Similarity analysis of membrane distillation utilizing dimensionless parameters derived from process-governing equations

There is a significant disparity in performance outcomes between the lab-scale and full-scale modules of membrane distillation (MD). Furthermore, extrapolating the performance of a lab-scale module to anticipate the performance of a large-scale MD system is misleading due to the non-linear relationship between different scales and several design and operating characteristics. By systematically analyzing and optimizing the key parameters affecting DCMD performance using dimensionless numbers, we can improve the design, operation, and scalability of DCMD systems. This approach allows for a deeper understanding of the underlying transport phenomena and achieves high-performance, energy-efficient DCMD processes. The dimensionless groups were obtained by normalizing the governing equations and compared with the π-theorem results. Some groups were adjusted, while others were redefined to clarify their physical significance. Additionally, new groups were added to be included in the DCMD, marking the first time this has been done. The Pi grouping mathematical technique resulted in the generation of seven additional dimensionless groups. The influence of dimensionless numbers on the performance of DCMD was evaluated using literature-validated data for four different scale modules. The results revealed the existence of a novel dimensionless parameter that can be employed to assess the efficiency of the spacer in the DCMD system. This work proposed two new dimensionless numbers that can define the DCMD performance, which would be vital for membrane comparison studies and DCMD scaling-up. Additionally, two correlations between heat and mass transmission in DCMD are presented, which are applicable irrespective of the size of the membrane module.