Developments in the understanding of South African style SAG mills

The South African style SAG (RoM) mills operate in a window that is almost exclusive from the operation of the Australian and North American mills that have been used for the development of SAG mill models. Combining good quality, test data from the RoM mills is extending and improving these models, and assisting in a practical manner in improving our understanding of SAG/AG milling. Data from high mill loads, both in absolute filling and ball loading, have been used to extend and improve the JK SAG mill model. This improved understanding has been successfully applied to increasing the throughput of a mill by 8%. Data is presented on relationships between power and load for high mill loading. Slurry pooling is common in closed-circuit RoM mills, and the detrimental effect of this has been dramatically demonstrated at ALCOA with a mill throughput increase of over 20%. Techniques for calculating the effects of slurry pooling have been developed and a new pulp lifter system designed to give optimal slurry discharge. The influence of mill speed in shifting the product size distribution has also been measured. (C) 2001 Elsevier Science Ltd. All rights reserved.

A modified pore-filling isotherm for liquid-phase adsorption in activated carbon

This article modifies the usual form of the Dubinin-Radushkevich pore-filling model for application to liquid-phase adsorption data, where large molecules are often involved. In such cases it is necessary to include the repulsive part of the energy in the micropores, which is accomplished here by relating the pore potential to the fluid-solid interaction potential. The model also considers the nonideality of the bulk liquid phase through the UNIFAC activity coefficient model, as well as structural heterogeneity of the carbon. For the latter the generalized adsorption integral is used while incorporating the pore-size distribution obtained by density functional theory analysis of argon adsorption data. The model is applied here to the interpretation of aqueous phase adsorption isotherms of three different esters on three commercial activated carbons. Excellent agreement between the model and experimental data is observed, and the fitted Lennard-Jones size parameter for the adsorbate-adsorbate interactions compares well with that estimated from known critical properties, supporting the modified approach. On the other hand, the model without consideration of bulk nonideality, or when using classical models of the characteristic energy, gives much poorer bts of the data and unrealistic parameter values.

The use of liquid phase adsorption isotherms for characterization of activated carbons

The characterization of three commercial activated carbons was carried out using the adsorption of various compounds in the aqueous phase. For this purpose the generalized adsorption isotherm was employed, and a modification of the Dubinin-Radushkevich pore filling model, incorporating repulsive contributions to the pore potential as well as bulk liquid phase nonideality, was used as the local isotherm. Eight different flavor compounds were used as adsorbates, and the isotherms were jointly fitted to yield a common pore size distribution for each carbon. The bulk liquid phase nonideality was incorporated through the UNIFAC activity coefficient model, and the repulsive contribution to the pore potential was incorporated through the Steele 10-4-3 potential model. The mean micropore network coordination number for each carbon was also determined from the fitted saturation capacity based on percolation theory. Good agreement between the model and the experimental data was observed. In addition, excellent agreement between the bimodal gamma pore size distribution and density functional theory-cum-regularization-based pore size distribution obtained by argon adsorption was also observed, supporting the validity of the model. The results show that liquid phase adsorption, using adsorptive molecules of different sizes, can be an effective means of characterizing the pore size distribution as well as connectivity. Alternately, if the carbon pore size distribution is independently known, the method can be used to measure critical molecular sizes. (C) 2001 Elsevier Science.

Characterization of activated carbons using liquid phase adsorption

A modification of the Dubinin-Radushkevich pore filling model by incorporation of the repulsive contribution to the pore potential, and of bulk non-ideality, is proposed in this paper for characterization of activated carbon using liquid phase adsorption. For this purpose experiments have been performed using ethyl propionate, ethyl butyrate, and ethyl isovalerate as adsorbates and the microporous-mesoporous activated carbons Filtrasorb 400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The repulsive contribution to the pore potential is incorporated through a Lennard-Jones intermolecular potential model, and the bulk-liquid phase non-ideality through the UNIFAC activity coefficient model. For the characterization of activated carbons, the generalized adsorption isotherm is utilized with a bimodal gamma function as the pore size distribution function. It is found that the model can represent the experimental data very well, and significantly better than when the classical energy-size relationship is used, or when bulk non-ideality is neglected. Excellent agreement between the bimodal gamma pore size distribution and DFT-cum-regularization based pore size distribution is also observed, supporting the validity of the proposed model. (C) 2001 Elsevier Science Ltd. All rights reserved.

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.

