Osmosis Model Research Articles

Enhanced osmosis model with bilateral total variation for effective shadow removal

This research paper presents an innovative technique for shadow images removal. The method involves redefining a contemporary osmosis model by incorporating bilateral total variation (TV) operators. This integration allows to take advantage of robust anisotropic diffusion, resulting in improved image restoration. The paper also outlines new mathematical derivation of the bilateral TV and a combination with nonlinear anisotropic transport term. The experimental results substantiate the effectiveness of the anisotropic osmosis model, showcasing its superior qualitative and quantitative performance when compared to current state-of-the-art techniques.

Time-fractionated anisotropic osmosis with bilateral total variation for effective shadow mitigation in image processing

This work introduces an innovative strategy for mitigating shadow effects in images through the utilization of a time-fractionated anisotropic osmosis equation. The method goes beyond conventional approaches by incorporating a newly derived bilateral total variation (BTV) term, coupled with a nonlinear anisotropic transport component. Theoretical insights are rigorously presented, accompanied by a meticulous exposition of the discretization scheme based on finite differences. In addition to the theoretical foundation, the paper conducts comprehensive numerical experiments to validate the proposed model's efficacy. These experiments not only affirm the qualitative advantages of the anisotropic osmosis model but also provide quantitative evidence of its superiority over existing state-of-the-art techniques.

Simulation of landfill leachate treatment systems involving self-designed disk tube reverse osmosis (DTRO) model integrated with mechanical vapor recompression (MVR)

Four landfill leachate treatment systems involving self-designed disk tube reverse osmosis (DTRO) module integrated with mechanical vapor recompression (MVR) were established in Aspen Plus. To assess the treatment efficiency and the economic feasibility of landfill leachate treatment techniques, simulation of leachate treatment by four systems were conducted, and the corresponding recovery rate Y, removal rate Rt, energy consumption and operating cost were obtained. Results indicate that for the two-stage DTRO system, the optimal operational pressures in compliance with emission standards are 5.6 MPa in the first stage and 3.5 MPa in the second stage. Adding an MVR system to further treat the membrane concentrate (MC) can greatly reduce the pollutant recharge and the energy consumption of the DTRO system. When Y in MVR is not strictly required, the single-stage MVR system is the most energy-saving one. When a high Y (≥80 %) is required, the series double-stage MVR system affords the highest energy-efficiency, offering a 3.14 % lower operating cost, a 3.27 % lower unit COD removal cost, and a 7.29 % lower unit water production cost as compared to the single-stage MVR system.

Optimization of seawater desalination processes with the ideal reverse osmosis equation

The optimization of a membrane seawater desalination system is used to be a very complicated and time consuming process because tedious calculations are required to determine permeate recovery of the membrane system. This process can be greatly streamlined when the ideal reverse osmosis model is used to calculate the recovery of the membrane system. With this model, the pressure for a designated recovery can be determined conveniently and accurately from the basic parameters of a membrane system. Then the specific cost under various conditions can be calculated for the recovery. Finally, the recovery that minimized the specific cost for the permeate production can be easily determined graphically. The impacts of energy, membrane, feed water pretreatment, and concentrate handling on the optimal recovery of a membrane desalination process are demonstrated. The avoidance of a large number of equations and numerical integration in the determination of permeate recovery can greatly facilitate the optimization of design and operation of seawater desalination processes.

A fractional osmosis model for image fusion

A fractional osmosis model for image fusion

A Lyapunov-Sylvester numerical method for solving a reverse osmosis model

<abstract><p>Clean water is a necessity for many organisms, especially human life. Due to many factors, there is a significant shortage of potable water. This has led to efforts involving recovering water from wastewater or the sea through different technologies. Recently, the desalination of seawater via the reverse osmosis system has shown to be a promising method for drinking water treatment and recovery. Such a technique relies on mathematical models based on many parameters, resulting in special PDEs to model the reverse osmosis system. This paper develops a numerical method to solve a reverse osmosis model. The governing PDE is converted into a Sylvester equation that is proved to be uniquely solvable, stable, consistent, and convergent. The numerical scheme developed is validated with experimental data from the literature, and some numerical simulations.</p></abstract>

