Multicomponent Adsorption Model Research Articles

Production of green methane by carbon dioxide capture from landfill biogas via pressure swing adsorption mediated by MOF ZIF-8

The growing interest in biomethane (bioCH4) as a sustainable replacement for conventional fossil fuels highlights the urgency to develop efficient CO2 capture methods from raw biogas, thereby enhancing the value of this renewable fuel source. This study investigates the efficacy of ZIF-8 as an adsorbent for CO2 capture through pressure swing adsorption (PSA) under non-isothermal conditions. ZIF-8 was synthesized and characterized using SEM, BET, FTIR, and XRD to understand and confirm its microstructures. A computational model was developed to simulate the dynamic behavior of ZIF-8 during adsorption, incorporating insights from its characterization. The model, based on the extended Langmuir model for multicomponent adsorption, also accounted for adjustments in the adsorption bed geometry. Dynamic simulations were performed employing the Aspen Adsorption platform to assess the impact of key parameters such as the CH4/CO2 ratio, length/diameter ratio, and adsorption time on bioCH4 purity. Utilizing the Design of Experiments framework, central composite design (CCD), and desirability functions, the interplay of these parameters was optimized to enhance bioCH4 purity and recovery rates. The optimized PSA system, utilizing ZIF-8, demonstrated impressive purity of 99.93% and recovery of 96.5% at CH4/CO2 ratio of 2.06, a length/diameter ratio of 2.76, and an adsorption time of 115 s. These results meet stringent quality criteria for vehicle fuel, aligning with the most rigorous emission standards. For future investigations, it is crucial to explore the long-term stability and regeneration capabilities of ZIF-8 in large-scale applications. Understanding its practical feasibility and sustainability as an adsorbent for biogas upgrading will provide valuable insights for further advancements in this field.

Activated carbon fibers of high surface area from corn husk: Mono and multicomponent adsorption studies of Pb2+ and Cu2+ ions from aqueous solution

The present work reports the preparation of activated carbon fibers (ACF) from corn husk through the slow pyrolysis process in the presence of H3PO4. The ACF were properly characterized, exhibiting morphological characteristics of microfibers, high surface area (SBET = 1824 m2/g), and acidic surface properties (pHpcz = 3.85). Adsorption studies for mono and multicomponent systems of Pb2+ and Cu2+ ions in aqueous solution were carried out and kinetic models of pseudo-first-order, pseudo-second-order, and Elovich, and equilibrium models of Langmuir, Freundlich, and Dubinin-Radushkevich, as well as, multicomponent adsorption models of modified Langmuir, extended Freundlich, and Sheindorf-Rebuhn-Sheintuch were fitted to the experimental data. The results showed the ACF exhibited high adsorption capacity in the monocomponent system (Pb2+= 210.6 mg g−1, Cu2+= 212.9 mg g−1), which decreased for the multicomponent system (Pb2+ = 101.6 mg g−1; Cu2+ = 56.1 mg g−1). Furthermore, the adsorption process involved both physisorption and chemisorption reactions and it was considered spontaneous and endothermic.

Equation-of-state-based lattice Boltzmann model of multicomponent adsorption onto fluid–fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid–fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid–fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.

Dynamic simulation and analysis of dichloromethane-acetone, dichloromethane-trichloromethane and dichloromethane-toluene VOC mixture abatement systems under transient feed conditions

Minimisation of environmental footprint in line with sustainability goals rests at the top of the agenda of the pharmaceutical industry. Volatile Organic Compounds (VOCs), while essential to primary pharmaceutical manufacturing, are solvents whose emissions pose a risk to human health and ecosystems. Adsorption on activated carbon beds is an established technology for end of pipe emissions control, which, however, faces efficiency limitations by quick and irregular bed saturation due to complex, transient feeds. This study employs a validated nonisothermal, multicomponent adsorption model to quantitatively assess the exact effect and potential value of waste stream feed sequencing towards activated carbon bed utilisation optimisation. Our results indicate that gradual increase of dichloromethane feed concentration in combination with a low, constant inlet concentration of the strongly adsorbing component leads to the latest breakthrough onset for the dichloromethane-acetone, dichloromethane-chloroform and dichloromethane-toluene mixtures. Transient vs. constant feeds usage and their interplay clearly affects bed behaviour, paving the way to industrial VOC emission abatement scheduling and process optimisation.

