Modeling, simulation, and characterization of spinning basket membrane module in recovery of proteins from synthetic wastewater
Introduction
Over the last few decennia, membrane separation technology has emerged as an alternative to the traditional separation processes in the recovery of different nutritional and therapeutic proteins from wastewater streams of pharmaceutical, biochemical, and food industries [1]. Pressure Driven Membrane Systems (PDMS), in specific, have gained considerable attention in this regard [2]. However, the projected growth of PDMS in protein recovery was majorly hindered because of the two well-known non-idealities, namely, concentration Polarization (CP) and membrane fouling [3]. CP refers to the reversible accumulation of solutes on the membrane surface, whereas solute adsorption and subsequent pore blocking are known as fouling. Fouling leads to irreversible loss of permeability. An elevated level of CP has been reported to increase the membrane fouling [4]. Those two non-idealities are primarily responsible for the transient flux decline observed from the very beginning of filtration [5]. Consequently, the flux levels off to a quasi-steady value towards the terminal stages of filtration. Flux can only be recovered through cleaning operation, of which chemical cleaning is most commonly practiced [6]. Therefore, all membrane-based water treatment units sequentially operate in filtration and cleaning modes. Frequent cleaning, on the other hand, alters the permeation property and often results in a drastic reduction of the service life [7]. Several remedial techniques were proposed over the years, which are generally classified into four major categories: (i) boundary layer manipulation; this is commonly accomplished either upon insertion of the static turbulent promoter(s) or by feed flow rate independent shear enhancement at the membrane surface (e.g., the DSE modules) [8] (ii) upstream techniques, like pretreatment of feed [9] (iii) Modification of the membrane surface properties [10] and (iv) external perturbations (e.g., backpulsing/backflushing/backwashing, pulsatile flow, gas sparging, use of electric field or ultrasound, etc.) [11,12].
The idea of shear enhancement at the membrane surface and disruption of the polarized layer was first implemented in much earlier cross-flow (CF) systems [13]. In CF modules, the membrane shear stress can be largely increased upon increasing the feed flow rate. Nevertheless, the transmembrane pressure (TMP) eventually decreases along the direction of feed flow, which results in a “non-optimal use of the membrane surface” [14]. Increased feed flow rate also increases the pumping cost. The idea of “dynamic shear enhancement” was introduced to decouple the membrane-shear stress from the feed flow rate. According to this strategy, shear was made independent of the feed rate by introducing a rotating or a reciprocating accessory. For example, a primitive dead-end module may be converted to a DSE filtration system upon placing a high-speed stirrer close to the membrane [15]. Flux was reported to increase in this upgraded design, known as “single-stirred cell” compared to its ‘unstirred’ counterpart [16]. The increasing need of processing heavy fouling feedstocks (e.g., concentrated protein or polymer solutions, oil-water emulsions, industrial effluents, etc.) has promoted the innovation, scale-up, and commercialization of different DSE modules since the 1970s. Some of the standard designs include rotating disk (RD), rotating disk-membrane (RDM), multi-shaft disk (MSD), and vibratory shear enhanced processing (VSEP) units [17]. A large number of performance characterization and hydrodynamic studies of several DSE modules with a wide range of feed and process conditions have been reported over the last two decades [18]. A comprehensive review of their performances in the treatment of various industrial and synthetic feedstocks, comparative analysis, shear production capacities, and energy usage profiles has been presented by Jaffrin [19]. A different group of DSE modules with an online cleaning facility was propped nearly a decade ago [20,21], of which the SBM unit was the baseline design. The module was tested in ultrafiltration (UF) of polyethylene glycol, polyvinyl alcohol, and bovine serum albumin. For all feedstocks, the maximum flux decline was restricted within 10 % even after three to five hours of continuous filtration [22]. Very recently, the upgraded design referred as the ‘intermeshed spinning basket membrane’ (ISBM) module, has also been reported [23].
Literature review on DSE modules indicates a plethora of performance characterization studies. Some of the investigations were also based on hydrodynamic simulation; nevertheless, majorly based on the standard CFD packages. Very few attempts were made to formulate a mathematical model, primarily owing to the complex hydrodynamic environment that generally prevails in any DSE module. The models mainly deal with the baseline designs, such as RD or RDM. Recently, a first-of-its-kind, but exceedingly simplified formulation is reported for the SBM filtration device [24]. A brief review of those models is presented as follows:
One of the early models of RD unit was proposed by Holechovsky and Cooney [25]. One dimensional convection-diffusion equation with variable diffusivity term was solved to obtain the system-specific mass transfer correlation. The dynamic feature of shear enhancement was established in terms of axial velocity independent mass transfer coefficient as the specific velocity component, according to its definition, was directly proportional to the feed flow rate. The formulation was grossly empirical indeed because it incorporates the experimental mass transfer correlation. Since then, several models of RD and RDM were proposed. Bhattacharjee and Dutta partially resolved the problem of empiricism associated with the mass transfer coefficient. They have introduced the concept of ‘back transport flux’ to account for the effects of shear enhancement. The back transport flux was semi-empirically considered to be proportional to the rotational speed of the stirrer [26]. A more realistic one-parameter model based on the similar idea was later proposed by Sarkar et al. [27]. The model was further extended to simulate the RDM filtration systems [28]. Alternative to the analytical studies, different numerical models are also available for RD and RDM pilots. Very recently, an elegant numerical model of a ‘rotodynamic’ (i.e., equivalent to RD module) RO filtration system has been proposed by Uppu et al. [29]. Different specific-purpose subroutines were incorporated in a commercial CFD package to simulate the complex hydrodynamic picture correctly. The simulated velocity field confirmed the presence of helical pathlines, which was rightly envisaged earlier by Sarkar et al. [27]. It is imperative to note that modeling studies of DSE units are majorly limited to simple and baseline designs (i.e., RD and RDM modules only). Only an elementary two-parameter, steady-state model of the SBM system has been recently proposed [24]. The formulation was based on lubrication theory, osmotic pressure model, and thermodynamic black-box model of membrane transport due to Spiegler and Kedem. The approach circumvented the solution of the fundamental convection-diffusion equation. Additionally, the physical picture of the cleaning run remained completely unexplored.
