Elsevier

Desalination

Volume 277, Issues 1–3, 15 August 2011, Pages 257-264
Desalination

An analytical model for spiral wound reverse osmosis membrane modules: Part II — Experimental validation

https://doi.org/10.1016/j.desal.2011.04.037Get rights and content

Abstract

This paper presents the experimental studies carried out for validation of a new mathematical model [1] developed for predicting the performance of spiral wound RO modules. Experiments were conducted on a laboratory scale spiral wound RO module taking chlorophenol as a model solute. Experiments were carried out by varying feed flow rate, feed concentration and feed pressure and recording the readings of permeate concentration, retentate flow rate, retentate concentration and retentate pressure. A total of 73 experimental readings were recorded. The membrane transport parameters Aw (solvent transport coefficient) and Bs (solute transport coefficient) and the feed channel friction parameter b were estimated by a graphical technique developed in this work. The mass transfer coefficient k, estimated using the experimental data, was found to be strongly influenced by solvent flux and solute concentration apart from the fluid velocity. Taking the effects of solvent flux, solute concentration and fluid velocity, a new mass transfer correlation for Sherwood number is proposed in this work for the estimation of mass transfer coefficient. Comparison of model predictions with experimental observations demonstrated that the model was capable of predicting permeate concentration within 10% error, retentate rate flow within 4% error and rejection coefficient within 5% error.

Research highlights

► Experiments were conducted on a spiral wound RO unit taking chlorophenol as a solute. ► Model parameters were estimated using the experimental data. ► A new correlation for estimation of mass transfer coefficient is proposed. ► Proposed correlation accounts for effect of solvent flux, velocity and concentration. ► Model predictions tested with experimental readings showed good agreement.

Introduction

Although reverse osmosis (RO) got established as a successful technology for sea water desalination [2] in the early 60s, it was only in the past 20 years that RO made inroads into other applications like removal of organics and treatment of waste water [3], [4], [5], [6]. With increasing applications of RO in the removal of organic compounds, studies on design and performance analysis of RO modules gain importance in the success of RO technology for separation of organic solutes. Spiral wound reverse osmosis membrane module [7] is widely used in industrial applications due to high packing density and lower capital and operating costs.

Development of mathematical models to predict the performance of spiral wound RO modules in removal of organic solutes is important for the optimal design and operation of these modules in such applications. Studies reported in the literature on development of mathematical models describing the performance of spiral wound RO modules include ‘Approximate analytical models’ [8], [9], [10], [11], [12], [13] and ‘Rigorous numerical models’ [14], [15], [16]. Although numerical models are more appropriate for describing complex situations, the analytical models are useful for gaining better physical insight and understanding of the system. A new analytical model for the spiral wound RO module was developed in this study and reported in Part I of this paper series [1]. In this model [1], variations of pressure, flow and solute concentration in the feed channel of the module were incorporated and the transport through the membrane was described by solution–diffusion model with concentration polarization [17].

Validation of the mathematical model with experimental data becomes essential for the model to get accepted as an analytical tool for the design and operation of spiral wound RO modules. Most of the studies on validation of models for spiral wound RO modules were confined to sea water desalination data [13], [15], [18] and not many works on model validation with experiments using organic solutes were found in the literature. In this paper, experimental studies (Section 2) conducted on laboratory scale spiral wound RO module with chlorophenol as a model solute is reported. Experimental readings recorded in this work were used for validation (Section 5) of the analytical model developed and reported in Part I [1].

Parameter estimation is an important aspect of any mathematical modeling work. Model parameters are usually estimated by matching the model predictions with experimental data. Estimation of membrane transport parameters Aw (solvent transport coefficient) and Bs (solute transport coefficient) using experimental measurements on ‘stirred membrane cells’ is reported in the literature [19], [20], [21]. In the present work, new analytical and graphical methods were developed for estimation of Aw, Bs and b (feed channel friction parameter) using the experimental readings taken on spiral wound RO module. Studies on estimation of these parameters are reported in Section 4.1.

Mass transfer coefficient k is the model parameter that characterizes the concentration polarization in membrane transport. The value of k is generally estimated using standard mass transfer correlations [22], [23]. Although many investigators [14], [15], [24] have justified the application of standard mass transfer correlations for estimation of k in membrane transport, there are a few [11], [25] who have strongly criticized their validity in concentration polarization layers of membrane stating that the mechanism of solute transport in these layers is more due to advection than due to convection. Assuming the validity of mass transfer correlations of the standard form, Murthy and Gupta [20], [24] have proposed a graphical method for estimation of k. However, correlations of different forms [10], [11], [26] have also been reported in the literature taking the effects of solvent flux, pressure and solute concentration on mass transfer coefficient. In the present work, a new correlation for estimation of k is proposed accounting for the influence of solvent flux and solute concentration in addition to fluid velocity and the validity of this correlation is justified from the experimental data.

Section snippets

Experimental setup

A commercial thin film composite polyamide RO membrane packed in a spiral wound module (Make: Ion Exchange, India) was used for the experimental studies. Detailed specifications of the membrane module are given in Table 1. The schematic diagram of the experimental setup used in this work is shown in Fig. 1. The feed solution kept in a stainless steel feed tank (FT) was pumped through the spiral wound RO module (M) by a high pressure pump (P) capable of developing pressure up to 20 atm. The

Model equations

The experimental data reported here was used for the analysis and validation of the mathematical model developed in this work for spiral wound RO modules. The model equations, presented in Part I of this paper series[1], were solved to yield analytical expressions for the prediction of retentate flow rate (Fo), retentate pressure (Po), retentate concentration (Co), permeate concentration (Cp) and solvent flux (Jv). The model has four parameters namely solvent transport coefficient Aw, solute

Estimation of model parameters

Parameter estimation for the analytical model developed in this work is an important aspect of this study. Analytical and graphical methods for parameter estimation were developed and reported in Part I of this paper series [1]. Applying these parameter estimation techniques, the values of model parameters Aw, Bs, b and k were calculated using the experimental readings reported in Table 2, Table 3, Table 4. The results of this parameter estimation study are outlined in this section.

Model predictions and experimental verification

Any mathematical model gets accepted as an appropriate analytical tool only if the model predictions match with the experimental measurements within some acceptable magnitude of error. Studies carried out in this work on validation of mathematical model with experimental data are presented in this section.

For specified values of feed pressure Pi, feed flow rate Fi, feed concentration Ci, permeate pressure Pp and feed temperature T, the model developed in this work can predict the values of

Conclusions

An analytical model for predicting the performance of spiral wound RO modules was developed and presented in part I of this paper series[1] assuming spatial variations of pressure, flow and solute concentration in feed channel and uniform condition of pressure in permeate channel. In this paper, which is Part II of this series, experimental studies on validation and analysis of this mathematical model were presented. Experiments were conducted on a laboratory scale spiral wound RO module taking

Symbols

    a

    Coefficient appearing in Eq. (23)

    a1

    Coefficient appearing in Eq. (30)

    Af

    Feed channel area (m2)

    Am

    Membrane area (m2)

    Ap

    Permeate channel area (m2)

    Aw

    Solvent transport coefficient (m/atm·s)

    b

    Feed channel friction parameter (atm·s/m4)

    Bs

    Solute transport coefficient(m/s)

    C

    Solute concentration in feed channel(kmol/m3)

    Cb

    Bulk solute concentration in the feed channel (kmol/m3)

    Ci

    Concentration of solute in the feed (kmol/m3)

    Co

    Concentration of solute in the retentate (kmol/m3)

    Cp

    Concentration of solute in the

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