessitating adjustments in reactor design or operating conditions. Understanding these principles of chemical reaction engineering ensures the successful translation of reactions from concept to industrial reality.

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Most popular questions from this chapter

Liquid \(n\) -pentane at \(25^{\circ} \mathrm{C}\) is burned with \(30 \%\) excess oxygen (not air) fed at \(75^{\circ} \mathrm{C}\). The adiabatic flame temperature is \(T_{\mathrm{ad}}\left(^{\circ} \mathrm{C}\right)\) (a) Take as a basis of calculation \(1.00 \mathrm{mol} \mathrm{C}_{5} \mathrm{H}_{12}(1)\) burned and use an energy balance on the adiabatic reactor to derive an equation of the form \(f\left(T_{\mathrm{ad}}\right)=0,\) where \(f\left(T_{\mathrm{ad}}\right)\) is a fourth-order polynomial \(\left[f\left(T_{\mathrm{ad}}\right)=c_{0}+c_{1} T_{\mathrm{ad}}+c_{2} T_{\mathrm{ad}}^{2}+c_{3} T_{\mathrm{ad}}^{3}+c_{4} T_{\mathrm{ad} \mathrm{d}}^{4}\right]\). If your derivation is correct, the ratio \(c_{0} / c_{4}\) should equal \(-6.892 \times 10^{14} .\) Use a spreadsheet program to determine \(T_{\mathrm{ad}}\) (b) Repeat the calculation of Part (a) using successively the first two terms, the first three terms, and the first four terms of the fourth-order polynomial equation. If the solution of Part (a) is taken to be exact, what percentage errors are associated with the linear (two-term), quadratic (three-term), and cubic (four-term) approximations? (c) Why is the fourth-order solution at best an approximation and quite possibly a poor one? (Hint: Examine the conditions of applicability of the heat capacity formulas in Table B.2.)

Methane is bumed with \(25 \%\) excess air in a continuous adiabatic reactor. The methane enters the reactor at \(25^{\circ} \mathrm{C}\) and 1.10 atm at a rate of \(550 \mathrm{L} / \mathrm{s}\), and the entering air is at \(150^{\circ} \mathrm{C}\) and 1.1 atm. Combustion in the reactor is complete, and the reactor effluent gas emerges at 1.05 atm. (a) Calculate the temperature and the degrees of superheat of the reactor effluent. (Consider water to be the only condensable species in the effluent.) (b) Suppose only 15\% excess air is supplied. Without doing any additional calculations, state how the temperature and degrees of superheat of the reactor effluent would be affected lincrease, decrease, remain the same, cannot tell without more information] and explain your reasoning. What risk is involved in lowering the percent excess air?

In the production of many microelectronic devices, continuous chemical vapor deposition (CVD) processes are used to deposit thin and exceptionally uniform silicon dioxide films on silicon wafers. One CVD process involves the reaction between silane and oxygen at a very low pressure. $$\mathrm{SiH}_{4}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g})$$ The feed gas, which contains oxygen and silane in a ratio \(8.00 \mathrm{mol} \mathrm{O}_{2} / \mathrm{mol} \mathrm{SiH}_{4},\) enters the reactor at 298 \(\mathrm{K}\) and 3.00 torr absolute. The reaction products emerge at \(1375 \mathrm{K}\) and 3.00 torr absolute. Essentially all of the silane in the feed is consumed. (a) Taking a basis of \(1 \mathrm{m}^{3}\) of feed gas, calculate the moles of each component of the feed and product mixtures and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the silane oxidation reaction (kJ). Then, taking the feed and product species at \(298 \mathrm{K}\left(25^{\circ} \mathrm{C}\right)\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in the component amounts (mol) and specific enthalpies (kJ/mol). (See Example 9.5-1.) Data $$\left(\Delta \hat{H}_{\mathrm{f}}\right)_{\mathrm{SiH}_{4}(\mathrm{g})}=-61.9 \mathrm{kJ} / \mathrm{mol}, \quad\left(\Delta \hat{H}_{\mathrm{f}}^{\mathrm{o}}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}=-851 \mathrm{kJ} / \mathrm{mol}$$ $$\left(C_{p}\right)_{\mathrm{SiH}_{4}(g)}[\mathrm{k} \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})]=0.01118+12.2 \times 10^{-5} T-5.548 \times 10^{-8} T^{2}+6.84 \times 10^{-12} T^{3}$$ $$\left(C_{p}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]=0.04548+3.646 \times 10^{-5} T-1.009 \times 10^{3} / T^{2}$$ The temperatures in the formulas for \(C_{p}\) are in kelvins. (c) Calculate the heat ( \(k\) J) that must be transferred to or from the reactor (state which it is). Then determine the required heat transfer rate ( \(\mathrm{kW}\) ) required for a reactor feed of \(27.5 \mathrm{m}^{3} / \mathrm{h}\).

