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Chapter 4: Problem 60

Under the FutureGen 2.0 project (http:///www.futuregenalliance.org/) sponsored by the U.S. Department of Energy, a novel process is used to convert coal into electricity with minimal greenhouse gas \(\left(\mathrm{CO}_{2}\right)\) emissions to the atmosphere. In the process, coal is combusted in a boiler with pure \(\mathrm{O}_{2}\); the heat released produces steam, which is then used for heating and to drive turbines that generate electricity. An excess of \(\mathrm{O}_{2}\) is supplied to the boiler to convert all the coal into a flue gas consisting of carbon dioxide, steam, and any unreacted oxygen. The mass flow rate of coal to the boiler is \(50 \mathrm{kg} / \mathrm{s}\), and \(\mathrm{O}_{2}\) is fed in \(8.33 \%\) excess. For the purposes of this analysis, the chemical formula of coal can be approximated as \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\) (a) Draw and label the flowchart and carry out the degree-of-freedom analysis using balances on atomic species. (b) Determine the molar flow of oxygen supplied to the boiler. (c) Solve for the remaining unknown flow rates and mole fractions. Determine the molar composition of the flue gas on a dry basis. (d) A feature that makes the FutureGen power plant unique is the intent to capture the \(\mathrm{CO}_{2}\) generated, compress it, and pump it into deep geological formations in which it will be permanently stored. List at least two safety or environmental issues that should be considered in the construction and operation of this plant. (e) List at least two pros and two cons of using pure \(O_{2}\) versus air.

Short Answer

Expert verified
The molar flow rate of oxygen supplied to the boiler is approximately 2095 mol/s. The molar flow rates for \(CO_{2}\) and \(H_{2}O\) are 1397 mol/s and 1118 mol/s. The molar composition of the dry flue gas (in mol%) is \(CO_{2}: 30.3\%, \(O_{2}\): 49.7\%, \(N_{2}\): 20\%. A major part of the FutureGen challenge is capturing the CO2, which raises potential issues of containment and safety. Using pure oxygen instead of air has advantages such as focus on combusting only the desired compound, however this brings challenges such as increased costs and safety measures.

Step by step solution

01

Stoichiometry

The combustion of the coal is represented by the reaction \(C_{5}H_{8}O_{2} + a \, O_{2}\) \(\rightarrow b \, CO_{2} + c H_{2}O + d \, O_{2}\). Through stoichiometry \(a=O_{2}=7.5, b=CO_{2}=5, c=H_{2}O=4, d=unreacted\, O_{2}=a-5-0.5(8)=0\).
02

Molar Flow, Oxygen Supply

The molar flow of oxygen supplied to the boiler can be calculated from the mass flow rate of the coal and the stoichiometry. As \(1 \, mol \, of \, C_{5}H_{8}O_{2} (194 g/mol) requires 7.5 \, mol \, of \, O_{2}\), one finds the stoichiometric flow rate: \([O_{2}]_{Stoich}=(50 \, kg/s)*(1 \, mol/0.194 \, kg) * 7.5 \, mol/mol = 1934 \, mol/s\). Due to the 8.33% excess of \(O_{2}\), the actual flow rate is \(F_{O_{2}}=[O_{2}]_{Stoich}*(1+0.0833)=2095\, mol/s\).
03

Unknown Flow Rates and Mole Fractions

Since the coal is converted completely, and the excess of \(O_{2}\) is known, the flow rates of \(CO_{2}\) and H2O are \(5/7.5*F_{CO_{2}}=1397鈭梞ol/s\) and \(4/7.5*F_{CO_{2}}=1118鈭梞ol/s\) .
04

Molar Composition of Flue Gas

The molar flow rates calculated in Step 3 can be summed up to calculate the total molar flow rate of the flue gas: \(F_{total} = F_{CO_{2}}+ F_{H_{2}O}+ F_{O_{2}})=1397+1118+2095=4610\,mol/s\). For dry basis, only CO2 and O2 are included, with fraction_X = F_X/F_total.
05

FutureGen power plant unique attributes

Safety and environmental considerations must include: possible leakage of captured CO2, careful monitoring of the reservoir, security measures during transportation, impact of extraction etc.
06

Pros and cons of using oxygen versus air.

