Flow rate of steam in power plants

[T C]

TL;DR

What's the flow rate of steam at 5 barA pressure in a 250 kW power plant?

I want to know what's the flow rate (in kg/s) of saturated steam at 5 barA pressure to the turbines of a 250 kW power plant.

 

[Chestermiller]

Summary: What's the flow rate of steam at 5 barA pressure in a 250 kW power plant?

I want to know what's the flow rate (in kg/s) of saturated steam at 5 barA pressure to the turbines of a 250 kW power plant.

What is the exit pressure from the turbine?

 

[T C]

Atmospheric pressure.

 

[Chestermiller]

Assuming that the turbine operates adiabatically and reversibly, from your steam tables, what is the change in enthalpy of the steam per unit mass in passing through the turbine?

 

[T C]

Can't tell that. What's the enthalpy change of the market available power plants using such parameters?

 

[Chestermiller]

Can't tell that. What's the enthalpy change of the market available power plants using such parameters?

Wadda you mean? Do you have steam tables or not?

 

[T C]

73.16 kJ/kg.

 

[anorlunda]

73.16 kJ/kg.

Good. Now since one joule per second is one watt, can you complete the calculation?

 

[Chestermiller]

73.16 kJ/kg.

Please provide details on how you obtained this result.

 

[T C]

By subtracting the gross enthalpy of saturated steam at 1 barA pressure from 5 barA pressure.

 

[Chestermiller]

By subtracting the gross enthalpy of saturated steam at 1 barA pressure from 5 barA pressure.

This is not correct. It neglects the fact that some of the steam condenses in the turbine. For the adiabatic reversible expansion occurring in the turbine, the entropy per unit mass of the mixture of saturated liquid and saturated vapor leaving the turbine at 1 Bar must equal the entropy per unit mass of the dry saturated vapor entering the turbine at 5 bars. So, on this basis, you need to determine the mass fractions of saturated liquid and saturated vapor exiting the turbine such that this condition is satisfied. Then, using these mass fractions, you need to determine the enthalpy per unit mass of the combined mixture exiting the turbine. For the enthalpy change of the water passing through the turbine, you will then get a value higher than that which you calculated.

 

[T C]

Just for the sake of simplicity, let's consider this as a non-condensing turbine i.e. the condensation factor to be nil or negligible.

 

[anorlunda]

Just for the sake of simplicity, let's consider this as a non-condensing turbine i.e. the condensation factor to be nil or negligible.

Yes, non-condensing non-reheat turbine is clear. Nevertheless, the moisture content of the saturated mixture changes a lot in the turbine. It may enter very dry with 2% moisture, and exit with very wet steam with high moisture content.

The significant parts that we are still neglecting are the steam seals and the water drains that remove excess moisture part way through the turbine. Because of those, the mass flow at the exit is significantly less than mass flow in.

Steam turbines are more complicated than we commonly imagine.

 

[Chestermiller]

Well, if you neglect condensation, then you end up with your value of 73.16 kJ/kg for the enthalpy change. With condensation considered, I calculate 275 kJ/kg. Don't you think that difference is significant?

 

[JBA]

Are there powerplant steam turbines that actually operate on saturated steam, from what little I know on the subject, I am under the impression they operate on steam with a significant level superheat to prevent high velocity moisture that can erode the blades an stators. In one case on this forum about the design of a turbine emergency shutdown valve the supply steam's superheat temperature was twice the saturation temperature.

 

[anorlunda]

Most nuclear power plant turbines run on saturated steam. Most fossil plants run on superheated steam, but they are also typically 250 MW or more. 250 KW is miniature in comparison, who knows what kind of boiler you are asking about? It also sounds like you are asking about an open-cycle plant that dumps steam to the atmosphere. That's far from the typical power plant turbine.Do we have some semantic confusion here? A condensing turbine is one that exhausts into a condenser vacuum (29 inches hg) in a closed-cycle. A non-condensing turbine exhausts to the atmosphere at 1 bar in an open-cycle. The OP said exit at atmosphere pressure, so I presume we are talking about an open-cycle.

Even in in the non-condensing turbine, a fraction of the steam can condense and raise the moisture content. We provide drains at intermediate points in the turbine to get rid of excessive moisture, and grooved moisture removal turbine blades to facilitate that removal.

 

[JBA]

@anorlunda Thanks for the feedback, my question was of a general nature, my only experience is with fossil fuel power plants. In one case, it was a dual service operation with the power plant turbines as the primary and the turbine exhaust steam piped to a pharmaceutical plant at a discharge pressure substantially higher than atmospheric.
Edited

 

[T C]

Well, if you neglect condensation, then you end up with your value of 73.16 kJ/kg for the enthalpy change. With condensation considered, I calculate 275 kJ/kg. Don't you think that difference is significant?

The difference is huge. What's the % of condensation that you have considered?

 

[Chestermiller]

The difference is huge. What's the % of condensation that you have considered?

9%

 

[T C]

Is it the average standard rate of condensation? Whatsoever, in that case the flow rate would be go below 1 kg/sec.

 

[Chestermiller]

I don't know what "average standard rate of condensation" means. But, yes, for the setup you describe, the flow rate would be below 1 kg/sec.

 

[anorlunda]

Is it the average standard rate of condensation? Whatsoever, in that case the flow rate would be go below 1 kg/sec.

Recall that I said that in comparison to power plant turbines, 250 KW is miniature.

 

[gmax137]

Just for comparison purposes, a nuclear plant I have some familiarity with was making about 750 MW (electric) with a steam flow of 12 million pounds per hour. As @anorlunda notes, the nuclear steam is saturated. Anyway, that works out to about 0.5 kg/second for 250 KWe. That is the total steam flow, servicing the secondary side auxiliaries (steam jet ejectors, gland sealing, etc.). I am not sure what the generator efficiency is (MWe to the turbine shaft power) but I think they're pretty high, close to 1.0.

This is not really representative of the OP's situation, since the nuclear plant's output is 3000 times the 250 KW in the OP. So, I'm offering it up as a lower-bound sanity check only.