or, It Depends …
This post started out as an e-mail answering a question from one of the folks taking the Existing Building Commissioning Workshop this year at the Pacific Energy Center. But as I worked on it, I realized that the question had come up before and that the answer and related concepts might be useful to others. On the surface, it seems like a simple question. But if you really want to understand, it is fairly complex. Thus, this blog post.
This ended up becoming quite a long post (surprise, surprise, surprise). So, I broke it up into several posts, which are still somewhat long. To minimize the pain for someone just wanting the bottom line, I have included a table of contents that will allow you to jump to a topic of interest. The “Return to Contents” link at the end of each section will bring you back here.
- The Question
- Confusing Units
- Asking the Source
- Using a Simplifying Assumption
- Seeking a More Exact Solution
- Energy and Phase Changes
- A Few New Terms
- Enthalpy Depends on Temperature and Pressure
- Focusing on p-h Diagrams
- Applying the p-h Diagram for Water and Steam
- Plotting the Initial Condition
- Plotting the Condition Entering the Control Valve
- Plotting the Condition Entering the Heat Exchanger
- Plotting the Leaving Condition
- Enthalpy Change = Energy Change
- ENERGYSTAR®, Conversion Factors, and Rules of Thumb
Students participating in the workshop are required to have access to a building that they can use as a living laboratory to apply the EBCx skills we teach in the class. One of the first things they do is benchmark their building in the LBNL Building Performance Database and ENERGYSTAR®. To benchmark, you typically need to convert the annual energy consumption of a facility into some sort of index, typically an EUI (Energy Use Intensity or sometimes also called an Energy Utilization Index).
EUIs can be stated in terms of site or source energy. If you want to know more about the difference, this blog post will provide the details. In the discussion that follows, I will be considering things in terms of site energy.
EUIs typically have engineering units in the form of energy use per unit area per year, such as kBtu/sq.ft. per year (kilo or thousands of British Thermal Units per square foot per year). Energy is not always billed directly as Btus. For instance electricity is billed in terms of kWh or kiloWatt Hours consumed. District steam is often billed as pounds of steam consumed. To create an EUI from the bill metrics , you need to convert the billing units to Btu’s.
In the industry, most people are pretty familiar with the conversion factor for kWh to Btus, which is 3.413 kWh per Btu and pretty invariable. But there is less familiarity with how to convert a pound of steam to Btus, and there can be some variability related to exactly how the thermal energy is billed (kBtus, pounds of steam, thousands of pounds of steam, etc.) and the nature of the steam source (district steam, central plant, or boilers on site). Bottom line, if you want an exact value, it can become more complex than the single factor used to make electrical conversion.
As you may have guessed by now, the question I was asked was how to go about converting pounds of steam to Btus. The answer is:
It depends ….
One of our students has a facility that purchases steam from a district steam system[i] and their bill states consumption in the form of Mlbs. For example,
Total usage invoiced in Mlbs – 301.3
Note the letter “M” which means the unit of measure is not simply pounds, it is some multiple of pounds.
So the first part of answering the question is to determine what the “M” stands for, because to correctly answer the question,
It depends on the units of measure.
Most of us (probably because of computers) would take the M to be the SI (System International; often referred to as metric) prefix denoting a factor of one million (1,000,000) as in the MBytes or MB associated with a file or hard drive size. Thus we might conclude the bill is stating that the facility was being invoiced for 301.3 x 1,000,000=301,300,000 pounds of steam.
Unfortunately, that turned out not to be true in this case.
It turns out that there is another system of units that uses “M” for a multiplier; the Roman Numeral System, where “M” is used to indicate thousands (1,000), not millions (1,000,000). And to make things interesting, the industry uses both systems and (to me at least), seems to figure you will simply know which one applies.
If you have been in the industry for a while, that is probably true. But if you are new to it all (or suffer from aging brain cells like I seem to), then it can be confusing.
For example, we have control systems that are moving and storing Mb or Megabytes of data (where mega is the SI prefix for millions, so millions of bytes). These systems can be monitoring and managing air handling systems that are moving cfm of air (where the “c” stands for “cubic”, not the SI prefix “centi” or hundredths, nor does it mean hundred, which is what it would stand for if it was a capital letter in the Roman Numeral system).
