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Chapter 9: Problem 34

Formaldehyde is produced by decomposing methanol over a silver catalyst: $$\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2}$$ To provide heat for this endothermic reaction, some oxygen is included in the feed to the reactor, leading to the partial combustion of the hydrogen produced in the methanol decomposition. The feed to an adiabatic formaldehyde production reactor is obtained by bubbling a stream of air at 1 atm through liquid methanol. The air leaves the vaporizer saturated with methanol and contains \(42 \%\)methanol by volume. The stream then passes through a heater in which its temperature is raised to \(145^{\circ} \mathrm{C} .\) To avoid deactivating the catalyst, the maximum temperature attained in the reactor must be limited to \(600^{\circ} \mathrm{C}\). For this purpose, saturated steam at \(145^{\circ} \mathrm{C}\) is metered into the air-methanol stream, and the combined stream cnters the reactor. A fractional methanol conversion of \(70.0 \%\) is achicved in the reactor, and the product gas contains 5.00 mole\% hydrogen. The product gas is cooled to \(145^{\circ} \mathrm{C}\) in a waste heat boiler in which saturated steam at 3.1 bar is generated from liquid water at \(30^{\circ} \mathrm{C}\). Several absorption and distillation units follow the waste heat boiler, and formaldehyde is ultimately recovered in an aqueous solution containing 37.0 wt\% HCHO. The plant is designed to produce 36 metric kilotons of this solution per year, operating 350 days/yr. (a) Draw the process flowchart and label it completely. Show the absorption/distillation train as a single unit with the reactor product gas and additional water entering and the formaldehyde solution and a gas stream containing methanol, oxygen, nitrogen, and hydrogen leaving. (b) Calculate the operating temperature of the methanol vaporizer. (c) Calculate the required feed rate of steam to the reactor \((\mathrm{kg} / \mathrm{h})\) and the molar flow rate and composition of the product gas. (d) Calculate the rate ( \(\mathrm{kg} / \mathrm{h}\) ) at which steam is generated in the waste heat boiler. (e) Enough saturated steam was added to the feed to the reactor to keep the reactor outlet temperature at \(600^{\circ} \mathrm{C}\). Explain in your own words (i) why adding steam lowers the outlet temperature, and (ii) the cconomic drawbacks of higher and lower outlet temperatures.

Short Answer

Expert verified
The operating temperature of the methanol vaporizer is 64.7掳C. The feed rate of steam, and the molar flow rate and composition of the product gas can be determined by conducting a mass balance over the system and considering the specific heat capacity of steam. The rate of steam generation in the waste heat boiler can also be determined using a mass balance. The addition of saturated steam helps to regulate the outlet temperature but any deviations in the temperature can have economic implications.

Step by step solution

01

Process Flowchart

The process flowchart needed is of formaldehyde production process. The methanol goes through a vaporizer and then through a heater which brings it to a temperature of 145掳C. The stream with methanol and air goes through a reactor, releasing a product gas with oxygen, nitrogen, hydrogen and methanol. This stream is cooled in a waste heat boiler to 145掳C. From this, it goes into absorption/distillation units where it produces an aqueous solution containing formaldehyde.
02

Operating Temperature of the Methanol Vaporizer

Assuming the methanol is saturated within the vaporizer, we can refer to the vapor pressure curve of methanol to find the operating temperature. The operating temperature of the methanol vaporizer is the temperature at which methanol gets vaporized, i.e. its boiling point is 64.7掳C.
03

Feed Rate of Steam to the Reactor

To calculate the feed rate of steam to the reactor, we need to first determine the required temperature increase. This comes from the temperature the steam needs to reach minus the initial temperature of the methanol/air stream, which is \(600 - 145 = 455\)掳C. Given the specific heat of steam, we can then calculate the amount of steam required to achieve this temperature increase.
04

Molar Flow Rate and Composition of the Product Gas

To find the molar flow rate and composition of the product gas, we need to conduct a mass balance calculation over the entire process, accounting for the feed, the steam injection, the methanol decomposition and the resulting product gases. This will enable us to calculate the composition of the gases in the product stream.
05

Steam Generation Rate in the Waste Heat Boiler

To calculate the rate of steam generation in the waste heat boiler, we'll again need to perform a mass balance over the boiler component. By considering the energy provided by the hot product gas and the energy required to vaporise water into steam, we'll be able to calculate the mass flow required.
06

Effect of Adding Saturated Steam and Consequences of Outlet Temperature

We add saturated steam to the feed to the reactor to keep the outlet temperature at \(600掳C\). The steam absorbs heat from the reactor, hence lowering the outlet temperature. The economic drawbacks of higher outlet temperatures include possible damage to the equipment, reduced efficiency due to heat loss, and higher energy costs. Lower outlet temperatures, on the other hand, may not provide sufficient heat for the reactions, leading to lower production rates.