Optimized hydrogen purification for fuel cell quality from quinary coke oven gas via layered pressure swing adsorption under non-isothermal conditions

Coke oven gas from steel industries offers a valuable hydrogen rich fuel but is accompanied by impurities, such as CH4 and CO2, that contribute to the environmental footprint. The process of extracting H2 from coke oven gas not only provides clean energy from the alternative source, but also prevents the release of these impurities. Motivated by the promising H2 source alternative, a 2-bed, 6-step pressure swing adsorption system operating under non-isothermal conditions was used to purify H2 from coke oven gas. A validated multi-component adsorption model was developed via Aspen Adsorption to simulate and optimize the process. The validated model revealed strong correlations between the factors (adsorption pressure, adsorption temperature, adsorption time, and H2 concentration) and responses (purity and recovery of H2). The findings indicated that increasing the H2 feed concentration resulted in an improvement in H2 purity but a decline in recovery. Conversely, an extended duration of adsorption exhibited an adverse influence on both the purity and recovery of H2. Furthermore, the study indicates that higher adsorption pressure and temperature were correlated with lower H2 purity but improved recovery performance. To optimize the pressure swing adsorption process, the desirability function was applied within the response surface methodology model, enabling the determination of optimal conditions for the purification process. The optimized H2 purity and recovery were found to be 99.995% and 62.758%, respectively, at H2 feed concentration of 49%, adsorption time of 160 s, pressure of 6 atm, and adsorption temperature of 293 K.

Research in Industrial Use of Ion Exchange and Simulation

We investigated the industrial use of ion exchange technology as well as the modeling of fixed bed, multicomponent ion exchange processes. In this paper we report on both fields of this research. We have developed a complex technology for the selective separation of the long-live radionuclides and the partial recycling of boric acid from radioactive evaporator bottom residue. A wastewater treatment system has been developed by using a cesium-selective inorganic ion exchanger. The selective separation of 137Cs, 134Cs from high salt concentration and strongly alkaline evaporator bottom residue in Paks NPP has a volume reduction factor of about 3500–6500 at the value of the decontamination factor DF > 100, for the samples of four evaporator bottom residue tanks of the NPP. Some important classes of ion exchangers do possess uniform internal pore structures and bring all parts of the solíd structure into much closer contact with the liquid. Such materials are porous organic resins. For these types of exchangers, we have modified Mansour's multicomponent adsorption model and developed a computer program to describe multicomponent breakthrough, cocurrent, and counter-current elution curves for ion exchangers. In addition, we have developed a subroutine for the calculation of multicomponent ion exchange kinetics according to Nernst-Planck equation and successfully tested it. This subroutine will be added to the multicomponent ion exchange breakthrough and elution simulation program to have a real multicomponent ion exchange simulation program. In this paper we report about these research results too.

Competitive adsorption law of multi-component gases during CO2 displacement of CH4 in coal seams

The CO2 enhanced coal bed methane recovery technology provides an excellent way to mitigate the greenhouse effect and energy crisis. The features and mechanism of CO2/CH4 competitive adsorption in the coal rock matrix have a critical impact on the production of CBM. For CO2/CH4 competitive adsorption process components and pressure changes, a multi-component gases competitive adsorption experiment was carried out with CO2 and CH4 binary gases as the study objects, and a multi-component adsorption model was developed by the expanded Langmuir equation. Based on the principles of molecular dynamics and thermodynamics, important parameters such as the average free range of gas molecules and adsorption potential are introduced to explain the competitive adsorption behavior from multiple perspectives and explore the competitive adsorption law of CH4 and CO2 under multiple component conditions, so as to provide some theoretical basis and field guidance for improving the extraction effect of CH4 in coal seams. The results show that: Under two critical conditions (100%CO2 +0%CH4 and 0%CO2 +100%CH4), the Langmuir volumes of CO2 for HN 1/3 coking coal and HL weakly caking coal respectively are 2.21 and 3.01 times higher than those of CH4; the overall adsorption capacity of binary gas is in between the adsorption capacities of both critical conditions and increases with increasing CO2 concentration in the gas source ratio; using E-L equation for binary gas component partitioning, the CH4 partition curves were all below CO2, the concentration of free-phase CH4 was always higher than that in the adsorbed phase, and coal samples had stronger adsorption ability for CO2 than CH4. CO2 has a stronger adsorption potential at the surface for HL weakly caking coal. CH4 has a slightly stronger adsorption potential at the surface for HN 1/3 coking coal. The higher coalification degree of the coal sample, the stronger the adsorption ability for CH4 and the weaker the adsorption ability for CO2. The slope of the overall adsorption curve of multi-component gases is analogous to the slope of the component with a high ratio of gas or strong adsorption capacity; the capacity of one-component adsorption for dual gas is closely related to the partial pressure of the free-phase gas and the separation factor α21. When the concentration ratio of CH4/CO2 in free phase is y2/y1 =α21, the concentration of both gases in adsorption phase is 50%, and α21 correlation is weakened, then the free phase gas partial pressure is dominant and there is a threshold value makes CH4 and CO2 adsorption capacity equal; when y2/y1 <α21, the coal preferentially adsorbs CO2 in the binary gas; when y2/y1 >α21, the coal preferentially adsorbs CH4 in the binary gas.

