### Abstract

Although ultrafiltration has replaced many liquid phase separation equipment, it is still considered as a "non-unit operation" process because the sizing of the 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 ultrafiltration 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 modeling is rate-based, the length of both modules could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer unit (NTU). The solution of the integral representing the NTU of ultrafiltration is found to be the difference between two exponential integrals (Ei(x)). The poles of the solution represent the flux extinction curves of ultrafiltration. The NTU for ultrafiltration is found to depend on three parameters: the rejection R, the recovery S, and the dimensionless gel concentration C_{g}. For any given C_{g} and R, the recovery, S is limited by the corresponding flux extinction curve. The NTU for ultrafiltration is found to be generally small and less than unity but increases rapidly to infinity near the poles due to flux extinction. The complete-mixing model is reformulated in terms of the same parameters used in the cross-flow model. The design of membrane modules for ultrafiltration taken from case-studies of previous authors is performed using both the complete-mixing and the cross-flow models developed in this paper and a comparative study of the results is carried out. The length of the hollow fiber module and the membrane area calculated using the cross-flow model for ultrafiltration are found to be always smaller than those given by the complete-mixing model.

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

Pages (from-to) | 1221-1238 |

Number of pages | 18 |

Journal | Separation Science and Technology |

Volume | 39 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- Cross-flow model
- Height of a transfer unit
- Hollow fiber module design
- Number of transfer unit
- Ultrafiltration

### ASJC Scopus subject areas

- Chemistry(all)
- Process Chemistry and Technology
- Chemical Engineering(all)
- Filtration and Separation

### Cite this

**Rate-Based Design of Non-fouled Cross-Flow Hollow Fiber Membrane Modules for Ultrafiltration.** / Wan Daud, Wan Ramli.

Research output: Contribution to journal › Article

*Separation Science and Technology*, vol. 39, no. 6, pp. 1221-1238. https://doi.org/10.1081/SS-120030479

}

TY - JOUR

T1 - Rate-Based Design of Non-fouled Cross-Flow Hollow Fiber Membrane Modules for Ultrafiltration

AU - Wan Daud, Wan Ramli

PY - 2004

Y1 - 2004

N2 - Although ultrafiltration has replaced many liquid phase separation equipment, it is still considered as a "non-unit operation" process because the sizing of the 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 ultrafiltration 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 modeling is rate-based, the length of both modules could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer unit (NTU). The solution of the integral representing the NTU of ultrafiltration is found to be the difference between two exponential integrals (Ei(x)). The poles of the solution represent the flux extinction curves of ultrafiltration. The NTU for ultrafiltration is found to depend on three parameters: the rejection R, the recovery S, and the dimensionless gel concentration Cg. For any given Cg and R, the recovery, S is limited by the corresponding flux extinction curve. The NTU for ultrafiltration is found to be generally small and less than unity but increases rapidly to infinity near the poles due to flux extinction. The complete-mixing model is reformulated in terms of the same parameters used in the cross-flow model. The design of membrane modules for ultrafiltration taken from case-studies of previous authors is performed using both the complete-mixing and the cross-flow models developed in this paper and a comparative study of the results is carried out. The length of the hollow fiber module and the membrane area calculated using the cross-flow model for ultrafiltration are found to be always smaller than those given by the complete-mixing model.

AB - Although ultrafiltration has replaced many liquid phase separation equipment, it is still considered as a "non-unit operation" process because the sizing of the 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 ultrafiltration 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 modeling is rate-based, the length of both modules could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer unit (NTU). The solution of the integral representing the NTU of ultrafiltration is found to be the difference between two exponential integrals (Ei(x)). The poles of the solution represent the flux extinction curves of ultrafiltration. The NTU for ultrafiltration is found to depend on three parameters: the rejection R, the recovery S, and the dimensionless gel concentration Cg. For any given Cg and R, the recovery, S is limited by the corresponding flux extinction curve. The NTU for ultrafiltration is found to be generally small and less than unity but increases rapidly to infinity near the poles due to flux extinction. The complete-mixing model is reformulated in terms of the same parameters used in the cross-flow model. The design of membrane modules for ultrafiltration taken from case-studies of previous authors is performed using both the complete-mixing and the cross-flow models developed in this paper and a comparative study of the results is carried out. The length of the hollow fiber module and the membrane area calculated using the cross-flow model for ultrafiltration are found to be always smaller than those given by the complete-mixing model.

KW - Cross-flow model

KW - Height of a transfer unit

KW - Hollow fiber module design

KW - Number of transfer unit

KW - Ultrafiltration

UR - http://www.scopus.com/inward/record.url?scp=2142660699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142660699&partnerID=8YFLogxK

U2 - 10.1081/SS-120030479

DO - 10.1081/SS-120030479

M3 - Article

AN - SCOPUS:2142660699

VL - 39

SP - 1221

EP - 1238

JO - Separation Science and Technology (Philadelphia)

JF - Separation Science and Technology (Philadelphia)

SN - 0149-6395

IS - 6

ER -