Membrane fouling in microfiltration of oil-in-water emulsions; a comparison between constant pressure blocking laws and genetic programming (GP) model
Graphical abstract
Introduction
Microfiltration of oil-in-water emulsions using membrane processes has been experimentally investigated in recent decades and demonstrated to be effective and possible [1], [2], [3], [4]; however, fouling mechanisms are not still fully understood and have remained challenging [5], [6]. These mechanisms have been studied to predict the variation in permeate flux rate with time during crossflow filtration. In other words, fouling models have been developed to describe the fouling behavior. Oil droplets are deformable and also coalescence and adsorption may occur in separation of emulsions. Oil droplet size, pore size distribution, and operating conditions are also the other factors that should be taken into account when considering the fouling mechanisms. Therefore, application of the filtration models in oily systems needs more investigations.
Deposition of the oil droplet inside the pore or on the top of the membrane surface can lead to fouling of a membrane [7], [8]. This phenomenon can be mechanically described by four types of models. First, standard blocking which assumes that the droplets deposit inside the membrane and constrict the pores, and then this constriction reduces permeability. Second, complete blocking which assumes that oil droplets block pore entrances and prevent flow. Third, intermediate blocking where some droplets are responsible for pore blocking and the rest accumulated on top of the other deposited particles. Finally, cake filtration occurs when particles accumulate on the surface of a membrane in a permeable cake of increasing thickness that adds resistance to flow. Each of these mechanisms has been used individually or in combinations to explain experimental observations [7].
These mechanical concepts were used to introduce the so-called “blocking laws” which are one of the most popular models in fouling mechanisms. They were first introduced by Hermans and Bredee and then further investigations were done [9], [10]. Then, Hermia revised the mentioned blocking mechanisms in a common frame of power-law non-Newtonian fluids [8]. Hermia's constant pressure blocking filtration laws were directly applicable to dead-end filtration, but with appropriate modification of the relevant mass balances, equivalent equations were derived for cross-flow filtration [11].
Arnot et al. [11] and Koltuniewicz et al. [12] reformulated the Hermia's equation in terms of flux and focused their theoretical analysis upon the dead-end filtration and the initial stages of the crossflow filtration. The following general equation was obtained:where k is the generalized filtration constant and the values of n, blocking index (constant), represents the different mechanisms; values of n being 1.5, 1.0 and 0 correspond to standard pore blocking, intermediate pore blocking, and cake filtration, respectively. This equation, in addition to resistance concept (R) and its first-order derivative with respect to time, (dR/dt), was used in some researches to analyze the fouling mechanisms [6], [12].
On the other hand, any of these classical models may explain a definite period of filtration [13], [14], [15], [16]. Tracey and Davis [14] fitted their BSA microfiltration data initially by complete model and subsequently by the cake model. Iritani et al. [17] reported that all the individual models were unable to fit their experimental observation and a combination of them may probably lead to better results; however, they did not proposed any combined models.
Ho and Zydney [18] developed the first model that used a two-stage mechanism to describe protein fouling during microfiltration. They found that “the complete pore blocking–cake filtration” model fitted by the experimental data. Following these works, Bolton et al. [7] generated five new fouling models that accounted for the combined effects of the different individual fouling mechanisms for both constant pressure and flux. They tested the applicability of the models to data for the sterile filtration of IgG and the viral filtration of BSA for which the cake–complete model provided the best data fits. It was concluded that the models derived by Bolton et al. [7] are less physically detailed than the model of Ho and Zydney [18]. Therefore, the models will be less useful for estimation of physical parameters. However, the new combined models were more numerically simple to implement.
It has been reported that these physical–mathematical models are typically process specific, and require detailed knowledge of the filtration process, largely depend on the nature of feed solution as well as operating ranges [19], [20]. In addition, some other techniques have been proposed to predict process performance by applying obtained data and extending it to a mathematical model for prediction of unavailable data without requiring detailed knowledge of the process. Genetic programming (GP) as a branch of genetic algorithm (GA) has shown to be a promising tool capable of modeling highly complex and non-linear systems in a wide variety of applications [21]. Modeling of membrane processes is one of such areas because of highly complex nature of such processes. However, there have been done some few remarkable works in the field of using GP in membrane technology [22], [23], [24], [25].
