/*! 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 44 Effluents from metal-finishing p... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 44

Effluents from metal-finishing plants have the potential of discharging undesirable quantities of metals, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal-finishing plant has identified a wastewater stream that contains 5.15 wt\% chromium (Cr) and devised the following approach to lowering risk and recovering the valuable metal. The wastewater stream is fed to a treatment unit that removes \(95 \%\) of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above \(4500 \mathrm{kg} / \mathrm{h}\) ) bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon. (a) Without assuming a basis of calculation, draw and label a flowchart of the process. (b) Wastewater leaves the finishing plant at a rate \(\dot{m}_{1}=6000 \mathrm{kg} / \mathrm{h}\). Calculate the flow rate of liquid to the waste lagoon, \(\dot{m}_{6}(\mathrm{kg} / \mathrm{h}),\) and the mass fraction of \(\mathrm{Cr}\) in this liquid, \(x_{6}(\mathrm{kg} \mathrm{Cr} / \mathrm{kg})\) (c) Calculate the flow rate of liquid to the waste lagoon and the mass fraction of Crin this liquid for \(\dot{m}_{1}\) varying from \(1000 \mathrm{kg} / \mathrm{h}\) to \(10,000 \mathrm{kg} / \mathrm{h}\) in \(1000 \mathrm{kg} / \mathrm{h}\) increments. Generate a plot of \(x_{6}\) versus \(\dot{m}_{1}\). (Suggestion: Use a spreadsheet for these calculations.) (d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination? (e) What concerns might need to be addressed regarding the waste lagoon?

Short Answer

Expert verified
The mass fraction of chromium in the waste lagoon will depend on the feed rate of the wastewater. For a given feed rate, part of the wastewater will bypass the treatment unit and part will be treated, with 95% of the chromium removed. The leftover chromium from the treatment unit and the chromium in the bypass flow will combine to form the output flow to the waste lagoon. To decide whether to add capacity to the treatment unit, one would need to consider the cost of expansion, potential reduction in contamination, value of recovered chromium, regulatory issues, and social and environmental impact. Concerns about the waste lagoon may include environmental and health risks, contamination, cleanup costs, and regulations.

Step by step solution

01

Draw and Label a Flowchart

Sketch a flowchart showing the wastewater from the finishing plant being fed into the treatment unit. The treatment unit removes and recycles a percentage of the chromium, with the remaining liquid sent to the waste lagoon. If the wastewater leaving the plant is above the treatment unit's capacity, the excess bypasses the unit and combines with the residual liquid, and this combined stream also goes to the waste lagoon.
02

Calculate the Flow Rate of Liquid to the Waste Lagoon and the Mass Fraction of Cr in This Liquid for \(\dot{m}_{1}=6000\)

Begin by determining what portion of the input will exceed the treatment unit's capacity. Since the unit can only handle 4500 kg/h, the excess is \(6000 - 4500 = 1500\) kg/h. The amount of chromium in this excess is \(1500 \times 0.0515\). The unit itself will treat \(4500 \times 0.0515 \times 0.05\) kg/h of Cr, with the remaining going to the waste lagoon. Sum these two amounts to get the total amount going to the lagoon. Divide this by the total weight of material going to the lagoon (\(1500 + 4500\)) to get the mass fraction \(x_{6}\).
03

Calculate the Flow Rate of Liquid and Mass Fraction for Different \(\dot{m}_{1}\) Values

Repeat the calculation in Step 2 for \(\dot{m}_{1}\) values ranging from 1000 to 10,000 in 1000 increments. Use a spreadsheet or other computational tool to perform these repeated calculations.
04

Generate a Plot of \(x_{6}\) versus \(\dot{m}_{1}\)

Use the data from Step 3 to generate a plot. The x-axis should represent \(\dot{m}_{1}\) (input rates), and the y-axis should represent \(x_{6}\) (mass fraction). This plot will show how the chromium concentration in the waste lagoon changes with different input rates.
05

Identify Factors for Decision-Making

To determine whether or not to add capacity to the treatment unit, you would need to know the cost of expanding the unit, the reduction in chromium content in the waste lagoon that would be achieved, the value of the recovered chromium, any relevant environmental regulations or fines, and the social and environmental impacts of the waste lagoon.
06

Identify Concerns Regarding the Waste Lagoon

Concerns may include potential contamination of surrounding areas, environmental impacts, costs of eventual cleanup or remediation, health risks to humans and wildlife, and regulatory issues.

