Modelisation of Membrane Distillation: Mass and Heat Transfer in Air Gap Membrane Distillation

Abstract

Membrane distillation (MD) is receiving recent attention as a technique to efficiently concentrate aqueous solution such as seawater. It has potential benefits of low temperature and pressure operation with high degrees of separation. In this work, the effect of the membrane thickness was studied to produce of the steam flow in the three different mass transfer mechanisms, and in the different possible combinations of its mechanisms in three different temperatures. The results have been carried using a polynomial approximation through MATLAB. A quite important increase in the flow in the model (DGM, Schofield, and KMPT) was observed with a decrease in the stream rating in the model (KMT). However, the Molecular model, DGM model, KMPT model, and Schofield model are not affected by the membrane's thickness. After, we have studied the effect of this parameter (Thickness of the membrane) on the transfer of conduction heat and latent heat. List of Symbols J v Local permeate flux at the hot side of membrane in vapor phase [Kg/m 2 .s] Ɛ Porosity of the membrane Τ Tortuosity γ p Membrane pore size [m] M v Molar mass [Kg/mol] R Universal gas constant [J/mol.K] T m Average temperature of the membrane [°C] P m Average pressure partial of the air [P a ] δ m Thickness of the membrane [m] P Pressure [P a ] D v/a Diffusion coefficient of the vapor in the vapor/air mixture [m 2 /s] µ Dynamic viscosity [Kg/m.s] P v Water vapor pressure [P a ] C s Mole fraction of NaCl hm Hot liquid/ membrane interface M Membrane mg Membrane/ air gap interface S Saline P Pores v/a Vapor/air C 1 Concentration in the feed part C 2 Concentration in the air gap part K Transfer coefficient [m/s] D eff Effective diffusion coefficient [m 2 s-1 ] R e Reynold number of the hot solution channel P r Prandlt number d h Half-width of the flow channel [m] H m Membrane length [m] T gf Temperature at the interface of hot feed and the membrane [°C] T f Feed bulk temperature [°C] T c Bulk temperature of the coolant [°C] Q s Total heat [KJ/m 2 h] Q c Flow of heat by conduction [KJ/m 2 h] Q v Latent heat flux [KJ/m 2 h] R m Gas constant of membrane [J/mol K] K cm Thermal conductivity of the materiel forming the membrane [W/m.K] K a Thermal conductivity of air [W/m.K] K m Thermal conductivity of membrane [W/m.K] J v Δh v J v Δh v Enthalpy of hot solution [J/Kg] T h Hot temperature [°C]