Long term filtration modelling and scaling up of mixed matrix ultrafiltration hollow fiber membrane: a case study of chromium(VI) removal

Mixed matrix membrane (MMM) belongs to the special class of filter where adsorptive removal of smaller sized solutes is realized by more open pore sized ultrafiltration grade membrane operated at higher throughput. Incorporation of nanoparticles having adsorption tendency towards a specific smaller sized solute in the polymer matrix is responsible for such a behavior. Since solute adsorption is the dominant mechanism of removal, the breakthrough behavior of the membrane dictates its life indicating its regeneration or eventual replacement. Thus, quantification of long time fouling behavior of a scaled up MMM filter is of utmost importance. A detailed two-dimensional transient model is formulated in this work starting from first principles using equations of continuity, motion and convective-diffusive-adsorption based solute transport for filtration through hollow fiber MMM module. The set of governing equations is solved using finite element method by COMSOL v5.3 (R) software package. A case study was considered for adsorptive removal of chromium(VI) using graphene oxide incorporated MMM hollow fibers. The model parameters were evaluated using the experimental long term filtration data of synthetic chromium(VI) solution. The same set of model parameters was used in predictive mode to quantify the long-term performance behavior of a real life chrome tanning effluent that showed remarkable predictive capability of the model in terms of throughput and rejection characteristics of chromium(VI). The validated model is further extended for simulation of large scale filter with high breakthrough volume interrelating number and length of fibers (n f and L) with the operating conditions (trans-membrane pressure drop, TMP and cross flow rates, CFR) so that the filter can sustain its performance over long period of time (i.e., long filter life). Based on the simulation, at a fixed TMP and CFR, a performance curve was generated linking n f , L and breakthrough volume of the filter that can be used as a guideline for designing of large scale filtration units with hollow fiber MMM for industrial applications. In general, the theoretical framework formulated in this work can be used as a foundation for design and scale up of any hollow fiber MMM based filtration system.