PROS: Higher combustion temperatures, flame stability, reduced flue gas volume, emissions control. CONS: Cost and energy demand of oxygen production, safely handling pure oxygen.

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Key Concepts

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

Stoichiometry in Chemical Process Engineering
Understanding stoichiometry is crucial for chemical engineers as it lays the foundation for balancing chemical equations and predicting the outcome of reactions. In a process like FutureGen 2.0, stoichiometry helps in determining the exact amount of reactants, like oxygen (O2), needed to combust coal completely.

The chemical reaction provided in the exercise illustrates the combustion of coal (C5H8O2) with pure oxygen. By balancing this chemical equation, engineers can derive the molar ratios between reactants and products. For instance, the stoichiometry used to determine the reactant oxygen is based on the coal's mass flow rate and its molecular weight. The exercise also includes an 8.33% excess of oxygen to ensure complete combustion, indicating practical operations often include safety margins.

To truly grasp this concept, one must practice balancing chemical equations, understand molar relations, and be able to translate mass flow rates into molar flow rates. Being well-versed in stoichiometry not only aids in the design of chemical processes but also in optimizing efficiency and minimizing waste.
Molar Flow Rates in Combustion Processes
The molar flow rate is a measure of the number of moles of a substance that pass through a given surface per unit time. It's a pivotal quantity in chemical engineering, vital for the design of reactors, and pipes, and for conducting environmental impact assessments.

In the context of the FutureGen 2.0 project, calculating molar flow rates allows engineers to design equipment to handle the appropriate volume of gases. From the mass flow rate of coal and its composition, you can determine the molar flow rate of oxygen needed for combustion. It's also important for determining the molar composition of the flue gas, as seen in this exercise, which is essential for pollutant control strategies. Knowing these flow rates helps in scaling up the process from a laboratory to an industrial scale, thus ensuring that the environmental performance targets, such as minimal greenhouse gas emissions, are met.

Practical tips for students include always checking units for consistency and envisioning the flow of substances through the system to better understand where molar flow rates fit into the bigger picture of process design.
Environmental Impact of Energy Production
Energy production processes, as seen in the FutureGen 2.0 project, can have significant environmental impacts. The capture and sequestration of CO2 aim to mitigate some of these effects by preventing this potent greenhouse gas from reaching the atmosphere and contributing to global warming.

Engineers and environmental scientists look at safety and environmental concerns such as the potential leakage of captured CO2, the integrity of geological formations used for storage, and the lifecycle emissions of the process itself. Moreover, the use of pure oxygen in coal combustion has implications such as higher energy demands for oxygen production and the need for specialized equipment that can safely handle the high temperatures and reactivity of pure oxygen environments.

Students should consider not only the immediate outputs of energy production but also the long-term sustainability and environmental footprint. Always weigh the pros and cons of each process modification or technological innovation, such as using pure oxygen instead of air for combustion, to deeply understand its potential environmental impacts.

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Most popular questions from this chapter

