Mini-series on material balance: what should be measured to get a good material balance?

Part 4

Mini-series on material balance – Part 4: what should be measured to get a good material balance?

Dec 21, 2021 | Process simulation

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 the part 4, we will explore what should be measured to get a good material balance and where.

Every measurement has a cost. Multiplying measurements increases the cost. Moreover, the cost increases with the precision sought. The more measurements and the higher the quality, the better the material balance. But such an ideal measurement system must generate enough revenue, or reduce losses sufficiently, to justify the costs and make a profit. This is where the problem lies.

Indeed, the material balance, as such, is not a direct element of production and its indirect role in the correct operation of an installation is very difficult to quantify or even justify. Therefore, all too often, when cost reduction is sought, it is measurement that is the first target, the approach being more often purely accounting. Fortunately, and increasingly, many measurements are essential for plant management, whether for regulatory reasons related to safety and the environment, real-time process control, or even accounting. However, these essential measurements are often not sufficient to establish a sufficiently detailed and accurate material balance.

Establishing a material balance also has a cost, but it is minimal compared to the cost of the measurement.

The objectives of the material balance

The objective of the material balance is to get a precise and complete assessment of a process over a more or less long period. As ore is a highly heterogeneous and variable raw material, this assessment must be repeated frequently in order to understand better:


  • The performances, step by step, in terms of recovery and content, to better understand the behaviour of the material and to constantly seek
       their improvement, source of income.
  • The losses of recoverable elements in the various waste streams, in order to try to reduce them and the associated loss of income, and also
       to avoid unduly accounting for part of them in stocks, which would result in overvaluing them and thus biaising the real value of the
       company, a source of financial risk.
  • The release of undesirable elements into the environment to better control them, and to monitor them more frequently than the simple
       regulatory controls which are not very representative of reality, and thus avoid unforeseen remediation costs.
  • The characteristics of the raw material, more precisely than by direct measurement, and to lead to an optimised management of the
      orebody mining by anticipating the expected performances and revenues.

All these elements lead to either an increase in income, a decrease in losses or a reduction in financial risk. The intangibility of the impact of the material balance on these elements makes it difficult to justify.

The best example of the reality of this impact comes from facilities that have stopped or reduced their material balance activity. Indeed, when a plant starts up, the measuring equipment is operational, and some additional measurements are carried out to check the conformity of the installations and validate their acceptance. But over time, additional measurements no longer seem necessary, the measuring and sampling devices break down without being repaired or replaced, or are not regularly calibrated and shows drifts. It may take several years to realise that profit is decreasing, despite the reduction in measurement costs, and even longer to question the technological reason. It appears then that the cumulative losses are much greater than the costs of the measurements and material balances that could have preventing them. The credibility of a mining company towards its shareholders and the regulatory authorities depends on its ability to control its production tool in the present, the future, and the past.

Numerous measurements or good measurements? That is the question

Finding the right balance between sufficient numbers of measurements of good quality and cost is not easy and deserves a step-by-step approach. Indeed, too many measurements can kill the measurement. The rare cases where instrumentation is highly developed from the time the plant is built show that it is not enough to have measuring equipment, but that it is also necessary to be able to manage, maintain and calibrate it, and, in the case of sampling, to collect and analyse the samples.

As a result, not all measuring devices are available or reliable, and key measurements are often missing. It is better to have a gradual ramp-up, giving the teams in charge of managing and using the system time to adapt and standardise routine operations. Nevertheless, planning for measurement at the design stage of the process makes it possible to prepare the locations of the measuring devices and samplers so that they can be installed later in the best possible conditions.

Since engineering companies are rarely aware of the rules for the correct installation of such equipment they must absolutely call on the experts of the most reliable suppliers. It is still all too common to find measuring devices, sometimes very expensive, badly installed and thus rendered inoperative. Likewise, far too many plant designs do not allow for retrofitting.

The general rule for the choice of measurements and their location:

A sufficient number of measurements of good quality measurements allowing for slight redundancy is always

better than a large number of lower quality.

Rules to determine reliable measurements for mass balancing

The concept of measurement quality for material balance includes: 


  • The absence of bias or at worst an acceptable bias (well below
    the standard deviation of the measurement error).
  • No drift leading to an unacceptable bias.
  • Acceptable reproducibility, constant and with known variance.

Firstly, it is good practice to identify all the measurement means needed to control the process and to assess their quality for use in a material balance. These measurements are usually not sufficient and other measurements must be added in order to have enough redundancy to improve the accuracy of the material balance through reconciliation algorithms (more information provided in the bonus part of the mini-series).