The air is often being cooled using electricity, which is often billed as kWh ( where the “k” means the metric prefix “kilo” or thousands of watt hours), and heated, perhaps, with steam generated by a boiler that might be rated in terms of MBtu (where the M is the Roman Numeral M and means thousands of Btu), or MMBtu(still the Roman Numeral M, but two of them, meaning thousand thousand, or million Btu).
If the boiler is fired using natural gas, then the gas might be billed in terms of MCF (thousands of cubic feet, where the M stands for the Roman Numeral, but the C stands for cubic not the Roman Numeral for 100 and F stands for feet), or in terms of therms (which stands for 100,000 Btus),
Or the consumption could be billed in terms of Dth (which combines therm with the metric prefix “Deka” or 10 to stand for 10 therms), which is approximately the same amount of energy as an MCF of natural gas (see above) depending on the exact heat content of the gas, which varies with the source of the gas.
Other than nuances like that, we have a pretty straight-forward system of units in the industry. So there should be little confusion about what things mean.
Asking the Source
The student who asked the question, went to the source (the utility representative) for clarification on the units on the bill. And in this case, they were told that the M (Roman Numeral) actually stands for K (Si Prefix) meaning that their bill was for thousands of pounds of steam.
So it seems that all that is needed now is to figure out how any Btu’s are released when you condense a pound (or a thousand pounds) of steam. Frequently, that is done by making an assumption about the amount of energy associated with the phase change. But if you want a more exact answer, it is a bit more complex than a single number.
It is also an interesting (in a nerdy sort of way) saturated system physics exercise. So I thought it would be worth looking at both techniques.
Using a Simplifying Assumption
There is nothing at all wrong with using a simplifying assumption. Being math-phobic and often pressed for time in terms of coming up with an answer, I do it all of the time. But if you do it, I think it is important to recognize the constraints that your assumption placed on the result so you don’t take yourself to seriously if the discussion becomes more precise. And you need to understand if the assumption can actually be used in the context of a given discussion.
In this case, our simplifying assumption might be based on the fact that most condensate return systems are open to atmospheric pressure at some point, usually at the condensate receiver. So, we could look at the amount of energy released if we were to condense 1 pound of steam at atmospheric pressure.
You can find this value in a steam table. Steam tables contain empirically derived values for the various properties of water under different conditions of temperature and pressure. You can find them in classic publications like Keenan and Keyes, on line, in the ASHRAE handbooks, or you can even build one yourself as a learning exercise using REFPROP, like I did to create the table below.
Note that the pressures in second column are in absolute pressure units, not the gauge pressure units we are probably more accustomed too. In other words, the pressures are referenced to a pure vacuum, o psia. So atmospheric pressure is 14.71 psia or 0 psig.
The value we are interested in is the latent heat of vaporization at atmospheric pressure (highlighted in orange above) which is the difference between the enthalpy of the water vapor (steam) and the enthalpy of the liquid water at the condition we are interested in. In this case, the value is 970.8 Btu/lb.
To estimate the amount of energy associated with a bill for 301.3 thousand pounds of steam based on the assumption that the steam was condensed at atmospheric pressure, we could do a bit of simple math, like this.
If we needed to convert this to millions of Btu, we would just divide the result by 1,000,000, like this.
We could even create a multiplier that we could directly apply to future bills to give us the answer.
In fact, the student who inspired this post was planning on using this multiplier. All I have done up to this point is illustrate where it came from and that there is an assumption behind it.
How much does that assumption impact the accuracy of the EUI and benchmark? Well,
It depends on the magnitude of the difference between the assumed value for the enthalpy change that occurs when the steam is condensed relative to the actual value of the enthalpy change produced by the thermodynamic processes used to extract energy from the steam at the facility.
It also depends on what you do with the condensate.
Seeking A More Exact Solution
Truth be told, in the olden days, folks (such as myself) would assume that condensing a pound of steam was worth about 1,000 Btus. It made the math easier if you were using a slide rule or four function calculator. And, if you contemplate the steam table above, you can see that it probably meant we were accurate to with-in 10% or better over a pretty broad range of conditions.
