Glass batch calculation or glass batching is the determination of the correct mix of raw materials (batch) for a glass melt.
Principle The raw materials mixture for glass melting is termed "batch". The batch must be measured properly to achieve a desired glass formulation. This batch calculation is based on the common linear regression equation
with and being the molarities, in the form of 1-column matrices of the batch and glass components respectively, and being the batching matrix.Y. B. Peng, Xingye Lei, D. E. Day: "A computer programme for optimising batch calculations"; Glass technology, vol. 32, 1991, no. 4, p 123–130.M. M. Khaimovich, K. Yu. Subbotin: "Automation of Batch Formula Calculation"; Glass and Ceramics, vol. 62, no 3-4, March 2005, p 109–112.A. I. Priven: "Calculating batch weights with a programmable microcalculator"; Glass and Ceramics, vol. 43, no 11, November 1986, p 488–491. The symbol "T" stands for the matrix transpose operation, "−1" indicates matrix inversion, and the sign "·" denotes matrix multiplication. From the molarity matrices , percentages by weight (wt%) can easily be derived using the appropriate molar masses.
Example calculation An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67 , 12 , 10 CaO, 5 , 1 , 2 MgO, 3 , and as raw materials are used sand, trona, lime, albite, orthoclase, dolomite, and borax. The formulas and molar masses of the glass and batch components are listed in the following table:
Formula of glass component Desired concentration of glass component, wt% Molar mass of glass component, g/mol Batch component Formula of batch component Molar mass of batch component, g/mol 67 60.0843 Sand 60.0843 12 61.9789 Trona 226.0262 CaO 10 56.0774 Lime 100.0872 5 101.9613 Albite 524.4460 1 94.1960 Orthoclase 556.6631 MgO 2 40.3044 Dolomite 184.4014 3 69.6202 Borax 381.3721
The batching matrix indicates the relation of the molarity in the batch (columns) and in the glass (rows). For example, the batch component adds 1 mol to the glass; therefore, the intersection of the first column and row shows "1". Trona adds 1.5 mol to the glass; albite adds 6 mol , 1 mol , and 1 mol , and so on. For the example given above, the complete batching matrix is listed below. The molarity matrix of the glass is simply determined by dividing the desired wt% concentrations by the appropriate molar masses, e.g., for 67/60.0843 = 1.1151.
The resulting molarity matrix of the batch, , is given here. After multiplication with the appropriate molar masses of the batch ingredients one obtains the batch mass fraction matrix :
or
The matrix , 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, then the desired composition given above is obtained.See also: Free glass batch calculator During glass melting, carbon dioxide (from trona, lime, dolomite) and water (from trona, borax) evaporate.
Simple glass batch calculation can be found at the website of the University of Washington.
Advanced batch calculation by optimization 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), then the batch composition must be determined by optimization techniques.
See also Glass ingredients Calculation of glass properties
References