| A fundamental study was conducted to examine concentration polarization (CP) and membrane fouling (MF)on an unstirred, one-dimensional (batch) reverse osmosis membrane process. A discrete-time finite element Galerkin method was employed to solve the nonlinear partial differential equation which arises from a mass balance. The model was developed to solve the problem for 1 or 2 non-interactive components. The formulation assumes that one component may be sparingly soluble. Particle formation, growth, and transport phenomena were incorporated. The one dimensional model was extended to consider two dimensional, steady state flow; axial diffusion was neglected. The one dimensional model was also formulated to predict membrane performance for a charged membrane, assuming that the membrane could be represented by an infinite sheet of charge. The solution diffusion (SD) model was used to describe water transport through the membrane. The standard expression was modified to include both osmotic pressure effects and flow resistance due to a fouling layer.; Solutions of NaCl, Na{dollar}sb{lcub}2{rcub}{dollar}SO{dollar}sb{lcub}4{rcub}{dollar}, PbSO{dollar}sb{lcub}4{rcub}{dollar}, Zn(OH){dollar}sb{lcub}2{rcub}{dollar}, and trichlorophenol (TCP)were studied experimentally. The model could predict the water flux quite well, with typical errors of 2-8% for most solutes. Errors of 15-30% occurred in the prediction of certain Zn(OH){dollar}sb{lcub}2{rcub}{dollar} data. This was due to variations in the morphology of flocculated precipitate. Prediction of permeate concentration data showed that a correction factor had to be applied to correct the time values used, due to membrane cell construction resulting in permeate dilution. Typical errors were 5-10%. Prediction of permeate data for the charged membrane case showed that the solute transport coefficient, B, in general may not be constant.; Oil shale retort wastewater treatment was studied. These waters had high-concentrations of ammonia, chloride, phenols, free and emulsified oils, etc. Membranes, coupled with conventional pretreatment steps, such as organics adsorption by activated carbon, were effective at removing up to 85-90% of the contaminants at water recoveries of 90%. Flux could be predicted to within 5-15%. Larger errors were due to the model being formulated for fouling precipitates which are discrete spheres, rather than oils or other macromolecules. |