But, if you consider what is really going on in the context of the data in the steam table, you realize that assuming the latent heat of vaporization is 970.8 Btu/lb or 1,000 Btu/lb could be wrong because:
It depends on the saturation temperature that the steam condenses at.
For instance, most steams systems deliver the steam to the loads they serve at a pressure that is above atmospheric pressure; pressures of 3-15 psig are common. For district steam systems, the delivery pressure can be significantly higher, perhaps as high as 60-150 psig or more, which is subsequently reduced to the 3-15 psig range at the end use facility.
If you look at the Tariff that defines the rate structure and nature of the service for the utility suppling steam to the facility in question, you find that there are two potential delivery pressure ranges available from their distribution network, 5-10 psig and 20-120 psig and that the company reserves the right to adjust the delivery pressure.
Note that I have assumed the pressures are gauge pressures vs. absolute pressures.
And, the term “quality” as used in the tariff is probably not the thermodynamic use of the term given the reference to chemical constituents. In other words, in a pure thermodynamic sense, the “quality” of saturated steam is a measure of it’s wetness; i.e. how much of the steam is pure vapor and how much of it is water that has yet to change phase. More on this to follow.
It is also worth noting that some utilities will deliver the steam in a superheated state, not a saturated state. All of these things have an impact on the energy content of the steam.
Energy and Phase Changes; Understanding the Process
If you perform the experiment I describe in this blog post, you will discover that it takes a whole lot more energy to change the state of water from a liquid to a vapor relative to what it takes to heat the liquid or vapor. Here is an image from that blog post depicting the results of the experiment. The paragraphs that follow describe the results.
The red line in the picture is temperature of the water in the tea kettle. The green dashed line and blue solid line are the temperature of the space above the water.[ii] Initially, this space is filled with a mix of air and water vapor. But once boiling starts, with the lid on the kettle, all of the air will be driven out and it will fill with steam.
Heating the Water
If you observe what happens, when I turn on the heat (the purple line is the watts into the burner on the stove), the temperature of the water and the water vapor mix both start to rise. Since the liquid water is at atmospheric pressure but below the boiling temperature (a.k.a. the saturation temperature) we say that it is subcooled. During this phase of the experiment the burner was supplying 1 Btu to raise the temperature of one pound of water 1°F.
When the water temperature reaches 212°F, the water begins to boil, which creates steam, filling the area above the water with pure steam, and creating a saturated system where the temperature of both the water and the steam are the same (notice how the green and red lines converge).
Heating the Mixture of Water and Steam
Now, even though the burner is applying a steady amount of energy, the temperature of the water/steam mix holds constant. That is because the energy from the burner is now being used to change the liquid water to steam (a.k.a. a phase change) and during a phase change the temperature remains constant at the saturation temperature. During this time, the burner was supplying 970.8 Btus for every pound of water that was converted to steam.
When the last drop of water changed to steam, the burner was still supplying energy at a steady rate. But since the mass of the steam contained inside the teapot at that point was quite low compared to the mass of water that was there when we started (most of that mass was now outside the teakettle condensing on the windows in the kitchen), there was a lot of energy being supplied to a very small mass.
Heating the Steam
At this point, the phase change is complete so all of the energy from the burner is applied to changing the temperature of the steam inside the pot. Since it only takes about 0.5 Btus to raise the temperature of a pound of steam 1°F at atmospheric pressure (and there was much, much less than a pound of steam contained in the pot) then the temperature spikes rapidly. This elevation in temperature above the saturation temperature is called superheat.
A Few New Terms
If you are new to thermodynamics, some of the terms that you observed in the steam table can be a little scary sounding. After all, how many dinner conversations (with normal people) have you had where the words “enthalpy” and “entropy” were bantered about.
We are accustomed to concepts like temperature and pressure because we apply them directly in our day to day lives. A weather forecaster may talk about a high pressure system moving into our area or that we can expect lower temperatures and humidity after a cold front moves through. Or the recipe we select to prepare for dinner likely specifies a temperature that we should cook the food at, perhaps suggesting that we bring a pot of water to boil in preparation for making some pasta.
