Application of heterogeneous vacancy solution theory to characterization of microporous solids

The vacancy solution theory of adsorption is re-formulated here through the mass-action law, and placed in a convenient framework permitting the development of thermodynamic ally consistent isotherms. It is shown that both the multisite Langmuir model and the classical vacancy solution theory expression are special cases of the more general approach when the Flory-Huggins activity coefficient model is used, with the former being the thermodynamically consistent result. The improved vacancy solution theory approach is further extended here to heterogeneous adsorbents by considering the pore-width dependent potential along with a pore size distribution. However, application of the model to numerous hydrocarbons as well as other adsorptives on microporous activated carbons shows that the multisite model has difficulty in the presence of a pore size distribution, because pores of different sizes can have different numbers of adsorbed layers and therefore different site occupancies. On the other hand, use of the classical vacancy solution theory expression for the local isotherm leads to good simultaneous fit of the data, while yielding a site diameter of about 0.257 nm, consistent with that expected for the potential well in aromatic rings on carbon pore surfaces. It is argued that the classical approach is successful because the Flory-Huggins term effectively represents adsorbate interactions in disguise. When used together with the ideal adsorbed solution theory the heterogeneous vacancy solution theory successfully predicts binary adsorption equilibria, and is found to perform better than the multisite Langmuir as well as the heterogeneous Langmuir model. (C) 2001 Elsevier Science Ltd. All rights reserved.

Applicability of molecular simulations for modelling the adsorption of the greenhouse gas CF4 on carbons

Tetrafluoromethane, CF4, is powerful greenhouse gas, and the possibility of storing it in microporous carbon has been widely studied. In this paper we show, for the first time, that the results of molecular simulations can be very helpful in the study of CF4 adsorption. Moreover, experimental data fit to the results collected from simulations. We explain the meaning of the empirical parameters of the supercritical Dubinin–Astakhov model proposed by Ozawa and finally the meaning of the parameter k of the empirical relation proposed by Amankwah and Schwarz.

Modelling water adsorption on Au(210) surfaces: II. Monte Carlo simulations

Canonical Monte Carlo simulations for the Au(210)/H(2)O interface, using a force field recently proposed by us, are reported. The results exhibit the main features normally observed in simulations of water molecules in contact with different noble metal surfaces. The calculations also assess the influence of the surface topography on the structural aspects of the adsorbed water and on the distribution of the water molecules in the direction normal to the metal surface plane. The adsorption process is preferential at sites in the first layer of the metal. The analysis of the density profiles and dipole moment distributions points to two predominant orientations. Most of the molecules are adsorbed with the molecular plane parallel to surface, while others adsorb with one of the O-H bonds parallel to the surface and the other bond pointing towards the bulk liquid phase. There is also evidence of hydrogen bond formation between the first and second solvent layers at the interface. (c) 2007 Elsevier B.V. All rights reserved.

Pressure Swing Adsorption on Carbon Molecular Sieves for Nitrogen Production: Modelling and Simulation with Aspen Adsorption

L’azoto è uno dei prodotti principali dell’industria chimica, utilizzato principalmente per assicurare un sicuro stoccaggio di composti infiammabili. Generatori con sistemi PSA sono spesso più economici della tradizionale distillazione criogenica. I processi PSA utilizzano una colonna a letto fisso, riempita con materiale adsorbente, che adsorbe selettivamente un componente da una miscela gassosa. L’ossigeno diffonde molto più velocemente dell'azoto nei pori di setacci molecolari carboniosi. Oltre ad un ottimo materiale adsorbente, anche il design è fondamentale per la performance di un processo PSA. La fase di adsorbimento è seguita da una fase di desorbimento. Il materiale adsorbente può essere quindi riutilizzato nel ciclo seguente. L’assenza di un simulatore di processo ha reso necessario l’uso di dati sperimentali per sviluppare nuovi processi. Un tale approccio è molto costoso e lungo. Una modellazione e simulazione matematica, che consideri tutti i fenomeni di trasporto, è richiesta per una migliore comprensione dell'adsorbente sia per l'ottimizzazione del processo. La dinamica della colonna richiede la soluzione di insiemi di PDE distribuite nel tempo e nello spazio. Questo lavoro è stato svolto presso l'Università di Scienze Applicate - Münster, Germania. Argomento di questa tesi è la modellazione e simulazione di un impianto PSA per la produzione di azoto con il simulatore di processo Aspen Adsorption con l’obiettivo di permettere in futuro ottimizzazioni di processo affidabili, attendibili ed economiche basate su computazioni numeriche. E' discussa l’ottimizzazione di parametri, dati cinetici, termodinamici e di equilibrio. Il modello è affidabile, rigoroso e risponde adeguatamente a diverse condizioni al contorno. Tuttavia non è ancora pienamente soddisfacente poiché manca una rappresentazione adeguata della cinetica ovvero dei fenomeni di trasporto di materia. La messa a punto del software permetterà in futuro di indagare velocemente nuove possibilità di operazione.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Discrimination of adsorption kinetic models for the description of hydrocarbon adsorption in activated carbon

