The Study Of Porosity Of Cake Layer Of MBR Based On The Collapsed Body-centered Cubic Sphere Packing Model

Membrane bioreactor (MBR), using membrane filter technology, is a new technology for wastewater treatment. The membrane fouling is the major problem restricting widespread application of MBR. Hitherto, former researches only focused on the change of membrane flux and trans-membrane pressure (TMP), or the qualitative analysis of extracelluar polymeric substances (EPS) and soluble microbial products (SMP) etc. However, the micro mechanism of membrane fouling and quantitative description of cake layer is rarely investigated. In this paper, in order to obtain a better understanding of the cake layer formation mechanism in the flocculants added MBRs, we developed a model on the basis of particle packing model considering cake collapse effect and a frictional force balance equation to predict the porosity and permeability of the cake layers. The important characteristic parameters of the floes (e.g., floc size, fractal dimensions) and operating parameters of MBRs (e.g., transmembrane pressure, cross-flow velocity) are considered in this model for the possibility of practical application.The main research conclusions are performed as follows:(1) Using the method of solid geometry and calculus, expressions of∈inter,∈intra c,∈cake and a with different ranges of drel (1> drel≥0.866,0.866＞drel≥0.816,0.816＞drel≥0.813 and drel＜0.813) on the basis of body-centered cubic packing model considering cake collapse effect was developed. Monte Carlo method confirmed the truth of the mathematical formula (R2=0.98).(2) A frictional force balance equation, which related drel with the important operating parameters of MBRs (e.g., transmembrane pressure, cross-flow velocity), was established:k(1-drel)da+1.257 x 10-12(dau)1/3+13.072d7/3au+1.061 x 109d4au2-k'ΔP=0.The values of k and k'was 1.23×10-3 N/Pa and 6.71×10-12 N/m, respectively.(3) Many crucial operating parameters played an important role for the properties of aggregate and cake layer. The fractal dimensions of aggregates decrease upon increasing the cross-flow velocity. The specific cake resistances increase gradually with increasing transmembrane pressure under constant cross-flow velocity. The cross-flow velocity increases under constant transmembrane pressure, the specific cake resistances decline slightly at the beginning and then increase progressively. When transmembrane pressure is 4904 Pa, cross-flow velocity has little effect on specific cake resistances; when the pressure rises to 7846 Pa, however, overhigh cross-flow velocity leads to significantly increasing cake resistance.(4) The values of∈cake,model were in good agreement with the values of∈cake,CLSM under various conditions. This result indicated that the model was a reliable and useful tool to calculate the specific cake resistances.(5) When the cake collapse effect was not considered, the model underpredicted the experimental data notably. In a word, the cake collapse effect should be thought over when analyzing and estimating the permeability of a cake layer in MBRs.