Integrated Pumped Hydro Reverse Osmosis System optimization featuring surrogate model development in Reverse Osmosis modeling

The pressure head generated by the upper reservoir of a pumped hydro energy storage system can be sufficient for creating the pressure gradient required for a reverse osmosis desalination plant. Combined with the fact that many drought-stricken coastal areas have nearby mountains at the necessary elevation for these upper (mountaintop) reservoirs, a symbiotic relationship can be ascertained through the co-location of a pumped storage hydropower (PSH) system with a reverse osmosis (RO) desalination system. Merging PSH and RO into one Integrated Pumped Hydro Reverse Osmosis System (IPHROS) instead of implementing each individually could result in a number of benefits, including reduced capital investment, lower maintenance costs, and a natural mechanism for diluting the highly saline brine discharge generated from the RO process. This paper extends the work of Slocum et al. in 2016, who first introduced the concept of IPHROS, by optimizing the amount of seawater sent to and diverted from the upper reservoir for maximal energy recapture and freshwater production, respectively, while also seeking to maximize the RO system recovery ratio. For this multiobjective optimization, a new reverse osmosis model is created that utilizes a blend of empirical and fundamental equations based on the solution–diffusion model of membrane transport and boundary layer effects that naturally occur along reverse osmosis membranes. Additionally, surrogate models are developed to predict the permeate flowrate and fractional salt rejection rate for a Seamaxx™-440 RO element. Optimizing the presented IPHROS model reveals a 16% decrease in the break even time for IPHROS compared to PSH and RO being implemented individually, and that at the best design with regards to the energy, freshwater, and RO system recovery objectives, 79.5 million kWh of energy and 5.79 million cubic meters of fresh water can be delivered to a population, significant amounts for a population seeking to transition to a renewable energy-based grid and alleviate dire freshwater conditions. Enhanced modeling and optimization, as was initiated in this paper, will eventually aid in IPHROS’ large-scale adoption into energy and freshwater infrastructures.

A hybrid modelling approach for reverse osmosis processes including fouling

A novel hybrid modelling approach, combining the strengths of a mechanistic reverse osmosis (RO) model and a data-driven fouling model, is developed on a unique long-term dataset from a full-scale RO installation to predict its performance. The mechanistic solution-diffusion model describes well understood phenomena in RO such as concentration polarisation, osmotic pressure and solutes transport throughout the membrane. This solution-diffusion model is combined with a data-driven model to cover the gaps in knowledge related to fouling phenomena. Several fouling models are tested to predict the membrane resistance over time and a thorough analysis of important input features was performed. A non-linear recurrent neural network with long short-term memory (RNN-LSTM) clearly outperformed (RMSE = 1.01e13) a linear autoregressive integrated moving average with exogenous variables (ARIMAX) model (RMSE = 1.97e13) for an 8 month testing period. The best performance was achieved when including membrane cleaning as two separate features representing short and long CIPs. Moreover, recovery setpoint, concentrate flow rate, feed temperature, feed conductivity and feed calcium concentration were shown to be important model input features. Fouling sensitive parameters of the solution-diffusion model (the water permeability, the feed spacer channel height and the solute permeability - determined by a global sensitivity analysis) were made function of the output (membrane resistance) of the RNN-LSTM thus leading to a serial hybrid model. The predictions of the hybrid model showed a clear improvement for all output variables when compared to a solution-diffusion model including temperature correction. The model was developed, calibrated and trained on measurements of standard sensors and can thus be used for real-time applications such as advanced control and predictive scenario analysis in a digital twin context.

