Modelling and Control of Membrane Systems

The interplay of fouling and concentration polarisation (CP) is recognized to be decisive for the performance of any ultrafiltration (UF) system. Large efforts have been made to understand these phenomena in order to better design practical units. On the other hand, ultrafiltration of protein solutions has been used as a model systems to gain insight into these complex fluids and its behaviour in pressure driven membrane separation.

Simple mass transfer models are inapplicable for these complex solutions due to strong membrane/solute/solvent interactions. Computational fluid dynamics (CFD) can be applied taking into account concentration dependent physical properties (solute/solvent interactions) and boundary conditions of the membrane flux (membrane/solute/solvent interactions).

In this study we performed ultrafiltration of aqueous BSA solutions using a lab-scale flat-sheet crossflow rig under various operating conditions and attempted to quantitatively simulate the experiments by means of a transient mathematical model. This study was to reveal if a predictive simulation was feasible, if this kind of mathematical model could replace empirical tests and serve as a design tool for practical applications in the future.

In order to achieve an optimal economic return from WPC production, the achievable control performance from a given process design needs to be determined before the actual feedback controller is implemented. This intrinsic property of the process design towards automatic control is called dynamic operability. Based on the dynamic behaviour of manipulated variables from an industrial whey UF process, the effects of the number of stages of the process and recycle streams on dynamic operability have been investigated by the researchers. However, given that industrial whey UF processes usually operate for 16 hours every day, the effects of long-term membrane fouling on dynamic operability is not well understood. The aim of this study is therefore to investigate the effects of long-term fouling on the dynamic operability of an industrial whey UF process, and the implications on process operation. The study is based on dynamic models of an industrial whey UF process developed by the UNSECO Centre for Membrane Science and Technology.

Dynamic operability of the industrial whey UF process indicates that the required adjustments in manipulated variables to deliver the same level of control performance increase with time during the 16 hours of operation. Given the physical constraints of the manipulated variables (e.g. recycle ratios are bounded between 0 and 1), the automatic feedback controllers are not able to mitigate fluctuations in feed flowrate and composition experienced by the whey UF process when long-term fouling becomes significant after long hours of operation.

While mid-run washing is often used during the industrial production of WPC to ensure that the desired specifications of WPC can be delivered in steady state, dynamic operability of the whey UF process suggests that mid-run washing is crucial to maintain the performance of automatic feedback controllers, especially after long hours of process operation.

Modifications in process design, such as the installation of a buffer tank to dampen the fluctuations of the fresh whey feed before supplying to the UF process, can also improve the achievable control performance of the automatic controllers when long-term fouling is significant. By studying the dynamic operability of the modified design, improvements on the achievable control performance can be assessed even before the modification is actually implemented.

Dynamic response of the total solids concentration in the retentate stream under automatic control when 7 stages are used in the process design

Ultrafiltration (UF) is proving to be a promising operation in the biopharmaceutical industry for both virus purification and clearance operations. In this work, we present a detailed model for virus UF that is based on population balance theory. The proposed model is validated experimentally using model particles.

Numerous process models have been presented in the literature that describe the performance of UF operations [1-6]. Typically UF models predict permeate flux decline, the percent rejection and solute concentration in the retentate under varying feed concentrations, membrane fouling and changes in pressure drop. The model of this work addresses these variables’ interactions and further takes into account particle suspension properties, more specifically particle polydispersity parameters. Population balance theory lays the foundation for this model where a discrete set of equations can be written to describe the population density of each particle size class of the permeate (or retentate).

The developed population balance equation (PBE) is accompanied by a specific initial condition, mass balance and other constitutive relations together forming the population balance model (PBM). In developing the PBM, several assumptions are considered including: tangential flow, laminar flow in pores, monodispersed pore sizes, constant feed flow and concentration. The model is solved using gPROMS package (Process Systems Enterprise, UK).

Experiments were conducted for the purpose of model validation. In all the experiments, the temperature was set to 25 C and specially prepared 0.1% Latex and silica particles at various pump speeds were used. Samples (from permeate and retentate) were collected at regular time intervals. These samples were analyzed for the particle size distribution using dynamic laser particle size measurement.

Preliminary modeling results are promising indicating that the mechanics of the PBM, which are to a large extent statistical in nature, are close to the region of the experimental data. The existing mismatch between the model and the experimental data is attributable to the simplifications of the assumptions involved. The PBM is simple yet serves as a powerful predictive tool for the study of the impact of the operating parameters on the permeate particle phase viz. quality of permeate. Particle mean size as well as other particle characteristics like particle size distribution etc can be derived from the PBM leading to better understanding of the underlying UF interactions and mechanisms.

A Computational Fluid Dynamics (CFD) model is being developed to simulate mass transfer in narrow channels in three-dimensions. Current simulations have been completed for a channel containing a novel non-woven 3-layer spacer (shown in figure 1) with a filament diameter to channel height ratio of 0.6, and a mesh length to channel height ratio of 4, positioned at 0° or 90° towards the bulk flow. Steady fluid flow for a solute with a Schmidt number of 600 (similar to NaCl) dissolving from the wall and hydraulic Reynolds numbers up to 200 were evaluated. These conditions are similar to those used in our previous two-dimensional simulations of spacers.

Conventional 2-layer ladder spacers and 3-Layer spacer meshes modelled: 90° (top-left), 45° (top-right), A3LS-0° (bot-left) and A3LS-90° (bot-right)

Spacer performance was evaluated via an approximate permeate processing cost analysis. The total direct costs of permeate production were estimated without taking into account pre-treatment costs. Although the CFD simulations did not calculate permeate flux directly, it was estimated using a relationship derived for the mass balance of the solute at the membrane surface.

Comparison of permeate processing costs, suggests that although the 90° orientation of the 3-layer spacer results in a higher channel pressure drop, lower processing costs are achieved due to the increase in mass transfer and therefore lower membrane area requirements. Moreover, the costs achieved by that orientation in the laminar flow regime are lower than those achieved with common 2-layer ladder or diamond type spacers. Further optimisation of the performance of the 3-layer spacer and reduction in processing costs may be achievable by varying the geometric ratios of the spacer mesh.

The shape and orientation of the middle spacer layer also lends itself to optimisation. Previous research shows that form drag in the bulk flow does not improve mass transfer. Thus, the performance of a series of multi-layer spacer designs shown in figure x was evaluated. For these designs, the filament diameter to channel height ratio of ‘traditional’ cylindrical spacers was reduced from 0.6 to 0.4 or 0.3, and one or two layers of elliptical filaments with various angles of attack were introduced in the middle region of the channel. Simulations were completed for a solute with a Schmidt number of 600. The hydraulic Reynolds number was varied from 50 to 800. Due to computational complexities, only two-dimensional flow was considered.

The permeate processing cost analysis indicates that the multi-layer configurations are able to increase productivity by enhancing mass transfer. However, lower permeate processing costs are generally obtained by using a simple 2D zigzag spacer (2L06) with the same filament diameter to channel height ratio. Better performance can be obtained for the multi-layer designs by changing the angle of attack until little or no recirculation regions are formed downstream. In addition, the multi-layer spacer achieves better performance when membrane costs are high. There are further opportunities to improve the performance of multi-layer spacers by optimising the trade-off between mass transfer enhancement and energy losses associated with changes in spacer design.