System scale analytical modeling of forward and assisted forward osmosis mass exchangers with a case study on fertigation

Abstract

Forward osmosis (FO) and assisted forward osmosis (AFO) mass exchangers are currently receiving considerable attention for their potential use in a variety of dilution and concentration applications in resource extraction, fertigation, and pharmaceutical process streams. In this work we develop analytical expressions for parallel and counterflow FO and AFO exchangers which can be used to quickly and accurately estimate the membrane area required for these applications in addition to determining the performance of existing exchangers. Unlike previous models, our analytical model accounts for internal and external concentration polarization in system scale exchangers with overall average errors of less than 10% against a numerical model and less than 35% validated against data from the literature. The performance of FO and AFO exchangers is compared, and an osmotic fertilizer dilution (fertigation) case study is investigated in which the trade-off between energy and membrane area requirements is quantified. We find that AFO exchangers yield a higher recovery relative to FO exchangers for a given energy input especially when the inlet draw-to-feed osmotic pressure ratio is low. Diminishing returns in recovery ratio are attained for increasing membrane area and increasing draw-to-feed mass flow rate ratio. We also find that for the same brackish feed water and recovery ratio, reductions in area of up to 40% relative to FO can be realized with 2 kWh/m 3 of energy input into an AFO system in the fertigation case study.

Molecular Dynamics Simulation of Transport Mechanisms and Desalination Performance of the PSF/UiO-66 Thin-film Composite Membrane

“…The Spiegler Kedem (SK) model was also proposed for osmotically driven membranes [9] to correct errors of total volume flux and other variables. The solute diffusion (SD) model was also used to predict the dilution factor and membrane area of the flat sheet needs [10], with considerations of the nonlinearity osmotic driving force, concentration polarization, and mass conservation. However, the pressure dropped through the membrane and the salt rejection was not properly predicted.…”

Hybrid Forward Osmosis–Nanofiltration for Wastewater Reuse: System Design

“…Operational parameters that highly influence the size of the system, its energy demands, and environmental impacts are, for example, the net driving force of the process, the inlet flow rate of the draw and feed solutions, and the recovery rate. Some modeling-based research was carried out to study the possible module design and to compare feasible configurations (e.g., cocurrent versus counter-current) [19,23,24,25,26]. These analyses are a step forward to understand the mass transfer mechanisms and they have not yet been developed to tackle the full scale of the potential treatment system.…”

One-Dimensional Analytical Modeling of Pressure- Retarded Osmosis in a Parallel Flow Configuration for the Desalination Industry in the State of Kuwait

“…As much of the literature focuses on lab-scale transport through a membrane by assuming that the concentrations along the membrane for both flow streams are constant, which might result in under-sizing exchangers for use in large systems because the average osmotic driving force across a long membrane is lower than the maximum osmotic driving force in a 0D transport model [23], therefore, a large system must be sized with a model that considers the change in driving force along the membrane length. In 2013, Shaqawy et al [24] developed a one-dimensional (1D) analytical expressions for parallel and counterflow PRO mass exchangers with respect to the recovery ratio of the membrane as a function of dimensionless parameters such as mass transfer units (MTU), mass flowrate ratio (MR) and osmotic pressure ratio (SR).…”

“…It was further extended later to estimate the required area of a PRO exchanger to determine the power production at a given feed and draw salinity by considering the effect of CP on the membrane performance [25]. Similar methods were also used by their research group to acquire the designated area of a forward osmosis (FO) and an assisted forward osmosis (AFO) system on the application of fertigation [23].…”

“…Furthermore, the maximum work simulated from these analytical expressions will be discussed, as well. Figure 1 shows the schematic diagram of a PRO mass exchanger device [23]. Herein, the feed solution of a lower concentration flows into the channel on one side, through a semipermeable membrane.…”