Mini-series on material balance – Part 1: the mass balance approach

Discover a CASPEO mini-series dedicated to the material balance in mineral processing: The material balance, a key step between measurement and process control. Follow us and learn everything you ever wanted to know about material balance. No promotion, it will describe the topic from a neutral point. In this first part, have a look to the basics and the mass balance approach. 

Material balance is the foundation of any understanding of the phenomena underlying, transformation processes of any material, whatever it is. It is a good tool to better orientate the means to move towards a better knowledge of the processes, which is the only way to make them more profitable in the short and long term.

Paradoxically, material balance has become so routinely used that it is often neglected in many industries as for mineral processing, metallurgy, or recycling. If it is established, whether for process control and monitoring or for metallurgical accounting, its reliability and accuracy are rarely questioned. And it is often very late, or even too late, for the reality to come to light.

What is mass balance?

A treatment process is a succession of operating units for material transformation, separation or mixing. This regards mineral material in our purpose. A set of material conservation laws is associated to each operation. These laws relate to the material as a whole, but above all and more specifically, to the components of that material. The ones that are used everywhere are the conservation laws for chemical elements, hence the adage: nothing is lost, nothing is created, everything is transformed. But other components of matter can be subject to a conservation law: conservation of molecules, minerals, size or density classes. Of course, these laws only apply if these components are not transformed.

Thus, the quantity of matter entering an operation is added to the quantity of matter already present, the whole being equal to the sum of the quantities of matter leaving the operation and remaining there. And this is true for each component that is conserved. If we disregard nuclear reactions, the quantity that is conserved is the mass. This is why a material balance will always be a mass balance.

What are the different types of material balance?

Three types of material balance are used for the process management at different stages of its life: the production balance, the dynamic balance, and the steady state balance (Figure 1).

• The production balance: mass balance of a component which is conserved over a production period

As there can be several input streams or several output streams in an operation, Q_i and Q_o are then the sum of the quantities on these different streams.

• The dynamic balance: material balance calculation over an infinitesimal period of time

• The steady state balance: the flowrates do not change and the variation in stock is zero

The sum of the input flowrates is then equal to the sum of the output flowrates:

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