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Flat sheet direct contact membrane distillation desalination system using temperature-dependent correlations: thermal efficiency via a multi-parameter sensitivity analysis based on Monte Carlo method

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Abstract

In this paper, a 1D model of direct contact membrane distillation is presented in which all fluid properties are temperature-dependent. In addition, a Nusselt number (Nu) relationship for developing flow in ducts (accounting for both thermal and hydrodynamic effects) is used to obtain the convective heat transfer coefficient at each side of the membrane. Simulated mass flux shows very good agreement with experimental measurements at various feed temperature, flow rate and concentration. A comprehensive sensitivity analysis of all operational and geometrical parameters, as well as Nu estimation parameters on water mass flux across the membrane \((J_{\text{m}} )\) and thermal efficiency, is also done. To determine the relative importance of each parameter, a multi-parameter sensitivity analysis (MPSA) based on the Monte Carlo method is applied, and the sensitivity index of each parameter at the defined range is computed. Results show that \(J_{\text{m}}\) is highly sensitive to bulk feed inlet temperature (\(T_{{{\text{in}},{\text{f}}}}\)) while both \(J_{\text{m}}\) and thermal efficiency are highly sensitive to membrane porosity. Results show that among all parameters, just membrane porosity is highly sensitive which affects both mass flux and thermal efficiency especially at low \(T_{{{\text{in}}.{\text{f}}}}\).

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Abbreviations

A :

Cross-sectional area (m2)

B :

Membrane flux coefficient (kg m−2 Pa−1 s−1)

D :

Water diffusion coefficient (m2 s−1)

dA :

Area element (m2)

Dz :

Length element (m)

F :

Friction factor

H :

Specific enthalpy (J kg−1)

\(h_{\text{ch}}\) :

Channel height (m)

\(h_{\text{m}}\) :

Membrane thickness \((\upmu{\text{m}})\)

\(h_{\text{t}}\) :

Convective heat transfer coefficients (W m−2 K−1)

\(J_{\text{m}}\) :

Membrane water vapor mass flux (kg m−2 s−1)

K :

Gain coefficient and thermal conductivity (W m−1 K−1)

L :

Channel length (m)

M :

Blending parameter

\(M_{\text{w}}\) :

Water molecular weight (kg mol−1)

\(\dot{m}\) :

Mass flow rate (kg s−1)

P :

Pressure (Pa)

\(Q\) :

Volume flow rate (L min−1)

Q :

Heat flux (W m−2)

R :

Gas constant (J K−1 mol−1)

\(r_{\text{p}}\) :

Pore size (\(\upmu{\text{m}}\))

S :

Salinity (ppm)

T :

Temperature (K or °C)

W :

Channel width (m)

Z :

Z-axis (flow direction) (m)

\(z^{*}\) :

Dimensionless position

\(\gamma\) :

Activity coefficient and shape parameter

\(\delta\) :

Membrane thickness (\(\upmu{\text{m}}\))

\(\varepsilon\) :

Aspect ratio of duct

\(\epsilon\) :

Membrane porosity

\(\eta\) :

Thermal efficiency

\(\kappa\) :

Sensitivity index

\(\tau\) :

Membrane tortuosity

a:

Air

ave:

Average

b:

Bulk

f:

Feed

g:

Gas

in:

Inlet

m:

Membrane

p:

Permeate

s:

Solid

v:

Vapor

w:

Water

AGMD:

Air gap membrane distillation

DCMD:

Direct contact membrane distillation

MD:

Membrane distillation

MPSA:

Multi-parameter sensitivity analysis

\({\text{Nu}}\) :

Nusselt no

\({ \Pr }\) :

Prandtl no

PTFE:

Polytetrafluoroethylene

Re:

Reynolds no

SGMD:

Swiping gas membrane distillation

VMD:

Vacuum membrane distillation

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Acknowledgements

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under grant No. (24-135-35-HiCi). The authors, therefore, acknowledge technical and financial support of KAU.

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Authors and Affiliations

  1. Center of Research Excellence in Renewable Energy and Power Systems, and Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

    Yusuf A. Al-Turki

  2. Department of Physics, Faculty of Sciences, University of 20 août 1955—Skikda, B. P 26 Road El-Hadaiek, Skikda 21000, Algeria

    Fateh Mebarek-Oudina

  3. Institute of IR 4.0, The National University of Malaysia, UKM, Bangi, Selangor, Malaysia

    Ali Ahmadian

  4. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele, Romania

    Dumitru Baleanu

  6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Dumitru Baleanu

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  1. Yusuf A. Al-Turki
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  2. Fateh Mebarek-Oudina
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Correspondence to Dumitru Baleanu.

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Al-Turki, Y.A., Mebarek-Oudina, F., Ahmadian, A. et al. Flat sheet direct contact membrane distillation desalination system using temperature-dependent correlations: thermal efficiency via a multi-parameter sensitivity analysis based on Monte Carlo method. J Therm Anal Calorim 144, 2641–2652 (2021). https://doi.org/10.1007/s10973-020-10503-6

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