The rules for determining which additional measurements to make and where to make them are:


  • The accessibility of the material stream or stock. Some streams or stocks are completely inaccessible to measurement (e.g. the stream of
    slurry between two flotation cells within a bank). Others are only accessible to a few types of measurement. Most often the flowrate cannot
    be measured, but a sample can be collected. It may also be a level in a tank that can be measured but a sample cannot be correctly collected.
  • A key stream or stock on which a quality effort (absence of bias and good precision) must be made:
  • The raw material feed to the mill should be fully characterised in terms of mass and composition, e.g. by belt weighing, on-line moisture
    measurement and automatic sampling for chemical composition and moisture verification.
  • Plant products should often be well measured because they are sold.
  • Tailing, too often neglected, without mass measurement and with unrepresentative sampling. However, these known loss streams must
    absolutely be correctly measured in terms of mass and composition in order to estimate the losses as accurately as possible. Only channelled
    discharges can be measured in this way. Non-channelled releases to the environment (such as dust, fumes, gases, and liquid leaks), which are
    difficult to measure, either in mass or in composition, must be reduced to a minimum (by containment and recovery of dust and leaks, by
    treatment of fumes and gases) and must be changed from unknown losses to known losses.
  • Stocks of raw materials and final products.
  • Intermediate streams that constitute main streams of the process, but offering the possibility of better measurement quality. This is the
    case, for example, of the product stream of the grinding circuit, before separation, where most of the raw material passes through, but
    offering  less sampling error compared to the plant feed.
  • Intermediate stocks and work-in-progress that are large in quantity, where even a small percentage uncertainty can have a significant
    impact on the overall material balance.
  • A secondary stream to better estimate an inaccessible stock or, conversely, a stock to better estimate an inaccessible stream.
  • A circulating load for which mass measurement is usually inaccessible (such as the underflow of a hydrocyclone directly into the mill) but for
    which a sample can be taken for composition determination.
  • The contents or concentrations of elements other than valuable ones, but which provide better measurement accuracy and sufficient
    separation to improve the mass estimates using the equivalent of the two-output formula. This is for instance the case for Si and Fe in base
    metal ores.

How to establish a material balance sheet and why it is important


For a dynamic balance, corresponding to a given moment, it is necessary to collect all the measurements corresponding to this moment and to express them in terms of quantity (mass flowrate for streams or mass variation for stocks and inventories) and composition. The steady-state balance is a special case of the dynamic balance for which stocks and work-in-progress do not vary.

For a production balance, all measurements corresponding to the considered production period are collected, including beginning and ending stocks and work in progress. They are consolidated over this period: the mass quantities are summed up (or integrated in case of flowrates), the compositions are averaged by quantities.

In all cases, the unmeasured parameters are then calculated and serve as an initialization for the reconciliation algorithm. If there is sufficient redundancy, several calculation methods can be used for the same parameter. In this case, the most accurate method must be used (e.g. a sum of quantities rather than a difference, which may be negative in some cases).

Each measurement is associated to a measurement error, usually expressed as a relative error (in percent), which is small or high depending on the precision of the measuring device, the measurement conditions, the level of representativeness of the sample on which the measurement is based, or the precision of the analytical protocol. The parameters consolidated over the period are then also subject to error, which can be calculated from the errors of the individual measurements, following the error propagation rules. On the other hand, the unmeasured variables, which are calculated as described above, are only estimates and are therefore associated to a large error.

The redundancy of the measurements, which are by definition imprecise, makes the consolidated data set inconsistent with the material conservation laws. The data reconciliation algorithm is there to make the set consistent by providing a set of estimators, as close as possible to the measured data, with respect to their error, but consistent with the conservation laws. The algorithm also calculates the errors associated to the estimates. It is observed that these estimates are much more accurate than the initial data. It is then possible to evaluate the contribution of redundancy and the importance of the good precision of some key variables.

All the reconciled data constitute the material balance itself and will serve as a basis for determining key performance indicators (KPIs):

  • Production of final products in quantity and quality.
  • Consumption of raw materials in quantity and quality.
  • Recovery and concentration ratio of valuable components.
  • Yields.
  • Stocks and work in progress in quantity and quality.
  • Consumption of reagents and water.
  • Losses of valuable components in tailings.
  • Discharges to the environment.
  • Workshop by workshop, operation by operation, estimation of performance indicators specific to each technology.
The material balance can therefore be used in near-real time for process control, over short periods such as a shift, a day or a week for process monitoring and production balance, in association with production planning, or over a month for metallurgical accounting ,as described in the following article.

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The material balance, a key step between measurement and process control

Subscribe now to our dedicated mailing list and receive directly in your email box articles on the material balance approach. No promotion, it will describe the topic from a neutral point.

The mini-series on material balance includes 5 parts + 1 bonus:

  • Part 1: The mass balance approach (this page)
  • Part 2: The material balance, a tool used throughtout the
    process life cycle
  • Part 3: Material balance in process control
  • Part 4: What should be measured to get a good material balance
  • Part 5: The material balance as the basis for metallurgical
  • Bonus: Redundancy and data reconciliation

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