Sankey Trees: Visualization of Energy Flows

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 to optimize 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, there 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. The diagrams show input flows, how energy is converted and into what 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 Sankey diagrams and make it straightforward to associate energy sources, sinks and waste flows. Unfortunately, Sankey diagrams do not convey all information required to support practical decision making for redirecting individual energy flows. Based only 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 on-site heat demand currently being met with paid-for, possibly carbon intensive fuel. However without augmenting 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 fluctuation or variability on different timescales (diurnal, seasonal, interannual). Currently, 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 season. 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 replaced with a time series. Branches of sustained and diminishing flows are represented through variation of the geometric properties of the branches of the trees. These branches are animated to indicate the direction of flow, and branch joints are used to indicate that a process is transporting one form of energy to multiple processes.