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# power plant system equations

## power plant system equations

(OP)
Could someone help me with equations to work out the following or lead me in the right direction

the percentage of steam bled of to the feed heater
the power generated by the turbines per unit mass of steam leaving the boiler
the energy available for low grade heating from the condenser

Many Thanks

### RE: power plant system equations

Look at the overall heat balance for a plant. It is usually a schematic that has steam temp, enthalpy, and flow at each location. It varies greatly by size of plant and weather low grade steam is desirable. I know of a plant that can divert 85% of the steam for heating applications, or send it all to the turbines.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

### RE: power plant system equations

(OP)
in a high pressure turbine i have steam expanding from 90 bar to 4.5 bar saturation at 412 celcius. i need to work out how much is bled off to the feed heater and how much is then expanded to the low pressure turbine at 1 bar and 0.93 dryness fraction.

So to work this out, basically I have to produce a schematic drawing along with a t-s diagram? to answer the above?

### RE: power plant system equations

(OP)
Thank you all for the pointers.

### RE: power plant system equations

Again, it's built into the operating structure of the design. You can't calculate this percentage from 1st principles, because it's a designed value. You need to look at design specs or operating parameters.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: power plant system equations

Hello PieD94,

Your "handle" suggests a response, and I intend no sarcasm.

You seem to be asking, "Someone is cutting up a pie. How big of a slice am I going to get?"

The question as posed mixes theory and practice, and somehow seems to presume an answer can be provided with only the information given...

The fact that in general pies are baked from raw ingredients into delicious treats is well known, and the means by which the flour, lard, filling, water, and other ingredients are combined and manipulated in the science of baking is both well understood and, when undertaken by a skilled practitioner, both predictable and repeatable.

The question of how big the different slices of a finished pie are lies entirely in the intent and the hand of the one wielding the knife. Similarly, steam flow can be divided into an almost infinitely huge ratio of turbine flow versus extraction, but what the final proportions of these steam flows will be is all a matter of design and how the plant is operated.

Plant and component efficiency can reasonably be considered to have reached their acme; determining heat balance, steam flow divisions and other such matters are standard industry practices involving the measurement of temperatures, the rate of condensate flow, and applied thermodynamics. There are numerous consulting firms out there that know how to do this and can be engaged to assist your firm in collecting and analyzing this information and recommending options based on the findings.

Hope this helps.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

### RE: power plant system equations

(OP)
Thanks for your response. The question I have raised is that of a past paper for my course. The course is energy based and leads into consultancy as you have mentioned. I have read through text books and a fair share of online articles to which i cant find a solution or information to help me solve the questions.

P.S. is it possible for an admin to edit posts? My post above had been changed to "thank you all for the pointers" which wasnt what I typed, also my login details seem to had been chsnged since that post.

### RE: power plant system equations

You apparently have not read board policies that discourage homework problems.

### RE: power plant system equations

(OP)
Im just reaching out for help. I havnt asked for the full answers, just a bit of guidance so that i can gain some understanding of the questions. But thanks for your input

Also, i stated it was a past paper question, not homework. Im trying to learn.

### RE: power plant system equations

Wouldn't happen if one had to participate in the forums for 30 days prior to posting.

### RE: power plant system equations

It seems that some information which appeared in this post on an earlier date has been deleted. I believe that the verbiage in the earlier version of this post indicated that in preparing your answer, you need to state your assumptions. This problem cannot be solved without making assumptions.

Based on my recollection of the earlier version, the HP Turbine inlet temperature is missing. You need the temperature at the inlet to the HP Turbine to determine the inlet enthalpy.

Here is a potential approach: (Please see the attached cycle diagram.)
• It is easier to work with a mass flow of steam than a percentage. Therefore, assume 100,000 kg/hr from the Boiler.
• Use the steam tables to determine the enthalpies at the HP turbine inlet, HP turbine exhaust and LP turbine exhaust.
• Assume no leakage of steam from the HP and LP Turbines.
• Assume the same pressure and temperature at the HP Turbine exhaust and LP Turbine inlet.
• Assume a typical pressure drop of 5% from the HP turbine exhaust to the Feedwater Heater shell. With the pressure at the heater, determine the saturation temperature in the heater shell.
• Assume values for the Terminal Temperature Difference (TTD) and Drain Cooler Approach (DCA) of the feedwater heater. Typical values are: TTD of 2.8 K and DCA of 5.6 K.
• Assume that condensate leaves the Condenser at the saturation temperature corresponding to the pressure of 1 bar (absolute) and that no heat is added or lost between the Condenser and the Feedwater Heater.
• Make a heat and mass balance around the heater to determine the mass flow of extraction steam.
• The difference between the mass flow from the boiler and the extraction is the Feedwater Heater is the flow through the LP Turbine.
• Using the enthalpies at the inlet and exhaust from each turbine (HP and LP) and flow through each turbine, calculate the power developed by each.
• Assume a Generator efficiency of 98% (for conversion from mechanical to electrical energy).

Pardon me if I have missed any other assumptions. Once you have made these assumptions and performed the related calculations, you should be able to answer all the questions in the original query.

Best of luck!

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