This model (which is also Pyrosim's newest feature) is a mass balance model which may be specified in much the same way as the equilibrium models are specified (from the main menu choose

Once Calculate has been pressed you will be prompted for various ratios. These ratios are user definable. Common ratios that could be specified in furnaces are typically the CO:CO_{2}, SO:SO_{2} and H_{2}:H_{2}O. These are not restricted to a phase and you could have the ratio of a species in one phase to a completely unrelated species in another phase if you so wished.

Pyrosim keeps count of the number of ratios which have been specified and subtracts these from the number of required composition specifications.

All these required specifications arise from the number of species present in each phase; each specie is a variable in the system of linear equations which needs to be constructed to solve the system. As this model is merely a mass balance routine what you are doing is giving Pyrosim just enough information so that it will be able to fill in all the remaining gaps.

The quantities and analyses of the feed streams are known, and once the number of specifications equals the number of remaining unknowns the system of equations can be solved (by pressing **Enter**).

The equations are formulated as follows:

- The number of unknowns equals the number of species in each phase i.e.,
*n*(this because the analyses are pre-defined and the feedrates specified). - The element balances provide
*y*equations. - Each mass or mole ratio is an equation
*r*. - Every composition is also an equation
*c*. - Once the number of equations equals the number of unknowns (
*n*=*y*+*r*+*c*) the system is soluble.

However the specification also must be mathematically independent. If you have a metal phase containing four elements, you can only make three composition specifications in this phase because the fourth specification can be inferred (as the sum of the compositions must total 100 %). Also note that composition specifications of zero percent are not acceptable as an input, (any composition of zero percent will be read by Pyrosim as an unknown and it will try and calculate a value for this variable)

If the system is not soluble the program will report the following message: *Error, try a different specification*. This means that you must change your specification and try again.

Some **rules of thumb** are being developed:

Any element reporting to more than one phase will require (*n-1*) specifications, where *n* is the number of components. This is true for all components except one, which will require (*n-2*) specifications.

If the program calculates **negative flowrates** it implies that the quantity of an element (available in the feed streams) is insufficient to satisfy the requirements according to the specifications you have made. This means that some changes may be necessary, either to the feed quantities, or to the specifications made. For example, when analysing the mass balance of a matte smelter we consistently got negative flowrates for sulphur in the system. We eventually found that the feed assays were erroneous and that the sulphur in the feed was greater than that which was originally reported.

Empirical balance models are not trivial to configure, but, once defined, these models can rapidly evaluate mass and energy balances.

This model has been applied to verfiying mass flows (when few measurements are made).

Pyrometallurgy Division, Mintek,

200 Hans Strijdom Drive, Randburg, 2125, South Africa

Private Bag X3015, Randburg, 2125, South Africa.

Phone: +27 (11) 709-4642

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Copyright © 1996-97 George la Grange, Mintek, glg@pyro.mintek.ac.za
19 June 2001*