/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 82 Acctylene is produced by pyrolyz... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 82

Acctylene is produced by pyrolyzing - decomposing at high temperature- -natural gas (predominantly methane): $$2 \mathrm{CH}_{4}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+3 \mathrm{H}_{2}$$ The heat required to sustain this endothermic reaction is provided by feeding oxygen to the reactor and burning a portion of the methane to form primarily CO and some \(\mathrm{CO}_{2}\) A simplified version of the process is as follows. A stream of natural gas, which for the purposes of this problem may be considered pure methane, and a stream containing 96.0 mole \(\%\) oxygen and the balance nitrogen are each preheated from \(25^{\circ} \mathrm{C}\) to \(650^{\circ} \mathrm{C}\). The streams are combined and fed into an adiabatic converter, in which most of the methane and all of the oxygen are consumed, and the product gas is rapidly quenched to \(38^{\circ} \mathrm{C}\) as soon as it emerges from the converter. The residence time in the converter is less than 0.01 s, low enough to prevent most but not all of the methane from decomposing to form hydrogen and solid carbon particles (soot). Of the carbon in the feed, \(5.67 \%\) emerges as soot. The cooled effluent passes through a carbon filter in which the soot is removed. The clean gas is then compressed and fed to an absorption column, where it is contacted with a recycled liquid solvent, dimethylformamide, or DMF (MW = 73.09). The off-gas leaving the absorber contains all of the hydrogen and nitrogen, \(98.8 \%\) of the \(\mathrm{CO}\), and \(95 \%\) of the methane in the gas fed to the column. The "lean" solvent fed to the absorber is essentially pure DMF; the "rich" solvent leaving the column contains all of the water and \(\mathrm{CO}_{2}\) and \(99.4 \%\) of the acetylene in the gas feed. This solvent is analyzed and found to contain 1.55 mole\% \(\mathrm{C}_{2} \mathrm{H}_{2}, 0.68 \% \mathrm{CO}_{2}, 0.055 \%\) CO, \(0.055 \% \mathrm{CH}_{4}, 5.96 \% \mathrm{H}_{2} \mathrm{O},\) and \(91.7 \% \mathrm{DMF}\) The rich solvent goes to a multiple-unit separation process from which three streams emerge. One-the product gas-contains 99.1 mole \(\% \mathrm{C}_{2} \mathrm{H}_{2}, 0.059 \% \mathrm{H}_{2} \mathrm{O},\) and the balance \(\mathrm{CO}_{2}\); the second \(-\) the stripper off-gas-contains methane, carbon monoxide, carbon dioxide, and water; and the third \(-\) the regenerated solvent- is the liquid DMF fed to the absorber. A plant is designed to produce 5.00 metric tons per day of product gas. Your assignment is to calculate (i) the required flow rates (SCMH) of the methane and oxygen feed streams; (ii) the molar flow rates (kmol/h) and compositions of the gas fed to the absorber, the absorber off-gas, and the stripper off- gas; (iii) the DMF circulation rate: (iv) the overall product yield (mol \(C_{2} \mathrm{H}_{2}\) in the product gas/mol \(\mathrm{CH}_{4}\) in feed to reactor) and the fraction that this quantity represents of its theoretical maximum value; (v) the total heating requirements (kW) for the methane and oxygen feed preheaters; (vi) the temperature attained in the converter. (a) Draw and label a flowchart of the process. Determine the degrees of freedom for the overall system, each individual process unit, and the feed- stream mixing point. (b) Write and number a full set of equations for the quantities specificd as (i)-(iv), identifying each one (e.g... \(C\) balance on converter, \(C H_{4}\) balance on absorber, ideal-gas equation of state for feed streams, etc.). You should end with as many equations as unknown variables. (c) Solve the equations of Part (b). (d) Calculate quantities (v) and (vi). (e) Speculate on what additional processing step(s) the absorber and stripper off-gases might be subjected to, and state your reasoning.

Short Answer

Expert verified
By setting up and solving a system of material balances, energy balances, and other relevant relationships based on the specified problem and the information given, one can calculate the required flow rates, heat requirements, DMF circulation rate, product yield, and other needed quantities. The maximum temperature for the conversion and the need for additional processing steps for the off-gases can also be identified.

Step by step solution

01

Write Full Set of Equations (i) to (iv)

Write the equations based on molar balance of every substance within reactor, absorber and stripper for quantities (i)-(iv) according to the given rules.
02

Determine degrees of freedom

Determine the degrees of freedom of the overall system based on the number of unknown variables minus the number of independent equations set.
03

Solve the equations

After achieving a system of equations with a number of equations equal to the number of unknowns, we can solve these equations, separately for reactor, absorber and stripper part.
04

Calculate (v) and (vi)

Calculate the total heating requirements using the temperature difference and specific heat capacity of methane and oxygen to heat them from initial to final temperature. By using adiabatic condition and considering all of the heat changes owing to reactions has been utilized to heat up the product gases, calculate the maximum temperature in the converter.
05

Propose additional steps in the process

Based on the composition of the off-gas, propose potential additional treatment steps that could be used, and give a rationale for their inclusion.

