Steam power plant cycle design, Mollier Diagram help

[Blaine]

Hi posted the question/cry for help in a regular thread but thought it might fit in here as well.
Hello All,
I am currently trying to optimize a steam power plant cycle and I am stuck... What I am unable to figure out is how to use a Mollier chart/diagram in order to determine the amount of steam I must tap off from my turbine to my feed water heater. I know my feed water heaters inlet and outlet temperatures, mass flow rate, TTD and DCA. I have drawn en expansion line in my Mollier chart, taking into consideration my isentropic efficiency. I have been told that from that line I should be able to make an energy balance and directly read off the bleed temperature, pressure and enthalpy of my steam to my feed water heater. Could someone please shed some light on the matter?? Regards Blaine


Forward preheater:
mass flow rate out = 50 kg/s
h out = 994.9 KJ/kg
t out = 231 deg C
h in = 771.9 KJ/Kg
t in = 182 deg C

Heat is added after the feed water heater in order to get the turbine steam entry data, see below.

Turbine steam entry data:
P in = 80 bar
t in = 500 deg C

During the expansion process steam is bled off from the turbine to the feed water heater in order to raise the feedwater temperature from 182 deg C to 231 deg C. The question is how much steam? At what pressure? At what temperature? How can this be read off from the expansion line in my Mollier diagram?

Steam data:
t out bled steam = 191 deg C
t in (bled steam) = unknown
mass flow (rate bled steam) = unknown

Hope this is clear and hope someone can shed some light as I am stuck... Thanks Blaine

 

[Astronuc]

Write out the definition/equation for efficiency of steam turbine system.

The work extracted is related to the change in enthalpy across turbine stages (2 in this case) and mass flow rate. Between the stages, one extracts some fraction of the total mass.

So there is an energy balance equation, and a mass balance equation.

 

[Blaine]

Given:

Condenser temperature: 97 deg C
Condenser pressure: 0.91 bar

Turbine:
T admin = 500 deg C
P admin = 80 bar
isentropic efficiency= 0.87

Final feedwater temperature = 0.9* (n/n+1) [t (sat at P admin) - t (cond)] + t (cond)
The above equation gives the final feed water temperature = 231 deg C
where n is the number of feed water (2) heaters including the tank (1). This in my case being 3.
The optimization temperatures to each section of the feed water is calculated by
[T (final feed water)] / [T (condenser)]^(1/n) This in degrees kelvin


I have drawn the expansion line starting at [500 deg C and 80 bar] and ending at [97 deg C, 0.91 bar, X= 0.947 and S = 7.066] KJ /KgK

At the last feed water heater I know the mass flow rate = 50 kg/s

Thus I have the following energy balance at the last feed water heater:
E in = E out
m bled steam( h in - 817.5) = 50 ( 994.9 - 771.9)

My two unknowens being the bled mass steam rate from the turbine and the temperature/pressure (enthalpy.)
I have been told that from my Mollier Chart I should be able to read what I am missing but I do not know how. I hope someone has had a simular type of problem and can assist me in. Happy holidays, Blaine

 

[Blaine]

Hey,
I see many have looked/read my problem but why no insight? I need to figure this problem out asap so ANY insight would be much appreciated. I have the answer to my problem but I do not understand why steam at such a high pressure and temperature are chosen instead of a lower temp/pressure and a greater mass flow to the feed water heater.

My questions are now these: How is the overall efficiency made better by bleeding off steam at a higher temperature and pressure, smaller mass flow rate v's lower temp/pressure and a greater mass flow rate? Secondly how does one calculate what temperature and pressure give the optimal efficiency based on a energy balance or from an expansion line when there are two unknowens; h, enthalpy and the mass flow rate??

Hope someone can shed some light?? The optimum pressure and temperature bled to the first feed water heater, for the above described problem, are;
P= 30.08 bar t= 369 deg C

 

[Astronuc]

What is the work for each turbine stage (set)?

For a turbine, the power out is related to the mass flowrate * change in enthalpy (in -> out).

Does "At the last feed water heater I know the mass flow rate = 50 kg/s" imply the flow out of the last feedwater heater, and therefore the flow into the first turbine stage is 50 kg/s. Then let x (or some suitable variable label) be the bleed rate.

If 50 kg/s is the total flow, the 50-x flows through the subsequent turbine stage(s) after the bleedoff.

 

[Blaine]

Thanks for your responce.
I have figured out how to use my mollier chart but only once I realized that I have to use it in conjunction with a steam table. Once I have the feed water temperature I can determine the enthalpy that will be extracted in the steam thus making my energy balance complete. By taking the saturation pressure at the feed water temperature and by following that pressure line until my expansion line I then have the enthalpy. Then a simple energy balance will give me the mass flow rate out.
Thanks for your time. Regards Blaine