Fast and stable schemes for non-linear osmosis filtering

We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general scalar function g with suitable properties, which allows to balance the diffusion intensity on the different regions of the image while preventing smoothing artefacts. For the proposed model, conservation properties (intensity and non-negativity) are proved and a variational interpretation is showed for specific choices of g. Upon suitable spatial discretisation, both an explicit and a semi-implicit iterative scheme are considered, for which convergence restrictions and unconditional stability are proved, respectively. To validate the proposed modelling and the computational speed of the numerical schemes considered, we report several results and comparisons for the problem of shadow/light-spot removal and compact data representation, showing that artefact-free and computationally efficient results are obtained in comparison to standard linear and anisotropic models, and state-of-the art approaches.

Data-driven forward osmosis model development using multiple linear regression and artificial neural networks

This work investigates the capability of multiple linear regression (MLR) and artificial neural networks (ANN) to model permeate flux in a thermodynamically complex forward osmosis (FO) process. Whey-permeate was concentrated to a dry matter content of more than 55 %, creating a highly supersaturated metastable solution and exceeding the established boundaries of conventional membrane technology. Different ANN architectures were trained and tested with a varying number of hidden layers and neurons to find an accurate structure.Furthermore, the evaluated significance of the input parameters was used to reduce the model's complexity. This work shows that both approaches (MLR: R²test = 0.9718, ANN: R²test = 0.9849) were able to model the FO's permeate flux accurately, even with a reduced number of inputs. Finally, due to its slightly better performance, the ANN was used to outline the influence of FS inlet flow and process temperature.

Modeling and Structural Optimization of MSF-RO Desalination System.

Based on the mathematical modeling and operational optimization studies of reverse osmosis (RO) and multistage flash (MSF) desalination, the structural optimization of the hybrid process was specially studied in this work with the consideration of reducing comprehensive expenses under given operational conditions. Firstly, according to the process mechanism and flowchart of the RO and MSF seawater desalination technologies, seven hybrid structures with different feed conditions were designed, and their connection equations were established for numerical calculation. Then, in order to evaluate the economic performance of the hybrid systems with different structures, the hourly average operational cost equations of RO and MSF processes were established and formulated as the comprehensive evaluation indicators. Next, with a given water production requirement, simulation calculations of the hybrid system with seven different structures were performed. The results show that the hybrid system with the fourth structure has the lowest operational cost of 4.6834 CNY/m3, and at the same time it has the lowest blowdown. However, if we take GOR or production water temperature as the target, the optimal structure of the hybrid system is the fifth or the seventh option. The obtained results are helpful in structural optimization of the hybrid system with aspects of operational cost reduction, maximum GOR, or minimizing the wastewater discharge.

Transport mechanisms and desalination performance of the PSF/UiO-66 thin-film composite membrane: a molecular dynamics study

ABSTRACT A novel non-equilibrium molecular dynamics (MD) model was presented to investigate the transport mechanisms and desalination performance of thin-film composite membranes (TFC). Firstly, polyamide (PA) and polysulfone (PSF), or PSF/UiO-66 models, were constructed as active and support layers. Subsequently, feed solution and draw solutions with 0.5, 1.0, and 1.5 M salt concentrations were generated. Thirdly, these aqueous and membranes were combined to build forward osmosis (FO) models. The FO process was simulated to anatomise the membrane fouling, water flux, and salt rejection, which JAVA and MD programs were combined to calculate. The results indicated that the PA-PSF/UiO-66 membrane exhibited a stable water transport and salt rejection performance compared to the pristine PA and PA-PSF membranes. Finally, experiments and simulations were compared, and the same trends were found. Therefore, this simulation work provided significant insight in guiding the design and synthesis of the FO membrane.

A nonlocal method for image shadow removal

This paper proposes a new model for image shadow removal. The model reformulates a recent osmosis model with nonlocal differential operators. This allows to benefit from distant pixels similarities and thus improves restoration results. Some properties of this model are established and discussed, making it suitable for our application. Experimental results show that the nonlocal model obtained very good qualitative and quantitative results compared with state-of-the-art techniques.