Hydrophobicity of Templated Silica Xerogels for Molecular Sieving Applications

Silica xerogels were prepared by a sol-gel process catalyzed by acid with tetraethylorthosilicate, and using an organic covalent ligand template (methyltriethoxysilane) or a noncovalent template C6 surfactant (triethylhexylammonium bromide). The influence of hydrotreatment on the structure of templated xerogels is examined in terms of surface area, micropore volume, average pore size, and pore size distribution, and compared against a blank xerogel (nontemplated). The role of surface functional groups was evaluated using Si-29 nuclear magnetic resonance. The structural integrity of the xerogel was maintained to a large extent in samples that had a high contribution of Q(4) species (siloxane groups). Xerogel matrix densification occurred when there was a large concentration of Q(3) and Q(2) species (silanol groups), which also were responsible for increased hydrophilicity. The templated xerogels resulted in up to a 25% concentration of methyl functional groups (T-3 and T-2 species), leading to hydrophobic xerogels. The best results in terms of structural integrity and hydrophobicity were obtained with templated xerogels prepared with the C6 surfactant. The results in this study suggest that surfactant-enhanced condensation reactions lead to structures with a high contribution of Q(4) groups, which are not susceptible to water attack, but are strong enough to oppose matrix densification during rehydration.

Characterisation of templated xerogels for molecular sieve application

This paper presents the results of the characterisation of templated silica xerogels as precursor material for molecular sieve silica membranes for gas separation. The template agent integrated in the xerogel matrix is a methyl ligand covalently bended to the siloxane network in the form of methyltriethoxysilane (MTES). Several surface and microstructural characterisation techniques such as TGA, FTIR, NMR, and nitrogen adsorption have been employed to obtain information on the reaction mechanisms involved in the sol-gel processing of such molecular sieves. The characterisation results show the effects of processing parameters such as heat treatment temperature, and the concentration of the covalently bonded template on the development of the pore structure. It was found that calcination temperature significantly enhanced the condensation reactions thus resulted in more Si-O-Si groups being formed. This was also confirmed with the data of FTIR characterisation showing enhanced silicon bands at higher heat treatment temperatures. As a result of the promoted densification and shrinkable pore network the micropore volume also reduced with increasing methyl ligand molar ratio. However, the mean pore diameter does not change significantly with calcination temperature. While the contribution of the templates towards controlling pore size is less precise, increasing the methyl ligand molar ratio results in the broadening of the pore size distribution and lower pore volume. Higher template concentration induces the collapse of the xerogel matrix due to capillary stress promoting dense xerogels with low pore volume (C) 2001 Elsevier Science B.V. All rights reserved.

The Dubinin-Radushkevich equation and the underlying microscopic adsorption description

The Dubinin-Radushkevich (DR) equation is widely used for description of adsorption in microporous materials, especially those of a carbonaceous origin. The equation has a semi-empirical origin and is based on the assumptions of a change in the potential energy between the gas and adsorbed phases and a characteristic energy of a given solid. This equation yields a macroscopic behaviour of adsorption loading for a given pressure. In this paper, we apply a theory developed in our group to investigate the underlying mechanism of adsorption as an alternative to the macroscopic description using the DR equation. Using this approach, we are able to establish a detailed picture of the adsorption in the whole range of the micropore system. This is different from the DR equation, which provides an overall description of the process. (C) 2001 Elsevier Science Ltd. All rights reserved.

Characterization of micro-mesoporous carbon media

A simple method to characterize the micro and mesoporous carbon media is discussed. In this method, the overall adsorption quantity is the sum of capacities of all pores (slit shape is assumed), in each of which the process of adsorption occurs in two sequential steps: the multi-layering followed by pore filling steps. The critical factor in these two steps is the enhancement of the pressure of occluded 'free' molecules in the pore as well as the enhancement of the adsorption layer thickness. Both of these enhancements are due to the overlapping of the potential fields contributed by the two opposite walls. The classical BET and modified Kelvin equations are assumed to be applicable for the two steps mentioned above, with the allowance for the enhanced pore pressure, the enhanced adsorption energy and the enhanced BET constant,all of which vary with pore width. The method is then applied to data of many carbon samples of different sources to derive their respective pore size distributions, which are compared with those obtained from DFT analysis. Similar pore size distributions (PSDs) are observed although our method gives sharper distribution. Furthermore, we use our theory to analyze adsorption data of nitrogen at 77 K and that of benzene at 303 K (ambient temperature). The PSDs derived from these two different probe molecules are similar, with some small differences that could be attributed to the molecular properties, such as the collision diameter. Permeation characteristics of sub-critical fluids are also discussed in this paper. (C) 2001 Elsevier Science B.V. All rights reserved.