The popularity of orange juice, especially as a breakfast drink, makes this beverage an important factor in the economy of orange-growing regions. Most marketed juice is concentrated and frozen and then reconstituted before consumption, and some is "not-from-concentrate." Although concentrated juices are less popular in the United States than they were at one time, they still have a major segment of the market for orange juice. The approaches to concentrating orange juice include evaporation, freeze concentration, and reverse osmosis. Here we examine the evaporation process by focusing only on two constituents in the juice: solids and water. Fresh orange juice contains approximately 10 wt\% solids (sugar, citric acid, and other ingredients) and frozen concentrate contains approximately 42 wt\% solids. The frozen concentrate is obtained by evaporating water from the fresh juice to produce a mixture that is approximately 65 wt\% solids. However, so that the flavor of the concentrate will closely approximate that of fresh juice, the concentrate from the evaporator is blended with fresh orange juice (and other additives) to produce a final concentrate that is approximately 42 wt\% solids. (a) Draw and label a flowchart of this process, neglecting the vaporization of everything in the juice but water. First prove that the subsystem containing the point where the bypass stream splits off from the evaporator feed has one degree of freedom. (If you think it has zero degrees, try determining the unknown variables associated with this system.) Then perform the degree- offreedom analysis for the overall system, the evaporator, and the bypass- evaporator product mixing point, and write in order the equations you would solve to determine all unknown stream variables. In each equation, circle the variable for which you would solve, but don't do any calculations. (b) Calculate the amount of product (42\% concentrate) produced per 100 kg fresh juice fed to the process and the fraction of the feed that bypasses the evaporator. (c) Most of the volatile ingredients that provide the taste of the concentrate are contained in the fresh juice that bypasses the evaporator. You could get more of these ingredients in the final product by evaporating to (say) 90\% solids instead of 65\%; you could then bypass a greater fraction of the fresh juice and thereby obtain an even better tasting product. Suggest possible drawbacks to this proposal.

Draw and label the given streams and derive expressions for the indicated quantities in terms of labeled variables. The solution of Part (a) is given as an illustration. (a) A continuous stream contains 40.0 mole\% benzene and the balance toluene. Write expressions for the molar and mass flow rates of benzene, \(\dot{n}_{\mathrm{B}}\left(\operatorname{mol} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right)\) and \(\dot{m}_{\mathrm{B}}\left(\mathrm{kg} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right),\) in terms of the total molar flow rate of the stream, \(\dot{n}(\mathrm{mol} / \mathrm{s})\) (b) The feed to a batch process contains equimolar quantities of nitrogen and methane. Write an expression for the kilograms of nitrogen in terms of the total moles \(n(\) mol) of this mixture. (c) A stream containing ethane, propane, and butane has a mass flow rate of \(100.0 \mathrm{g} / \mathrm{s}\). Write an expression for the molar flow rate of ethane, \(\dot{n}_{\mathrm{E}}\left(\text { Ib-mole } \mathrm{C}_{2} \mathrm{H}_{6} / \mathrm{h}\right)\), in terms of the mass fraction of this species, \(x_{\mathrm{E}}\). (d) A continuous stream of humid air contains water vapor and dry air, the latter containing approximately 21 mole \(\% \mathrm{O}_{2}\) and \(79 \% \mathrm{N}_{2}\). Write expressions for the molar flow rate of \(\mathrm{O}_{2}\) and for the mole fractions of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{O}_{2}\) in the gas in terms of \(\dot{n}_{1}\left(\mathrm{lb}-\mathrm{mole} \mathrm{H}_{2} \mathrm{O} / \mathrm{s}\right)\) and \(\dot{n}_{2}(\text { lb- mole dry air/s })\) (e) The product from a batch reactor contains \(\mathrm{NO}, \mathrm{NO}_{2},\) and \(\mathrm{N}_{2} \mathrm{O}_{4} .\) The mole fraction of \(\mathrm{NO}\) is 0.400. Write an expression for the gram-moles of \(\mathrm{N}_{2} \mathrm{O}_{4}\) in terms of \(n(\mathrm{mol}\) mixture) and \(y_{\mathrm{NO}_{2}}\left(\operatorname{mol} \mathrm{NO}_{2} / \mathrm{mol}\right)\)