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Key Concepts

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

Metal Finishing Wastewater Treatment
Metal finishing processes often use a variety of metallic substances such as cadmium, nickel, lead, manganese, and chromium. These metals are part of the production processes and can end up in wastewater streams. Proper treatment of this wastewater is essential to mitigate environmental impact and comply with regulations.
Metal finishing wastewater treatment generally involves several key steps:
  • Precipitation and Clarification: Metals are precipitated out of the solution, usually in the form of hydroxides.
  • Filtration: Solid particles formed during precipitation are removed.
  • Ion Exchange or Membrane Filtration: Additional removal of dissolved metals using ion exchange resins or membrane processes.
  • Neutralization: Balancing the pH of the treated water before release or reuse.
Each step helps in capturing the metals, preventing them from reaching natural water bodies where they could harm aquatic life and the environment. The treatment efficiency significantly impacts whether metals can be reclaimed or the treatment meets regulatory standards.
Chromium Recovery
Chromium, a valuable metal, is often recovered from wastewater streams in metal finishing plants to prevent environmental harm and reclaim economic value. The recovery process is a critical environmental engineering task that involves several techniques:
  • Reduction and Precipitation: Chromium is typically present as hexavalent chromium (\(Cr^{6+}\)). It is often reduced to trivalent chromium (\(Cr^{3+}\)), which can be more easily precipitated out of solution.
  • Electrochemical Recovery: Utilizing an electric current to attract metal ions to electrodes for recovery.
  • Crystallization: Chromium can be recovered by inducing crystal growth from the treatment solutions.
Recovering chromium reduces waste disposal costs and minimizes risks associated with hazardous waste management. Effective chromium recovery contributes to sustainable industrial practices by enabling recyclability and reducing dependency on raw material extraction.
Wastewater Flow Rate Analysis
Analyzing the flow rates of wastewater is important in sewage treatment to ensure the capacity of treatment units is not exceeded, leading to inefficient operations or environmental fallback. In the metal finishing plant scenario, understanding wastewater flow rate involves:
  • Calculating Flow Rates: Determining the volume of wastewater and the amount that exceeds treatment capacity. For example, with an inflow of \(6000 \ \text{kg/h}\) and a capacity of \(4500 \ \text{kg/h}\), \(1500 \ \text{kg/h}\) bypasses treatment.
  • Mass Balance Calculations: Performing calculations to determine the amount of chromium not captured by the treatment unit, which could enter waste streams, impacting environmental quality.
  • Modeling Variability: Varying the input rates and studying their effect on the treatment process efficiency through computational models or spreadsheets.
Detailed flow rate analysis ensures optimal operation of treatment units and minimizes untreated discharge, maintaining environmental compliance and operational efficiency.

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Most popular questions from this chapter

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 \(y_{\mathrm{NO}_{2}}\left(\operatorname{mol} \mathrm{NO}_{2} / \mathrm{mol}\right)\)

Liquid methanol is fed to a space heater at a rate of \(12.0 \mathrm{L} / \mathrm{h}\) and burned with excess air. The product gas is analyzed and the following dry-basis mole percentages are determined: \(\mathrm{CH}_{3} \mathrm{OH}=0.45 \%\) \(\mathrm{CO}_{2}=9.03 \%,\) and \(\mathrm{CO}=1.81 \%\) (a) Draw and label a flowchart and verify that the system has zero degrees of freedom. (b) Calculate the fractional conversion of methanol, the percentage excess air fed, and the mole fraction of water in the product gas. (c) Suppose the combustion products are released directly into a room. What potential problems do you see and what remedies can you suggest?

Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The fresh feed to the process contains 32.0 mole \(\%\) CO, \(64.0 \%\) H \(_{2}\), and \(4.0 \%\) Ne. This stream is mixed with a recycle stream in a ratio 5 mol recycle/ 1 mol fresh feed to produce the feed to the reactor, which contains 13.0 mole\% \(\mathrm{N}_{2}\). A low single-pass conversion is attained in the reactor. The reactor effluent goes to a condenser from which two streams emerge: a liquid product stream containing essentially all the methanol formed in the reactor, and a gas stream containing all the \(\mathrm{CO}, \mathrm{H}_{2}\), and \(\mathrm{N}_{2}\) leaving the reactor. The gas stream is split into two fractions: one is removed from the process as a purge stream, and the other is the recycle stream that combines with the fresh feed to the reactor. (a) Assume a methanol production rate of \(100 \mathrm{kmol} / \mathrm{h}\). Perform the DOF for the overall system and all subsystems to prove that there is insufficient information to solve for all unknowns. (b) Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design.

A stream consisting of 44.6 mole \(\%\) benzene and \(55.4 \%\) toluene is fed at a constant rate to a process unit that produces two product streams, one a vapor and the other a liquid. The vapor flow rate is initially zero and asymptotically approaches half of the molar flow rate of the feed stream. Throughout this entire period, no material accumulates in the unit. When the vapor flow rate has become constant, the liquid is analyzed and found to be 28.0 mole\% benzene. (a) Sketch a plot of liquid and vapor flow rates versus time from startup to when the flow rates become constant. (b) Is this process batch or continuous? Is it transient or steady-state before the vapor flow rate reaches its asymptotic limit? What about after it becomes constant? (c) For a feed rate of 100 mol/min, draw and fully label a flowchart for the process after the vapor flow rate has reached its limiting value, and then use balances to calculate the molar flow rate of the liquid and the composition of the vapor in mole fractions.

A liquid mixture contains \(60.0 \mathrm{wt} \%\) ethanol \((\mathrm{E}), 5.0 \mathrm{wt} \%\) of a dissolved solute \((\mathrm{S}),\) and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream to contain 90.0 wt\% ethanol and no S. (a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don't do any calculations yet.) (b) Calculate (i) the mass fraction of \(S\) in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., \(\mathrm{kg} \mathrm{E}\) in bottom stream/kg \(\mathrm{E}\) in feed) if the process operates as designed. (c) An analyzer is available to determine the composition of ethanol-water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, \(x\) (kg E/kg mixture), versus analyzer reading, \(R\). The line passes through the points \((R=15, x=\) 0.100) and \((R=38, x=0.400)\). Derive an expression for \(x\) as a function of \(R(x=\cdots\) ) based on the calibration, and use it to determine the value of \(R\) that should be obtained if the top product stream from the distillation column is analyzed. (d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in Part (c). Assume that the calculation in Part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between \(R_{\text {measured and }} R_{\text {prediced }}\), including several assumptions made when writing the balances of Part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.
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