Energy Management
Practical lesson 3
Sankey diagrams are a type of flow diagram, in which the width of the arrows is shown
proportionally to the flow quantity. They are typically used to visualize energy or material or
cost transfers between processes. A schematic representation of how a Sankey diagram can be
designed is shown in Figure 1. When available, all quantities or shares of flows and losses
should be specified.
Figure 1- Schematic representation of a Sankey diagram
1. Reading a book requires the conversion from primary energy to light. Assume that the
electricity used is produced from coal with 37% efficiency and transported with 94% efficiency.
Assume that the efficiency of the light bulbs is 50% and that only 20% of the light produced is
used for reading the book, with the rest being dispersed in the environment and from poor use
of the lights.
a) Draw the Sankey diagram of this process;
b) What are the total losses associated with this activity?
2. A trip performed by a driver is represented in Table 1, divided in 4 segments. For this trip, a
gasoline car was used. Assume that the energy content of gasoline is 31.8 MJ / l, the
conversion of oil to gasoline has an efficiency of 88% and that the efficiency of a gasoline car
from final energy to movement is 20%.
Table 1 – Trip characterization
Segment 1 Segment 2 Segment 3
Average speed (km/h)
35
80
110
Time (min)
20
15
40
Consumption (l / 100 km)
10.0
7.3
8.5
Segment 4
65
10
7.5
a) Calculate the average final energy consumption in MJ / km.
b) Assuming that 25% of the energy used in segment 1, 10% of segment 2, 5% of segment
3 and 15% of segment 4 was lost due to traffic, how much final energy was lost due to
traffic?
c) Draw the Sankey diagram, specifying all losses (conversion from oil to gasoline, from
gasoline to movement and in traffic losses).
d) What was the conversion factor from primary energy to useful energy?
3. A gas plant produces electricity with 42% efficiency, while the rest is converted into heat.
The electricity is then transported to the final consumers with 94% efficiency.
a) Draw the Sankey diagram for the process described.
b) Calculate the conversion efficiency from primary to final energy.
c) In a CHP plant, the electricity is produced with an efficiency of 35%. However, from the
heat produced at the plant, 62% is reused in a district heating system which has a
transmission efficiency of 80%. Draw the Sankey diagram for this plant.
d) What is the overall efficiency from primary to final energy in the case of the CHP plant?
4. Consider a factory that consumes electricity and propane. Electricity has the following
applications: 20% pressurized air, 10% lightning, 70% productive equipment. Propane is used
in ovens with an efficiency of 60%. Around 20% of the electrical consumption in the air
compressors is being wasted because there is no associated production. There are losses in the
network that transports the compressed air due to bad maintenance. These losses correspond
to 30% of the effective needs. Also there are losses in the final product that correspond to 5%.
Consider that the efficiency in producing electricity is 35% and that the conversion of primary
into final energy for the propane is achieved with 95% efficiency. Draw the Sankey diagrams,
quantifying all stages, for:
a) the ovens;
b) the compressed air.
5. Consider a residential heat pump with a COP = 3 (COP = heat produced / electricity
consumed). Draw the Sankey diagram assuming that the electricity is produced from natural
gas at a power plant and that 20% of the heat produced at the heat pump is lost. Specify all
energy consumption in the system.