Inside a distillation column (see Problem 4.8), a downward-flowing liquid and an upward-flowing vapor maintain contact with each other. For reasons we will discuss in greater detail in Chapter \(6,\) the vapor stream becomes increasingly rich in the more volatile components of the mixture as it moves up the column, and the liquid stream is enriched in the less volatile components as it moves down. The vapor leaving the top of the column goes to a condenser. A portion of the condensate is taken off as a product (the overhead product), and the remainder (the reflux) is returned to the top of the column to begin its downward journey as the liquid stream. The condensation process can be represented as shown below: A distillation column is being used to separate a liquid mixture of ethanol (more volatile) and water (less volatile). A vapor mixture containing 89.0 mole \(\%\) ethanol and the balance water enters the overhead condenser at a rate of \(100 \mathrm{lb}\) -mole/h. The liquid condensate has a density of \(49.01 \mathrm{b}_{\mathrm{m}} / \mathrm{ft}^{3},\) and the reflux ratio is \(3 \mathrm{lb}_{\mathrm{m}}\) reflux/lb \(_{\mathrm{m}}\) overhead product. When the system is operating at steady state, the tank collecting the condensate is half full of liquid and the mean residence time in the tank (volume of liquid/volumetric flow rate of liquid) is 10.0 minutes. Determine the overhead product volumetric flow rate (ft \(^{3}\) /min) and the condenser tank volume (gal).

Mammalian cells can be cultured for a variety of purposes, including synthesis of vaccines. They must be maintained in growth media containing all of the components required for proper cellular function to ensure their survival and propagation. Traditionally, growth media were prepared by blending a powder, such as Dulbecco's Modified Eagle Medium (DMEM) with sterile deionized water. DMEM contains glucose, buffering agents, proteins, and amino acids. Using a sterile (i.e., bacterial-, fungal-,and yeast-free) growth medium ensures proper cell growth, but sometimes the water (or powder) can become contaminated, requiring the addition of antibiotics to eliminate undesired contaminants. The culture medium is supplemented with fetal bovine serum (FBS) that contains additional growth factors required by the cells. Suppose an aqueous stream (SG = 0.90) contaminated with bacteria is split, with 75\% being fed to a mixing unit to dissolve a powdered mixture of DMEM contaminated with the same bacteria found in the water. The ratio of impure feed water to powder entering the mixer is 4.4:1. The stream leaving the mixer (containing DMEM, water, and bacteria) is combined with the remaining 25\% of the aqueous stream and fed to a filtration unit to remove all of the bacteria that have contaminated the system, a total of \(20.0 \mathrm{kg}\). Once the bacteria have been removed, the sterile medium is combined with FBS and the antibiotic cocktail PSG (Penicillin-Streptomycin-L-Glutamine) in a shaking unit to generate 5000 L of growth medium (SG = 1.2). The final composition of the growth medium is 66.0 wt\% H_O, 11.0\% FBS, 8.0\% PSG, and the balance DMEM. (a) Draw and label the process flowchart. (b) Do a degree-of-freedom analysis around each piece of equipment (mixer, filter, and shaker), the splitter, the mixing point, and the overall system. Based on the analysis, identify which system or piece of equipment should be the starting point for further calculations. (c) Calculate all of the unknown process variables. (d) Determine a value for (i) the mass ratio of sterile growth medium product to feed water and (ii) the mass ratio of bacteria in the water to bacteria in the powder. (e) Suggest two reasons why the bacteria should be removed from the system.