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Key Concepts

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

Chemical Engineering Processes
Chemical engineering processes are the backbone of manufacturing and production industries. In the context of formaldehyde production, the chemical reactions are carefully managed to transform methanol into formaldehyde using a silver catalyst. Formaldehyde is produced by decomposing methanol, a process that requires precise control of conditions such as temperature and pressure to maximize yield and ensure safety. Catalysts, like silver, play a crucial role in facilitating reactions by lowering the energy barriers, thus increasing reaction rates without being consumed within the process. Engineering these reactions involves a deep understanding of thermodynamics, kinetics, and material properties, to optimize performance while minimizing waste and energy consumption.
Mass and Energy Balances
Mass and energy balances are essential tools for chemical engineers to understand and evaluate the efficiency of any given process. For formaldehyde production, a mass balance calculates the input and output of methanol, formaldehyde, and by-products like hydrogen and water vapor in the system. It ensures that mass is conserved throughout the process. By doing so, one can verify that the correct proportion of each substance is being used and produced.
Energy balances, on the other hand, focus on the heat and work interactions within the reactor. They are used to calculate the energy required to achieve the reaction temperature and to maintain optimal conditions. For instance, in this process, heat is needed to maintain a high enough temperature in the reactor for the decomposition of methanol, while the waste heat boiler recaptures energy from cooled gases to be reused.
Process Flowchart Design
Designing a process flowchart is a critical step in visualizing and planning the production setup. It involves outlining each stage of the formaldehyde production pathway 鈥� from the methanol vaporizer, heater, reactor, to the waste heat boiler, and finally to the absorption/distillation units. Each step must be precisely labeled to understand the movement and transformation of substances within the plant.
The flowchart simplifies complex processes, making it easier to identify potential areas for improvement or troubleshooting. It serves as a blueprint for plant operations and helps engineers communicate process details effectively to contractors, operators, and stakeholders.
Reactor Temperature Control
Reactor temperature control is vital for the stability and safety of chemical processes. In the production of formaldehyde, maintaining a maximum temperature of 600掳C in the reactor prevents catalyst deactivation and ensures reaction efficiency. Temperature control is achieved by managing steam addition, which absorbs excess heat and minimizes temperature fluctuations.
Effective temperature control can avert issues like thermal runaway, where temperatures could spiral out of control, leading to dangerous conditions. Additionally, maintaining precise temperatures enhances reaction selectivity and yield, reducing the formation of undesired by-products. Thus, understanding and implementing temperature control strategies are key in the safe and efficient design of chemical reactors.

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Most popular questions from this chapter

A fuel gas containing 85.0 mole\% methane and the balance ethane is burned completely with pure oxygen at \(25^{\circ} \mathrm{C},\) and the products are cooled to \(25^{\circ} \mathrm{C}\). (a) Suppose the reactor is continuous. Take a basis of calculation of \(1 \mathrm{mol} / \mathrm{s}\) of the fuel gas, assume some value for the percent excess oxygen fed to the reactor (the value you choose will not affect the results), and calculate \(-\dot{Q}(\mathrm{k} \mathrm{W}),\) the rate at which heat must be transferred from the reactor. (b) Now suppose the combustion takes place in a constant-volume batch reactor. Take a basis of calculation of 1 mol of the fuel gas charged into the reactor, assume any percent excess oxygen, and calculate \(-Q(\mathrm{kJ}) .\) (Hint: Recall Equation 9.1-5.) (c) Briefly explain why the results in Parts (a) and (b) do not depend on the percent excess \(\mathrm{O}_{2}\) and why they would not change if air rather than pure oxygen were fed to the reactor.

The production of most of the steel manufactured in the United States begins with the reduction of hematite ore (mostly ferric oxide) with coke (carbon) in a blast furnace to obtain pig iron. The basic reaction is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=2.111 \times 10^{5} \mathrm{Btu}$$ Suppose that stoichiometric amounts of ferric oxide and carbon are fed at \(77^{\circ} \mathrm{F}\), the reaction is complete, the iron emerges as a liquid at \(2800^{\circ} \mathrm{F}\), and \(\mathrm{CO}\) emerges at \(570^{\circ} \mathrm{F}\). Perform the following calculations for a basis of 1 ton of iron produced. (a) Draw and label a flowchart and perform all the material balance calculations needed to determine the amounts (lb-mole) of each feed and product stream component. (b) Taking the reactant and product species in their normal states at \(77^{\circ} \mathrm{F}\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in all unknown component specific enthalpies (Btu/lb- mole). Use the following physical property data for iron: \(\mathrm{Fe}(\mathrm{s}): \quad C_{p}\left[\mathrm{B} \operatorname{tu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=5.90+1.50 \times 10^{-3} T\left(^{\circ} \mathrm{F}\right)\) \(T_{\mathrm{m}}=2794^{\circ} \mathrm{F}, \quad \Delta \hat{H}_{\mathrm{m}}\left(T_{\mathrm{m}}\right)=6496 \mathrm{Btu} / \mathrm{lb}-\mathrm{mole}\) \(\mathrm{Fe}(\mathrm{l}): \quad C_{p}\left[\mathrm{Btu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=8.15\) (c) Estimate the furnace heat requirement (Btu/ton Fe produced). (d) List the assumptions that make the value calculated in Part (c) only an approximate estimate of the furnace heat requirement. (One of the assumptions has something to do with the reactor pressure.)

