A porous media approach based on the volume-averaging theory has been proposed to investigate solute diffusion and ultrafiltration processes associated with hemodialysis using a hollow fiber membrane dialyzer. A general set of macroscopic governing equations has been derived for the three individual phases, namely, the blood phase, the dialysate phase, and the membrane phase. Thus, conservations of mass, momentum, and species are considered for blood compartments, dialysate compartments, and membranes within a dialyzer to establish a three concentration equation model. These macroscopic equations can be simultaneously solved for the various cases of inlet velocities of blood and dialysate. An analytic expression for the solute clearance was obtained for the one-dimensional case, in which important dimensionless parameters controlling the dialyzer system are identified for the first time.
Issue Section:
Porous Media
References
1.
Kedem
, O.
, and Katchalsky
, A.
, 1958, “Thermodynamics Analysis of the Permeability of Biological Membranes to Non-Electrolytes
,” Biochim. Biophys. Acta
, 27
, pp. 229
–246
.2.
Lu
, J.-F.
, and Lu
, W.-Q.
, 2010, “A Numerical Simulation for Mass Transfer Through the Porous Membrane of Parallel Straight Channels
,” Int. J. Heat Mass Transfer
, 53
, pp. 2404
–2413
.3.
Tu
, J.-W.
, Ho
, C.-D.
, and Chuang
, C.-J.
, 2009, “Effect of Ultrafiltration on the Mass-Transfer Efficiency Improvement in a Parallel-Plate Countercurrent Dialysis System
,” Desalination
, 242
, pp. 70
–83
.4.
Tu
, J.-W.
, Ho
, C.-D.
, and Yeh
, H.-M.
, 2006, “The Analytical and Experimental Studies of the Parallel-Plate Concurrent Dialysis System Coupled With Ultrafiltration
,” J. Membr. Sci.
, 281
, pp. 676
–684
.5.
Yeh
, H. M.
, 2009, “Numerical Analysis of Mass Transfer in Double-Pass Parallel-Pale Dialyzers With External Recycle
,” Comput. Chem. Eng.
, 33
, pp. 815
–821
.6.
Legallais
, C.
, Catapano
, G.
, Von Harten
, B.
, and Baurmeister
, U.
, 2000, “A Theoretical Model to Predict the Vitro Performance of Hemodiafilters
,” J. Membr. Sci.
, 168
, pp. 3
–15
.7.
Palaty
, Z.
, Zakova
, A.
, and Petrik
, P.
, 2006, “A Simple Treatment of Mass Transfer Data in Continuous Dialyzer
,” Chem. Eng. Proc.
, 45
, pp. 806
–811
.8.
Galach
, M.
, Ciechanowska
, A.
, Sabalinska
, S.
, Waniewski
, J.
, Wojcicki
, J.
, and Werynski
, A.
, 2003, “Impact of Convective Transport on Dialyzer Clearance
,” J. Artif. Organs
, 6
, pp. 42
–48
.9.
Yeh
, H. M.
, Cheng
, T.-W.
, and Wu
, H.-H.
, 1998, “Membrane Ultrafiltration in Hollow-Fiber Module With the Consideration of Pressure Declination Along the Fibers
,” Sep. Purif. Technol.
, 13
, pp. 171
–180
.10.
Sigdell
, J. E.
, 1982, “Calculation of Combined Diffusive and Convective Mass Transfer
,” Int.J. Artif. Organs
, 5
(6
), pp. 361
–372
.11.
Waniewski
, J.
, 2006, “Mathematical Modelling of Fluid and Solute Transport in Hemodialysis and Peritoneal Dialysis
,” J. Membr. Sci.
, 274
, pp. 24
–37
.12.
Ding
, W.-P.
, He
, L.-Q.
, Zhao
, G.
, Zhang
, H.-F.
, Shu
Z.-Q.
, and Gao
, D.-Y.
, 2004, “Double Porous Media Model for Mass Transfer of Hemodialyzers
,” Int. J. Heat Mass Transfer
, 47
, pp. 4849
–4855
.13.
Shirazian
, S.
, Moghadassi
, A.
, and Moradi
, S.
, 2009, “Numerical Simulation of Mass Transfer in Gas-Liquid Hollow Fiber Membrane Contactors for Laminar Flow Conditions
,” Simul. Modell. Pract. Theory
, 17
, pp. 708
–718
.14.
Wang
, Y.
, Brannock
, M.
, Cox
, S.
, and Leslie
, G.
, 2010, “CFD Simulations of Membrane Filtration Zone in a Submerged Hollow Fiber Membrane Bioreactor Using a Porous Media Approach
,” J. Membr. Sci.
, 363
, pp. 57
–66
.15.
Kumar
, V.
, and Upadhyay
, S. N.
, 2000, “Computer Simulation of Membrane Processes: Ultrafiltration and Dialysis Units
,” Comput. Chem. Eng.
, 23
, pp. 1713
–1724
.16.
Cheng
, P.
, 1978, “Heat Transfer in Geothermal Systems
,” Advances in Heat Transfer
, Vol. 14
, Academic Press
, New York
, pp. 1
–105
.17.
Quintard
, M.
, and Whitaker
, S.
, 1993, “One and Two Equation Models for Transient Diffusion Processes in Two-Phase Systems
,” Adv. Heat Transfer
, 23
, pp. 369
–465
.18.
Nakayama
, A.
, 1995, PC-Aided Numerical Heat Transfer and Convective Flow
, CRC Press
, Boca Raton, FL
.19.
Vafai
, K.
, and Tien
, C. L.
, 1981, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media
,” Int. J. Heat Mass Transfer
, 24
, pp. 195
–203
.20.
Nakayama
, A.
, and Kuwahara
, F.
, 2008, “A General Bioheat Transfer Model Based on the Theory of Porous Media
,” Int. J. Heat Mass Transfer
, 51
, pp. 3190
–3199
.21.
Nakayama
, A.
, Kuwahara
, F.
, and Kodama
, Y.
, 2006, “An Equation for Thermal Dispersion Flux Transport and Its Mathematical Modelling for Heat and Fluid Flow in a Porous Medium
,” J. Fluid Mech.
, 563
, pp. 81
–96
.22.
Kuwahara
, F.
, Nakayama
, A.
, and Koyama
, H.
, 1996, “A Numerical Study of Thermal Dispersion in Porous Media
,” ASME J. Heat Transfer
, 118
, pp. 756
–761
.23.
Yang
, C.
, and Nakayama
, A.
, 2010, “A Synthesis of Tortuosity and Dispersion in Effective Thermal Conductivity
,” Int. J. Heat Mass Transfer
, 53
(15–16), pp. 3222
–3230
.24.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2009, “Forced Convection With Counterflow in a Circular Tube Occupied by a Porous Medium
,” J. Porous Media
, 12
, pp. 657
–666
.25.
Waniewski
, J.
, Werynski
, A.
, Ahrenholtz
, P.
, Lucjanek
, O.
, Judycki
, W.
, and Esther
, G.
, 1991, “Theoretical Basis and Experimental Verification of the Impact of Ultrafiltration on Dialyzer Clearance
,” Artif. Organs
, 15
, pp. 70
–77
.26.
Jaffrin
, M. Y.
, Ding
, L.
, and Laurent
, J. M.
, 1990, “Simultaneous Convective and Diffusive Mass Transfer in a Hemodialyzer
,” J. Biomech. Eng.
, 112
, pp. 212
–219
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
