/*! 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 45 In a coal gasification process, ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 45

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 \(710 \mathrm{kJ} / \mathrm{kg}\).

Short Answer

Expert verified
In the coal gasification process, the oxygen lowers synthesis gas yield but is necessary for the complete reaction of coal. Based on the given details for a basis of 1.00 kg of coal fed, \(n_0\) can be determined through a compiled energy balance on the system. The standard heat of formation of the coal is about -1510 kJ/kg.

Step by step solution

01

Understand the Effect of Oxygen on Synthesis Gas Yield

Oxygen lowers the yield of synthesis gas because its reaction with carbon yields \(CO_2\) (reaction 2), a combustion product, rather than \(CO\) and \(H_2\) which make up synthesis gas (reaction 1). Oxygen, however, is still supplied to ensure complete reaction of the coal, as reaction 1 alone, without sufficient heat, would not be capable of completely converting the carbon in coal to synthesis gas.
02

Drawing the Flowchart and Derive Molar Flow Rates

Draw a block diagram to represent the coal gasification process, including all input and output streams. Label the mass and mole flow rates of each component on the respective stream. Express the molar flow rates of the output gas species in terms of \(n_0\). Use the stoichiometric ratios given by the reactions and the mass balance of carbon and hydrogen to derive these. The partial solution suggests that \(n_{H_2} = (51.3 - n_0)\) mol, indicating that all of the hydrogen either ends up as \(H_2O\) (in combination with \(O_2\) in the coal and the feed) or as \(H_2\) (when carbon reacts with steam).
03

Determine the Standard Heat of Formation

Begin by calculating the heat of combustion per mole of carbon and hydrogen in the coal. This can be done by dividing the standard heat of combustion by the molar mass of the coal and then using the weight percentages of carbon and hydrogen. After that, calculate the heat of formation per kg of coal by adding the heat of combustion and the heats of reaction for each of the species in the coal.
04

Energy Balance to Calculate \(n_0\)

Estimate the energy content of the inlet and outlet using heat capacities and heats of reaction. The energy should be conserved throughout, meaning that the total energy in the inlet streams should equal the total energy in the outlet streams. This can be written as an energy balance equation. From this equation, the value of \(n_0\) can be determined.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Chemical Engineering Principles
Chemical engineering is the discipline that combines natural sciences with life sciences, mathematics, and economics to produce, transform, transport, and properly use chemicals, materials, and energy. When examining the coal gasification process, these principles come into play as engineers work to optimize the transformation of coal into valuable synthesis gas (syngas), involving chemical reactions and energy considerations.

A key aspect is understanding how materials behave and how they interact with energy. By implementing an energy balance, an engineer ensures that all the energy provided or generated in the system either goes into synthesizing desired products, maintaining the process conditions, or is accounted for in the losses, a topic we will discuss further in a later section on energy balance. One of the core challenges is to manage the reaction conditions such that the maximum yield of desirable products is maintained. This often involves a trade-off, as seen in the exercise where the addition of oxygen ensures the completion of the reaction but reduces the yield of syngas due to the formation of CO2.
Stoichiometric Calculations
Stoichiometric calculations are pivotal in chemical engineering for they quantify the relationship between reactants and products in a chemical reaction. Understanding stoichiometry allows us to predict the amounts of substances consumed and produced during a reaction, which in turn helps in designing and scaling up processes.

In the coal gasification exercise, precise stoichiometric calculations would enable the estimation of reactant amounts required for the desired products. For example, the relationship between carbon, oxygen, and the resultant synthesis gas components is based on the stoichiometric coefficients from the balanced equations. When utilizing the provided partial solution for hydrogen gas, n_{H_2} = (51.3 - n_0) moles, it is clear that this calculation relies on an understanding of the molar ratios of the reactants to hydrogen in the product, which is derived from the balanced equations for the gasification reactions.
Energy Balance
An energy balance is a fundamental principle in chemical engineering, necessary for designing and operating chemical reactors. It is the application of the first law of thermodynamics which states that energy cannot be created or destroyed, only transformed. In the context of the coal gasification exercise, an energy balance would ensure that the total energy entering the system (in the form of chemical potential energy in reactants) is equal to the energy leaving the system (as chemical energy in products, thermal energy, and energy lost to surroundings).

