This presentation from 2015 by Alicia Valero of the Spanish Research Centre for Energy Resources and Consumption (CIRCE, Zaragoza) is on critical materials, minerals scarcity, recycling and a “thermodynamic cradle-to-cradle approach”.

It features two Sankey-style diagrams depicting the mineral balance of the European Union (UE).

This first one is a Sankey diagram for the mineral balance without fossil fuels (‘Diagrama de Sankey para el balance mineral de la UE sin combustibles fósiles’).

Data is for the year 2011, Flows are shown in tons. Iron and limestone dominate the picture with 77% of the input. Limestone is produced (extracted) mainly within Europe, while iron is mostly imported.

The second Sankey diagram is a scarcity diagram (‘Diagrama de rareza para el balance mineral de la UE sin combustibles fósiles’) and takes into account thermodynamic exergy to obtain (mine) the minerals. Although it depicts aluminium, gold, ion, nickel and the likes, flows are shown in an en(x)ergy unit (Mtoe).

Iron and limestone which seemed to be the most important mass-wise only constitute some 10% of the input. Aluminium and potash seem to be much more difficult to produce. Rare earth elements (REE) are not included in this diagram.

The author points out that it is important to not only look at materials from a mass perspective. Looking at materials availability taking into account thermodynamic exergy paints a different picture of the real cost and scarcity.

For those interested, please check out the presentation (in Spanish) here.

From a July 2013 article titled ‘Energy and exergy analyses of a Zero emission coal system’ by Linbao Yan, Boshu He, Xiaohui Pei, and Chaojun Wang of Beijing Jiaotong University, available at Researchgate. This Sankey diagram is for “the exergy flow of the improved Z[ero] E[mission] C[oal] system at benchmark condition”.

Fig. 4. Sankey diagram of the exergy flow of the improved ZEC system at the benchmark condition.

All flows are in kJ. The individual process steps if the system are only labeled with acronyms. They are explained in the article: GF is gasifier, CL is cleaner, RF is a reformer, and CH is a CO2 heater. The article also features the energy flow Sankey diagram.

I have presented several examples of Sankey diagrams in the field of maritime technology before (see here).

This recent article (Baldi, F., Ahlgren, F., Nguyen, T., Gabrielii, C., Andersson, K. (2015): Energy and exergy analysis of a cruise ship. In: Proceedings of ECOS 2015 – the 28th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems) confirms that “the complexity of the energy system of a [cruise] ship where the energy required by propulsion is no longer the trivial main contributor to the whole energy use thus makes this kind of ship of particular interest for the analysis of how energy is converted from its original form to its final use on board.”

The authors conduct a thorough energy and exergy analysis for a cruise ship in the Baltic Sea. The ship has different operation modes (sea-going, manoeuvring, port stay). The energy analysis “allows identifying propulsion as the main energy user (41% of the total) followed by heat (34%) and electric power (25%) generation”. Nevertheless, “it can be seen that the energy demand for auxiliary power is comparable in size to that for propulsion.”

The data for this Sankey diagrams in the annex of the paper and shows that flows are in TJ for an operation period of 11 months. Blue, yellow and green arrows depict energy use, while the orange arrows reveal heat losses to the environment.

The study continues with an exergy analysis of the ship, since it reveals more on the system inefficiencies. The exergy analysis is shown as a Grassmann diagram in the paper. This is structured similarly to the Sankey diagram above, but has dark orange arrows representing the exergy destruction. This is mainly from the Diesel engines and the oil-fired boilers.

I recommend this paper not only to naval engineers, but to everyone who wishes to get a better understanding of exergy and Grassmann diagrams. Can we consider Grassman diagrams a subset of Sankey diagrams? What do you reckon?

The scientific paper ‘A Sankey Framework for Energy and Exergy Flows’ by Kamalakannan Soundararajan, Hiang Kwee Ho, Bin Su (Energy Studies Institute, National University of Singapore) features these two Sankey diagrams.

Energy flow in an open rack vaporiser (ORV):

Exergy flow in an open rack vaporiser (ORV):

The authors explain that “ORVs regasify liquefied natural gas (LNG) from temperatures below -160°C to room temperature through a heat exchange process with sea water at room temperature and pressure. (…) The Sankey representation of energy and exergy flows here presents a large potential for energy savings that could be realised in the regasification process.”

Found the two Sankey diagrams on the website of the Exergy Design Joint Research Lab of Osaka University in Japan. The diagrams are for enthalpy and exergy in a Solid Oxide Fuel Cell (SOFC). Can’t fully understand what it means, but both are simple breakout Sankey diagrams that could also be presented as a pie chart.

The first one is titled “Enthalpy Sankey Diagram”:

The second one is a “Exergy Sankey Diagram”:

Anybody care to explain more?
Looking at the choice of color one could be led to believe that enthalpy is female, while exergy is male.