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Key Concepts

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

Chemical Process Analysis
Chemical process analysis is a critically important part of chemical engineering education, which entails examining the sequence of chemical and physical operations involved in transforming raw materials into desired products. It often begins with a conceptual representation of the entire process, such as a flowchart, as described in step (a) of the original exercise. Understanding the process analysis allows students to identify various streams and operations, as well as the connections between them.

In the context of the given problem, the flowchart would visualize inputs such as methane and oxygen, the adiabatic converter where reactions take place, subsequent cooling, filtration, and separation processes. Each operation and stream is studied to manage and optimize the conversion of methane to acetylene and to minimize by-products like soot through careful control of reaction conditions.

Process analysis often requires a combined understanding of several disciplines, such as thermodynamics, kinetics, and material transfer. It lays the foundation for the more quantitative aspects of chemical engineering, like material balance calculations, and guides process design and optimization efforts.
Material Balance Calculations
Material balance calculations are at the heart of chemical engineering and essentially involve accounting for all materials entering and exiting a system. It is based on the law of conservation of mass: mass can neither be created nor destroyed. The key is to ensure that the amount of each substance entering a process must be accounted for in the products, by-products, or waste streams leaving the process.

In the given exercise, material balances must be computed for methane, oxygen, acetylene, hydrogen, carbon monoxide, carbon dioxide, soot, and DMF. The problem requires calculating the flow rates and compositions of the feed and off-gases, which hinges on conducting a detailed material balance around each unit (e.g., reactor, absorber, stripper) as well as the overall system, as mentioned in steps (b) and (c). This helps in determining necessary input amounts to achieve a specific production target, such as the stated 5.00 metric tons per day of product gas.

Carrying out a material balance is a step-by-step method which may involve linear algebra for solving sets of equations or iterative techniques for more complicated processes. It's a fundamental concept that enables more advanced topics like reaction engineering and process design.
Chemical Reaction Engineering
Chemical reaction engineering focuses on the engineering aspects of reactions to produce desired products economically and safely. It includes designing and optimizing reactors based on kinetic data, ensuring the desired reaction pathways are favored while avoiding undesirable side reactions and by-products.

In the pyrolysis of methane to produce acetylene as illustrated in the exercise, key considerations would involve reaction kinetics, reactor design, reaction thermodynamics, and catalyst presence. It also requires an understanding of how various operating conditions, such as temperature, pressure, and residence time (as mentioned, less than 0.01 s in the converter), impact the conversion and selectivity of the desired product.

Chemical reaction engineering principles are critical in calculating the overall product yield relative to the theoretical maximum as demanded by the exercise's part (iv). These principles aid in predicting the behavior of the reaction system under different operating conditions, which is essential for process optimization and scale-up from lab-scale to production-scale processes.
Process Design and Optimization
Process design and optimization are about creating an efficient, economical, and environmentally benign process that meets production goals. Utilizing the principles of chemical engineering, it requires integrating individual unit operations into a cohesive process that conforms to specified product quality, capacity, and regulatory requirements.

In the context of creating acetylene, process design would address the flow rates, temperatures, pressures, and compositions for each part of the system, ensuring stable operation and quality product as demanded in parts (i), (ii), and (iv) of the exercise. Additionally, optimization efforts may focus on energy usage as required by part (v) for preheaters' heating requirements and part (vi) for the temperature achieved in the converter.

Modern process design also employs software tools for simulation and modeling, allowing the designer to explore the impacts of changing different parameters on the overall process efficiency and output before implementation. In the exercise, speculating on further processing steps as in step (e) is also a component of process design, where engineers consider the fate of off-gas components and opportunities for resource recovery or pollution control.

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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.)

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 \(7.5 \mathrm{MPa}\).