This energy accounting is crucial when considering the endothermic and exothermic reactions, by including the heats of reaction for the formation of syngas and CO2. Additionally, there are thermal energies related to the temperature changes of reactants and products, as well as phase changes, such as the formation of slag from ash. By calculating heat duties for each of these components and applying the energy conservation principle, one can ensure the reactor operates effectively and safely.
Synthesis Gas Production
Synthesis gas, or syngas, is a mixture of carbon monoxide (CO) and hydrogen (H2) that is a key intermediate in the production of a variety of chemicals and as a fuel source itself. The production of syngas through coal gasification involves the controlled reaction of coal with oxygen and steam at high temperatures. The goal is to maximize the output of CO and H2, while minimizing the production of CO2 and other byproducts. Hence, it's essential to carefully control the reaction conditions, including temperature, pressure, and reactant ratios, based on chemical engineering principles and energy balance considerations.

The exercise implies that to increase yield, one may need to optimize the ratio of oxygen provided to the reactor, since oxygen is necessary to support the reaction but also competes with steam for the available carbon, influencing the composition of the syngas produced. This interplay showcases the need for careful design and operation of gasification processes to produce a high-quality syngas efficiently.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Methane and \(30 \%\) excess air are to be fed to a combustion reactor. An inexperienced technician mistakes his instructions and charges the gases together in the required proportion into an evacuated closed tank. (The gases were supposed to be fed directly into the reactor.) The contents of the charged tank are at \(25^{\circ} \mathrm{C}\) and 4.00 atm absolute. (a) Calculate the standard internal energy of combustion of the methane combustion reaction. \(\Delta \hat{U}_{c}^{\circ}(\mathrm{kJ} / \mathrm{mol}),\) taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) as the presumed products. Then prove that if the constant-pressure heat capacity of an ideal-gas species is independent of temperature, the specific internal energy of that species at temperature \(T\left(^{\circ} \mathrm{C}\right)\) relative to the same species at \(25^{\circ} \mathrm{C}\) is given by the expression $$\hat{U}=\left(C_{p}-R\right)\left(T-25^{\circ} \mathrm{C}\right)$$ where \(R\) is the gas constant. Use this formula in the next part of the problem. (b) You wish to calculate the maximum temperature, \(T_{\max }\left(^{\circ} \mathrm{C}\right),\) and corresponding pressure, \(P_{\max }(\text { atm }),\) that the tank would have to withstand if the mixture it contains were to be accidentally ignited. Taking molecular species at \(25^{\circ} \mathrm{C}\) as references and treating all species as ideal gases, prepare an inlet-outlet internal energy table for the closed system combustion process. In deriving expressions for each \(\dot{U}_{i}\) at the final reactor condition \(\left(T_{\max }, P_{\max }\right),\) use the following approximate values for \(C_{p_{i}}\left[\mathrm{k} J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]: 0.033 \mathrm{for} \mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052 \mathrm{for} \mathrm{CO}_{2},\) and \(0.040 \mathrm{for} \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) .\) Then use an energy balance and the ideal-gas equation of state to perform the required calculations. (c) Why would the actual temperature and pressure attained in a real tank be less than the values calculated in Part (a)? (State several reasons.) (d) Think of ways that the tank contents might be accidentally ignited. The list should suggest why accepted plant safety regulations prohibit the storage of combustible vapor mixtures.