Formaldehyde may be produced in the reaction between methanol and oxygen: $$2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{HCHO}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta H_{\mathrm{r}}^{\circ}=-326.2 \mathrm{kJ}$$ The standard heat of combustion of hydrogen is $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta \hat{H}_{\mathrm{c}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}$$ (a) Use these heats of reaction and Hess's law to determine the standard heat of the direct decomposition of mcthanol to form formaldchyde: $$\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l}) \rightarrow \mathrm{HCHO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ (b) Explain why you would probably use the method of Part (a) to determine the heat of the methanol decomposition reaction experimentally rather than carrying out the decomposition reaction and measuring \(\Delta H_{f}^{\circ}\) directly.

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.

Various uses for nitric acid are given in Problem \(6.43,\) along with information about how this important chemical is synthesized industrially. The key reactions are oxidations of ammonia to nitric oxide and of nitric oxide to nitrogen dioxide, followed by dissolution of \(\mathrm{NO}_{2}\) in water: $$\begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) & \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \\ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \\ 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1) & \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{aligned}$$ Nitric oxide generated on dissolution of \(\mathrm{NO}_{2}\) in water is oxidized to produce additional \(\mathrm{NO}_{2},\) which is then combined with water to form more \(\mathrm{HNO}_{3}\). In this problem we neglect side reactions that would lower the product yield. Ammonia vapor at \(275^{\circ} \mathrm{C}\) and 8 atm is mixed with air, also at \(275^{\circ} \mathrm{C}\) and 8 atm, and the combined stream is fed to a converter. Fresh air entering the system at \(30^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(50 \%\) is compressed to \(100^{\circ} \mathrm{C}\) and 8 atm, and the compressed air then exchanges heat with the product gas leaving the converter. The quantity of oxygen in the feed to the converter is \(20 \%\) in excess of the amount theoretically required to convert all of the ammonia to \(\mathrm{HNO}_{3}\). The entire process after the compressor may be taken to operate at a constant pressure of 8 atm. In the converter, the ammonia is completely oxidized, with a negligible amount of \(\mathrm{NO}_{2}\) formed. The product gas leaves the converter at \(850^{\circ} \mathrm{C}\), and, as described in the preceding paragraph, exchanges heat with the air entering the system. The product gas then is fed to a waste-heat boiler that produces superheated steam at \(200^{\circ} \mathrm{C}\) and 10 bar from liquid water at \(35^{\circ} \mathrm{C}\). The product gas leaving the wasteheat boiler is cooled further to \(35^{\circ} \mathrm{C}\) and fed to an absorption column in which the NO is completely oxidized to \(\mathrm{NO}_{2},\) which in turn combines with water (some of which is present in the product gas). Water is fed to the absorber at \(25^{\circ} \mathrm{C},\) at a rate sufficient to form a 55 wt\% aqueous nitric acid solution. The NO formed in the reaction of \(\mathrm{NO}_{2}\) to produce \(\mathrm{HNO}_{3}\) is oxidized, and the NO \(_{2}\) produced is hydrated to form still more \(\mathrm{HNO}_{3}\). The off-gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (a) Construct a flowchart showing all process streams, including input and output from the process and the following equipment: converter, air compressor, exchanger recovering heat from the converter product, waste-heat boiler producing superheated steam, exchanger cooling the product gas before it is fed to the absorber, and absorber. (b) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, develop spreadsheets (preferably incorporating the use of APEx) to determine the following: (i) Molar amounts (kmol) of oxygen, nitrogen, and water vapor in the air fed to the process, cubic meters of air fed to the process, and kmol of water fed to the absorber. (ii) Molar amounts, molar composition, and volume of the off-gas leaving the absorber. (iii) Mass (kg) of product nitric acid solution. (iv) Molar amounts and composition of the gas leaving the converter. (v) Heat removed from or added to (state which) the converter. (vi) Temperature of the product gas after it has exchanged heat with the air, assuming no heat is transferred between the heat exchanger and the surroundings. (vii) Production rate of superheated steam if the gas temperature leaving the boiler is \(205^{\circ} \mathrm{C}\). Before performing this calculation, determine if condensation of water occurs when the gas is cooled to \(205^{\circ} \mathrm{C}\). Since the superheated steam temperature is \(200^{\circ} \mathrm{C}\), explain why the selected temperature of the product gas is reasonable. (viii) Heat removed from the product gas before it is fed to the absorber (Hint: Check the condition of the gas at \(35^{\circ} \mathrm{C}\) ) and mass of cooling water required to remove that heat if the water temperature can only be increased by \(5^{\circ} \mathrm{C}\). Assume no heat is transferred between the heat exchanger and the surroundings. (ix) Heat removed from or added to the absorber. Assume the heat capacity of the nitric acid solution is approximately the same as that of liquid water and the outlet temperatures of the off-gas and product streams are \(25^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\), respectively. (c) Scale up the results calculated in Part (b) to determine all stream flow rates and heat transfer rates for a production rate of \(5.0 \times 10^{3} \mathrm{kg} / \mathrm{h}\) of the product solution.
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