Direct-drive ocean wave-powered batch reverse osmosis

Ocean waves provide a clean, reliable source of energy making them a viable energy source for desalination, especially in coastal communities and island nations. However, large capital costs render current wave-powered desalination technologies economically infeasible. This work presents a configuration for ocean-wave-energy-powered batch reverse osmosis. The proposed system uses seawater as the working fluid in a hydro-mechanical coupling and replaces the reverse osmosis high-pressure pump with a hydraulic converter for direct-drive, allowing for minimal intermediary power conversions, which leads to fewer parts necessary for operation and higher efficiencies. The concept was analyzed with MATLAB and Simulink to model the transient energy dynamics of the wave energy converter, power take-off system, and desalination load. The coupling, incorporating energy recovery, could achieve an SEC and LCOW as low as 2.30 kWh/m3 and $1.96/m3, respectively, for different sea states and a second law efficiency of 0.461. The results of the model were validated at the sub-system level against existing literature on wave energy models and previous work completed on batch reverse osmosis models. This system is the first to combine these two technologies. SEC and LCOW values were validated by comparing to known and predicted values for various types of RO systems.

Modeling of forward osmosis for microalgae harvesting

In this study, a transport-based model capable of predicting water flux in microalgae harvesting in forward osmosis (FO) system was developed. Based on Carman-Kozeny resistance model, steady state hydraulic resistance of cake layer comprised of microalgae cells was calculated; by means of control volume approach growth rate of the cake layer was also quantitatively obtained at transient state. Cake-enhanced concentration polarization (CECP), which arises from cells, along with dissolved compounds, deposited on membrane surface and acts to degrade FO performance, was estimated in real time. Model parameters related to a feed solution of microalgae cells were evaluated on the basis of empirical and theoretical data. It was found that deposition rate constant of microalgal cells was at least two orders of magnitude higher than diffusion rate constant under the experimental condition. Among microalgae related parameters, the porosity and thickness of cake layer were found to be the most influential on the water flux according to sensitivity analysis; and therefore they were calibrated by a statistical technique to improve model accuracy. Based on the estimated parameters, the developed model was validated through batch FO operations, and it was in good alignment with quasi-steady state data. There have been quite a few FO modeling studies thus far; and yet to the best of our knowledge, this study is the first one that elucidates actual fouling phenomenon with an actual feed solution, which may offer both theoretical and practical understandings needed for the development of FO-based microalgae harvesting process.

Mathematical and experimental modeling of reverse osmosis (RO) process

This paper provides a mathematical simulation model for the reverse osmosis (RO) process with series elements. A mathematical simulation model was developed based on the mass, material and energy balances considering the concentration polarization. The simulation model is open-source and easy to couple with other computational tools like optimization algorithms and SCADA1 applications. An RO laboratory pilot was also set up in the Hydraulic Lab of Shahid Chamran University of Ahvaz to validate the simulation results. Comparing the results of the simulation model with the experiments and ROSA commercial software, the proposed simulation model functions well and is reliable. The comparisons indicate that the simulation results are over 96% close to ROSA and over 80% close to experimental results.

Comparison between pressure retarded osmosis model using batch and continuous water supply sources

Pressure retarded osmosis (PRO) is a novel renewable energy technology that generates electricity from two water sources. Due to the osmotic pressure difference, freshwater permeates across a membrane to the other side, where the high-pressure seawater flows and drives a turbine to generate power. Many mathematic models have been proposed to evaluate the performance of a PRO. However, it was found that most performance of the PRO that have been reported were performance by using freshwater with limited supply (batch) in the model. It is not accurate as, in practice, the supply of freshwater occurs in a continuous manner. In this work, the influence of batch and continuous supply of fresh water on the performance of PRO was demonstrated. The effect of flow direction, i.e., concurrent and counter-current flows, was also examined. The model simulation was performed by using MATLLAB program, and the performance of PRO is expressed in terms of average power density. The results revealed that the batch and continuous supplies of freshwater had a strong impact on the performance of the PRO. However, the performance of concurrent and counter-current flow were not significantly different.