But in the course of day to day conversation, we seldom discuss enthalpy or entropy, even though those properties are also changing as we go about our daily lives. For instance, the weather forecaster could have said that the enthalpy of the air is going to drop after the cold front passes. And the recipe could have suggested that we increase the enthalpy of a pot of water until it reached saturation and then continue to add energy so that the water changes phase.
The point is that enthalpy, while an unfamiliar term in day to day life, is a property used to measure the total available energy in a substance at a given condition. So, if we know the enthalpy change that a substance goes through in a given process, we know the energy change.[iii]
Enthalpy is challenging to measure directly. But since it is related to things that we can more readily measure, like temperature and pressure and moisture, some very dedicated individuals have been able to experimentally determine enthalpies for various substances and develop relationships that allow us to predict enthalpy based on other measurements and coefficients that are developed via the experiments. The thermodynamic diagrams that follow are simply graphical representations of these results.
Enthalpy Depends on Temperature and Pressure
If you study the steam table I inserted previously, you will discover that the latent heat of vaporization – i.e. the energy it takes to convert a pound of water to a pound of water vapor (a.k.a. steam) – varies as a function of the saturation temperature and pressure. Stated another way, the enthalpy change associated with a phase change will vary with the temperature and pressure that the phase change occurs at.
For example, if the pressure is about 60 psig (or about 75 psia), then the latent heat of vaporization is more like 905 Btu/lb vs. the 970.8 Btu/lb we have discussed for water at atmospheric pressure. Similar considerations apply for sub-atmospheric pressures. And, as our experiment revealed, the amount of heat associated with changing the temperature of a subcooled liquid or a superheated vapor is different from the phase change value and will also vary a bit with temperature and pressure.
The steam table above is focused on water at saturation. There are other tables that document the properties for water that is superheated or subcooled.
All of this can be quite complex to wrap your head around. But a picture can be worth a thousand words, and in the context of our discussion, a thermodynamic diagram can be worth a thousand words. Using one, you can plot a process and read all of the thermodynamic properties of water (or other substances) directly from the diagram. And the process plot gives you a “visual” on what is going on.
Psychrometric charts are a form of thermodynamic diagram that HVAC engineers use to assess an HVAC process.
Skew T log P diagrams are used by meteorologists to understand the atmosphere.
To understand what happens to a substance as it goes through a process, encountering various various conditions and states, we can use pressure-enthalpy (p-h) diagrams (what follows uses water as an example) …
… temperature entropy (t-s) diagrams …
… and enthalpy-entropy (h-s) diagrams (a.k.a Mollier diagrams) ….
These diagrams are extremely intimidating.
But if you can stay calm and continue to breath normally, they can be quite useful because if you can plot a process on them, you can read all of the properties for the various states directly from the chart. When you compare it to the other options, like playing with the equations of state, which can look like this …
… or working through multiple tables like the one pictured below and interpolating values …
… they can become quite attractive and you may find yourself inspired to learn how to use them.
The Spreadsheet Behind the Diagrams
If you are really curious about the diagrams above, you can find the spreadsheet behind them at this link. Personally, I learned a lot by developing them. And now that I have them, I can plot processes on them pretty precisely, which lends itself to using a graphical solution to solve and visualize complex thermodynamic processes.
Focusing on p-h Diagrams
P-h diagrams are a very common way to look at thermodynamic processes like refrigeration cycles.
They can give you a “visual” on a complex process and make it less intimidating for math phobic folks like me. If you want an example of how useful a diagram like the one above is, take a look at this engineering application guide from Sporlan.
I don’t want to get to far a-field here, but the point is that diagrams like these can make the analysis of cycles much easier to accomplish once you learn to work with them. There was a point in my career where I was somewhat terrified of a psych chart. But now, it is my “go to” tool for understanding air handling system processes. Similarly, I use the various thermodynamic diagrams I illustrated above to help me understand different HVAC and building system processes.
