I highly recommend the following textbook for the flashing topic:

Don W. Green; Robert H. Perry (2008). Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill publisher.

Please chapter 4 on Thermodynamics.

I use this textbook in teaching my course on chemical engineering processes at Yale University.

Hope this helps answer your question and good luck.

Well, to get the humorous answer out of the way . . . Just go to the park and look for an unkempt guy in a trench coat with bare ankles.

But seriously, a good, recent treatment is:

Title: Working Guide to Vapor-Liquid Phase Equilibria Calculations

Author(s): Tarek Ahmed (Auth.)

Publisher: Gulf Professional Publishing, Year: 2010

ISBN: 978-1-85617-826-6

By Chapter 2, you'll have the math necessary to set up the appropriate calculations, either for a stable but slow-converging single-variable approach or a faster but sometimes less stable multi-variable approach. From there, the author delves into increasing detail on the calculational aspects.

For a deeper dive into the fundamentals behind the equations you'll be using, one can do no better than:

Title: Molecular Thermodynamics of Fluid-Phase Equilibria

Author(s): Prausnitz J.M., Lichtenthaler R.N., de Azevedo E.G.

Publisher: PH PTR

Year: 1999

Edition: 3ed

Language: English

Pages: 886\886

ISBN: 0139777458, 9780139777455

Thanks all

I only want to understand about non equilibrium allowance (NEA) in flashing process and read an example....

That is a very specific question, and I would suggest a literature search. You have asked a previous question on this topic and been provided with a good reference. There are several more accessible here or via any literature search engine. I suggest that you read some of the articles and then, if necessary, ask a more nuanced question that shows you have taken the time to do so. Without more information than you have provided, I don't know which reference is "perfect" for you, and I suspect no one else does, either.

Paul Bryan

Thanks a lot...I think i have been searching it more than a week....!

There are so many conflicts in literature.....So i confused...

One sample:

first check 1st file........Is it true?

If it is true so why outlet temperature in 2nd file is different as we have calculated it in the first file?

Dear Paul Bryan

Please see page 3 of the attached file....

The NEA applies to the BRINE stream for effects 2, 3, 4, ... N, and the authors show that when they develop the governing equations on page 13 (page 5 of the file you sent), particularly in Equation 25. NEA is very simply the difference between the brine temperature that would be in equilibrium with the vapor leaving the stage and the actual temperature of the brine. The difference exists because real equipment does not allow sufficient contact time for equilibrium to be reached. Where it gets difficult is in estimating NEA, because it will vary with the design of the equipment and several operating parameters. In this case, Equation 24 is a simple correlation based on the values of three other temperatures in / around a given stage.

On Fig. 2, where you have your question, you are pointing to the COOLING WATER temperature, which is not subject to NEA. And in any case, the labels on Fig. 2 are simply variable names. Any relationships among these variables are laid out in the development of the model in the succeeding pages.

I do find the notation of Fig. 2 confusing, and I wouldn't swear there wasn't a typo somewhere, but in these systems, I have always / only seen NEA applied to the temperature of the BRINE.

Thanks

That is not COOLING WATER. That's the outlet of flash box. the authors of the paper have assumed it Tc

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Consider the stream(brine not distillate) leaving the evaporator "i"(Ti=Tvi+BPE)

Is the following conclusion true?

If we want to calculate Ti accurately we must consider the thermal equilibrium between two streams:

1.one stream from top of the stage with the temperature equal to Tvi+BPE

2. another stram from the previous stage with the temperature equal to Tvi+BPE+NEA

We must write the energy balance between them and calculate Ti

When the temperature increased by NEA, Is it stable or just after flashing(evaporation), NEA disappears?

When the brine flashes, the liquid always leaves that effect at a temperature higher than that of the vapor. At true equilibrium, liquid and vapor would have to have the same temperature, but in a real evaporator, flows are always too fast to allow time for 100% attainment of equilibrium. NEA does not "disappear" -- it is a correction used to estimate the ACTUAL temperature of the brine leaving the effect. If the vapor temperature leaving the effect is 100 C and NEA is 2 C, then the actual liquid temperature is 102 C. The calculated NEA is just an estimate, of course, the actual NEA can only be measured when the evaporator is operating. But for design purposes, the NEA estimates allow for more accurate design calculations than if true thermal equilibrium was assumed.

