/*! 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

Methanol is formed from carbon monoxide and hydrogen in the gas-phase reaction The mole fractions of the reactive species at equilibrium satisfy the relation where \(P\) is the total pressure (atm), \(K_{c}\) the reaction equilibrium constant (atm \(^{-2}\) ), and \(T\) the temperature (K). The equilibrium constant \(K_{c}\) equals 10.5 at 373 K, and \(2.316 \times 10^{-4}\) at \(573 \mathrm{K}\). A semilog plot of \(K_{\mathrm{c}}\) (logarithmic scale) versus 1/ \(T\) (rectangular scale) is approximately linear between \(T=300 \mathrm{K}\) and \(T=600 \mathrm{K}\) (a) Derive a formula for \(K_{\mathrm{c}}(T),\) and use it to show that \(K_{\mathrm{e}}(450 \mathrm{K})=0.0548 \mathrm{atm}^{-2}\) (b) Write expressions for \(n_{A}, n_{B},\) and \(n_{C}\) (gram-moles of each species), and then \(y_{A}, y_{B},\) and \(y_{C},\) in terms of \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0},\) and \(\xi,\) the extent of reaction. Then derive an equation involving only \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, P, T,\) and \(\xi_{e},\) where \(\xi_{e}\) is the extent of reaction at equilibrium. (c) Suppose you begin with equimolar quantities of CO and \(\mathrm{H}_{2}\) and no \(\mathrm{CH}_{3} \mathrm{OH}\), and the reaction proceeds to equilibrium at 423 K and 2.00 atm. Calculate the molar composition of the product ( \(y_{\mathrm{A}}\), \(\left.y_{\mathrm{B}}, \text { and } y_{\mathrm{C}}\right)\) and the fractional conversion of \(\mathrm{CO}\) (d) The conversion of CO and \(\mathrm{H}_{2}\) can be enhanced by removing methanol from the reactor while leaving unreacted CO and \(\mathrm{H}_{2}\) in the vessel. Review the equations you derived in solving Part (c) and determine any physical constraints on \(\xi_{c}\) associated with \(n_{\mathrm{A} 0}=n_{\mathrm{B} 0}=1\) mol. Now suppose that 90\% of the methanol is removed from the reactor as it is produced; in other words, only 10\% of the methanol formed remains in the reactor. Estimate the fractional conversion of CO and the total gram moles of methanol produced in the modified operation. (e) Repeat Part (d), but now assume that \(n_{\mathrm{B} 0}=2\) mol. Explain the significant increase in fractional conversion of CO. (f) Write a set of equations for \(y_{\mathrm{A}}, y_{\mathrm{B}}, y_{\mathrm{C}},\) and \(f_{\mathrm{A}}\) (the fractional conversion of \(\mathrm{CO}\) ) in terms of \(y_{\mathrm{A} 0}, y_{\mathrm{B} 0}, T,\) and \(P(\) the reactor temperature and pressure at equilibrium). Enter the equations in an equation-solving program. Check the program by running it for the conditions of Part (c), then use it to determine the effects on \(f_{\mathrm{A}}\) (increase, decrease, or no effect) of separately increasing, (i) the fraction of \(\mathrm{CH}_{3} \mathrm{OH}\) in the feed, (ii) temperature, and (iii) pressure.

The reaction between ethylene and hydrogen bromide to form ethyl bromide is carried out in a continuous reactor. The product stream is analyzed and found to contain 51.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\) and 17.3\% HBr. The feed to the reactor contains only ethylene and hydrogen bromide. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is \(165 \mathrm{mol} / \mathrm{s}\), what is the extent of reaction?

A garment to protect the wearer from toxic agents may be made of a fabric that contains an adsorbent, such as activated carbon. In a test of such a fabric, a gas stream containing \(7.76 \mathrm{mg} / \mathrm{L}\) of carbon tetrachloride (CCl_) was passed through a 7.71-g sample of the fabric at a rate of 1.0 L/min, and the concentration of \(\mathrm{CCl}_{4}\) in the gas leaving the fabric was monitored. The run was continued for \(15.5 \mathrm{min}\) with no \(\mathrm{CCl}_{4}\) being detected, after which the \(\mathrm{CCl}_{4}\) concentration began to rise. (a) How much CCl_ was fed to the system during the first 15.5 min of the run? How much was adsorbed? Using this information as a guide, sketch the expected concentration of \(\mathrm{CCl}_{4}\) in the exit gas as a function of time, showing the curve from \(t=0\) to \(t \gg 15.5\) min. (b) Assuming a linear relationship between amount of \(\mathrm{CCl}_{4}\) adsorbed and mass of fabric, what fabric mass would be required if the feed concentration is \(5 \mathrm{mg} / \mathrm{L},\) the feed rate \(1.4 \mathrm{L} / \mathrm{min},\) and it is desired that no \(\mathrm{CCl}_{4}\) leave the fabric earlier than 30 min?

A Claus plant converts gaseous sulfur compounds to elemental sulfur, thereby eliminating emission of sulfur into the atmosphere. The process can be especially important in the gasification of coal, which contains significant amounts of sulfur that is converted to \(\mathrm{H}_{2}\) S during gasification. In the Claus process, the \(\mathrm{H}_{2}\) S-rich product gas recovered from an acid-gas removal system following the gasifier is split, with one-third going to a furnace where the hydrogen sulfide is burned at 1 atm with a stoichiometric amount of air to form SO \(_{2}\). $$\mathrm{H}_{2} \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ The hot gases leave the furnace and are cooled prior to being mixed with the remainder of the \(\mathrm{H}_{2}\) S-rich gases. The mixed gas is then fed to a catalytic reactor where hydrogen sulfide and \(\mathrm{SO}_{2}\) react to form elemental sulfur. $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+3 \mathrm{S}$$ The coal available to the gasification process is 0.6 wt\% sulfur, and you may assume that all of the sulfur is converted to \(\mathrm{H}_{2} \mathrm{S}\), which is then fed to the Claus plant. (a) Estimate the feed rate of air to the Claus plant in \(\mathrm{kg} / \mathrm{kg}\) coal. (b) While the removal of sulfur emissions to the atmosphere is environmentally beneficial, identify an environmental concern that still must be addressed with the products from the Claus plant.

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.
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