Applying the p-h Diagram For Water and Steam
To gain a deeper understanding of the amount of heat represented by a condensed pound of steam, I’m going to plot out a pressure reducing process on a p-h diagram. I could plot it on any of the diagrams, but I chose the p-h diagram because we want to demonstrate what happens as steam is throttled to reduce its pressure and a throttling process can be considered a constant enthalpy process. So, the two things we are going to work with are represented by the primary axis of the chart.
Let’s look at what happens if the utility serving the facility we are considering is delivering saturated steam to it from their high pressure system at 120 psig. And let’s assume:
- The facility uses a pressure reducing valve to drop the pressure to 12 psig to serve an insulated pipe header that delivers the lower pressure steam to a heat exchanger, and
- That the heat exchanger condenses the steam to make 180°F hot water, which is then distributed to to the various loads in the facility, and
- That the pressure reducing valve, heat exchanger, and its control valve are all in close proximity to each other so that there is no meaningful pressure drop between the pressure reducing valve and control valve nor is there any meaningful heat loss through the insulation between those points, and
- That the design supply water temperature to the loads is 180°F with the heat exchanger was selected for a 20°F temperature rise on the water side using saturated steam at atmospheric pressure (0 psig, 14.7 psia), and
- As a result, the condensate leaving the heat exchanger is at 212°F, and
- That the condensate is discharged to a system that is vented to atmospheric pressure.
The process is plotted out on the p-h diagram below.
Plotting the Initial Condition
The initial condition is on the saturation line at the delivery pressure of 120 psig or 134.7 psia. Knowing that the steam is saturated (red saturated vapor curve) at a specific pressure (value on the vertical axis) allows us to plot the entering condition on the chart, and we can read the enthalpy of 1,193 Btu/lb at this condition from the p-h diagram.
Plotting the Condition Entering the Control Valve
The condition entering the control valve represents the result of the throttling processes associated with the pressure reducing valve. Throttling processes are constant enthalpy processes, so knowing that and that the leaving condition that the pressure reducing valve is controlling for (12 psig, 26.7 psia), we can plot this point on our chart.
Note that we assumed there was no meaningful pressure drop or heat loss in the piping header due to its short length. Had there been a meaningful pressure drop and thermal loss in the piping system, that would have shifted the entering control valve point down and to the left slightly from where we plotted it.
Plotting the Condition Entering the Heat Exchanger
The entering condition in the heat exchanger represents the throttling processes associated with the control valve, which was selected based on an entering steam pressure of 12 psig and a pressure in the heat exchanger of 0 psig. This results in an initial condition in the heat exchanger that is at the same enthalpy as the control valve entering condition (because throttling processes occur at constant enthalpy) but at the pressure used to select the heat exchanger (o psig, 14.7 psia). Thus, we can plot this point on the chart based on these two parameters.
Note that the steam entering the heat exchanger is superheated as a result of the two throttling processes in the delivery chain. As a result, it has a bit more energy content than it would if it was saturated steam at atmospheric pressure.
Plotting the Leaving Condition
Because the heat exchanger was selected to deliver the design performance requirement using steam at atmospheric pressure, the condensate coming off of the process will be at atmospheric pressure and 212°F, the saturation temperature associated with atmospheric pressure. This is also the condition in the condensate return main. As a result, we can plot this point on the chart, which allows us to read the enthalpy of the condensed steam leaving the process.
Enthalpy Change = Energy Change
If we know the enthalpy change between two conditions, then we know the energy change. In this case, the change in enthalpy was from 1,193 Btu/lb t0 181 Btu/lb or 1,012 Btu/lb.
Good News and Bad News
Taking a closer look at the specifics of the process revealed that for every pound of steam that was condensed in this scenario, we received 42 more Btu’s than our rule of thumb would have suggested or about 4% more. In the context of the Btu’s received for your dollar, that sounds like a good thing. In other words, the pounds of steam you purchased delivered more Btus than the rule of thumb suggested.
But in the context of a benchmark, it means that you actually used more energy than the rule of thumb suggested. Thus, in this case, if we were to calculate an EUI based on our more specific assessment of how the steam was actually used in the facility, the EUI will be higher and the benchmark score will be lower.
