Modelling of a transmembrane evaporation module for desalination of seawater

Transmembrane evaporation (often called membrane distillation) carried out in a countercurrent flow module, in which incoming cold seawater is heated by the condensing product water flow, is a promising technology for low-cost seawater desalination. This paper presents a model for preliminary design calculations for such a module. The model calculates temperature profiles alongside and across the module, heat and vapour fluxes through the membrane and the total product flow. Mass transfer of the water vapour through the membrane and the air gap is described with molecular diffusion through stagnant air. Estimated properties and constants have been used to calculate the energy transport. Calculations with variable temperatures, membrane fibre diameter and diffusion distance have been performed. From the calculation results can be concluded that the model is able to describe the process of interest in a qualitative way. The calculations indicate that the highest productivity will be obtained with high temperatures, small membrane fibres and a small air gap.

A model has been developed for preliminary calculations on a countercurrent transmembrane evaporation module. The model is able to — — cp d D h Hvap J k L m M P Ptot Pmax — — — — — — — — — — — — — Q R Ru — — — s T v Y — — — — half the distance between the centre two fibres, m distance between the centre of a fibre and the cooling surface, m heat capacity of seawater, J/kg K thickness, m diffusion coefficient, m2/s heat transfer coefficient, W/m2 K heat of vaporisation of water (J/kg) water vapour flux, kg/m2 s thermal conductivity, W/m K length (height) of the module, m mass flow, kg/s molar mass of water, kg/kmol water vapour pressure, Pa total vapour pressure, Pa hydraulic pressure drop over the membrane module, Pa heat flux, J/m2 s universal gas constant, J/kmol K outside radius of the membrane fibres, m mass fraction of salt temperature, K streaming velocity, m/s air mole fraction — — membrane porosity (mean) viscosity seawater, Pa s Greek — — density of seawater, kg/m3 membrane tortuosity Subscripts ag c cp h ln m p z — — — — — — — — air gap incoming cold seawater cooling plate hot seawater log mean membrane product, pure water (layer) z-dependent