Conference Agenda

Polymeric membranes for liquid separation are recognized as a promising technology in various industrial separation applications. Two important characteristics of polymeric membranes are selectivity and permeability – higher permeability leads to high recovery, while higher selectivity translates to high purity. However, polymeric membranes exhibit an inherent tradeoff between selectivity and permeability [1]. Therefore, simultaneously achieving high recovery and high purity with a single-stage membrane is often impractical or leads to increased operating and capital costs. To address this limitation, a network with multiple membrane stages must be synthesized.

Multiple potential network configurations, with different stream connections and a distinct number of membrane stages, can be designed for a given separation task. However, the operating and capital costs of these configurations can differ significantly [2]. Therefore, the economic feasibility of membrane separation is heavily influenced by the decisions made during network synthesis. Thus, an optimization-based framework can be employed to synthesize globally optimal membrane networks. Additionally, a membrane unit model is a critical element to a membrane network optimization framework. However, nonidealities present in liquid mixtures pose difficulties in describing membrane permeation. As a result, existing computationally tractable unit models are valid only for separation of either binary liquid mixtures or multicomponent ideal gas mixtures.

In this work, we present a novel approach to design globally optimal membrane networks for multicomponent liquid separation. We propose a generalized optimization framework to recover multiple target components from the feed liquid mixture. First, we present a physics-based nonlinear surrogate unit model to describe membrane permeation for multicomponent liquid mixtures. Second, we formulate a highly interconnected superstructure to represent the broad spectrum of potential network configurations. Third, we propose an optimization model to determine the network configuration, along with the operating conditions, that minimizes the total required membrane area. The resulting optimization model is a nonconvex mixed integer nonlinear programming (MINLP) model, which is generally challenging to solve; hence, we introduce solution methods to improve computational efficiency. Finally, through multiple applications, we showcase how the proposed approach can obtain globally optimal solutions.

[1] L.M. Robeson, The upper bound revisited, J. Membr. Sci. 320 (2008) 390–400. https://doi.org/10.1016/j.memsci.2008.04.030.
[2] R. Spillman, Chapter 13 Economics of gas separation membrane processes, in: R.D. Noble, S.A. Stern (Eds.), Membr. Sci. Technol., Elsevier, 1995: pp. 589–667. https://doi.org/10.1016/S0927-5193(06)80015-X.

In the drive towards a circular economy, the reuse of waste materials for pollutant mitigation is a critical area of research. This study investigates the adsorption of lead, an EPA priority pollutant, onto reclaimed mine water sludge (RMWS), a sustainable and low-cost adsorbent from a water desalination plant. The focus was on modeling the internal diffusion mechanisms governing adsorption kinetics, offering a comprehensive model that tracks the diffusion of lead onto the RMWS adsorbent in both space and time. This was done to by exploring the influence of different transport phenomena playing a role within the system.

The adsorption process typically involves the occurrence of three steps: the transport of the adsorbate from the bulk liquid phase to the boundary layer, movement to the adsorbent surface (external mass transfer) as well as diffusion through the material's pores (internal mass transfer). This analysis builds on the understanding that in liquid–solid adsorption, fluid film diffusion often plays a secondary role compared to intraparticle diffusion, especially in mesoporous adsorbents such as RMWS. Parameter optimisation previously conducted showed external mass transfer effects becomes less significant under sufficient agitation conditions.

Traditional kinetic models used for adsorption modelling typically assume that both external and internal mass transfer are negligible, this is not always justified. Only in the context of intrinsic kinetics, where the system’s behaviour depends solely on the physical or chemical interactions between the adsorbate and adsorbent, can this assumption hold true. In the study conducted, diffusion was examined in great depth. It was assumed that the contaminant concentration at the moth of the adsorbent’s pore is greater than that inside the pore as adsorption takes place. Consequently, the rate throughout the particles will vary. The model derived is based on a mole balance on the RMWS as the lead is adsorbed. This will give insight into the application of a species balance over volume segments in a packed bed.

Incorporating both surface and pore diffusion effects, our model captures the dynamics of Pb(II) diffusion from the bulk solution to the RMWS surface and further into its pore structure. These findings are crucial for the design of large-scale adsorption units, where oversimplified kinetic models can lead to suboptimal system performance. The validated diffusion model highlights RMWS's potential as a circular economy solution for heavy metal removal, promoting resource efficiency and environmental sustainability.