Spinning basket filtration systems (i.e., SBM and ISBM units) are pretty effective in the treatment of heavy-fouling feed solutions [[20], [21], [22], [23]]. The modules are also capable of intermittent flux regeneration using their inbuilt physical cleaning facility. Furthermore, both SBM and ISBM filtration units have been established to be techno-economically suitable specifically for protein recovery compared to other DSE systems [22,23]. Accordingly, a thorough understanding of their mass transfer picture is necessary beyond the mere performance characterization and elementary CFD simulation for appropriate scale-up. A modeling attempt, from the perspective of the fundamental convection-diffusion archetype, is, therefore necessary to be explored. Additionally, the basic physics of the physical cleaning mechanism must be understood from a quantitative point of view for further improvement and upgradation.
In this article, we have presented a two-parameter unsteady-state analytical model of the SBM pilot, which can simulate the device operating in repeated filtration and cleaning modes in sequence. The transient two-dimensional convection-diffusion equation was solved to obtain the protein concentration profile under the time-varying boundary condition at the membrane surface. A functional form (: flux, : membrane surface, and permeate concentrations of protein, : time), derived thereof was incorporated with two other constitutive equations arising from osmotic pressure and Spiegler-Kedem black box models. The governing system equations were simultaneously solved to simulate the device in filtration mode. On the other hand, a lumped parameter cleaning model was formulated in terms of . A force balance between the dislodging mechanical draft on the deposited solute layer due to reversed directional basket spinning, the flow-induced lift force, and the solute-solute DLVO interactions was considered to formulate the cleaning rate. The model has been validated with the experimental profiles of and obtained in ultrafiltration of protein-bearing synthetic wastewater (i.e., an aqueous solution of BSA) conducted in a standard SBM pilot.
Section snippets
Materials and analytical techniques
Reagent grade (99 % pure); IgG, endotoxin, and fatty acid-free BSA of average molecular weight 66 kDa was procured from SRL, India. The synthetic wastewater feedstock was prepared upon dissolving BSA powder in the Tris buffer. The buffer was prepared upon mixing 151.14 g of Tris base per 1000 mL of deionized water [30]. The pH was adjusted around the neural range (i.e., 7.0–7.3). Additionally, 0.012 w % sodium azide was also added to prevent bacterial growth. Asymmetric, semi-permeable, moist
Model formulation
Primarily, it is necessary to outline the objectives of the present model. In the filtration mode, variations of the flux () and the permeate concentration () with time are to be principally simulated for a fixed set of parametric conditions (i.e., TMP,, and ) as the two quantities could be experimentally measured. The membrane surface concentration profile was also predicted to initialize the next cleaning run; nevertheless, it is impossible to measure in the present
Simulation scheme
Transient profiles of , and during the filtration run were simulated by solving Eqs. 8, 11 and 12 simultaneously. The multivariate Newton-Raphson scheme was employed for this purpose. Complete profiles were generated by repeatedly solving the set of equations over . For all filtration experiments, the permeate flux was observed to attain its quasi-steady state around 120 min. Therefore, we have chosen to be 120 min. Time increment to execute repeated solution was fixed
Results and discussion
The SBM filtration pilot was simulated under a different set of , , and (Table 1) to obtain the transient profiles of , , and over the three sequential filtration runs. The adjustable parameters (i.e., and ) were appropriately tuned to minimize and . The Response Surface Methodology (RSM) was used to decipher the functional relations between the adjustable and the operating parameters. Furthermore, the standard correlation between the time-averaged permeate flux (
Conclusion
Nearly a decade ago, we proposed the design of a dynamic shear enhanced filtration device with an inbuilt membrane cleaning facility. The unit was named as 'Spinning Basket Membrane' (SBM) module. The SBM pilot was characterized in ultrafiltration of different synthetic wastewater streams [[20], [21], [22]]. An elementary mathematical model was also previously developed to simulate the flux profile under steady-state [24]. Closer investigation revealed that the perpetual sequence of filtration
Declaration of Competing Interest
The authors report no declarations of interest.
References (47)
- et al.
Reduced membrane fouling in a novel bio-entrapped membrane reactor for treatment of food and beverage processing wastewater
Wat. Res.
(2011) - et al.
Biofouling on RO-membranes used for water recovery in the dairy industry
J. Wat. Pros. Eng.
(2018) - et al.
In situ monitoring techniques for concentration polarization and fouling phenomena in membrane filtration
Adv. Coll. Interf. Sci.
(2004) - et al.
Concentration polarization in ultrafiltration and reverse osmosis: a critical review
Desalination
(2001) - et al.
Chemical cleaning/disinfection and ageing of organic UF membranes: a review
Wat. Res.
(2014) - et al.
Fouling and cleaning of ultrafiltration membranes: a review
J. Wat. Proc. Eng.
(2014) - et al.
Enhancement of surface properties and performance of reverse osmosis membranes after surface modification: a review
Desalination
(2017) - et al.
Membrane fouling in desalination and its mitigation strategies
Desalination
(2018) - et al.
Productivity enhancement in a cross-flow ultrafiltration membrane system through automated de-clogging operations
J. Membr. Sci.
(2006) - et al.
Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes
J. Membr. Sci.
(2002)