Okhovat and Mousavi [22] have successfully used GP as a novel approach for explicit formulation of nanofiltration (NF) process performance. They applied GP for prediction of the membrane rejection of arsenic, chromium and cadmium ions in a NF pilot-scale system as a function of feed concentration and transmembrane pressure. The results showed quite satisfactory accuracies of the proposed models and nominated GP as a potential tool for identifying the behavior of a membrane process.
Shokrkar et al. [23] studied treatment of oily wastewaters with synthesized mullite ceramic microfiltration membranes and developed a new approach for modeling of the membrane flux using GP. The model used input parameters for operating conditions (flux and filtration time) and feed oily wastewater quality (oil concentration, temperature, trans-membrane pressure and cross-flow velocity). From the results, the model predictions were satisfactory.
Suh et al. [24] investigated the application of GP to develop a model for estimating membrane damage in the membrane integrity test. They used GP as an alternative approach to develop a model to predict the area of membrane breach with other experimental conditions (concentration of fluorescent nano-particle, the permeate water flux and transmembrane pressure). The GP based model predictions were satisfactory in predicting the area of the membrane breach and, with the simple membrane integrity test, the GP technique provided a practical way for estimating the degree of membrane damage.
Hwang et al. [25] applied GP as a tool for modeling and prediction of the microfiltration (MF) membrane fouling rate in a pilot-scale drinking water production system. The presented model used input parameters for operating conditions and feed water quality to discover the mathematical function for the pattern of the membrane fouling rate. From their results, GP well predicted the investigated MF process.
To the best of our knowledge, there is no detailed investigation on fitting the individual and combined models in constant pressure for oil-in-water emulsions. In addition, GP has not been used as a predictive method in this field. The present study is aimed at evaluating performance of both individual and combined blocking laws as well as the GP model. Different models have been applied to determine if they would provide acceptable fits of the experimental data in microfiltration of oil-in-water emulsions. The dominant fouling mechanisms have also been identified based on the combined blocking models. This work is the first attempt comparing blocking laws and GP in membrane science and technology.
Section snippets
Constant pressure individual and combined blocking models
Permeate volume per unit filtration area, V, can be calculated as a function of time. As discussed, four different approaches have been used and different assumptions have been made to obtain the individual classical models [8]. These classical models include standard, complete pore blocking, intermediate, and cake filtration model which have been given in Table 1. The detailed derivations of these equations as well as relevant assumptions have been given elsewhere [7].
As mentioned in previous
Feed preparation and analyses
The oil-in-water emulsion was made using gasoil (Tehran Refinery) with the dispersed oil prepared by mixing gasoil and surfactant at a mixing rate of 12,000 rpm for 30 min. The surfactant used was polyoxyethylene (80) sorbitanmonooleate (Tween 80, Merck) at concentration of 100 ppm. A wide range of oil concentration, varied from 1000 to 20,000 ppm, was considered. The oil concentration in the feed andpermeate solution were analyzed using UV/VIS spectrophotometer (Jasco, V-550) at absorbance
Individual models
The individuals and combined models were applied to the constant pressure microfiltration of oil-in-water emulsion to determine if they would provide acceptable fits of the experimental data. Sixteen experiments were performed to investigate the fouling behavior of oil droplets in different concentrations and TMPs. The permeate volume was measured as a function of time until the flux reached to an almost constant value. Fig. 3 describes the typical behavior of permeate flux versus time for a
Conclusions
Individual and combined blocking laws were compared with GP model to investigate the fouling mechanisms and predict the permeate volume in lab-scale experiments for microfiltration of oil-in-water emulsion. The intermediate model obtained the best predictions in individual models and the cake model failed to provide any fit of the experimental data in all data sets. The combined models did not provide better fitting results than the classical ones. For more accurate fit, the GP model was
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