91Ó°ÊÓ

Seawater containing 3.50 wt\% salt passes through a series of 10 evaporators. Roughly equal quantities of water are vaporized in each of the 10 units and then condensed and combined to obtain a product stream of fresh water. The brine leaving each evaporator but the tenth is fed to the next evaporator. The brine leaving the tenth evaporator contains \(5.00 \mathrm{wt} \%\) salt. (a) Draw a flowchart of the process showing the first, fourth, and tenth evaporators. Label all the streams entering and leaving these three evaporators. (b) Write in order the set of equations you would solve to determine the fractional yield of fresh water from the process \(\left(\mathrm{kg} \mathrm{H}_{2} \mathrm{O} \text { recovered } / \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\) in process feed) and the weight percent of salt in the \right. solution leaving the fourth evaporator. Each equation you write should contain no more than one previously undetermined variable. In each equation, circle the variable for which you would solve. Do not do the calculations. (c) Solve the equations derived in Part (b) for the two specified quantities. (d) The problem statement made no mention of the disposition of the 5 wt\% effluent from the tenth evaporator. Suggest two possibilities for its disposition and describe any environmental concerns that might need to be considered.

Step by step solution

01

Drawing a Flowchart

To draw the flow chart, each evaporator can be represented as a square box. Salt water is entering the first evaporator and water vapor is being removed from each unit, which can be represented by arrows. The concentrated brine is transferred to the next evaporator. This is done repetitively from the first to fourth and then to tenth evaporator, where the effluent containing 5% of salt is finally released. The condensed water vapor from all the units is combined and considered as the product stream.

02

Setting Up Equations

To find the fractional yield of fresh water, we will consider the total water entering the process, denoted by \(W_{total}\), and the total water vapor removed, denoted by \(W_{removed}\). We can then calculate the fraction of water recovered, \(frac_{water}\), as \(frac_{water} = W_{removed}/W_{total}\). For the weight percent of salt in the solution leaving the fourth evaporator, denote the initial and final weight percentages as \(P_{initial}\) and \(P_{final}\), respectively. Using the concentration change principle, we can set up the equation \(P_{final} = P_{initial} \cdot W_{total} / (W_{total} - W_{removed})\). In both equations, the circled variable to solve for is the one on the left side.

03

Solving The Equations

To solve the equations, remember that for every evaporator, the mass of water removed is roughly equal. The equations set up in the previous step should be used to derive the fractional yield of fresh water and the weight percent of salt.

04

Disposition of The Effluent

Two possible dispositions of the effluent from the tenth evaporator could be: (1) Discharging it directly to the sea, which may affect marine life due to salinity changes; (2) using it to extract valuable salts and minerals. The latter option would involve significant energy and equipment costs.

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Key Concepts

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

Process Flowchart Creation

Creating a process flowchart is an essential step in understanding and communicating the stages involved in seawater treatment for fresh water extraction.Making the process visual through a flowchart aids in grasping the complexities of the treatment process, readily identifying where each part of the system links to the next, and sequentially showcasing the progression from one stage to another.

A flowchart for seawater treatment could begin with an intake where sea water enters the treatment facility. It would then progress through representation of the series of evaporators, where each evaporator is a node in the flowchart, interconnected by lines depicting the flow of water and brine. For each of these evaporators—first, fourth, and tenth—specific streams entering and leaving are illustrated. These would include streams for the incoming seawater, vaporized water, and the increasingly concentrated brine moving from one evaporator to the next. It's essential that all relevant streams are clearly labelled to establish a clear understanding for anyone analyzing the flow of materials through the evaporators.

Fractional Yield of Fresh Water

The fractional yield of fresh water is a critical parameter in any desalination process as it measures the efficiency of the water recovery. It is defined as the ratio of the mass of fresh water recovered to the mass of the original seawater fed into the process.

To calculate the fractional yield, \( frac_{water} \), equations are set up considering the total mass of water entering the process, \( W_{total} \), and the mass of water vapor removed and subsequently condensed, \( W_{removed} \). The key to these calculations is to ensure that the equations contain only one undetermined variable at a time, thereby simplifying the problem solving for variables step by step. For instance, if we know the total water input and the water lost to evaporation, we can use the provided values to solve for the fractional yield. If the process operates efficiently, we should observe a high fractional yield, indicating that a significant portion of the input water has been converted into fresh water.

Environmental Impact of Brine Effluent

The disposal of brine effluent is one of the main environmental concerns associated with seawater treatment processes. Brine, being a highly concentrated salt solution, can have detrimental effects on marine ecosystems if not managed properly. For instance, discharging brine back into the ocean can increase local salinity levels, which can harm marine flora and fauna.

When discussing the environmental impact of brine effluent, two primary disposal methods are often considered: direct discharge into the sea, which is cost-effective but potentially harmful to aquatic life, and further treatment to extract valuable minerals, which can mitigate environmental risks but with higher capital and operating costs. It's important for students to understand that the chosen method of brine disposal should carefully consider the surrounding environment, regulatory requirements, and potential recovery of resources to reduce negative environmental impacts. These solutions underscore the need for sustainable practices in water treatment to protect our oceans and marine biodiversity.