Evaluation of membrane fouling models based on bench-scale experiments: A comparison between constant flowrate blocking laws and artificial neural network (ANNs) model
Introduction
Development of predictive/simulative models in membrane filtration process has become an important area in recent years. Models play an important role in predicting/simulating the membrane filtration performance, accomplishing efficient and economical process design, facilitating upscaling membrane systems, and especially explaining the phenomena of membrane fouling [1].
The oldest fouling and flux decline mathematical model is resistance-in-series model:where Δp is the pressure drop across the membrane (the transmembrane pressure drop, or TMP), σk an empirical constant, Δ∏ the osmotic pressure that is from the rejection of materials by the membrane and is, to a first approximation, inversely proportional to the molecular weight of the rejected species, μ the absolute viscosity (of the water), Rm the hydraulic resistance of the clean membrane with dimensions of reciprocal length, Rcp the concentration polarization resistance, Rc the cake resistance, Q the flowrate, D the diffusivity of the material in the concentration polarization layer, and δc is the thickness of the cake (or gel) layer. The resistance-in-series model resulted from Darcy's law:However, it is difficult to calculate the resistances caused by the concentration polarization layer or the cake/deposit on the membrane surface. An alternative approach is to analyze the fouling behavior in steady state, in which particles convectively driven to the membrane wall are balanced by some diffusive transport letting them to return to the bulk suspension. Then the concentration polarization model is obtained after some simplifications of the convection–diffusion equation:where Cw is the particle concentration at the membrane surface; CP the concentration in the permeate; Cb the concentration in the bulk solution; k(x) is the mass-transfer coefficient, which is estimated by Leveque solution [2]:where x is the distance from the membrane inlet; γW the shear rate at the membrane wall; DB is the diffusion coefficient. These models assume that the membrane fouling occurs in sequence. Concentration polarization acts as the dominant role in the initial period of rapid fouling till it reaches a relative steady stage. Following the initial period, the more gradual fouling is attributed to membrane fouling [3]. Later, a membrane transport model incorporating both resistance-in-series model and concentration polarization model was developed by Tu et al. [4].
Blocking laws are one of the most popular models used in recent years. They were first introduced by Hermans and Bredée [5]. With the further works done by Gonsalves [6], Grace [7], Shirato et al. [8], Hermia [9] finally revised all blocking mechanisms in a common frame of power-law non-newtonian fluids [10]. The following general equations were obtained:orwhere t is the duration of membrane filtration, V the total filtered volume, k (time−1) is a filtration constant, J can be expressed asand exponent n characterizes the filtration model, with n = 0 for cake filtration, which assumes that the resistance is increasing due to particle accumulation in the form of a cake on the filter media; n = 1 for intermediate blocking (long-term adsorption), witch assumes that particle build-up is sealing the membrane pores; n = 3/2 for pore constriction (also called standard blocking), which assumes that the pore volume decreases proportionally with filtrate volume by internal deposition; and n = 2 for complete pore blocking.
Later, Hlavacek and Bouchet [11] expended the blocking laws to constant flux mode asThe theory is based on the following assumptions. The membrane is considered as a bundle of parallel and straight pores with a radius r0 and a length L. The flow regime is assumed to be laminar and filtrate flowrate Q is a constant equal to the ratio of the volume of filtrate V to the time t(Q = V/t). Each particle entering the membrane is captured.
However, the mechanisms of the blocking laws are purely mechanical and they were derived from physical descriptions and understanding of the membrane process [11]. These models are mathematically complex, computationally expensive and they ideally require a very detailed knowledge of the filtration process as well as characterization of the membranes [12]. To apply these models usually rely on a number of fixed assumptions as mentioned before. As a result of these assumptions, existing models are typically process specific and are only valid within a limited operating range [13]. Therefore, there is a need to find an alternative means for predicting process performance by exploiting available process data and extending it to unavailable data. Artificial neural networks (ANNs) is one of tools are capable of modeling highly complex and non-linear systems for membrane system. ANNs have successfully been applied to different types of the membranes: microfiltration [14], [15], [16], ultrafiltration [17], [18], [19], [20], [21], [22], [23], [24], [25] and nanofiltration [26].
The aim of this study is to evaluate the performance of both blocking laws and ANNs model and identify the dominant fouling mechanisms in specific experimental periods based on the individual model fitting performance.
Section snippets
The configuration of constant flowrate blocking laws
In this section, the different forms of blocking laws are summarized based on the Refs. [26], [27] in Table 1, Table 2.
To account for the combined effects of different individual fouling mechanisms, five combined models were further generated by Bolton et al. [26].
The complete blocking assumes that particles seal off pore entrances and prevent flow. The intermediate blocking is similar to complete blocking but assumes that a portion of the particles seal off pores and the rest accumulate on top
Theory of neural network
Neural networks are statistical tools used for non-linear multivariate regression and they do not need an explicit formulation of the physical relationship of the problem. A particular input can lead to a specific target output data by training or adjusting the network. Their properties make them a promising way to model complex phenomena where numerous and complicated date occur.
The essential theory of neural network comes from biological information transfer process. In this way, neural
Materials and methods
Outside-in polyvinylidene fluoride (PVDF) hollow fiber membrane (Kolon, Korea) with an average pore size of 0.1 μm and 17.3 cm2 of effective filtrated area is used throughout. A single hollow fiber housed in a plastic tube of 6 mm inner diameter with the upper part sealed by epoxy resin forms a dead-end module.
The DEMF system installed vertically is shown in Fig. 2. Constant flow is pumped into membrane module via a variable speed peristaltic pump (MasterFlex® L/S, Model 7014-20). The TMP is
Results and discussion
The bench-scale experiments are conducted under different constant flowrate conditions with synthetic raw water, which characteristics are similar to the surface waters.
Conclusions
The blocking laws and ANNs model were evaluated based on bench-scale experiments with synthetic water in this study. The single blocking law could not fit the experimental data well in whole experimental period, but it fitted much better in separate specific experimental periods. The combined cake-complete and the cake-intermediate models demonstrated relative high consistency with experimental TMP data. The excellent agreement between experimental data and prediction has been obtained with
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