Modeling and optimal operation of batch closed-loop diafiltration processes
Graphical abstract
Introduction
Membrane separation processes as described in Cheryan (1998) and Zeman (1996) serve for separation of two or more different molecules from a solution using semi-permeable membranes. One of the techniques of membrane separation is diafiltration. Diafiltration is applied when reduction in concentration of certain components is required. It is frequently used in food and pharmaceutical industries in product concentration and impurity/toxin reduction. It has applications in pharmaceutical manufacturing (Sheth et al., 2003), purification of nanoparticles (Limayem et al., 2004), separating saccharides from salt solution (Wang et al., 2002, Yin et al., 2011), purifying oligosaccharides from monosaccharides (González-Muñoz et al., 2011), clearance of protein extractables (Magarian et al., 2016), etc.
The membrane separation processes can be operated in different modes (Jungbauer, 2013), such as batch (Mulder, 2012), feed-bleed (Hu and Dickson, 2015), or continuous (Farizoglu and Uzuner, 2011, Kurt et al., 2012) mode. The processing mode is chosen depending on various criteria to be achieved, e.g. concentration factor, volume reduction, permeate quality, processing time, cleaning frequency, etc. The batch type of operation includes simple batch (also known as straight batch (Rapaport, 2006)) and modified batch (also known as topped-off batch (Jungbauer, 2013)).
In this paper we study the so-called batch closed-loop configuration, also known as a membrane system with partial recirculation (Mulder, 2012, Bhave, 2014, Mallevialle et al., 1996). This configuration employs two pumps, i.e. feed and the recirculation pump. The feed pump is used to pressurize the feed and the recirculation pump adjusts the cross flow velocity and compensates for pressure drop. The batch closed-loop operation has following advantages over traditional batch (open-loop) operating mode:
- 1.
Regardless of the degree of fouling and changes in feed composition, this configuration provides a controlled and defined flow rate (Rapaport, 2006).
- 2.
The pipe diameter can be smaller than in conventional batch (Cheryan, 1998, Rapaport, 2006).
- 3.
The feed tank size can also be smaller for the closed-loop setup as part of the solution volume is permanently inside the loop. This reduces problems of foaming (Cheryan, 1998, Tamime, 2012). Temperature and quality of sensitive retentate products can be maintained which can be difficult in open-loop batch (AWWA, 2005).
- 4.
For large systems with remote tankage this setup can save quite a lot of large piping and with a small pressurizing feed pump, a large amount of energy by keeping the loop pressure high (Rapaport, 2006; Dow Water & Process Solutions; Jornitz and Meltzer, 2007).
- 5.
In membrane bioreactors, partial recycle of retentate resulted in higher nutrient uptake, which helped producing a higher biomass concentration (Bilad et al., 2014).
The majority of the work dealing with batch closed-loop in literature only mentions its properties and suggests the above mentioned advantages. However, theoretical properties are hardly explored except of our preliminary study (Sharma et al., 2015) on modeling issues and control suggestions. This paper deals with unsteady-state modeling of the process, while showing its differences to a batch open-loop mode. Optimization part of the paper proposes optimal operation of the process using two manipulated variables: diluant rate and recirculation ratio. The paper tries to give answers when it is more suitable to use batch open-loop or closed-loop configuration. Optimization goals include weighted minimization of processing time, diluant consumption, and power consumption.
The methodology of the paper follows the approach of optimal control (Paulen and Fikar, 2016, Paulen et al., 2015) where only processes without recirculation are studied. Optimal operation will be determined numerically in simulations.
The content of the paper is as follows. Section 2 describes the studied process and proposes its modeling from mass balances using ordinary differential equations. Control and optimization goals are defined in Section 3. Simulation results from multiple case studies are presented in Section 4. Finally, the last section concludes the paper.
Section snippets
Process description and modeling
The membrane processing separates the solution fed into two portions, i.e. retentate and permeate. Retentate forms the concentrated stream rejected by the membrane, while permeate stream is allowed to pass through, and hence leaves the system. The retentate returns back to the feed tank in the batch mode. In the batch closed-loop mode, some portion of the retentate can be directed to the loop with the aid of an extra recirculation pump. The basic differences between a batch membrane plant
Manipulated inputs
Traditional control of batch diafiltration plants keeps piece-wise constant diluant rate α using three simple modes (Jaffrin and Charrier, 1994, Foley, 2006)
- •
no addition of diluant (α = 0), i.e. concentration mode (C),
- •
diluant flow rate equals the flow rate of permeate leaving the system (α = 1), i.e. constant volume diafiltration mode (CVD (Luo et al., 2016)),
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diluant flow rate is proportional to the flow rate of permeate leaving the system and less than it (0 < α < 1), i.e. variable volume diafiltration
Case studies
We present three case studies differing in permeate flow models that are taken from literature. These demonstrate different aspects of optimization and optimal operation.
In all cases, we consider that the membrane is completely impermeable to the macro-solute. Therefore, its rejection coefficient as defined by (3) is R1 = 1. The micro-solute completely passes the membrane, thus R2 = 0.
Conclusions
In this paper, a membrane configuration with the possibility of partial recirculation of retentate was studied. In the first part, the process was rigorously modeled using material balances to obtain a system described by combined differential and algebraic equations.
The second part discussed control strategies, optimization goals, and analyzed the optimal operation both quantitatively as well as qualitatively. Three case studies with permeate models of increased complexity were considered.
The
Acknowledgements
We sincerely thank the anonymous reviewers for the help in the improvement and clarification of this manuscript. We also gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11 and the Scientific Grant Agency of the Slovak Republic (project 1/0004/17).
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