Found the Sankey diagram below in an article on ‘Exergetic efficiency analysis of pyrometallurgical processes’. It is from a master thesis by Bart Klaasen (PDF file), that contains several Sankey diagrams.

The main diagram is titled ‘Exergetic Sankey diagram for a zinc recycling process’. Input streams are in blue, emission streams are in red. Internal flows are colored green, while yellow represents the actual product.

The flows don’t show arrow heads, but a general left-to-right direction can be assumed. No values in the above overall Sankey diagram, but for each process step individual input/output Sankey digrams can be found that feature exergy data in KJ. They look like this one:

In contrast to Sankey diagrams that represent energy flows, the input output flows into a process node don’t have to have the same magnitude. Exergy is synonymously called “available energy”.

“Energy is never destroyed during a process; it changes from one form to another (see First Law of Thermodynamics). In contrast, exergy accounts for the irreversibility of a process due to increase in entropy (see Second Law of Thermodynamics). Exergy is always destroyed when a process involves a temperature change. This destruction is proportional to the entropy increase of the system together with its surroundings.” (Wikipedia)

So it is understandable that the exergy represented by the flow magnitude at the output of the process is less than the one of the flows on the input side.

NB: Bart’s article reminded me of some bookmarks to exergy diagrams I have, will try to post these in the near future too.

This post on the Pinhead’s Progress blog makes my day (if not my whole weekend!). ptuft draws the attention to a slide presented by Wes Hermann from Stanford at the SciFoo 2007 conference. You can see the original photo on flickr and the presentation slides “Earth’s Exergy Resources – Energy Quality, Flow, and Accumulation in the Natural World” by Wes Hermann here.

Slide from a presentation by Wes Herman (uploaded to flickr by zippy)

While I am not yet sure if this qualifies fully as a Sankey diagram, I find it really really fascinating! The diagram is titled “Exergy flux, accumulation, destruction, and use” and shows “where all the energy on the earth comes from, where it gets stored, and where it goes”. It distinguishes by colors the following exergy resources: Thermal, Nuclear, Radiation, Gravitational, Kinetic, Chemical.

The diagram type could be called a hybrid Sankey-Grassmann diagrams (see this post). The upper part is where radiation exergy is shown: 162000 TW of solar radiation and another 62500 TW of extra-solar radiation arriving on planet earth, being lost through atmospheric absorption, evaporation and surface heating. The green part (Chemical exergy) is what we focus on when we talk about energy consumption today. Hermann calls it “exergy destruction for energy services” (measured in ZJ). Accumulated exergy is shown with elliptic pouches on the arrow. Nuclear exergy features in the diagram as “bubbles”, most of it not accessible for human use as energy. One can find many other interesting details in this diagram.

I am tempted to challenge my e!Sankey tonight to see if I can draw this. Two different units (in this case TW and ZJ) can be displayed in one diagram. Biggest visualization issue will certainly be to handle the large differences in scale. Let’s see if I find the time, or if I prefer to enjoy radiation exergy of the summer sun at the poolside instead…

I have been asked whether ‘Grassmann Diagrams’ are the same as ‘Sankey Diagrams’, or what distinguishes them from Sankey diagrams. Frankly speaking, I only came across Grassmann Diagrams one or two years ago, and I hadn’t heard (or had I overheard?) this term during my studies. So here is a short summary of what I found out about this special type of diagram.

Grassmann diagrams are usually referred to as ‘exergy diagrams’. Exergy, in thermodynamics, are being “defined as a measure of the actual potential of a system to do work” (see Wikipedia entry), or the maximum amount of work that can be extracted from a system. (For those who are looking for a well-written introductory article on exergy, I recommend the first chapters of this one by Wall and Gong, which also shows links to LCA, economics and desalination).

Coming back to Sankey diagrams, they were in the very first place used to show the energy balance, or energy efficiency of a machine or a system. (Today, however, the use of Sankey diagrams has been extended beyond displaying energy flows, and they are also used for any kind of material flows, CO2 emission, value flows, persons, cars, pig halves, and the like).

Thus the difference between Grassmann and Sankey diagrams is mainly that the first depict exergy, the latter energy. Taking this, it is understandable that the width of the flow gets less at each stage, while in Sankey diagrams the width of the arrow at a process (transformation, machine) should be maintained, as energy is only being transformed, but never being consumed (First Law of Thermodynamics).

Let’s forget about the semantics and their primary use for a second, and look primarily to the visualization aspect of both diagram types. Then, in a more general perception of Sankey diagrams as flow diagrams that display arrow widths proportionally to the flow quantities, Grassmann diagrams could be understood as a special subset of Sankey diagrams. Indeed, some authors refer to them Sankey-Grassmann diagrams, or as an adaptation of Sankey diagrams, or as the counterpart to Sankey diagrams.

This article “On the efficiency and sustainability of the process industry” from Green Chemistry is recommended for further reading. It also and contains some nice Grassmann (- or should I say Sankey) diagrams. Enjoy!