The significance of granular activated carbon pore structure in modeling dissolved organic carbon removal in fixed-bed filters

A reliable model that describes DOC removal during biological-active granular activated carbon filtration for advanced wastewater treatment has to cover several aspects that influence biological and adsorptive removal processes. For this purpose, this work introduces a two-domain internal diffusion approach to a multicomponent adsorption model, which is combined with a traditional biofilm model for the first time. DOC was divided into fictive components according to biodegradability and adsorbability to calculate multicomponent adsorption equilibrium based on the ideal adsorbed solution theory. Adsorption kinetics included external mass transfer (diffusion through a boundary layer and a biofilm) and internal mass transfer (fast pore diffusion in the larger pores and slow surface diffusion in the micropores). Mass transfer in the micropore domain was implemented by adjusting the adsorptive driving force depending on the available internal surface area for DOC adsorption based on an empirical surface diffusion model. Simulated DOC breakthrough curves were sensitive to model parameters related to the pore structure of the granular activated carbon (GAC). The model was validated with two GAC types and empty bed contact times ranging between 6 and 33 min. The model results showed a good agreement with measured DOC breakthrough curves over the entire operation time, demonstrating the applicability and transferability of the model. In particular, the initial DOC breakthrough was well represented. However, some systematic deviations between measured and simulated DOC breakthrough curves were observed, which are probably due to the level of detail of the implemented biofilm model.

Highly selective adsorption of 5-hydroxymethylfurfural from multicomponent mixture by simple pH controlled in batch and fixed-bed column studies: Competitive isotherms, kinetic and breakthrough curves simulation

Fixed-bed column adsorption is one of the most promising technologies for the separation and purification of 5-hydroxymethylfurfural (5-HMF) from biomass hydrolysate from the point of view of industrial application. However, one of the most pressing issues to be resolved is how to improve the separation factor of 5-HMF and its by-product levulinic acid (LA) and formic acid (FA). In this study, we used poly (BDM-alt-DVB) resin (BD-11) as an adsorbent and a simple pH control in batch and fixed-bed column to explore the competitive adsorption behavior and mechanism of 5-HMF from multicomponent solution. Without adjustment for solution pH, the separation factors of α5-HMF/LA, α5-HMF/FA, α5-HMF/Glucose were 2.6, 11.3, and 22.2, respectively. Interestingly, the separation factors of α5-HMF/LA, α5-HMF/FA, α5-HMF/Glucose increased dramatically to 73.0, 72.2, and 49.2 by merely adjusting the solution pH to 7.02. Furthermore, when the pH was adjusted to 7.02, the equilibrium time of 5-HMF adsorption on the BD-11 resin was within 20 min, and the adsorption capacity reached 69.7 mg/g, which was 118 % of the equilibrium adsorption capacity of the unadjusted pH value. In addition, the proposed fixed-bed column multicomponent competitive adsorption model was shown to agree well with the experimental data and successfully simulated the adsorption behavior of 5-HMF under a variety of experimental conditions. In conclusion, the fixed-bed column had great potential in 5-HMF selective adsorption from an aqueous solution by simple pH control.

A Review of the Modeling of Adsorption of Organic and Inorganic Pollutants from Water Using Artificial Neural Networks