The confusion may be the designation of "flash box." The flash box is just a way to recoup a very small amount of vapor from cooling water that is warm and at a higher pressure than the next effect. Flashing this stream to the pressure of the next effect generates a small vapor stream whose latent heat can be used on the tube side of the next effect to slightly increase evaporation there (in thermal desalination, every accessible increment of energy must be used, and every small hurdle [BPE, DEA, Approach Temperatures, etc.] must be accounted for). But despite this name, the "flash" in "flash evaporation" really refers to the flashing of the BRINE as it flashes from each higher-pressure effect to the next, lower-pressure effect in series.

Thanks @Paul Bryan

I think as the NEA is negligible articles didn't consider all details about it and neglect temperature change according to NEA and only consider evaporation effect.

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For my final question:

Is the following conclusion true?

consider two streams entering a flashing box.

The pressure of the 1st steam is equal to the flash box pressure (P1=Pflash chamber, T1) so no flashing occurs and we don't have any temperature change.

The pressure of the 2nd stream is higher than the flash box pressure (P2>Pflash chamber, T2) so flashing occurs and temperature reaches T'2=Tsat+NEA

Stream 3 is the outlet stream of the flash box (and also we have outlet stream 4 for the saturated vapor leaving the box)

If we want to calculate the stream 3 temperature should we write an energy balance like the following?

h1(@T1,P1=Pflash chamber)+h'2(@T'2=Tsat+NEA,P1=Pflash chamber)=h3(T3=?,P1=Pflash chamber)+hsaturated vapor(@P1=Pflash chamber)

A flash box has TWO outlet streams. Also, as previously noted, NEA applies to the evaporator itself, in particular the brine stream, not to the "flash box." The evaporator has MULTIPLE inlet streams (2 for effect #1, 4 for effects #2, #3, . . . N), based on the process shown in Mutaz & Wazeer, Desalination (2014).

My last example is general and autonomous....

I've corrected my solution...Is it not clear and true?

h1(@T1,P1=Pflash chamber)+h'2(@T'2=Tsat+NEA,P1=Pflash chamber)=h3(T3=?,P1=Pflash chamber)+hsaturated vapor(@P1=Pflash chamber)

I don't understand this sentence:" NEA applies to the evaporator itself "

I don't understand this sentence:" NEA applies to the evaporator itself "

I have applied it here: h'2(@T'2=Tsat+NEA,P1=Pflash chamber)

Your equation may or may not be correct, but I can't offer an opinion because it is not clear, at least not to me. To what does "h" refer? What do the subscripts 1, 2, and 3 mean? Is the "flash chamber" the evaporator or the flash box? Putting @ and = in variable descriptions is not standard, etc., etc.

When I say "NEA applies to the evaporator itself," I mean that it does not apply to the "flash box." The FLASH evaporator is the large vessel with Brine streams flowing in and out, and NEA is an estimate of the difference between T(i) and T(vi) in Figure 2. From some of your comments, it seemed that you might be connecting NEA with the operation of the "flash box," rather than with the evaporator.

The flash boxes are essentially energy-recovery units, and depending on the economics of a particular project, they may not even be included . As noted in Equations 24 (evaporator) and 28 (flash box), there is also an NEA for the flash boxes, although this one I imagine is so small an effect that it may usually be negligible

Could you recommend me a book about this field of NEA?

In my personal library, I find these all useful:

H.T. El-Dessouky, H.M. Ettouney

Fundamentals of Salt Water Desalination

Elsevier Science

2002

691 pages

English

Woldai, Abraha

Engineering systems and sustainability series Multi-stage flash desalination : modeling, simulation, and adaptive control CRC Press

2015

352 pages

English

Vassilis Belessiotis, Soteris Kalogirou, Emmy Delyannis

Thermal Solar Desalination. Methods and Systems [1 ed.] Academic Press

2016

382 pages English

The first one - El-Dessouky & Ettouney - is probably best for your question.