Filter cake yield equation using lmt dimensional analyses

An equation expressing filterability in terms of Filter Cake Yield has been derived using Buckingham- method of LMT Dimensional Analysis. The model equation developed (Equation 27) shows that the cake yield from a filter press is directly proportional to the filter area of the pressure vessel, applied pressure and initial solids content of the sludge while being inversely proportional to specific resistance of the filtrate, viscosity of filtrate, compressibility coefficient of the sludge and pressing time. This is in agreement with scientific reasoning and experimental observation. The new equation enables performance of a pressure filter (Filter Press) to be predicted from a simple laboratory determination of cake yields. Curves derived from the model show how filter cake yield depends on a number of these parameters, for instance, figures 3,4,5 and 6 respectively illustrates the effects of pressing time, pressures, conditioner dosages and initial solids content on the filter cake yield. It was observed that increasing ferric chloride dosage from 11.87% to 22.61% increased filter cake yield from 3.785 x 10-4g/Cm2.S to 4.4118 x 10-4g/Cm2.S while reducing specific resistance from 1.7372 x 1010Cm/g to 1.5940 x 1010Cm/g. The optimum dosages from the graph to attain acceptable filtrate quality is 19.63% for an operating pressure of 6628.18g/Cm2. Considering the differences in the parameters tested, it is significant that they all responded similarly when compared with previous research works. Moreover, experimental verification of the equation and the derived curves has been described and it may be concluded that for practical purposes, the predicted performance agrees with measured values with a correlation coefficient of 0.998. Although, the scope of the experimental verification was somewhat limited, it was sufficient enough to demonstrate the use of the equation and curves derived in this study. The method can be applied in predicting full-scale performance for any sludge from laboratory experiments and the procedure has been fully described and comparatively analyzed.