Carbon disulfide, a key component in the manufacture of rayon fibers, is produced in the reaction between methane and sulfur vapor over a metal oxide catalyst: $$\begin{array}{c}\mathrm{CH}_{4}(\mathrm{g})+4 \mathrm{S}(\mathrm{v}) \rightarrow \mathrm{CS}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \\ \Delta H_{\mathrm{r}}\left(700^{\circ} \mathrm{C}\right)=-274 \mathrm{kJ} \end{array}$$ Methane and molten sulfur, each at \(150^{\circ} \mathrm{C}\), are fed to a heat exchanger in stoichiometric proportion. Heat is exchanged between the reactor feed and product streams, and the sulfur in the feed is vaporized. The gascous methane and sulfur leave the exchanger and pass through a second preheater in which they are heated to \(700^{\circ} \mathrm{C}\), the temperature at which they enter the reactor. Heat is transferred from the reactor at a rate of \(41.0 \mathrm{kJ} / \mathrm{mol}\) of feed. The reaction products emerge from the reactor at \(800^{\circ} \mathrm{C}\), pass through the heat exchanger, and emerge at \(200^{\circ} \mathrm{C}\) with sulfur as a liquid. Use the following heat capacity data to perform the requested calculations: \(C_{p}\left[J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \approx 29.4\) for \(\mathrm{S}(1), 36.4\) for \(\mathrm{S}(\mathrm{v}), 71.4\) for \(\mathrm{CH}_{4}(\mathrm{g}), 31.8\) for \(\mathrm{CS}_{2}(\mathrm{v}),\) and 44.8 for \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) (a) Estimate the fractional conversion achieved in the reactor. In enthalpy calculations, take the feed and product species at \(700^{\circ} \mathrm{C}\) as references. (b) Suppose the heat of reaction at \(700^{\circ} \mathrm{C}\) had not been given. What would be different in your solution to Part (a)? (Be thorough in your explanation.) Sketch the process paths from the feed to the products built into both the calculation of Part (a) and your alternative calculation. Explain why the result would be the same regardless of which method you used. (c) Suggest a method to improve the energy economy of the process.

An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen, nitrogen, oxygen, and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Dulong formula: $$H H V(\mathrm{k} J / \mathrm{kg})=33,801(\mathrm{C})+144,158[(\mathrm{H})-0.125(\mathrm{O})]+9413(\mathrm{S})$$ where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125(O) term accounts for the hydrogen bound in the water contained in the coal. (a) Derive an expression for the higher heating value ( \(H H V\) ) of a coal in terms of \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{S},\) and compare your result with the Dulong formula. Suggest a reason for the difference. (b) A coal with an ultimate analysis of \(75.8 \mathrm{wt} \% \mathrm{C}, 5.1 \% \mathrm{H}, 8.2 \% \mathrm{O}, 1.5 \% \mathrm{N}, 1.6 \% \mathrm{S},\) and \(7.8 \%\) ash (noncombustible) is burned in a power-plant boiler fumace. All of the sulfur in the coal forms \(\mathrm{SO}_{2}\) The gas leaving the furnace is fed through a tall stack and discharged to the atmosphere. The ratio \(\phi\) (\(\mathrm{kg} \mathrm{SO}_{2}\) in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate \(\phi\), using the Dulong formula for the heating value of the coal. (c) An earlier version of the EPA regulation specified that the mole fraction of \(\mathrm{SO}_{2}\) in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.

A culture of the fungus aspergillus niger is used industrially in the manufacture of citric acid and other organic species. Cells of the fungus have an ultimate analysis of \(\mathrm{CH}_{1,79} \mathrm{N}_{0.2} \mathrm{O}_{0.5}\), and the heat of formation of this species is necessary to approximate the heat duty for the bioreactor in which citric acid is to be produced. You collect a dried sample of the fungus and determine its heat of combustion to be \(-550 \mathrm{kJ} / \mathrm{mol} .\) Estimate the heat of formation \((\mathrm{kJ} / \mathrm{mol})\) of the dried fungus cells.

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.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.