A new diffusion and flow theory for activated carbon from low pressure to capillary condensation range

In this paper, we develop a theory for diffusion and flow of pure sub-critical adsorbates in microporous activated carbon over a wide range of pressure, ranging from very low to high pressure, where capillary condensation is occurring. This theory does not require any fitting parameter. The only information needed for the prediction is the complete pore size distribution of activated carbon. The various interesting behaviors of permeability versus loading are observed such as the maximum permeability at high loading (occurred at about 0.8-0.9 relative pressure). The theory is tested with diffusion and flow of benzene through a commercial activated carbon, and the agreement is found to be very good in the light that there is no fitting parameter in the model. (C) 2001 Elsevier Science B.V. All rights reserved.

Characterisation of pore structure of carbon adsorbents using regularisation procedure

The constrained regularisation procedure was applied to compute the pore size distributions (PSDs, f(x)) for a variety of activated carbons using overall adsorption equation based on the combination of the Kelvin equation and the statistical adsorbed film thickness. The impact of the boundary values of relative nitrogen pressure p/p(0) was analysed on the basis of the corresponding alterations in the PSDs. Changes in microporosity and mesoporosity of activated carbons can be described adequately only when the range of p/p(0) is as wide as possible, as at a high initial p/p(0) value, the f(x) curves can be broadened with shifted maxima especially for micropores and narrow mesopores. Comparative analysis of the PSDs and the adsorption potential, adsorption energy and fractal dimension distributions gives useful information on the complete description of the adsorbent characteristics. (C) 2001 Elsevier Science B.V. All rights reserved.

Population balance modelling of granulation with a physically based coalescence kernel

It was previously published by the authors that granules can either coalesce through Type I (when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch) or Type II (when granules are slowed to a halt during rebound, after their surfaces have made contact) (AIChE J. 46 (3) (2000) 529). Based on this coalescence mechanism, a new coalescence kernel for population balance modelling of granule growth is presented. The kernel is constant such that only collisions satisfying the conditions for one of the two coalescence types are successful. One constant rate is assigned to each type of coalescence and zero is for the case of rebound. As the conditions for Types I and II coalescence are dependent on granule and binder properties, the coalescence kernel is thus physically based. Simulation results of a variety of binder and granule materials show good agreement with experimental data. (C) 2002 Elsevier Science Ltd. All rights reserved.

Use of liquid phase adsorption for characterizing pore network connectivity in activated carbon

A simple percolation theory-based method for determination of the pore network connectivity using liquid phase adsorption isotherm data combined with a density functional theory (DFT)-based pore size distribution is presented in this article. The liquid phase adsorption experiments have been performed using eight different esters as adsorbates and microporous-mesoporous activated carbons Filtrasorb-400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The density functional theory (DFT)-based pore size distributions of the carbons were obtained using DFT analysis of argon adsorption data. The mean micropore network coordination numbers, Z, of the carbons were determined based on DR characteristic plots and fitted saturation capacities using percolation theory. Based on this method, the critical molecular sizes of the model compounds used in this study were also obtained. The incorporation of percolation concepts in the prediction of multicomponent adsorption equilibria is also investigated, and found to improve the performance of the ideal adsorbed solution theory (IAST) model for the large molecules utilized in this study. (C) 2002 Elsevier Science B.V. All rights reserved.

Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO2 and SO2 on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO2 and SO2, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies. (C) 2002 Elsevier Science Ltd. All rights reserved.

Vacancy solution theory for binary adsorption equilibria in heterogeneous carbon

A heterogeneous modified vacancy solution model of adsorption developed is evaluated. The new model considers the adsorption process through a mass-action law and is thermodynamically consistent, while maintaining the simplicity in calculation of multicomponent adsorption equilibria, as in the original vacancy solution theory. It incorporates the adsorbent heterogeneity through a pore-width-related potential energy, represented by Steele's 10-4-3 potential expression. The experimental data of various hydrocarbons, CO2 and SO2 on four different activated carbons - Ajax, Norit, Nuxit, and BPL - at multiple temperatures over a wide range of pressures were studied by the heterogeneous modified VST model to obtain the isotherm parameters and micropore-size distribution of carbons. The model successfully correlates the single-component adsorption equilibrium data for all compounds studied on various carbons. The fitting results for the vacancy occupancy parameter are consistent with the pressure change on different carbons, and the effect of pore heterogeneity is important in adsorption at elevated pressure. It predicts binary adsorption equilibria better than the IAST scheme, reflecting the significance of molecular size nonideality.