The application of artificial neural networks on adsorption modeling has significantly increased during the last decades. These artificial intelligence models have been utilized to correlate and predict kinetics, isotherms, and breakthrough curves of a wide spectrum of adsorbents and adsorbates in the context of water purification. Artificial neural networks allow to overcome some drawbacks of traditional adsorption models especially in terms of providing better predictions at different operating conditions. However, these surrogate models have been applied mainly in adsorption systems with only one pollutant thus indicating the importance of extending their application for the prediction and simulation of adsorption systems with several adsorbates (i.e., multicomponent adsorption). This review analyzes and describes the data modeling of adsorption of organic and inorganic pollutants from water with artificial neural networks. The main developments and contributions on this topic have been discussed considering the results of a detailed search and interpretation of more than 250 papers published on Web of Science ® database. Therefore, a general overview of the training methods, input and output data, and numerical performance of artificial neural networks and related models utilized for adsorption data simulation is provided in this document. Some remarks for the reliable application and implementation of artificial neural networks on the adsorption modeling are also discussed. Overall, the studies on adsorption modeling with artificial neural networks have focused mainly on the analysis of batch processes (87%) in comparison to dynamic systems (13%) like packed bed columns. Multicomponent adsorption has not been extensively analyzed with artificial neural network models where this literature review indicated that 87% of references published on this topic covered adsorption systems with only one adsorbate. Results reported in several studies indicated that this artificial intelligence tool has a significant potential to develop reliable models for multicomponent adsorption systems where antagonistic, synergistic, and noninteraction adsorption behaviors can occur simultaneously. The development of reliable artificial neural networks for the modeling of multicomponent adsorption in batch and dynamic systems is fundamental to improve the process engineering in water treatment and purification.

Role of heat dissipation on carbon dioxide capture performance in biomethane upgrading system using pressure swing adsorption

The generation of huge amount of heat from the processes adversely affects the separation and purification performance. The scarcity of studies on the heat transfer effects on breakthrough curves and bed temperature profile of biomethane upgrading process in the literature prompt us to investigate these effects in a greater detail. In this work, a multi-component adsorption model is built to emulate the heat transfer effects on the performance of biomethane upgrading process under three heat dissipation systems i.e., rigorous, thin wall, and adiabatic. Adiabatic system represents the existing industrial purification technology being practiced today. Adiabatic system prohibits heat exchange between beds. In this work, the rigorous system which allows maximum heat transfer between adsorbing and desorbing beds shows the highest methane purity of 97%, followed by thin wall (93%) and adiabatic (92%) systems. The rigorous system also is capable of reaching the highest methane recovery of 80%, followed by thin wall (77%) and adiabatic (76%) systems. The highest biomethane upgrading performance is largely due to the comprehensive nature and efficient heat dissipation by the rigorous system.

Adsorption for efficient low carbon hydrogen production: part 1\u2014adsorption equilibrium and breakthrough studies for H2/CO2/CH4 on zeolite 13X

Reforming of fossil fuels coupled with carbon capture and storage has the potential to produce low-carbon H2 at large scale and low cost. Adsorption is a potentially promising technology for two key separation tasks in this process: H2 purification and CO2 capture. In this work, we present equilibrium adsorption data of H2 and CH4 on zeolite 13X, in addition to the already established CO2 isotherms. Further, we carry out binary (CO2–CH4) and ternary (H2–CO2–CH4) breakthrough experiments at various pressures and temperatures to estimate transport parameters, assess the predictive capacity of our 1D column model, and compare different multi-component adsorption models. CO2 adsorbs strongly on zeolite 13X, CH4 adsorbs less, and H2 adsorbs very little. Thus, H2 breaks through first, CH4 second (first in the binary breakthrough experiments) and CO2 last. Linear driving force (LDF) mass transfer coefficients are estimated based on a single breakthrough experiment and mass transfer is found to be fast for H2, slower for CH4, and slowest for CO2. The LDF parameters can be used in a predictive manner for breakthrough experiments at varying pressures, temperatures, flows, and, though with lower accuracy, even compositions. Heat transfer inside the column is described well with a literature correlation, thus yielding an excellent agreement between simulated and measured column temperatures. Ideal and real adsorbed solution theories (IAST and RAST, respectively) both model the observed breakthrough composition profiles well, whereas extended isotherms are inferior for predicting the competitive behavior between CH4 and CO2 adsorption. This study provides the groundwork necessary for full cyclic experiments and their simulation.

Adsorption in the context of clean hydrogen production: process intensification by integrating H2 purification and CO2 capture - A modeling and experimental study of multi-component adsorption

Coupling fossil-based H2 production with carbon capture and storage can produce H2 with low associated CO2 emissions, which is urgently needed to decarbonize industry, the energy sector, and the transportation sector. Vacuum pressure swing adsorption (VPSA) allows for the integration of two key separation tasks in this process, H2 purification and CO2 capture. In this work, we compare experimental and simulation results of a cyclic VPSA process. Our focus is the evaluation of different approaches for modeling multi-component adsorption. In particular, we use a three process Langmuir model for CO2 adsorption and Langmuir model for H2 and CH4 adsorption. We assess the different options for energetic site matching. The results indicate that energetic site matching of H2 and CO2 is of little importance. In contrast to that, only two models with a different energetic site matching for CO2 and CH4 result in a reasonable prediction of the experimental results, i.e. uncorrelated (UC) and uncorrelated unselective B (UCUS B). Both extended Sips isotherms and the use of the real adsorbed solution theory (RAST), however, result in a better prediction of the experimental results.

