### Abstract

Although hyperfiltration has replaced many liquid phase separation equipment, it is still considered as a 'non-unit operation' process because the sizing of hyperfiltration equipment could not be calculated using either the equilibrium stage or the rate-based methods. Previous design methods using the dead-end and the complete-mixing models are unsatisfactory because the dead-end model tends to underestimate the membrane area due to the use of the feed concentration in the driving force while the complete-mixing model tends to overestimate the membrane area due to the use of the more concentrated rejection concentration in the driving force. In this paper, a cross-flow model for hyperfiltration is developed by considering mass balance at a differential element of the cross-flow module and then integrating the expression over the whole module to get the module length. Since the modelling is rate-based, the length of the module could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer units (NTU). The solution of the integral representing the NTU of hyperfiltration is found to be the difference between two hypergeometric functions. The poles of the solution represent the flux extinction curves of hyperfiltration. The NTU for hyperfiltration is found to depend on four parameters: the rejection, R, the recovery, S, the polarization, β, and the dimensionless applied pressure difference, ψ. For any given ψ and R, the recovery, S, is limited by the corresponding flux extinction curve. The NTU for hyperfiltration is found to be generally small and less than unity, but increases rapidly to infinity near the poles due to flux extinction. Polarization is found to increase the NTU and hence the length and membrane area of the hollow fibre module for hyperfiltration.

Original language | English |
---|---|

Pages (from-to) | 993-997 |

Number of pages | 5 |

Journal | Chemical Engineering Research and Design |

Volume | 82 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2004 |

### Fingerprint

### Keywords

- Cross-flow model
- Height of a transfer unit
- Hollow fibre module design
- Hyperfiltration
- Number of transfer unit
- Reverse osmosis

### ASJC Scopus subject areas

- Polymers and Plastics

### Cite this

**Rate-based design of non-fouled cross-flow hollow-fibre membrane modules for hyperfiltration.** / Wan Daud, Wan Ramli.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Rate-based design of non-fouled cross-flow hollow-fibre membrane modules for hyperfiltration

AU - Wan Daud, Wan Ramli

PY - 2004/8

Y1 - 2004/8

N2 - Although hyperfiltration has replaced many liquid phase separation equipment, it is still considered as a 'non-unit operation' process because the sizing of hyperfiltration equipment could not be calculated using either the equilibrium stage or the rate-based methods. Previous design methods using the dead-end and the complete-mixing models are unsatisfactory because the dead-end model tends to underestimate the membrane area due to the use of the feed concentration in the driving force while the complete-mixing model tends to overestimate the membrane area due to the use of the more concentrated rejection concentration in the driving force. In this paper, a cross-flow model for hyperfiltration is developed by considering mass balance at a differential element of the cross-flow module and then integrating the expression over the whole module to get the module length. Since the modelling is rate-based, the length of the module could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer units (NTU). The solution of the integral representing the NTU of hyperfiltration is found to be the difference between two hypergeometric functions. The poles of the solution represent the flux extinction curves of hyperfiltration. The NTU for hyperfiltration is found to depend on four parameters: the rejection, R, the recovery, S, the polarization, β, and the dimensionless applied pressure difference, ψ. For any given ψ and R, the recovery, S, is limited by the corresponding flux extinction curve. The NTU for hyperfiltration is found to be generally small and less than unity, but increases rapidly to infinity near the poles due to flux extinction. Polarization is found to increase the NTU and hence the length and membrane area of the hollow fibre module for hyperfiltration.

AB - Although hyperfiltration has replaced many liquid phase separation equipment, it is still considered as a 'non-unit operation' process because the sizing of hyperfiltration equipment could not be calculated using either the equilibrium stage or the rate-based methods. Previous design methods using the dead-end and the complete-mixing models are unsatisfactory because the dead-end model tends to underestimate the membrane area due to the use of the feed concentration in the driving force while the complete-mixing model tends to overestimate the membrane area due to the use of the more concentrated rejection concentration in the driving force. In this paper, a cross-flow model for hyperfiltration is developed by considering mass balance at a differential element of the cross-flow module and then integrating the expression over the whole module to get the module length. Since the modelling is rate-based, the length of the module could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer units (NTU). The solution of the integral representing the NTU of hyperfiltration is found to be the difference between two hypergeometric functions. The poles of the solution represent the flux extinction curves of hyperfiltration. The NTU for hyperfiltration is found to depend on four parameters: the rejection, R, the recovery, S, the polarization, β, and the dimensionless applied pressure difference, ψ. For any given ψ and R, the recovery, S, is limited by the corresponding flux extinction curve. The NTU for hyperfiltration is found to be generally small and less than unity, but increases rapidly to infinity near the poles due to flux extinction. Polarization is found to increase the NTU and hence the length and membrane area of the hollow fibre module for hyperfiltration.

KW - Cross-flow model

KW - Height of a transfer unit

KW - Hollow fibre module design

KW - Hyperfiltration

KW - Number of transfer unit

KW - Reverse osmosis

UR - http://www.scopus.com/inward/record.url?scp=4243128279&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243128279&partnerID=8YFLogxK

U2 - 10.1205/0263876041580721

DO - 10.1205/0263876041580721

M3 - Article

AN - SCOPUS:4243128279

VL - 82

SP - 993

EP - 997

JO - Chemical Engineering Research and Design

JF - Chemical Engineering Research and Design

SN - 0263-8762

IS - 8

ER -