Numerical simulation of heat and mass transfer in direct membrane distillation in a hollow fiber module with laminar flow

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Abstract

The heat and mass transfer processes in direct contact membrane distillation (MD) under laminar flow conditions have been analyzed by computational fluid dynamics (CFD). A two-dimensional heat transfer model was developed by coupling the latent heat, which is generated during the MD process, into the energy conservation equation. In combination with the Navies–Stokes equations, the thermal boundary layer build-up, membrane wall temperatures, temperature polarization coefficient (TPC), local heat transfer coefficients, local mass fluxes as well as the thermal efficiency, etc. were predicted under counter-current flow conditions. The overall performance predicted by the model, in terms of fluxes and temperatures, was verified by single hollow fiber experiments with feed in the shell and permeate in the lumen.

Simulations using the model provide insights into counter-current direct contact MD. Based on the predicted temperature profiles, the local heat fluxes are found to increase and then decrease along the fiber length. The deviation of the membrane wall temperature from the fluid bulk phase on the feed and the permeate sides predicts the temperature polarization (TP) effect. The TP coefficient decreases initially and then increase along the fiber length. It is also found that the local Nusselt numbers (Nu) present the highest values at the entrances of the feed/permeate sides. Under the assumed operating conditions, the feed side heat transfer coefficients hf are typically half the hp in the permeate side, suggesting that the shell-side hydrodynamics play an important role in improving the heat transfer in this MD configuration. The model also shows how the mass transfer rate and the thermal efficiency are affected by the operating conditions. Operating the module at higher feed/permeate circulation velocities enhances transmembrane flux; however, the thermal efficiency decreases due to the greater heat loss at a higher permeate velocity. The current study suggests that the CFD simulations can provide qualitative predictions on the influences of various factors on MD performance, which can guide future work on the hollow fiber module design, module scale-up and process optimization to facilitate MD commercialization.

Highlights

CFD simulations were conducted to analyze heat and mass transfers in DCMD process. ► The newly developed model was firstly verified by experiments. ► Temperature polarization coefficient decreased and then increased along fiber length. ► Hydrodynamics in feed side play an important role in improving the heat transfer. ► A trade-off relationship exists between mass transfer rate and thermal efficiency.

Introduction

Membrane distillation (MD), a thermally driven process that integrates mass and heat transfers for high-quality water production, is an emerging technology for seawater desalination. Amongst the four typical MD configurations, direct contact membrane distillation (DCMD) attracts the most attention as no external devices are needed for permeate condensation. With the spike in energy prices in recent years, the MD process has become a potential substitution for the conventional desalination technologies such as reverse osmosis (RO), provided there is access to waste heat. However, there remain several major obstacles to the widespread commercialization of MD process, which include the relatively low permeate flux and low thermal efficiency of MD modules [1].

To properly understand the complicated combination of mass and heat transfers in the MD process, the temperature distributions adjacent to the membrane surfaces along the module length should be fully described. Unfortunately, it is impossible to attain temperature information via the most widely used non-intrusive experimental approaches such as the flow visualization with dye, Particle Image Velocimetry (PIV) and Direct Observation through the Membrane (DOTM), etc. These observational techniques are not able to provide sufficient flow and thermal field information in the boundary layers [2]. To acquire heat transfer coefficients in the MD process, some researchers [3] have replaced the membranes with aluminum film and others [4], [5], [6], [7], [8] have conducted mathematical modeling using semi-empirical correlations and resistance-in-series model to predict the temperature distributions.

However, the efficacy of these semi-empirical correlations has been questioned recently. This is mainly because the correlations used were developed based on non-porous and rigid tube–shell heat exchangers which are not coupled with mass transfer [1]. Also, the variations of the temperature distribution along the module length have been ignored by treating the hollow fiber module as a whole heat transfer unit. In the radial direction, the temperature distributions have been simplified as mean fluid temperatures and membrane surface temperatures calculated based on boundary layer development, and these mean values were used to explain the temperature polarization effect [4], [9], [10]. Since the heat transfer coefficients, especially under low permeate flux, are strongly affected by the accuracy and applicability of these semi-empirical correlations, efforts have been made to modify the model parameters to improve the accuracy of the empirical correlations [11].

