Modeling of pressure drop in reverse osmosis feed channels using multilayer artificial neural networks

Supercomputing and machine learning-aided optimal design of high permeability seawater reverse osmosis membrane systems

Concentration polarization (CP) should limit the energy and cost reducing benefits of high permeability seawater reverse osmosis (SWRO) membranes operating at a water flux higher than normal one. Herein, we propose a multiscale optimization framework coupling membrane permeability, feed spacer design (sub-millimeter scale) and system design (meter scale) via computational fluid dynamics and system level modeling using advanced supercomputing in conjunction with machine learning. Simulation results suggest energy consumption could be reduced by 27.5% (to 1.66 kWh m^-3) predominantly through the use of high permeability SWRO membranes (12.2%) and a two-stage design (14.5%). Without optimization, CP approaches 1.52 at the system inlet, whereas the optimized CP is limited to 1.20. This work elucidates the optimized permeability, module design, operating scheme and benefits of high permeability SWRO membranes in seawater desalination.

Multiscale Analysis of Permeable and Impermeable Wall Models for Seawater Reverse Osmosis Desalination

In recent years, high permeability membranes (HPMs) have attracted wide attention in seawater reverse osmosis (SWRO) desalination. However, the limitation of hydrodynamics and mass transfer characteristics for conventional spiral wound modules defeats the advantage of HPMs. Feed spacer design is one of the effective ways to improve module performance by enhancing permeation flux and mitigating membrane fouling. Herein, we propose a multiscale modeling framework that integrates a three-dimensional multi-physics model with a permeable wall and an impermeable wall, respectively, at a sub-millimeter scale and a system-level model at a meter scale. Using the proposed solution framework, a thorough quantitative analysis at different scales is conducted and it indicates that the average errors of the friction coefficient and the Sherwood number using the impermeable wall model are less than 2% and 9%, respectively, for commercial SWRO membrane (water permeability 1 L m−2 h−1 bar−1) and HPMs (3 L m−2 h−1 bar−1, 5 L m−2 h−1 bar−1 and 10 L m−2 h−1 bar−1) systems, compared to the predictions using the permeable wall model. Using both the permeable and impermeable wall models, the system-level simulations, e.g., specific energy consumption, average permeation flux, and the maximum concentration polarization factor at the system inlet are basically the same (error < 2%), while the impermeable wall model has a significant advantage in computational efficiency. The multiscale framework coupling the impermeable wall model can be used to guide the efficient and accurate optimal spacer design and system design for HPMs using, e.g., a machine learning approach.

A Neural Network Based Superstructure Optimization Approach to Reverse Osmosis Desalination Plants

An ever-growing population together with globally depleting water resources pose immense stresses for water supply systems. Desalination technologies can reduce these stresses by generating fresh water from saline water sources. Reverse osmosis (RO), as the industry leading desalination technology, typically involves a complex network of membrane modules that separate unwanted particles from water. The optimal design and operation of these complex RO systems can be computationally expensive. In this work, we present a modeling and optimization strategy for addressing the optimal operation of an industrial-scale RO plant. We employ a feed-forward artificial neural network (ANN) surrogate modeling representation with rectified linear units as activation functions to capture the membrane behavior accurately. Several ANN set-ups and surrogate models are presented and evaluated, based on collected data from the H2Oaks RO desalination plant in South-Central Texas. The developed ANN is then transformed into a mixed-integer linear programming formulation for the purpose of minimizing energy consumption while maximizing water utilization. Trade-offs between the two competing objectives are visualized in a Pareto front, where indirect savings can be uncovered by comparing energy consumption for an array of water recoveries and feed flows.

Robust and universal predictive models for frictional pressure drop during two-phase flow in smooth helically coiled tube heat exchangers

There is a lack of well-verified models in the literature for the prediction of the frictional pressure drop (FPD) in the helically coiled tubes at different conditions/orientations. In this study, the robust and universal models for estimating two-phase FPD in smooth coiled tubes with different orientations were developed using several intelligent approaches. For this reason, a databank comprising 1267 experimental data samples was collected from 12 independent studies, which covers a broad range of fluids, tube diameters, coil diameters, coil axis inclinations, mass fluxes, saturation temperatures, and vapor qualities. The earlier models for straight and coiled tubes were examined using the collected database, which showed absolute average relative error (AARE) higher than 21%. The most relevant dimensionless groups were used as models' inputs, and the neural network approach of multilayer perceptron and radial basis functions (RBF) were developed based on the homogenous equilibrium method. Although both intelligent models exhibited excellent accuracy, the RBF model predicted the best results with AARE 4.73% for the testing process. In addition, an explicit FPD model was developed by the genetic programming (GP), which showed the AARE of 14.97% for all data points. Capabilities of the proposed models under different conditions were described and, the sensitivity analyses were performed.

Modeling and optimization of chlorophenol rejection for spiral wound reverse osmosis membrane modules

This study shows an artificial neural network (ANN) model of chlorophenol rejection from aqueous solutions and predicting the performance of spiral wound reverse osmosis (SWRO) modules. This type of rejection shows complex non-linear dependencies on feed pressure, feed temperature, concentration, and feed flow rate. It provides a demanding test of the application of ANN model analysis to SWRO modules. The predictions are compared with experimental data obtained with SWRO modules. The overall agreement between the experimental and ANN model predicted was almost 99.9% accuracy for the chlorophenol rejection. The ANN model approach has the advantage of understanding the complex chlorophenol rejection phenomena as a function of SWRO process parameters.