ABSTRACT : World Mining Congress in Montréal, Aug 2013.
Sankey Trees: Visualization of energy flows
and Dean Millar
Innovation Rehabilitation and Applied Research Corporation, Sudbury, Ontario, Canada
of Engineering , Laurentian University, Sudbury, Ontario, Canada
Mining operations consume a considerable amount of energy, and while reduced energy consumption is
desirable, it is not always clear how to achieve this goal. Understanding the opportunities
energy consumption is crucial, and the key to understanding is visualization. One option is the Sankey
diagram, which has been used for over 100 years to visualize the flow of energy, materials, or cost
through various processes. However, ther
e are drawbacks to this approach that must be addressed.
In a Sankey diagram, each flow is represented by an arrow possessing a width proportional to the
magnitude of the flow it represents.
he diagrams show input flows
how energy is converted and into
hat form, and also output flows. As per the first law of thermodynamics, the total energy output is
equivalent to the total energy input, so any energy that is not transferred to another process is
considered to be wasted. These waste flows are depicted in
and make it
straightforward to associate energy
, sinks and waste flows.
, Sankey diagrams do not
required to support
individual energy flows
on a Sankey diagram
it may become evident
that a significant flow of waste heat is of the appropriate grade (temperature) and volume to meet an
site heat demand currently being met with paid
for, possibly carbon intensive fuel. However without
ng the Sankey diagram with 3D spatial, true geometric analysis, the practicalities of the
concept or idea may not be fully appreciated.
Another issue with a Sankey diagram is that the magnitude of the energy flowing between processes
may have temporal fluc
tuation or variability on different timescales (diurnal, seasonal, inter
Sankey diagrams only provide a static picture of energy conversion and consumption, so that,
for example, 4 separate diagrams could have to be prepared for each se
A new energy flow visualization technique which we have called Sankey Trees has been developed.
Process locations are defined within a 3D model of the site being studied, and the magnitude of the flow
between each pair of processes considered is repl
aced with a time series. Branches of sustained and
diminishing flows are represented through variation of the geometric properties of the branches of th
trees. These branches are animated to indicate the direction of flow, and branch joints are used to
dicate that a process is transporting one form of energy to multiple processes.