ENERGYSTAR®, Conversion Factors, and Rules of Thumb
In an effort to try to create consistency, ENERGYSTAR® publishes conversion factors for various energy sources including district steam.
If I understand it correctly (I don’t actually do a lot of ENERGYSTAR® benchmarks), when you are entering your data into ENERGYSTAR®, an “Add Meter Wizard” will guide you to the 1,194 Btu number for a meter that was reporting KLbs (thousands of pounds) of steam.
As you can see, this would result in a consumption value that is higher than the rule of thumb we developed based on an assumption of condensing steam a atmospheric pressure (1,194 vs. 970.8 Btu/lb) as well as the rule of thumb used by old engineers like myself sometimes (1,194 vs. 1,000 Btu/lb) .
It is also higher than reality for the situation we explored in the p-h diagram (1,194 vs. 1,012 Btu/lb). So if you where to benchmark in ENERGYSTAR® using their metrics, it would seem like they would over-state the energy use of your facility if it was a facility where the steam delivery followed the process we traced out.
That means your EUI would be higher and your benchmark would be lower than it would be if you could insert your actual energy use in terms of the Btus released by the condensed steam vs. the thousands of pounds of steam you used into the ENERGYSTAR® database.
Benchmarks are Approximations, not Exactamates[iv]
The preceding may want you to cry “Foul”. After all, you are trying to do a good job in terms of running your facility efficiently and it seems unfair to have your score penalized by an arbitrary conversion factor.
But you need to remember that benchmarks are intended to provide a broad-brush comparison of similar facilities in similar climates serving similar occupancies with similar use patterns. There are a lot of variables at play. For example, the heat content of gas and other fuels will vary with the source and ENERGYSTAR® applies arbitrary conversion factors to them just like it does to district steam.
The endnotes in the referenced ENERGYSTAR® conversion factors document indicate the source for the conversion factors, with the International District Energy Association being the source for the district steam energy conversion factor.
Why so High?
If you study the steam table, you may find yourself wondering why the International District Energy Association recommended a conversion factor of 1,194 Btu/lb. After all, that appears to be the latent heat of vaporization associated with an extremely low saturation temperature and pressure.
That is because there is more than the latent heat of vaporization to be recovered. For instance, in the example I plotted out on the p-h diagram, the condensate left the process at 212°F. There are quite a few things that you could do with a stream of water at that temperature. For example, you could run it through a heat exchanger to recover sensible energy and preheat or even heat domestic hot water.
So, in a way, the answer to a modified version of the original question, perhaps along the lines of …
How can I go about capturing the energy that the ENERGYSTAR® conversion factor for district steam metered as pounds of steam implies is available?
It depends on what you do with steam and condensate you receive from the utility
The Basis of the ENERGYSTAR® Conversion Factor
If you dig around a bit, you can discover the basis behind the ENERGYSTAR® conversion factor. I found it in a footnote in a technical reference they provide about Greenhouse Gas Emissions.
What that is saying is that the ENERGYSTAR® conversion factor is equal to the enthalpy of saturated steam at 150 psig. It is important to realize that this is different from saying it is equal to the latent heat of vaporization of 150 psig steam, which is the enthalpy change associated with condensing saturated vapor to saturated liquid, or about 858 Btu/lb.
In our field, we are typically interested in changes in enthalpy through a process rather that the specific enthalpy at a given state. And, because enthalpy cannot be measured directly, we state the values of enthalpy for a substance referenced to a particular state. For instance the specific enthalpy of water or steam is referenced to water at 0.01°C and atmospheric pressure.
In the context of this discussion, that means that if we really wanted to capture all of the energy associated with the ENERGYSTAR® conversion rate for district steam metered as pounds, then we need to not only condense the steam we receive, we need to receive the steam at 150 psig as saturated steam and we need to cool it to just above freezing.
So, the ENERGYSTAR® Folks are Crazy
You may be thinking at this point that the ENERGYSTAR® folks are nuts. After all, your local utility may not deliver steam at 150 psig, with the delivery pressure of 120 psig in the utility tariff we looked at being an example of that.
