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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

Formaldehyde is produced commercially by the catalytic oxidation of methanol. In a side reaction, methanol is oxidized to \(\mathrm{CO}_{2}\) $$\begin{array}{l}\mathrm{CH}_{3} \mathrm{OH}+\mathrm{O}_{2} \rightarrow \mathrm{CH}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \\\\\mathrm{CH}_{3} \mathrm{OH}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\end{array}$$ A mixture containing 55.6 mole \(\%\) methanol and the balance oxygen enters a reactor at \(350^{\circ} \mathrm{C}\) and \(1 \mathrm{atm}\) at a rate of \(4.60 \times 10^{4} \mathrm{L} / \mathrm{s}\). The reaction products emerge at the same temperature and pressure at a rate of \(6.26 \times 10^{4} \mathrm{L} / \mathrm{s} .\) An analysis of the products yields a molar composition of \(36.7 \% \mathrm{CH}_{2} \mathrm{O}, 4.1 \% \mathrm{CO}_{2}\) \(14.3 \% \mathrm{O}_{2},\) and \(44.9 \% \mathrm{H}_{2} \mathrm{O} .\) The required reactor cooling rate is calculated to be \(1.05 \times 10^{5} \mathrm{kW}\) (a) Is the calculated cooling rate correct for the given stream data? (b) The stream data cannot be correct. Prove it.

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).

Lime (calcium oxide) is widely used in the production of cement, steel, medicines, insecticides, plant and animal food, soap, rubber, and many other familiar materials. It is usually produced by heating and decomposing limestone (CaCO \(_{3}\) ), a cheap and abundant mineral, in a calcination process: $$\mathrm{CaCO}_{3}(\mathrm{s}) \stackrel{\text { heat }}{\longrightarrow} \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ (a) Limestone at \(25^{\circ} \mathrm{C}\) is fed to a continuous calcination reactor. The calcination is complete, and the products leave at \(900^{\circ} \mathrm{C}\). Taking 1 metric ton \((1000 \mathrm{kg})\) of limestone as a basis and clemental species \(\left[\mathrm{Ca}(\mathrm{s}), \mathrm{C}(\mathrm{s}), \mathrm{O}_{2}(\mathrm{g})\right]\) at \(25^{\circ} \mathrm{C}\) as references for enthalpy calculations, prepare and fill in an inlet-outlet enthalpy table and prove that the required heat transfer to the reactor is \(2.7 \times 10^{6} \mathrm{kJ}\) (b) In a common variation of this process, hot combustion gases containing oxygen and carbon monoxide (among other components) are fed into the calcination reactor along with the limestone. The carbon monoxide is oxidized in the reaction $$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})$$ Suppose the combustion gas fed to a calcination reactor contains 75 mole \(\% \mathrm{N}_{2}, 2.0 \% \mathrm{O}_{2}, 9.0 \% \mathrm{CO},\) and \(14 \% \mathrm{CO}_{2}\) the gas enters the reactor at \(900^{\circ} \mathrm{C}\) in a feed ratio of \(20 \mathrm{kmol}\) gas/kmol limestone; the calcination is complete; all of the oxygen in the gas feed is consumed in the CO oxidation reaction; the reactor effluents are at \(900^{\circ} \mathrm{C}\) Again taking a basis of 1 metric ton of limestone calcined, prepare and fill in an inlet-outlet enthalpy table for this process [don't recalculate enthalpies already calculated in Part (a)] and calculate the required heat transfer to the reactor. (c) You should have found that the heat that must be transferred to the reactor is significantly lower with the combustion gas in the feed than it is without the gas. By what percentage is the heat requirement reduced? Give two reasons for the reduction. State another benefit of feeding the combustion gas, besides the reduction of the heating requirement.

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?

A methanol-synthesis reactor is fed with a gas stream at \(220^{\circ} \mathrm{C}\) consisting of 5.0 mole\% methane, \(25.0 \%\) CO, \(5.0 \% \mathrm{CO}_{2},\) and the remainder hydrogen. The reactor and feed stream are at \(7.5 \mathrm{MPa}\). The primary reaction occurring in the reactor and its associated equilibrium constant are $$\begin{array}{l}\mathrm{CO}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH} \\\K=\frac{y_{\mathrm{CH}, \mathrm{OH}} y_{\mathrm{H}_{2}}}{y_{\mathrm{CO}} y_{H_{2}}^{2} P^{2}}=\exp \left(\begin{array}{c}21.225+\frac{9143.6}{T}-7.492 \ln T \\ +4.076 \times 10^{-3} T-7.161 \times 10^{-8} T^{2}\end{array}\right)\end{array}$$ where \(T\) is in kelvins. The product stream may be assumed to reach equilibrium at \(250^{\circ} \mathrm{C}\). (a) Determine the composition (mole fractions) of the product stream and the percentage conversions of CO and \(\mathrm{H}_{2}\). (b) Neglecting the effect of pressure on enthalpies, estimate the amount of heat (kJ/mol feed gas) that must be added to or removed from (state which) the reactor. (c) Calculate the extent of reaction and heat removal rate (kJ/mol feed) for reactor temperatures between \(200^{\circ} \mathrm{C}\) and \(400^{\circ} \mathrm{C}\) in \(50^{\circ} \mathrm{C}\) increments. Use these results to obtain an estimate of the adiabatic reaction temperature. (d) Determine the effect of pressure on the reaction by evaluating extent of conversion and rate of heat transfer at \(1 \mathrm{MPa}\) and \(15 \mathrm{MPa}\). (e) Considering the results of your calculations in Parts (c) and (d), propose an explanation for selection of the initial reaction conditions of \(250^{\circ} \mathrm{C}\) and \(7.5 \mathrm{MPa}\).
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