Five kinetic models for adsorption of hydrocarbons on activated carbon are compared and investigated in this study. These models assume different mass transfer mechanisms within the porous carbon particle. They are: (a) dual pore and surface diffusion (MSD), (b) macropore, surface, and micropore diffusion (MSMD), (c) macropore, surface and finite mass exchange (FK), (d) finite mass exchange (LK), and (e) macropore, micropore diffusion (BM) models. These models are discriminated using the single component kinetic data of ethane and propane as well as the multicomponent kinetics data of their binary mixtures measured on two commercial activated carbon samples (Ajax and Norit) under various conditions. The adsorption energetic heterogeneity is considered for all models to account for the system. It is found that, in general, the models assuming diffusion flux of adsorbed phase along the particle scale give better description of the kinetic data.

Simulation methods in the modelling of bioaffinity assays

Computational model-based simulation methods were developed for the modelling of bioaffinity assays. Bioaffinity-based methods are widely used to quantify a biological substance in biological research, development and in routine clinical in vitro diagnostics. Bioaffinity assays are based on the high affinity and structural specificity between the binding biomolecules. The simulation methods developed are based on the mechanistic assay model, which relies on the chemical reaction kinetics and describes the forming of a bound component as a function of time from the initial binding interaction. The simulation methods were focused on studying the behaviour and the reliability of bioaffinity assay and the possibilities the modelling methods of binding reaction kinetics provide, such as predicting assay results even before the binding reaction has reached equilibrium. For example, a rapid quantitative result from a clinical bioaffinity assay sample can be very significant, e.g. even the smallest elevation of a heart muscle marker reveals a cardiac injury. The simulation methods were used to identify critical error factors in rapid bioaffinity assays. A new kinetic calibration method was developed to calibrate a measurement system by kinetic measurement data utilizing only one standard concentration. A nodebased method was developed to model multi-component binding reactions, which have been a challenge to traditional numerical methods. The node-method was also used to model protein adsorption as an example of nonspecific binding of biomolecules. These methods have been compared with the experimental data from practice and can be utilized in in vitro diagnostics, drug discovery and in medical imaging.

Element speciation and behaviour in metal-rich Boreal river and estuarine systems using ultrafiltration and chemical modelling

The bioavailability of metals and their potential for environmental pollution depends not simply on total concentrations, but is to a great extent determined by their chemical form. Consequently, knowledge of aqueous metal species is essential in investigating potential metal toxicity and mobility. The overall aim of this thesis is, thus, to determine the species of major and trace elements and the size distribution among the different forms (e.g. ions, molecules and mineral particles) in selected metal-enriched Boreal river and estuarine systems by utilising filtration techniques and geochemical modelling. On the basis of the spatial physicochemical patterns found, the fractionation and complexation processes of elements (mainly related to input of humic matter and pH-change) were examined. Dissolved (<1 kDa), colloidal (1 kDa-0.45 μm) and particulate (>0.45 μm) size fractions of sulfate, organic carbon (OC) and 44 metals/metalloids were investigated in the extremely acidic Vörå River system and its estuary in W Finland, and in four river systems in SW Finland (Sirppujoki, Laajoki, Mynäjoki and Paimionjoki), largely affected by soil erosion and acid sulfate (AS) soils. In addition, geochemical modelling was used to predict the formation of free ions and complexes in these investigated waters. One of the most important findings of this study is that the very large amounts of metals known to be released from AS soils (including Al, Ca, Cd, Co, Cu, Mg, Mn, Na, Ni, Si, U and the lanthanoids) occur and can prevail mainly in toxic forms throughout acidic river systems; as free ions and/or sulfate-complexes. This has serious effects on the biota and especially dissolved Al is expected to have acute effects on fish and other organisms, but also other potentially toxic dissolved elements (e.g. Cd, Cu, Mn and Ni) can have fatal effects on the biota in these environments. In upstream areas that are generally relatively forested (higher pH and contents of OC) fewer bioavailable elements (including Al, Cu, Ni and U) may be found due to complexation with the more abundantly occurring colloidal OC. In the rivers in SW Finland total metal concentrations were relatively high, but most of the elements occurred largely in a colloidal or particulate form and even elements expected to be very soluble (Ca, K, Mg, Na and Sr) occurred to a large extent in colloidal form. According to geochemical modelling, these patterns may only to a limited extent be explained by in-stream metal complexation/adsorption. Instead there were strong indications that the high metal concentrations and dominant solid fractions were largely caused by erosion of metal bearing phyllosilicates. A strong influence of AS soils, known to exist in the catchment, could be clearly distinguished in the Sirppujoki River as it had very high concentrations of a metal sequence typical of AS soils in a dissolved form (Ba, Br, Ca, Cd, Co, K, Mg, Mn, Na, Ni, Rb and Sr). In the Paimionjoki River, metal concentrations (including Ba, Cs, Fe, Hf, Pb, Rb, Si, Th, Ti, Tl and V; not typical of AS soils in the area) were high, but it was found that the main cause of this was erosion of metal bearing phyllosilicates and thus these metals occurred dominantly in less toxic colloidal and particulate fractions. In the two nearby rivers (Laajoki and Mynäjoki) there was influence of AS soils, but it was largely masked by eroded phyllosilicates. Consequently, rivers draining clay plains sensitive to erosion, like those in SW Finland, have generally high background metal concentrations due to erosion. Thus, relying on only semi-dissolved (<0.45 μm) concentrations obtained in routine monitoring, or geochemical modelling based on such data, can lead to a great overestimation of the water toxicity in this environment. The potentially toxic elements that are of concern in AS soil areas will ultimately be precipitated in the recipient estuary or sea, where the acidic metalrich river water will gradually be diluted/neutralised with brackish seawater. Along such a rising pH gradient Al, Cu and U will precipitate first together with organic matter closest to the river mouth. Manganese is relatively persistent in solution and, thus, precipitates further down the estuary as Mn oxides together with elements such as Ba, Cd, Co, Cu and Ni. Iron oxides, on the contrary, are not important scavengers of metals in the estuary, they are predicted to be associated only with As and PO4.

Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

Modelling the inorganic nitrogen behaviour in a small Mediterranean forested catchment, Fuirosos (Catalonia)

The aim of this work was to couple a nitrogen (N) sub-model to already existent hydrological lumped (LU4-N) and semi-distributed (LU4-R-N and SD4-R-N) conceptual models, to improve our understanding of the factors and processes controlling nitrogen cycling and losses in Mediterranean catchments. The N model adopted provides a simplified conceptualization of the soil nitrogen cycle considering mineralization, nitrification, immobilization, denitrification, plant uptake, and ammonium adsorption/desorption. It also includes nitrification and denitrification in the shallow perched aquifer. We included a soil moisture threshold for all the considered soil biological processes. The results suggested that all the nitrogen processes were highly influenced by the rain episodes and that soil microbial processes occurred in pulses stimulated by soil moisture increasing after rain. Our simulation highlighted the riparian zone as a possible source of nitrate, especially after the summer drought period, but it can also act as an important sink of nitrate due to denitrification, in particular during the wettest period of the year. The riparian zone was a key element to simulate the catchment nitrate behaviour. The lumped LU4-N model (which does not include the riparian zone) could not be validated, while both the semi-distributed LU4-R-N and SD4-R-N model (which include the riparian zone) gave satisfactory results for the calibration process and acceptable results for the temporal validation process.

Modelling thermodynamic properties of banana waste by analytical derivation of desorption isotherms

Banana is an agricultural product of great economic importance for various developing countries. The relationship between moisture content and water activity provides useful information for the processing and storage of banana waste. The water activity and moisture content of three banana (Mussa spp. Haploid AAB cv. Nanica) waste items were analyzed to determine the desorption isotherms at six different temperatures (20, 30, 40, 50, 60 and 70°C). The desorption isotherms of the peel, pedicel and pulp of overripe bananas were determined in wide ranges of moisture content (0.001-6.360 kg kg-1 d.b.) and water activity (0.02-0.907). The theoretical GAB model was used for modelling the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to compute the isosteric heat of sorption, the differential entropy and Gibbs' free energy by way of the GAB model when the effect of temperature on the hygroscopic equilibrium was considered. © 2012 de Gruyter. All rights reserved.

Modelling the fate of chromated copper arsenate in a sandy soil

A pulse of chromated copper arsenate (CCA, a timber preservative) was applied in irrigation water to an undisturbed field soil in a laboratory column. Concentrations of various elements in the leachate from the column were measured during the experiment. Also, the remnants within the soil were measured at the end of the experiment. The geochemical modelling package, PHREEQC-2, was used to simulate the experimental data. Processes included in the CCA transport modelling were advection, dispersion, non-specific adsorption (cation exchange) and specific adsorption by clay minerals and organic matter, as well as other possible chemical reactions such as precipitation/dissolution. The modelling effort highlighted the possible complexities in CCA transport and reaction experiments. For example, the uneven dosing of CCA as well as incomplete knowledge of the soil properties resulted in simulations that gave only partial, although reasonable, agreement with the experimental data. Both the experimental data and simulations show that As and Cu are strongly adsorbed and therefore, will mostly remain at the top of the soil profile, with a small proportion appearing in leachate. On the other hand, Cr is more mobile and thus it is present in the soil column leachate. Further simulations show that both the quantity of CCA added to the soil and the pH of the irrigation water will influence CCA transport. Simulations suggest that application of larger doses of CCA to the soil will result in higher leachate concentrations, especially for Cu and As. Irrigation water with a lower pH will dramatically increase leaching of Cu. These results indicate that acidic rainfall or significant accidental spillage of CCA will increase the risk of groundwater pollution.