Optimal artificial neural network design for simultaneous modeling of multicomponent adsorption

In this work, ultrasound-modified chitin (UM-chitin) was used to adsorb cobalt (Co2+), methylene blue (MB), and nickel (Ni2+) in single, binary and ternary systems, at different temperatures. The single adsorption isotherms showed that the affinity of the UM-chitin towards the metals was higher than that of the dye. Antagonist adsorption was found for the binary adsorption of Co2+ and MB; however, the presence of Ni2+ in the ternary system promoted the adsorption of MB and inhibited the adsorption of Co2+. Therefore, an optimal artificial neural network was developed to predict these synergistic and antagonistic interactions simultaneously. Different ANN configurations were tested using the initial concentration of each adsorbate (0–650 mg L−1) and the solution temperature (298–328 K) as input variables. The optimal ANN structure, which uses 2 hidden layers with 5 and 10 neurons, tangent sigmoid activation function (tansig) at both hidden and output layers, and Bayesian Regulation as its backpropagation algorithm demonstrated suitable ability in simultaneously predict the adsorption capacity for each adsorbate (MSE < 0.0003 and R > 0.9995).

Modeling the effect of dynamic adsorption on the phase behavior of hydrocarbons in shale and tight reservoirs

It is known that in shale and tight reservoirs, adsorption significantly affects hydrocarbon reserves and the processes of their production. This fact is reflected in the methods for calculating reserves and evaluating the production potential of shale and tight deposits. To calculate the initial content of the components, multi-component adsorption models are used. The impact on hydrocarbon production is taken into account through special dynamic permeability models for shale reservoirs. According to laboratory studies, adsorption can lead to significant changes not only in volume, but also in the composition of the produced fluids and their phase behavior. Previously, this effect could not be reproduced on the basis of mathematical models. The method proposed in this article allows modeling the phase behavior of a hydrocarbon mixture taking into account the dynamic adsorption/desorption of components in the process of pressure change. The method is applicable in the simulations of multi-component (compositional) flow and PVT-modeling on real objects. The phase behavior of hydrocarbons with pressure depletion in shale reservoirs has been simulated. It is shown that the neglect of the dynamic effect of adsorption / desorption leads to significant errors in predicting the saturation pressure, as well as the dynamics of changes in the composition of the produced fluid and of hydrocarbon component recovery.

Parametric study of CO2 separation using carbon molecular sieve, zeolite and silica gel

Performances of Pressure swing adsorption (PSA) dependent on the type of adsorbent and efficiency of the regeneration cycle. In this work, a model describing CO2 mixture flow, mass and heat transfer with multi-component adsorption model are developed in Aspen Adsorption environment to compare the performance of PSA cycles with three different adsorbents (CMS 3K, zeolite 13x and silica gel). Adsorption capacity of CO2 for three adsorbents was found to be in the order of CMS>zeolite>silica gel. Hence, CMS was chosen as the adsorbents to evaluate PSA performances on different feed flowrate and pressure based on the purity, recovery and productivity of the CO2 separation. The result shows that, within a certain range, higher adsorption pressure will increase all purity, recovery and productivity of CO2 while higher feeding rate leads to increase recovery but lower purity and productivity.

The rigid adsorbent lattice fluid model for pure and mixed gas adsorption

The ability of macroscopic models to predict correctly multicomponent systems from pure component isotherms alone remains a major challenge in adsorption engineering. A new fundamental thermodynamic model for multicomponent adsorption of molecules of different size in nanoporous materials is derived from a modified lattice fluid model. Expressions for the fugacity coefficients are derived and the resulting equilibrium relationships are shown to be consistent with a type I adsorption isotherm. Expressions are obtained for the saturation capacity, the Henry law constant and the adsorption energy. The model is applied to silicalite and the parameters for the adsorbent are obtained from crystal properties, the adsorption energy of n‐alkanes and Henry law constants for six gases. Model predictions for gas adsorption up to 20 bar are shown to be comparable to empirical adsorption isotherm equations. Extension to binary and quaternary systems shows good a priori predictive capability when compared to experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1304–1314, 2019

Quantification and isotherm modelling of competitive phosphate and silicate adsorption onto micro-sized granular ferric hydroxide.

