Thermodynamics!

 "What man can you show me who places any value on his time, who reckons the worth of each day, who understands that he is dying daily?  For we are mistaken when we look forward to death; the major portion of death has already passed, whatever years are behind us are in death's hands." - Lucius Annaeus Seneca

I recently had a sudden desire to determine the efficiency of the steam cycle here at work.  I also thought it might be good practical experience for the new guys here to learn how to calculate these values.  As a guy with gray hair and experience operating way too many different power plants, part of my job is to prepare these guys to take over the show at some point in the near future. 

Figuring out efficiency brings us to Thermodynamics, which I will *very lightly* brush over as the topic of today's post.  To be honest, I don't remember a lot of what I was taught so long ago, since it's not routinely needed. 

Thermodynamics is just a big word for movement of heat.  Like many other power plant operators, I know just enough to get by.  It's a complex subject, and I don't pretend to understand it deeply.

There are four laws of thermodynamics, each of which make sense - once you think about them for a bit.  Unfortunately the laws don't have much practical application to an operator's daily routine - they are mostly theoretical concepts.  What a power plant operator needs to calculate efficiency of a steam cycle is a set of steam tables.  Steam tables provide us with thermodynamic properties of water and steam at various temperatures and pressures.  

Years ago, power plant operators were commonly issued a small, inexpensive booklet containing steam tables when they started working in a power plant.  These booklets were usually published by Combustion Engineering, a major power plant component manufacturer back in the day.

Sadly, that era of deeper knowledge seems to be going the way of the woolly mammoth.  I don't know, maybe there is an app for that now (I looked it up, and there is.  Of course!  LOL).  Modern power plants use their installed control system to gather data and calculate overall efficiency in real-time.  It's unfortunate though, that this knowledge of how to figure it out on your own is gradually being lost to anyone other than those who program the computers.

I scrounged around the facility for a steam table booklet, but was unable to locate one, so I ordered one off eBay (linked eBay search).  Fortunately, it was inexpensive - being somewhat arcane knowledge at this point.

I am not interested in doing calculus to solve problems that can be dealt with using algebra or even simpler math.  This is from the front section that nobody at my level ever works with.

Below:  The meat of the matter.  What we need to know to calculate efficiency in the steam cycle.  The Enthalpy column in the next three images shows the energy content of steam and water at various pressures and temperatures under saturation conditions.

Below:  Superheated steam table.

Water and steam are weird.  If you boil water in a sealed vessel, it eventually heats up and begins to steam off.  This of course raises the pressure inside the vessel.  The temperature and pressure rise together as heat energy is added.  As long as there is still liquid water boiling in the vessel, conditions are "at saturation conditions", regardless of the temperature and pressure.  

Once the water has completely boiled off, and you continue to add heat to the steam, the steam is in a  "superheated" condition, meaning that the pressure-temperature relationship no longer exists - you can heat the steam further than when you could when water was still present, without raising the pressure.  Superheating steam increases efficiency - creating steam takes a lot of energy (which is lost as waste heat when the steam is condensed), but superheating steam does not take nearly as much energy, and the superheat energy is not lost during the condensing process.

Superheated steam was once called "Live Steam".  It's dangerous when it leaks out of a steam system, because it is too hot to create steam vapor.  It just sounds like an air leak hissing, but it can burn you quite badly, and you cannot see it, other than by noticing heat density waves above it.  Locating a superheated steam leak is done by tying a rag to a broom handle and waving the rag around until it blows sideways. 

Water also has a triple point - the pressure and temperature at which it can be solid, gas and liquid at the same time.  And there is a critical point - the temperature and pressure at which steam and liquid water have identical characteristics.  It's a weird thing, but real.  The critical point for steam/water is 3200 psi ( 220 bar) and 705 degrees F (374 C).  Some power plants are supercritical plants, and the term "steam" isn't used.  It's called a "working fluid", because what enters the turbine isn't steam, nor is it water.

Back to thermodynamics and the steam tables, and an overview of how to figure it out.  

The steam tables are used to determine how much energy is contained at each step of the steam cycle:

The water in the main condenser hotwell, the steam drum water, the steam leaving the steam drum, the superheater outlet, and the steam exiting the turbine exhaust.  All along the way you can see how energy is added and removed.  The math is not difficult, but it's also been several decades since I've had to do this.  Still, it's very helpful to understanding how it all works!

One cool thing the book came with, in a pocket inside the back cover, was a mollier diagram, also known as an enthalpy/entropy chart.  

Once you unfold it, it's quite large.

Again, I've slept a few times since I used one of these, so I'll have to re familiarize :)

One interesting thing about the mollier diagram is that the steam and water cycling through the power plant slide along a path following the lines.  Where the steam or water is at a particular moment on the diagram depends on where it is in the power plant - is it being boiled, superheated, or condensed?  This tells us where it is on the diagram.  The diagram below is for an ammonia refrigerant cycle, but the same principle applies to steam systems.

 Below is a diagram explaining the location in the power plant with respect to position on the mollier enthalpy diagram.

Can't say I needed this documentation, but it's still nice reference material in the unlikely event that it's ever needed.  BTW, I also added the phone app, just because :)