But if you compare the enthalpy of 12o psig steam with 150 psig steam, you will find that it is only about 3 Btu/lb different; about a quarter of a percent. So in the bigger picture, receiving steam at a lower delivery pressure would not make that much difference in the factor that you would use.
You may think, O.K. I’ll buy that, but it just does not seem practical to cool the condensate to just above freezing in a way that delivered anything useful to the building. In other words, to provide heat, the source (in this case the condensate) needs to be warmer than what you are trying to heat.
Given that we are trying to maintain space temperatures in the mid 60°F to mid 70°F range in most of our buildings, a fluid stream that is at or below that temperature range could not be used directly to heat. Some sort of heat pump (and energy input) would be required to move the heat from the condensate to the place that needed it.
Actually, the ENERGYSTAR® Folks are Not Crazy
If you take the time to think it through, you will realize that the ENERGYSTAR® conversion factor is simply forcing us to take a hard look at what it means in terms of energy and resources if our facility uses steam as an energy source.
There is a subtilty associated with how most (not all) commercial district steam systems work that we need to consider. You get a clue about it if you read the tariff for the facility we have been discussing closely (note my highlight).
What that is saying is that the condensate (condensed steam) delivered from the utility will not go back to the utility. Rather, it will go to the sewer. That means that all of the energy associated with the hot condensate is literally dumped down the drain and eventually is dissipated to the environment with out serving any useful purpose in the building that consumed the steam (a.k.a. energy and water vapor; two different resources).
In fact, depending on the temperature of the condensate and the requirements of the local plumbing code and the material in your sanitary piping system, you may actually have to cool the condensate before discharging it. Typically this is done using domestic cold water (directly or via a heat exchanger) which is then dumped to the sewer along with the cooled condensate.
Bottom line, if you received district steam at 150 psig, saturated, you actually did receive 1,194 Btus with every pound of steam (and a pound of water for every pound of steam). The challenge is to understand how to capture as many of those Btu’s as possible before discarding the condensed fluid stream to the sewer. Because what ever you don’t recover really is wasted energy (and water).
So painful as it may be for this type of system the 1,194 Btu/lb factor allows your steam consumption to be legitimately and fairly compared to the other types of steam systems I will describe in the next blog post.
[i] A district steam system is a network of piping served by a central plant that provides steam to a large area like the downtown area of a city.
[ii] The blue line is data from a very low mass thermocouple so that it would react quickly because I wanted to capture the very rapid increase in steam temperature that I anticipated once all of the liquid water had been converted to steam. (For more on how sensor mass can impact the data it produces, see this blog post).
I had the logger set for a very rapid sampling rate and did no have enough memory to allow it to log data for the entire time it took to boil off all of the water. So I did not start the logger associated with that sensor until nearly all of the water was evaporated, which is why the blue line only shows up towards the end of the graph.
[iii] Entropy is a bit more complicated to grasp, like, I almost flunked thermo because I struggled with it so much. I think that is not unusual and often take comfort in something John von Neumann said (emphasis is mine):
You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
They way I have come to think of it is that its basically nature’s way of saying:
There’s no such thing as a free lunch
When we turned on the burner to boil the water, energy flowed from it to the water because the burner was hotter than the water. But, with out some sort of process that involves doing work, we can not get the energy that flowed into the water converted back into heat or electricity. Heat does not flow from cold to hot, only from hot to cold.
If you want a bit more detail about all of this, you may want to review a string of blog posts I did that look at saturated multiphase systems. The experiment I mention and use to illustrate what happens when water boils is part of one of the posts.
[iv] You may also find the Chapters in Roy Dossat’s book Principles of Refrigeration titled Internal Properties of Matter and Properties of Vapors to be insightful. He writes about thermodynamic concepts in a very understandable way. When I found the book, early in my career, my first thought was where were you when I took thermodynamics, which I almost flunked because of my struggle with the math and concepts initially.
[iv] When I worked for Murphy Company, Mechanical Contractors, more than once, I heard Pat Murphy, our chief estimator mentor some of the younger estimators, saying
we were doing estimates, not exactamates.
When I first heard him say it, I felt it was really insightful. And I also think the same is true for a benchmark.