Here is a good example of how Sankey diagram and pie chart are used side-by-side. In fact, the Sankey diagram picks up one particular piece of information that is already in the Sankey diagram.

This is from a German research report titled ‘Entwicklung eines EnergieReduzierten Verfahrens für den Erwärmungs- und Umformungsprozess von Parabel-Lenkerfedern durch Verkürzung der Verfahrenskette („EnRed“)’ published in 2010. [Note: no English abstract present, but title translates to sth like ‘Development of an energy-reduced process for heating and forming of…’ and from what I understand it is a hot rolling process]

It compares a conventional process with a new, energy reduced process. Here is the Sankey diagram for the conventional process and the pie chart right below.

The unit is kWh/kg, primary energy per kg of final product. The three colors are picked up again in the pie chart that shows the breakdown of primary energy lost in the provision of heat (brown, 12.3%) and in the ovens (red, 74.3%). Only 13.4% of the primary energy is actually used for heating of the rolled material (yellow).

Now, the pieces of the pie chart correspond to the widths of the brown, red and yellow output arrows as part of the primary energy input at the left. We are, however, typically much more used to percentages being represented in a pie chart.

A nice detail in the Sankey diagram is the split for the three ovens and the losses from the three ovens (red). The flows run in parallel and then are joined again at a bar that reminds me of a bridge, or the nut of a guitar … or the Brandenburg gate turned sideways as my nephew suggested 😉

From my collection of Sankey diagrams here are three very similar samples depicting energy flows in a building. All three are from Germany (did I mention that more than half of the Sankey diagrams seem to be from Germany or Austria?).

These are all very simple Sankey diagrams. This first one is a hand-drawn goodie from the times when reports were still done with a typewriter. It shows use of fuel oil (‘Heizol’) in a school building, and interesting to see, the flows are given in kilograms fuel oil rather than to represent the heating value. The school building consumes 80 tonnes of fuel oil per year.

Note that flows are not to scale (arrow for equivalent of 10580 kg fuel oil annual heat loss through walls is about the same width as the one representing 31770 kg heat loss through windows). So this Sankey diagram doesn’t deserve an A…

The next building energy flow Sankey diagram shows flows in Watts (W). Not sure where I found this one. Flows again are not proportional (spot the 470 W flow and compare it to the others). Main inputs are radiation (‘Strahlung’) and electric energy. A heat pump cycling energy can be seen, so it seems that this one is maybe for a passive house.

This last one done with a Sankey diagram software hence flows are to scale in this one (although I have some doubts regarding the width of the fuel oil input arrow on the left). Flows are in kWh per year. Main fuel type is natural gas (red), some district heating (blue). Electric energy in yellow, consumed by IT, lighting, air compressors, and so on. This energy flow Sankey diagram is probably for a factory building or complex.

I will try to add the sources where I found these three diagrams. Please forgive my negligence this time.

A research project at Technical University Dresden in collaboration with a paper manufacturer aims at detecting and implementing energy saving measures for paper machines.

“Better monitoring of process variables, improvement in the operating point (or range) of the process, installation of heat recovery systems (e.g. at heat exchangers), use of heat pumps and replacement of high energy streams (steam) with waste heat streams. Most of these techniques are standard recipes which are readily available in the market. However they are designed without giving any consideration to the specific aspects of a manufacturing facility and also provide no quantitative evidence of the potential benefits. “

This is why they came up with a mass and energy balance model and are using the following Sankey diagram to visualize where energy could be recovered.

Flows are labeled as enthalpy flows, showing the changes in thermodynamic (heat) energy at each process step, hence losses. The Sankey diagram is for a balance period of six hours. No absolute figures are given. Several heat exchangers are installed along the wet section of the paper machine. In the drying section, a large part of the energy is lost as steam/humid air.

Here is another one … enjoy!

Same topic as in my previous post, heat flows and losses, this time in a continous furnace. Recovered heat loop is strange: arrows gets wider in the curves, as if painted by hand. Funny serpent arrow for opening (radiation) losses. No values given. All arrows have the same colour. Source: Article ‘Quest for Fire – Combustion Basics’ by by Daniel H. Herring. Published October 2, 2009 on Industrial Heating. The International Journal of Thermal Technology.

Found this Sankey-like diagram accompanying an abstract submitted for the 2001 International Conference on Thermal Engineering and Thermogrammetry. Posting it here on the blog before this site eventually vanishes. This Sankey diagram is a good example of how not to draw Sankey diagrams, I think. Or, as a Japanese friend would put it politely: “Maybe… [turn head at 30° degree angle, make slight air-sucking noise by inhaling through open mouth] … maybe not so good”.

