Solute Transport in Hemodiafiltration: A New Mathematical Model to Analyse Dialyser Performance

Author(s):  
H. H. Vincent ◽  
M. C. Vos ◽  
W. A. van Duyl
1987 ◽  
Vol 252 (3) ◽  
pp. F393-F402 ◽  
Author(s):  
J. Taniguchi ◽  
K. Tabei ◽  
M. Imai

We simulated profiles of water and solute transport along the descending limb of the long-loop nephron by a mathematical model based on mass balance equations for water, sodium, potassium, and urea, using phenomenological coefficients reported for hamsters. We assumed that interstitial concentration of sodium, potassium, and urea increased linearly along the descending limb from 150 to 350, from 5 to 50, and from 5 to 300 mM, respectively. Under this condition an increase in osmolality at the end-descending limb was mainly accounted for by the absorption of water. Considerable amounts of potassium and urea were secreted along the descending limb. Sodium was reabsorbed rather than secreted along the descending limb by both diffusion and solvent drag. The secreted amounts of urea and potassium were comparable to those observed by micropuncture studies. The sodium concentration in the lumen was higher than in the interstitium, with the transmural sodium gradient being 15 meq/liter at the hairpin turn. The potassium mass flow rate at the end-descending limb increased by 2.4 times. Large variations in potassium concentration of the delivered fluid scarcely changed the potassium mass flow rate at the end-descending limb. The secretion of urea and potassium and the reabsorption of sodium were increased as a function of delivered flow rate. An increase in corticomedullary urea gradient decreased the net potassium secretion along the descending limb. When the transport parameters for rabbits were used, both reabsorption of sodium and addition of urea were decreased, but a similar amount of potassium was secreted. These analyses indicate that the mathematical model that takes the species difference and internephron heterogeneity into consideration is useful in illustrating the transport processes along the descending limb of Henle's loop under various physiological and pathophysiological conditions.


2007 ◽  
Vol 21 (6) ◽  
Author(s):  
Wei Chieh Huang ◽  
Chris Clause ◽  
Peter Brink ◽  
Benjamin Walcott ◽  
Leon C Moore

1999 ◽  
Vol 21 (3) ◽  
pp. 156-164
Author(s):  
Nguyen Phi Khu

In this paper a model for solute transport in groundwater, including physic-co-mathematical basis, numerical method some simple example simulations is briefly presented. This model has been gradually improved in both simulation and methodology.


2016 ◽  
Vol 13 (2) ◽  
pp. 48-57
Author(s):  
Baghdad Science Journal

In this study, a mathematical model for the kinetics of solute transport in liquid membrane systems (LMSs) has been formulated. This model merged the mechanisms of consecutive and reversible processes with a “semi-derived” diffusion expression, resulting in equations that describe solute concentrations in the three sections (donor, acceptor and membrane). These equations have been refined into linear forms, which are satisfying in the special conditions for simplification obtaining the important kinetic constants of the process experimentally.


SPE Journal ◽  
2017 ◽  
Vol 23 (03) ◽  
pp. 704-718 ◽  
Author(s):  
A.. Padin ◽  
M. A. Torcuk ◽  
D.. Katsuki ◽  
H.. Kazemi ◽  
A. N. Tutuncu

Summary The objective of this research is to determine the physicochemical processes underlying water and solute transport in organic-rich source rocks. To achieve this goal, a custom-designed experimental apparatus was constructed to conduct flow tests, founded on a high-pressure triaxial assembly. The apparatus is capable of maintaining core samples at reservoir pressure, temperature, and confining stress. We conducted several 120-day low-salinity osmotic tests in low-clay, organic-rich Eagle Ford carbonate-shale samples. Test results showed gradual, slow increase of pressure within the samples. Because this pressure behavior could not be explained properly with classical models, we formulated a mass-transport mathematical model that relies on fundamental chemical osmosis principles driving low-salinity brine into high-salinity core samples. Our mathematical model was articulated to simulate flow into the core as a 3D porous medium rather than transport across a thin, molecule-selective membrane. The model is dependent on the following principles: The low-salinity brine selectively enters the pores by diffusion mass transport, and the pre-existing, ionized dissolved salt molecules within the core are restrained by internal electrostatic forces to counterdiffuse in the direction opposite to that of the low-salinity-brine molecules entering the pore network. Critical model input data, such as permeability, porosity, and rock compressibility, were obtained from flow experiments on twin cores, and the diffusion coefficient was chosen by history matching. The strengths of the numerical simulation include reliance on mass-transport fundamental principles; not requiring the use of an ambiguously defined membrane-efficiency term; and relying on chemical-potential gradient as the driving force for the low-salinity brine to enter the high-salinity core, generating osmotic pressure within the pore network. The latter implies that osmotic pressure is the consequence of water entering the cores, not the cause. Results of this research have provided a more plausible explanation of pore-scale mass transport in organic-rich shales, and provide useful insights for design of effective enhanced-oil-recovery (EOR) processes.


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