A stream containing \(\mathrm{H}_{2} \mathrm{S}\) and inert gases and a second stream of pure \(\mathrm{SO}_{2}\) are fed to a sulfur recovery reactor, where the reaction $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 3 \mathrm{S}+2 \mathrm{H}_{2} \mathrm{O}$$ takes place. The feed rates are adjusted so that the ratio of \(\mathrm{H}_{2} \mathrm{S}\) to \(\mathrm{SO}_{2}\) in the combined feed is always stoichiometric. In the normal operation of the reactor the flow rate and composition of the \(\mathrm{H}_{2} \mathrm{S}\) feed stream both fluctuate. In the past, each time either variable changed the required \(\mathrm{SO}_{2}\) feed rate had to be reset by adjusting a valve in the feed line. A control system has been installed to automate this process. The \(\mathrm{H}_{2} \mathrm{S}\) feed stream passes through an electronic flowmeter that transmits a signal \(R_{\mathrm{f}}\) directly proportional to the molar flow rate of the stream, \(\dot{n}_{\mathrm{f}}\). When \(\dot{n}_{\mathrm{f}}=100 \mathrm{kmol} / \mathrm{h}\), the transmitted signal \(R_{\mathrm{f}}=15 \mathrm{mV}\). The mole fraction of \(\mathrm{H}_{2} \mathrm{S}\) in this stream is measured with a thermal conductivity detector, which transmits a signal \(R_{\mathrm{a}} .\) Analyzer calibration data are as follows: $$\begin{array}{|l|c|c|c|c|c|c|}\hline R_{\mathrm{a}}(\mathrm{mV}) & 0 & 25.4 & 42.8 & 58.0 & 71.9 & 85.1 \\ \hline x\left(\mathrm{mol} \mathrm{H}_{2} \mathrm{S} / \mathrm{mol}\right) & 0.00 & 0.20 & 0.40 & 0.60 &0.80 & 1.00 \\\\\hline\end{array}$$ The controller takes as input the transmitted values of \(R_{\mathrm{f}}\) and \(R_{\mathrm{a}}\) and calculates and transmits a voltage signal \(R_{\mathrm{c}}\) to a flow control valve in the \(\mathrm{SO}_{2}\) line, which opens and closes to an extent dependent on the value of \(R_{c} .\) A plot of the \(S O_{2}\) flow rate, \(\dot{n}_{c},\) versus \(R_{c}\) on rectangular coordinates is a straight line through the points \(\left(R_{c}=10.0 \mathrm{mV}, \dot{n}_{c}=25.0 \mathrm{kmol} / \mathrm{h}\right)\) and \(\left(R_{c}=25.0 \mathrm{mV}, \dot{n}_{c}=60.0 \mathrm{kmol} / \mathrm{h}\right)\) (a) Why would it be important to feed the reactants in stoichiometric proportion? (Hint: \(\mathrm{SO}_{2}\) and especially \(\mathrm{H}_{2} \mathrm{S}\) are serious pollutants.) What are several likely reasons for wanting to automate the \(\mathrm{SO}_{2}\) feed rate adjustment? (b) If the first stream contains 85.0 mole \(\% \mathrm{H}_{2} \mathrm{S}\) and enters the unit at a rate of \(\dot{n}_{\mathrm{f}}=3.00 \times 10^{2} \mathrm{kmol} / \mathrm{h}\) what must the value of \(\dot{n}_{c}\left(\mathrm{kmol} \mathrm{SO}_{2} / \mathrm{h}\right)\) be? (c) Fit a function to the \(\mathrm{H}_{2} \mathrm{S}\) analyzer calibration data to derive an expression for \(x\) as a function of \(R_{\mathrm{a}}\) Check the fit by plotting both the function and the calibration data on the same graph. (d) Derive a formula for \(R_{\mathrm{c}}\) from specified values of \(R_{\mathrm{f}}\) and \(R_{\mathrm{a}},\) using the result of Part (c) in the derivation. (This formula would be built into the controller.) Test the formula using the flow rate and composition data of Part (a). (e) The system has been installed and made operational, and at some point the concentration of \(\mathrm{H}_{2} \mathrm{S}\) in the feed stream suddenly changes. A sample of the blended gas is collected and analyzed a short time later and the mole ratio of \(\mathrm{H}_{2} \mathrm{S}\) to \(\mathrm{SO}_{2}\) is not the required 2: 1 . List as many possible reasons as you can think of for this apparent failure of the control system.
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