Here’s the diagram:

The idea was to display heat losses at a slab furnace in a Turkish steel plant. Heat losses were identified in exhaust gases (22 %), at the cooling pipes (2.90 %), and at the furnace walls (0.47 %).

The fact that the widths of the arrows displaying the heat losses were chosen arbitrarily give a completely wrong idea of the proportions. The powerpointish curved arrows don’t really contribute to a better understanding.

All in all, not a very good one. Adding this to my “Lying with Sankey diagrams” mini series (see part 1, part 2), which has been neglected recently.

The Mexican National Commission on Energy Saving (Comisión Nacional para el Ahorro de Energía (CONAE) present several success stories (casos exitosos) on their website.

One success story dates back to 1997, and describes how an energy efficiency study of fired heaters (i.e. boilers) was carried out in a Nafta producing facility in the Veracruz state of Mexico. As a result of the study, several suggestions for optimization were implemented. Fuel consumption could be reduced by 23-24 %, while the efficiency of the ovens could be raised by 13% (calentador BA-2001 B) and 16% respectively (calentador BA-2001 A).

Para los hispanoparlantes: el título oficial del proyecto fue “estudio técnico económico e ingeniería conceptual realizada a los calentadores a fuego directo BA-2001 A/B de la planta hidrodesulfuradora de naftas, del C.P.Q. “La Cangrejera”, ubicado en Coatzacoalcos, Veracruz” (otro candidato para el concurso mundial de titulos largos).

The heat losses are shown as Sankey diagrams. The first describes the optimal situation, with an energy efficiency of 82,4 % “as guaranteed” by the maker of the fired heater.

The two other Sankey diagrams show the energy balance of the heaters A and B before the implementation of the measures. They run with an efficiency of 60,6 % and 62,35 %, a “real world situation of one fired heater” />

The arrows branching off at the top show the heat losses. I like the fancy icons that show how energy is lost through the walls, because of deteriorated or insufficient insulation, and heat energy in the effluent gases. The flows are given in MMBTU/h (millions of BTU per hour).

Unfortunately two of the diagrams are not to scale: The arrow to the right in the second diagram should be roughly 2/3 of the width on the left side. It is about 4/5 (or 80 %) of the width, similar to the width in the first Sankey diagram. This is a visual exaggeration of the inefficiency. However, I refrained from featuring this in my informal “Lying with Sankey diagrams” series. 😉

Edit 05/2015: the web pages are not acessible any more. I had to restore the image from a local copy, and removed references to two other diagrams I had references to. -Phineas

A few months ago I had found this b/w Sankey diagram on the website of the Institut de Génie Thermique (IGT) de la Haute Ecole d’Ingénierie et de Gestion du Canton de Vaud (HEIG-VD) in Switzerland, showing the energy or heat balance (bilan thermique) of an average family home.

It visualizes the sources of heat as Sankey flows into the building (in MJ per square metre) with the largest chunk being the combustible for the heating system, other inputs are from solar radiation and internal sources. On the right side it shows how and where heat is being lost: windows (fenétres) 122 MJ/m², ventilation (aéreation) 113 MJ/m² or roof (toit) 57 MJ/m². Also, the technical losses from the heating equipment (pertes techniques, shown as Sankey arrow from the heater to the top) are quite significant (57 MJ/m²).

A similar Sankey diagram in German was presented on the e!Sankey forum recently.

This diagram submitted by one of their users is explained as follows:

In the diagram the group of flows in red colors are heat losses due to transmissions through walls, windows, doors, etc. The dark blue arrow shows heat loss through ventilation. The stacked purple/mauve flow represents heat losses at equipment and pipes.

While a little more detailed in the number of flows, it shows the same general situation: In many houses “a lot of the heat gets lost due to heat leaks (thermal bridges) or insufficient external insulation.”

This article on the FAO website shows a comparison of several types of simples stoves and their energy balance using Sankey diagrams.

The Sankey diagrams show how the energy (typically from wood firing) is lost, and that only a small fraction of 12 to 20 % is actually being used as “useful heat”.

More of these “heat flow diagrams” can be found in chapter 4.2. of the article.

A rather special feature of the diagrams shown in this article is that the percentile values given for the flows cover a range (e.g. Ash and Char 5,97% – 12,15%), rather than a specific absolute value. This is rather untypical. Also, it can be noted, that the width of the arrows are not always to scale: compare, for example, the width of the “Surface” arrrow to that of the “Thermal Mass” arrow. It should be roughly four times wider.

The same Sankey diagram created with a Sankey software tool shows the arrow widths correctly.