Basically, the empirical correlations and conservation equations used in earlier studies provided simplified one dimensional solutions. To further improve model applicability and accuracy, computational fluid dynamics (CFD) simulations involving Navier–Strokes equations in two dimensional (2D) and three dimensional (3D) domains have been employed to provide more reliable and comprehensive information on flow fields. For example, Charfi et al. [12] have used numerous submodels, such as the Ergun model, Knudsen-molecular diffusion model, momentum/energy and mass transport equations, in their CFD modeling to study the heat and mass transfer in the sweeping gas membrane distillation process. However, this model is rather complicated for industrial applications due to its high computational workload.

Commonly used simplifications for numerical simulation of the mass transfer process include estimating the mass transfer coefficients using empirical equations [13], assuming a constant mass flux condition [14], or applying Henry's law constant to describe the equilibrium state of the targeted compound partitioning between water and the membrane phases [14]. Zhang et al. [15], [16] suggested treat the transfer processes associated with the membrane and two surrounding fluids as a conjugate problem, and they have simulated the heat and mass transfer in membrane-based ventilators without considering phase changes. More widely used CFD models ignored the permeate flow and only focused on the mass/heat transfer in the bulk feed flow and/or simplify the transfer model across the membranes [2]. In summary, there has been no report on CFD modeling of all three simultaneous heat transfer steps taking place in the feed, permeate and membrane, respectively, in the DCMD process.

The present work describes CFD simulations that couple the Navies–Stokes equations with the energy conservation equation in a two-dimensional domain to describe the hydrodynamic and thermal conditions in a single hollow fiber module with laminar flow for DCMD process. A newly developed heat transfer model, which allows the latent heat transfer due to the evaporation/condensation processes during the MD process, but ignores the transmembrane mass flux itself, has been used to estimate the heat transfer coefficients at different fluid conditions, temperature profiles, temperature polarization coefficients (TPC), mass flux distribution, heat loss and MD thermal efficiency. The aim of this work is to provide a deeper insight into the heat and mass transfer phenomena in the DCMD process and to guide further optimization of MD operation for performance enhancement.

Section snippets

Governing transport equations and boundary conditions

In general, the DCMD process can be described by three steps: (1) vapor evaporates on the feed side at the membrane surface; (2) vapor crosses the membrane; (3) vapor condenses on the permeate side near membrane surface. The transmembrane mass flux is the key issue in the MD process. However, it should be noted that the transmembrane mass flux of a single fiber has a negligible contribution to both the feed and permeate when compared to the operating feed flow rate. For example, the typical

Experimental

This section describes measurements and experiments used to validate the CFD simulation model.

Comparison between experimental data and simulation results

Firstly, the simulated average bulk temperatures were compared with the experimental results to verify the validity of the newly built heat transfer model. The experimental data and the simulation results are listed in Table 4, where Tfo, and Tpo are bulk temperatures at the exits of the feed side and the permeate side, respectively. The simulation conditions were the same as that listed in Section 3.2. It can be seen that the simulation data agrees well with the experimental values. The

Conclusions

A two-dimensional heat transfer model has been established for the DCMD process. Based on single-fiber module tests, the validity of the CFD model was verified. Using this model, numerical simulations of the thermal boundary layer build-up, membrane wall temperatures, TPC, local heat transfer coefficients, local mass fluxes as well as the thermal efficiency, etc. along the hollow fiber module length have been conducted and the results are discussed in details.

Based on the temperature profiles

Acknowledgments

Support from Siemens Water Technology is gratefully acknowledged. The authors also thank the Singapore Economic Development Board (EDB) for funding the Singapore Membrane Technology Centre (SMTC) where this study was performed.

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