The Bureau of Mines, in its alumina miniplant project to investigate alumina recovery from domestic, nonbauxitic ores, has conducted research on the use of a hydrochloric acid leaching, gas sparging crystallization technology. An important element of this research is the efficient separation of undissolved, siliceous residue from alcl3-bearing leach liquors by continuous, horizontal, countercurrent vacuum belt filtration. In an effort to calculate material balances quickly and to predict material balances based on different belt filtration configurations, the perfect-mixing-cells- in-series model (pmcs) for calculating material balances around belt filters was used. Because of the porous nature of the solids, the model produced erroneous material balances. Therefore a reliable model, the shrinking voids model, was developed postulating the presence of an unwashable voids liquor volume that decreases with decreasing liquor alcl3 concentration. This volume decrease postulation is equivalent to assuming that dilute liquors flow more freely, causing more voids liquor volume to become washable. Least- squares based computer programs are provided, which are useful not only in producing material balances from plant data but also in predicting balances for untested configurations using the same feed materials.