Cross-flow and dead-end microfiltration of oily-water emulsions: Part II. Mechanisms and modelling of flux decline

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Abstract

The focus of this paper is on the mechanisms and modelling of flux decline. Three distinct forms of modelling flux decline of cross flow filtration at constant transmembrane pressure (ΔP) were examined. The best fit to the data sets examined was obtained with the model developed previously by Field [9], [10]. The general equation is (dJ/dt) = kj(J  J*)J(2  n) where n depends upon the fouling mechanism and J* is the steady-state flux. This approach to the analysis of flux data has the ability to identify the dominant mechanism, which has been shown to depend upon the membrane used and the operating conditions. In order not to give undue emphasis to early or late times, the data were fitted in both flux and resistance form simultaneously. The dominant fouling mechanism was found to be either incomplete pore blocking (n = 1) or ‘cake’ filtration (n = 0). Trends in the model parameters are also discussed in relation to operating conditions such as mode of filtration, cross-flow velocity and transmembrane pressure. For dead-end filtration, the initial rate of flux decline was found to be proportional to ΔP3, as suggested by theory. The model of Wu et al. [11] was shown to have limited predictive performance and discarded as being empirical. The model of Koltuniewicz [12] was shown to have limited application and unrealistic performance in this filtration application. The two most significant practical observations on the oily-water data are (1) the initial rate of fouling is significantly lower for cross-flow velocities of 0.8 m s−1 or greater and (2) a ΔP of 1 bar can lead to excessive fouling. With regard to microfiltration modelling generally, further comparison between the three models with other data sets is recommended.

Introduction

This contribution focuses on the mechanisms and modelling of flux decline. The data used is that given in our previous paper [1] but the method of analysis will be of wider interest. This data is for a dispersion of oil-in-water, there is therefore a range of droplet sizes, and the potential for changes in this distribution both globally and locally at the membrane interface. The complications that arise will be discussed later. Firstly the background to this work is outlined in the second part of this section, whilst the equations for flux decline (and associated increase in resistance) are given in the first half of the Section 2.

When initially analysing the data for the three different types of membranes used, it was relatively easy to discern the different modes of flux decline [1]. However, the lack of a clear relationship between the parameters in the flux decline models on the one hand, and pressure and cross-flow velocity on the other, lead to a refinement in our methods of data analysis and a clear procedure for the discrimination between the different modes of fouling. This progress will be of general interest for all concerned with the methods for analysing flux decline.

The discharge of crude oily wastewater into the sea or rivers has been under increasingly careful scrutiny in recent years. In addition to oily wastes from the petrochemical, metallurgical and processing industries, it should be remembered that the production of crude oil is often accompanied, on average, by an equal volume of water. A production separator that separates most of the oil from the water is usually used to give an initial separation of oil and water. The small quantity of remaining oil in the water must be reduced to an acceptable limit before the water can be discharged into sea or rivers or re-injected for water flooding. Onshore, the separation can be done by the use of large gravity settling vessels, because large hold-up volumes are acceptable. Offshore space and weight are at a premium. In the past separation was done with air induced flotation tank based systems, where a fine mist of air is injected in conjunction with surfactants to float oil droplets to the surface. This method and other conventional technologies, including parallel plate coalescers and granular media filtration, do not produce effluent that consistently meets the discharge limits and re-injection requirements [2]. Offshore the oil industry has been increasingly using liquid–liquid hydro-cyclones to separate the oily water to cut down the operating cost as well as solving the problem of space and weight. However, hydro-cyclones are more efficient at high operating pressure and large oil droplets. It is therefore necessary to develop alternative technologies [3], [4], [5], [6], [7]. The extent to which this is necessary can be gauged by the fact that the offshore oil industry is prepared to use centrifuges for some duties [8].

There is thus an opportunity for membranes and other new technology that can meet current limits across a variety of old fields, as well as further lower limits.

Section snippets

Summary of previous developments

The three flux decline models that are to be subsequently compared against data, are introduced. The most comprehensive and theoretically sound framework is the one developed by Field [9], [10] for constant pressure filtration with due allowance for cross-flow. The general equation isdJdt=−kJ(J−J*)J(2−n)where n = 2.0 for ‘complete’ blocking; n = 1.5 for standard blocking; n = 1.0 for incomplete pore blocking (intermediate fouling) and n = 0 for cake filtration.

J is the membrane flux, and in the context

Experimental

The experimental methods and materials were as previously described by Koltuniewicz et al. [1] and the data sets are also as reported in that paper. However, it may be useful for current readers to summarise the experimental apparatus and conditions here for completeness.

Three types of microfiltration membrane were tested: Millipore 0.45 μm (hydrophilic PVDF), Gelman 0.1 μm (hydrophilic polysulphone), Ceramesh 0.1 μm (hydrophilic zirconia coated, nickel alloy mesh composite membrane). Experiments

Modelling

Three distinct forms of modelling equation for flux decline in cross flow filtration can be found in the literature, namely , , . These flux decline models were compared using the oil-in-water emulsion data. Although, the reproducibility of filtration performance is poor for emulsion systems, the same data is being used to test the three models and so the comparison is still valid.

Modelling was carried out using a commercial package called Scientist™ (version 2.0) supplied by MicroMath

Effect of membrane material

This section will address four sets of dead-end and cross-flow experiments, which can be treated as two pairs with similar operating conditions but different membrane materials. Table 1 summarises the experimental conditions and the estimated model parameters for the Field model (Eq. (9)), and Table 2 provides the model parameters and correlation coefficients for the models of Wu et al. (Eq. (4)) and Koltuniewicz (, ). These tables should be referred to in relation to the whole of this section.

Discussion

The earlier observations [1] that the influence of cross-flow was much greater for the Ceramesh membrane than for either the Millipore or Gelman membranes has been confirmed by the use of the Field model (Eq. (9)) to identify the dominant fouling mechanisms for the different modes of operation. Additionally the interpretation that pore blocking was more prevalent for both Gelman and Millipore membranes than for the Ceramesh has also been supported through this method of analysis. This approach

Conclusions

  • 1.

    Three distinct forms of modelling flux decline have been examined and the Field model was found to be superior; it makes due allowance for different fouling mechanisms.

  • 2.

    The Koltuniewicz model is not a physically realistic representation of the fouling process that appertained with the oil-in-water emulsion experiments. Examination of data for well-defined systems is required in order to ascertain whether the Field model is generally superior to the Koltuniewicz’s model in terms of its ability to

List of symbols used

    A

    membrane area (m2)

    a

    accumulation (fouling) constant in Koltuniewicz’s model (h−1)

    J

    flux (l m−2 h−1)

    J0

    flux at time t = 0 (l m−2 h−1)

    J*

    limiting or ‘steady-state’ flux (l m−2 h−1) in Field model

    J*d

    terminal flux in dead-end operation (i.e. a leakage flux) in Koltuniewicz’s model (l m−2 h−1)

    kf

    constant in Wu et al.’s model (h−1)

    kJ

    constant in Field’s original model (dimensions vary with n)

    kj

    constant in Field’s model as presented in Eq. (9) (h−1)

    kp

    constant in Wu et al.’s model (h−1)

    n

    constant in Field’s model, as

Acknowledgements

The above study was started when Dr A. Koltuniewicz visited the University of Bath in the summer of 1993. The experimental work was supported from Royal Academy of Engineering/Shell Research Fellowship funds, and subsequent discussion of the results and modelling has been possible through exchange visits between the UK and Poland supported by a British Council travel grant. The authors are grateful to those concerned for their initiative and support.

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