A mixture of methane, ethane, and argon at \(25^{\circ} \mathrm{C}\) is burned with excess air in a power-plant boiler. The hydrocarbons in the fuel are completely consumed. The following variable definitions will be used throughout this problem: \(x_{\mathrm{M}}=\) mole fraction of methane in the fuel \(x_{\mathrm{A}}=\) mole fraction of argon in the fuel \(P_{\mathrm{xs}}(\%)=\) percent excess air fed to the furnace \(T_{\mathrm{u}}\left(^{\circ} \mathrm{C}\right)=\) temperature of the entering air \(T_{\mathrm{s}}\left(^{\circ} \mathrm{C}\right)=\) stack gas temperature \(r=\) ratio of \(\mathrm{CO}_{2}\) to \(\mathrm{CO}\) in the stack gas \(\left(\mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO}\right)\) \(\dot{Q}(\mathrm{k} \mathrm{W})=\) rate of heat transfer from the furnace to the boiler tubes (a) Without doing any calculations, sketch the shapes of the plots you would expect to obtain for plots of \(\dot{Q}\) versus (i) \(x_{\mathrm{M}, \text { (ii) } x_{\mathrm{A}}, \text { (iii) } P_{\mathrm{xs}}, \text { (iv) } T_{\mathrm{a}},(\mathrm{v}) T_{\mathrm{s}}, \text { and }(\mathrm{vi})} r,\) assuming in each case that the other variables are held constant. Briefly state your reasoning for each plot. (b) Take a basis of 1.00 mol/s of fuel gas, draw and label a flowchart, and derive expressions for the molar flow rates of the stack gas components in terms of \(x_{\mathrm{M}}, x_{\mathrm{A}}, P_{\mathrm{xs}},\) and \(r .\) Then take as references the elements at \(25^{\circ} \mathrm{C}\), prepare and fill in an inlet-outlet enthalpy table for the furnace, and derive expressions for the specific molar enthalpies of the feed and stack gas components in terms of \(T_{\mathrm{a}}\) and \(T_{\mathrm{s}}\) (c) Calculate \(\dot{Q}(\mathrm{kW})\) for \(x_{\mathrm{M}}=0.85 \mathrm{mol} \mathrm{CH}_{\mathcal{J}} / \mathrm{mol}, x_{\mathrm{A}}=0.05 \mathrm{mol} \mathrm{Ar} / \mathrm{mol}, P_{\mathrm{xs}}=5 \%, r=10.0 \mathrm{mol}\) \(\left.\mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO}, T_{\mathrm{a}}=150^{\circ} \mathrm{C}, \text { and } T_{\mathrm{s}}=700^{\circ} \mathrm{C} \text { (Solution: } \dot{Q}=-655 \mathrm{kW} .\right)\) (d) Prepare a spreadsheet that has columns for \(x_{\mathrm{M}}, x_{\mathrm{A}}, P_{\mathrm{xs}}, T_{\mathrm{a}}, r, T_{\mathrm{s}},\) and \(\dot{Q},\) plus columns for any other variables you might need for the calculation of \(\dot{Q}\) from given values of the preceding six variables (e.g., component molar flow rates and specific enthalpies). Use the spreadsheet to generate plots of \(\dot{Q}\) versus each of the following variables over the specified ranges: $$\begin{aligned}&x_{\mathrm{M}}=0.00-0.85 \mathrm{mol} \mathrm{CH}_{4} / \mathrm{mol}\\\ &x_{\mathrm{A}}=0.01-0.05 \mathrm{mol} \mathrm{Ar} / \mathrm{mol}\\\ &P_{\mathrm{xs}}=0 \%-100 \%\\\ &T_{\mathrm{a}}=25^{\circ} \mathrm{C}-250^{\circ} \mathrm{C}\\\ &r=1-100 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO} \text { (make the } r \text { axis logarithmic) }\\\ &T_{\mathrm{s}}=500^{\circ} \mathrm{C}-1000^{\circ} \mathrm{C}\end{aligned}$$ When generating each plot, use the variable values given in Part (c) as base values. (For example, generate a plot of \(\dot{Q}\) versus \(x_{\mathrm{M}}\) for \(x_{\mathrm{A}}=0.05, P_{\mathrm{xs}}=5 \%,\) and so on, with \(x_{\mathrm{M}}\) varying from 0.00 to 0.85 on the horizontal axis.) If possible, include the plots on the same spreadsheet as the data.

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).

Methanol vapor is burned with excess air in a catalytic combustion chamber. Liquid methanol initially at \(25^{\circ} \mathrm{C}\) is vaporized at 1.1 atm and heated to \(100^{\circ} \mathrm{C}\); the vapor is mixed with air that has been preheated to \(100^{\circ} \mathrm{C},\) and the combined stream is fed to the reactor at \(100^{\circ} \mathrm{C}\) and 1 atm. The reactor effluent emerges at \(300^{\circ} \mathrm{C}\) and 1 atm. Analysis of the product gas yields a dry-basis composition of \(4.8 \% \mathrm{CO}_{2}\) \(14.3 \% \mathrm{O}_{2},\) and \(80.9 \% \mathrm{N}_{2}\) (a) Calculate the percentage excess air supplied and the dew point of the product gas. (b) Taking a basis of 1 g-mole of methanol burned, calculate the heat ( \(k\) J) needed to vaporize and heat the methanol feed, and the heat (kJ) that must be transferred from the reactor. (c) Suggest how the energy economy of this process could be improved. Then suggest why the company might choose not to implement your redesign.
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