Modeling and optimal operation of batch closed-loop diafiltration processes

https://doi.org/10.1016/j.cherd.2017.04.016Get rights and content

Highlights

  • Batch membrane diafiltration with partial recirculation (closed loop) is studied.

  • Complete mathematical model with various possible simplifications is derived.

  • Optimal values of diluant inflow and recirculation are analyzed for different objectives.

  • Literature models are used to solve cases, in order to get insights into the economics.

Abstract

The paper derives mathematical model and optimal operation of batch diafiltration processes with partial recirculation of retentate, i.e. batch closed-loop membrane processes. A generalized mathematical model of the process is developed in the form of a set of non-linear ordinary differential and algebraic equations. Two process variables are used as manipulated and optimized degrees of freedom: recirculation rate and diluant addition rate. Optimal operation aims to minimize a weighted combination of processing time, power consumption, and diluant consumption. A theoretical analysis of the process is combined with numerical optimization techniques. Based on selected case studies, conclusions are drawn on economics of the process operation to identify when the process design with recirculation adds substantial benefits compared to the classical (open-loop) design without recirculation. Simulation studies suggest that minimum time operation does not require recirculation loop. On the other hand, minimum power operation consumes about 70–95% less power in closed-loop design when compared to open-loop setup.

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)),

  • 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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