In a coal gasification process, carbon (the primary constituent of coal) reacts with steam to produce carbon monoxide and hydrogen (synthesis gas). The gas may either be burned or subjected to further processing to produce any of a variety of chemicals. A coal contains 10.5 wt\% moisture (water) and 22.6 wt\% noncombustible ash. The remaining fraction of the coal contains 81.2 wife \(\mathrm{C}, 13.4 \%\) O, and \(5.4 \%\) H. A coal slurry containing \(2.00 \mathrm{kg}\) coal/kg water is fed at \(25^{\circ} \mathrm{C}\) to an adiabatic gasification reactor along with a stream of pure oxygen at the same temperature. The following reactions take place in the reactor: $$\begin{array}{l}\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=+131.3 \mathrm{kJ} \\\\\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=-393.5 \mathrm{kJ} \\ 2 \mathrm{H}(\mathrm{in} \mathrm{coal})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta H_{\mathrm{r}}^{\circ} \approx-242 \mathrm{kJ}\end{array}$$ Gas and slag (molten ash) leave the reactor at \(2500^{\circ} \mathrm{C}\). The gas contains \(\mathrm{CO}, \mathrm{H}_{2}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}^{14}\) (a) Feeding oxygen to the reactor lowers the yield of synthesis gas, but no gasifier ever operates without supplementary oxygen. Why does the oxygen lower the yield? Why it is nevertheless always supplied. (Hint: All the necessary information is contained in the first two stoichiometric equations and associated heats of reaction shown above.) (b) Suppose the oxygen gas fed to the reactor and the oxygen in the coal combine with all the hydrogen in the coal (Reaction 3) and with some of the carbon (Reaction 2), and the remainder of the carbon is consumed in Reaction 1. Taking a basis of 1.00 kg coal fed to the reactor and letting \(n_{0}\) equal the moles of \(\mathrm{O}_{2}\) fed, draw and label a flowchart. Then derive expressions for the molar flow rates of the four outlet gas species in terms of \(n_{0}\). [Partial solution: \(n_{\mathrm{H}_{2}}=\left(51.3-n_{0}\right)\) mol \(\mathrm{H}_{2} . \mathrm{J}\) (c) The standard heat of combustion of the coal has been determined to be -21,400 kJ/kg, taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) to be the combustion products. Use this value and the given clemental composition of the coal to prove that the standard heat of formation of the coal is \(-1510 \mathrm{kJ} / \mathrm{kg}\). Then use an energy balance to calculate \(n_{0},\) using the following approximate heat capacities in your calculation: Take the heat of fusion of ash (the heat required to convert ash to slag) to be \(710 \mathrm{kJ} / \mathrm{kg}\).

Sulfur dioxide is oxidized to sulfur trioxide in a small pilot-plant reactor. SO \(_{2}\) and \(100 \%\) excess air are fed to the reactor at \(450^{\circ} \mathrm{C}\). The reaction proceeds to a \(65 \% \mathrm{SO}_{2}\) conversion, and the products emerge from the reactor at \(550^{\circ} \mathrm{C}\). The production rate of \(\mathrm{SO}_{3}\) is \(1.00 \times 10^{2} \mathrm{kg} / \mathrm{min}\). The reactor is surrounded by a water jacket into which water at \(25^{\circ} \mathrm{C}\) is fed. (a) Calculate the feed rates (standard cubic meters per second) of the \(\mathrm{SO}_{2}\) and air feed streams and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the SO_ oxidation reaction, \(\Delta H_{\mathrm{t}}^{\mathrm{r}}(\mathrm{kJ}) .\) Then, taking molecular species at \(25^{\circ} \mathrm{C}\) as references, prepare and fill in an inlet-outlet enthalpy table and write an energy balance to calculate the necessary rate of heat transfer ( \(\mathrm{kW}\) ) from the reactor to the cooling water. (c) Calculate the minimum flow rate of the cooling water if its temperature rise is to be kept below \(15^{\circ} \mathrm{C}\) (d) Briefly state what would have been different in your calculations and results if you had taken elemental species as references in Part (b).
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