An improved analytical method for the design of spiral-wound modules

Modeling of flat-sheet and spiral-wound nanofiltration configurations and its application in seawater nanofiltration

“…For the mass transfer coefficient, the expression given by [29,30] for spiral wound membranes (which includes the effect of spacers) was used as given by Eq.…”

Modeling of flat-sheet and spiral-wound nanofiltration configurations and its application in seawater nanofiltration

“…For the mass transfer coefficient, the expression given by [29,30] for spiral wound membranes (which includes the effect of spacers) was used as given by Eq.…”

Capillary hollow fiber nanofiltration membranes

“…Table 5 summarizes the parameters at which both modules were operated. The mass transfer coefficients and the concentration polarization modulus for the rejection of MgSO 4 are estimated from experimental rejection data procedures described in literature [5,6]. The data indicate higher mass transfer coefficients for the spiral-wound module and higher susceptibility for concentration polarization for the hollow fiber module.…”

Mathematical Analysis of the Meso-Scale Flow Field in Spiral-Wound Membrane Modules

“…Over the years several approximate analytical solutions have been proposed for particular problem formulations, either for the pure hydrodynamics problem or as part of modeling the filtration operation. − In the general case, these equations must be solved numerically, but according to the suggestion of Aris an equation must be first analyzed mathematically in order to derive all possible simplifications as well as analytical and asymptotic results, and, thus, understand the structure of the problem. This knowledge is usually important even for the appropriate numerical handling of the problem.…”

Modeling of flat-sheet and spiral-wound nanofiltration configurations and its application in seawater nanofiltration

“…For the mass transfer coefficient, the expression given by [29,30] for spiral wound membranes (which includes the effect of spacers) was used as given by Eq.…”

Capillary hollow fiber nanofiltration membranes

“…Table 5 summarizes the parameters at which both modules were operated. The mass transfer coefficients and the concentration polarization modulus for the rejection of MgSO 4 are estimated from experimental rejection data procedures described in literature [5,6]. The data indicate higher mass transfer coefficients for the spiral-wound module and higher susceptibility for concentration polarization for the hollow fiber module.…”

Mathematical Analysis of the Meso-Scale Flow Field in Spiral-Wound Membrane Modules

“…Over the years several approximate analytical solutions have been proposed for particular problem formulations, either for the pure hydrodynamics problem or as part of modeling the filtration operation. − In the general case, these equations must be solved numerically, but according to the suggestion of Aris an equation must be first analyzed mathematically in order to derive all possible simplifications as well as analytical and asymptotic results, and, thus, understand the structure of the problem. This knowledge is usually important even for the appropriate numerical handling of the problem.…”

Modeling of flat-sheet and spiral-wound nanofiltration configurations and its application in seawater nanofiltration

“…For the mass transfer coefficient, the expression given by [29,30] for spiral wound membranes (which includes the effect of spacers) was used as given by Eq.…”

Capillary hollow fiber nanofiltration membranes

“…Table 5 summarizes the parameters at which both modules were operated. The mass transfer coefficients and the concentration polarization modulus for the rejection of MgSO 4 are estimated from experimental rejection data procedures described in literature [5,6]. The data indicate higher mass transfer coefficients for the spiral-wound module and higher susceptibility for concentration polarization for the hollow fiber module.…”

Mathematical Analysis of the Meso-Scale Flow Field in Spiral-Wound Membrane Modules

“…Over the years several approximate analytical solutions have been proposed for particular problem formulations, either for the pure hydrodynamics problem or as part of modeling the filtration operation. − In the general case, these equations must be solved numerically, but according to the suggestion of Aris an equation must be first analyzed mathematically in order to derive all possible simplifications as well as analytical and asymptotic results, and, thus, understand the structure of the problem. This knowledge is usually important even for the appropriate numerical handling of the problem.…”