Mass and energy balance models (M&EBs) are the foundation of working with any pyrometallurgical process. It is the tool that engineers turn to when designing a new plant, when making changes to raw materials on an existing operation, or to help identify why things don’t go as planned.
Process failures may cause serious injuries to personnel, and often result in extended periods of downtime. Despite this, most M&EBs used in industry contain significant shortcomings. Assumptions are unavoidable in the development of these models. Reaction kinetics and mass transfer limit the extent to which materials react. Such details may be difficult and even impossible to incorporate in a mass and energy balance. However, if an aspect of the process can be quantified and calculated, we should make use of the opportunity.
Thermochemical software and process models can be relatively expensive. However, the cost of lost production due to a failure, and lower process efficiency far outweighs the cost of developing and integrating such a tool into an operation. Depending on the size of the plant, payback periods can be in the order of days or weeks.
Heat losses account for a significant part of the process energy consumption. This value is normally assumed when starting to develop an M&EB, but is later updated to be the difference between the actual energy input and the calculated process energy requirement. One can use the measurements from process instruments to calculate the furnace heat loss. This should be similar to the heat loss component in the M&EB. However, this is hardly ever the case, which indicates that some significant aspects have been omitted from the M&EB, or that some assumptions in the calculations are incorrect. A correction factor is therefore incorporated in the M&EB to account for the heat losses and any other uncertainties.
The furnace heat loss should remain fairly constant if the process is stable. However, some omitted items may change over time, thereby necessitating a change in the correction factor. Some critical items that are often excluded from M&EBs are:
Moisture: Although moisture is usually included in a M&EB, its variability is often not accounted for. Moisture content may change on a shift-to-shift basis. Process control parameters should be adjusted at similar intervals.
Oxidation state of metal oxides: Ore XRF and ICP assays do not distinguish between different oxidation states. Metal oxides are reported in the form in which the majority of the metal is expected to be present. This is the case for iron, chromium, manganese and other reducible oxides. Failing to account for different oxidation states of these oxides will result in an incorrect estimation of the energy and reductant requirements. This will also affect the gas volume.
Ore mineralogy: While the ore mineralogy does not have a notable effect on the mass balance, the enthalpy of formation of minerals can be significantly different from that of their simple components.
Reductant gross calorific value (GCV): Carbonaceous reductants are usually included in the M&EB as pure elements, which have enthalpies of formation of zero. This is incorrect and may have a notable impact on the energy balance.
Heat of solution: The energy required to heat and melt ore is normally included in M&EBs. However, additional heat will be generated or consumed to bring the ore into solution. The energy balance needs to account for this
Incorporating these items into your M&EB will reduce the impact that their variability has on your process. This should result in a more stable operation. As a result product grades will be more consistent and recovery will be higher over time.
Preliminary calculations have shown that some of these omissions can affect the energy balance by up to 10%. In a follow-up post, I will quantify some of these aspects to indicate the potential impact that their omission may have on a process. If you would like to share any case studies or examples on this topic, or if there are any additional items that are normally not considered in the M&EB, please let us know at firstname.lastname@example.org, or look us up on LinkedIn (https://www.linkedin.com/company/ex-mente/).