Simulation of momentum, heat and mass transfer in direct contact membrane distillation: A computational fluid dynamics approach

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Highlights

  • The effects of Knudsen diffusion, free molecular diffusion and viscous flow in a CFD model were considered.

  • Quantitative comparison of two MD configurations was performed.

  • The effects of different parameters on temperature polarization coefficient were studied.

  • Concentration polarization in DCMD was considered.

  • A fast algorithm for initial guess preparation was proposed.

Abstract

Membrane distillation is one of the newest methods for water purification. In this study, the behavior of direct contact membrane distillation (DCMD) process under various operating conditions was mathematically modeled using computational fluid dynamics (CFD) method. The effects of different parameters on transmembrane flux and temperature polarization coefficient (TPC) were measured by global sensitivity analysis technique. The sensitivity analysis results indicated that the most affecting design parameters in DCMD are membrane thickness and feed temperature.

Introduction

Membrane distillation (MD) is a fairly new process that is expected to be a competitive desalination process in the near future [1], [2], [3], [4]. The main advantages of MD can be mentioned as low operating pressure, theoretically complete rejection of ions and other non-volatiles and accommodating high separation area compared to conventional thermal techniques. The only function of membrane is to support a vapor–liquid interface, and it does not contribute in separation mechanism [5]. Direct contact membrane distillation (DCMD) is known as a type of MD which requires less auxiliary unit operations such as condenser compared to other configurations. In DCMD, a porous hydrophobic membrane with liquids in direct contact with both surfaces of the membrane is used [6], [7]. Mass transfer driving force is the vapor pressure difference caused by temperature difference of different streams on each side of the membrane [7].

Tang et al. [8] developed a CFD model for a single fiber in a hollow fiber module. They assumed that heat transfer has no effect in this process. Therefore, the fluid mechanic properties could be investigated in their model. Yu et al. [9] studied the effect of turbulence promoters on tubular membranes in DCMD process with CFD approach. They solved heat and momentum transfer equations simultaneously and assumed that mass transfer is independent from them. Ghadiri et al. [10] presented a comprehensive two dimensional model and considered different transport phenomena for DCMD in a flat sheet membrane module. However, the effect of concentration polarization was not considered in their model. They used COMSOL, which is a finite element based software package, to solve the complicated equations in the model.

It seems that development of a model including all transport phenomena and solving fluid properties simultaneously are essential. In the present study, a two dimensional axisymmetric model is presented for modeling of DCMD in a hollow fiber module. Simulation cell geometry is determined by Happel's free surface model. Raoult's law is applied to predict vapor pressure. Both convective and conductive contributions of heat and mass transfer are considered along the membrane. Effect of feed concentration on the feed membrane interface is also investigated. The developed model is capable to compute surficial temperature of membrane. Therefore effects of different parameters on temperature polarization coefficient can be predicated. In addition, global sensitivity analysis is carried out to quantify the contributions of the main design parameters.

Section snippets

Model development

The experimental data reported by Bonyadi et al. [11] for DCMD is used to validate the simulation. For the corresponding experiments, a hollow fiber module with 10 PVDF hollow fibers was used. The hot feed solution was circulated outside the fiber, while the cold sweeping permeate was flowed co-currently inside the fiber. Inlet feed solution consisted of 3.5 wt% NaCl solution. Inlet permeate temperature (Tp) was kept at 17 °C in all the experiments. Thickness, pore diameter, porosity and length

Results and discussion

A comparison between experimental results and model predictions is presented in Fig. 1. A good agreement between experimental and simulation data is shown in Fig. 1 (average deviation between simulated results and experimental results is 12%). Simulation results indicate that the viscous flow contribute in less than 5% of the total mass transfer across the membrane, while more than 95% of mass transfer is carried out by the combination of Knudsen and free diffusion flow.

Temperature distribution

Conclusion

A simulation based on CFD techniques was carried out in this simulation. The simulation results were in a good agreement with the experimental results. Global sensitivity analysis was also performed for five parameters; membrane thickness, feed temperature, feed flow rate, permeate flow rate and feed concentration. The results obtained by this analysis are concluded as following:

  • -

    Contribution of viscous flow across the membrane compared to diffusive flow is negligible.

  • -

    Membrane thickness and feed

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