A novel UiO-66/PSF-composite membrane for the rejection of multiple antibiotics: Numerical simulation and experiment verification

UiO-66 nanoparticles were fabricated and applied to the support layer of a novel, thin-film nanocomposite membrane for treatment of wastewater containing antibiotics. The incorporation of the UiO-66 particle structure improved the stability and permeability of the membrane. When the membrane with 0.5 wt% of UiO-66 particles was used to treat antibiotic wastewater by a forward-osmosis process, the water flux reached 50.78 LMH (L·m−2·h−1), an increase of 46% compared with the membrane without UiO-66 particles. The rejections of six types of antibiotics improved to over 99.94%. Even trimethoprims rejection rate enhanced to 100% because antibiotics exposed on the surface of the UiO-66 nanoparticles. The forward osmosis model could explain the mechanism of permeation, and predict water flux and rejection. Thus, a novel mathematical model with Gaussian pore distribution and different potential functions was proposed to process multiple-solute transportation and rejection on the charged surface of the membrane. The rejection of six antibiotics was predicted by the iteration algorithm, and the errors of water flux, salt flux, and rejection rates were less than 1.3 LMH, 0.2 gMH (g·m−2 h−1), and 1.7% between the predictions and the experiments, respectively. The accuracy of the proposed model was higher than the model published before. Therefore, the experimental results and the theoretical model provide a significant insight into the synthesis thin-film composite membranes and application of water purification.

A generic reverse osmosis model for full-scale operation

Mathematical models can be a powerful tool in the operation of reverse osmosis (RO) facilities which is often challenged by a varying feed water quality. Most models, however, do not consider both full-scale and good modelling practice, which makes them less suited in practice. In this paper, a generic steady state model for RO was set-up and applied to a unique three-year data set from a full-scale RO process according to state-of-the-art good modelling practice. It was found that the model outputs are most sensitive towards the water and the solute permeability, and the feed spacer channel height, and therefore, only these parameters were calibrated. Furthermore, manufacturer's tests do not always reflect the full-scale situation, which highlights the importance of calibration. The model was validated with online conductivity data as input taking into account the uncertainty originating from online sensors, and compared to the commercial software Winflows. Despite the lack of long-term predictive power since fouling was not included, the model with online conductivity data as input showed satisfactory results, i.e. an average deviation from the data of 2.7%, 12.7%, 34.1% and 18.7% for respectively the recovery, the concentrate pressure, the permeate and concentrate solute concentration.

A comparison of five surface mixed layer models with a year of observations in the North Atlantic

Five upper ocean mixed layer models driven by ERA-Interim surface forcing are compared with a year of hydrographic observations of the upper 1000 m, taken at the Porcupine Abyssal Plain observatory site using profiling gliders. All the models reproduce sea surface temperature (SST) fairly well, with annual mean warm biases of 0.11 °C (PWP model), 0.24 °C (GLS), 0.31 °C (TKE), 0.91 °C (KPP) and 0.36 °C (OSMOSIS). The main exception is that the KPP model has summer SSTs which are higher than the observations by nearly 3°. Mixed layer salinity (MLS) is not reproduced well by the models and the biases are large enough to produce a non-trivial density bias in the Eastern North Atlantic Central Water which forms in this region in winter.All the models develop mixed layers which are too deep in winter, with average winter mixed layer depth (MLD) biases between 160 and 228 m. The high variability in winter MLD is reproduced more successfully by model estimates of the depth of active mixing and/or boundary layer depth than by model MLD based on water column properties. After the spring restratification event, biases in MLD are small and do not appear to be related to the preceding winter biases.There is a very clear relationship between MLD and local wind stress in all models and in the observations during spring and summer, with increased wind speeds leading to deepening mixed layers, but this relationship is not present during autumn and winter. We hypothesize that the deepening of the MLD in autumn is so strongly driven by the annual cycle in surface heat flux that the winds are less significant in the autumn. The surface heat flux drives a diurnal cycle in MLD and SST from March onwards, though this effect is much more significant in the models than in the observations.We are unable to identify one model as definitely better than the others. The only clear differences between the models are KPP’s inability to accurately reproduce summer SSTs, and the OSMOSIS model’s more accurate reproduction of MLS.