Adsorption onto ferric hydroxide is a known method to reach very low residual phosphate concentrations. Silicate is omnipresent in surface and industrial waters and reduces the adsorption capacity of ferric hydroxides. The present article focusses on the influences of silicate concentration and contact time on the adsorption of phosphate to a micro-sized iron hydroxide adsorbent (μGFH) and fits adsorption data to multi-component adsorption isotherms. In Berlin drinking water (DOC of approx. 4 mg L−1) at pH 7.0, loadings of 24 mg g−1 P (with 3 mg L−1 initial PO43−–P) and 17 mg L−1 Si (with 9 mg L−1 initial Si) were reached. In deionized water, phosphate shows a high percentage of reversible bonds to μGFH while silicate adsorption is not reversible probably due to polymerization. Depending on the initial silicate concentration, phosphate loadings are reduced by 27, 33 and 47% (for equilibrium concentrations of 1.5 mg L−1) for 9, 14 and 22 mg L−1 Si respectively. Out of eight tested multi-component adsorption models, the Extended Freundlich Model Isotherm (EFMI) describes the simultaneous adsorption of phosphate and silicate best. Thus, providing the means to predict and control phosphate removal. Longer contact times of the adsorbent with silicate prior to addition of phosphate reduce phosphate adsorption significantly. Compared to 7 days of contact with silicate (c0 = 10 mg L−1) prior to phosphate (c0 = 3 mg L−1) addition, 28 and 56 days reduce the μGFH capacity for phosphate by 21 and 43%, respectively.

Artificial neural network-based surrogate modeling of multi-component dynamic adsorption of heavy metals with a biochar

This paper reports the application of four neural network surrogate models for the correlation and prediction of asymmetric breakthrough curves obtained from the multi-component adsorption of cadmium, nickel, zinc and copper ions on a biochar. Artificial neural networks namely: Feed forward back propagation neural network, Feed forward back propagation neural network with distributed time delay, Cascade forward neural network and Elman neural network have been assessed and compared where their limitations and capabilities have been discussed. The impact of the architecture of these surrogated models, including the activation functions and training algorithms, has been analyzed using error and residuals analyses in different zones of the adsorption breakthrough curves obtained from single, ternary and quaternary solutions of tested heavy metals. Overall, the bed adsorption capacities for these metals ranged from 2.01 to 5.40, 0.16 to 4.46 and 0.03 to 2.15 mmol/g in single, ternary and quaternary feeds, respectively, at tested operation conditions. Highest adsorption capacities were obtained for copper in single and multi-metallic solutions and they ranged from 2.15 to 5.4 mmol/g. Results of this paper showed that Cascade forward neural network was the best model for multi-metallic adsorption breakthrough curve modeling. This neural network showed the lowest modeling errors for the multi-component adsorption breakthrough curves. This paper introduces new results on the application of ANNs surrogate models for the simulation of multi-component adsorption process involved in water treatment and purification.

An explicit multicomponent adsorption isotherm model: accounting for the size-effect for components with Langmuir adsorption behavior

The extended Langmuir (EL) model is a popular multicomponent adsorption equilibria model, which can be based on single component Langmuir isotherms fitted on pure component data. Such explicit models are preferred over their implicit counterparts due to a lower computational requirement. An important shortcoming of the EL model is its inability to capture the adsorbate size effect occurring when the saturation capacities of pure component Langmuir isotherms are dissimilar. In contrast, this size effect is captured by the ideal adsorbed solution theory (IAST), which is centered on a set of implicit equations. In this work, we present an explicit multicomponent adsorption model for components with uneven saturation capacities obeying the Langmuir isotherm equation. This model predicts the expected change in selectivity with mixture composition, and even a selectivity reversal at high pressure when the adsorbates have significantly different molecular sizes. The model is extendable to any number of components, reduces to the Langmuir equation for pure components and to the EL equation when all saturation capacities are equal. The newly proposed model can be used to approximate the IAST and upgrade the EL model without introducing new parameters. Especially for binary mixtures, this model (Eqs. 12–14) offers a simple improvement of the EL model in predicting the experimental adsorption of light alkanes on 13X and 5A zeolites. The presented model is also applied to describe phase-changing adsorbents, in combination with the osmotic framework adsorbed solution theory (OFAST).