The raw materials mixture for glass melting is termed "batch".
The batch must be measured properly to achieve a given, desired glass formulation.
This batch calculation is based on the common linear regression equation:
The desired glass composition in wt% is: 67 SiO2, 12 Na2O, 10 CaO, 5 Al2O3, 1 K2O, 2 MgO, 3 B2O3, and as raw materials are used sand, trona, lime, albite, orthoclase, dolomite, and borax.
For example, the batch component SiO2 adds 1 mol SiO2 to the glass, therefore, the intersection of the first column and row shows "1".
The molarity matrix NG of the glass is simply determined by dividing the desired wt% concentrations by the appropriate molar masses, e.g., for SiO2 67/60.0843 = 1.1151.
The resulting molarity matrix of the batch, NB, is given here.
After multiplication with the appropriate molar masses of the batch ingredients one obtains the batch mass fraction matrix MB:
The matrix MB, normalized to sum up to 100% as seen above, contains the final batch composition in wt%: 39.216 sand, 16.012 trona, 10.242 lime, 16.022 albite, 4.699 orthoclase, 7.276 dolomite, 6.533 borax.
If this batch is melted to a glass, the desired composition given above is obtained.
Simple glass batch calculation can be found at the website of the University of Washington.
[5] If the number of glass and batch components is not equal, if it is impossible to exactly obtain the desired glass composition using the selected batch ingredients, or if the matrix equation is not soluble for other reasons (i.e., the rows/columns are linearly dependent), the batch composition must be determined by optimization techniques.