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By D. G. Hulbert

"Mineral processes are complex operations that have been modelled, controlled and simulated by diverse technologies. A review is given of some models of mineral processes in the literature. A new variation of a dynamic process model of flotation is presented. Process models, describing real and relevant physical variables, give a good understanding and good qualitative simulations, but can sometimes require prohibitively difficult and extensive parameter estimations. Process control is usually best done on operational plants by the fitting of system models, which can home in on the plant?s observability, controllability and optimisation. System models can be of a form amenable for use in appropriate techniques for controller design and implementation. The control of milling circuits is discussed in some detail. While simulators use models to predict dynamic or steady-state information, part of their strength lies in their ease of use and their ability to test different types of specifications. Some results are given for a flotation circuit simulator that can be made to solve virtually any permutation of specifications.INTRODUCTIONThe development and application of appropriate technology can lead to better operation of mineral processing plants in industry, so that substantial benefits can be obtained from improved throughputs, efficiencies and product qualities. This paper addresses some of the principles and methods used in the quest for the development and exploitation of such technology. Although the design of processes is often the motivation for modelling and simulation, this paper also targets the use of modelling and simulation for the control and optimum operation of mineral processes. The two processes given the most attention here are flotation and milling.Technologies used in mineral processing range from simple to very complex. Simple technical principles, such as mass and component balances, can yield some simple and effective strategies for modelling and control. However, minerals in particulate form have such complex physical and chemical properties that there appears no end to the complexity that emerges, as more and more factors are taken into consideration in the pursuit of better results and understanding. The situation is aggravated by the complexity of mineral processing plants, which have spatially variable conditions within process units, and complicated interactions between these units."

Jan 1, 2003

By R. L. Pascual, W. J. Whiten

"The froth flotation process is not well understood. Both flotation models, and the parameters used to describe the stream flows are not well defined. They in fact vary considerably in different applications. This creates difficulties is designing a simulation program suitable for use by plant personnel, consultants, and researchers. In addition to simulation, an effective simulation program can be expected to provide a range of other services.This paper shows how a process circuit simulator can be designed with sufficient flexibility to satisfy these needs, and discusses some of the additional services.OVERVIEWThe development of a simulation program for froth flotation circuits faces several challenges as flotation models and the associated stream descriptions are not well defined. There is little agreement on the best form for a flotation model, or on how the plant streams should be defined.In addition to simulation, a flotation simulator is generally expected to provide other services such as data input, data reconciliation, model fitting, and accuracy estimation. Additional services may also be needed beyond what might initially be envisaged. A summary of some of these possibilities is included.To apply simulation to a flotation circuit it is necessary to develop a flotation cell model, for instance based on the general outline given in the appendices. Experimental data, usually from the plant, is needed to determine cell model parameters. This is generally done by first undertaking data reconciliation to determine if mass flow constraints are sufficiently closely satisfied. At the same time the data is inspected for outliers that might bias subsequent calculations. Next the data is fitted to a model to back calculate ore characteristics. If there is sufficient agreement between the fitted model and the data, the model can then used to make predictions of the effect of changes to the plant. The changes, that the simulation shows are beneficial, can be applied to improve plant performance"

Jan 1, 2003

By Akira Nishikawa

During the twentieth century the copper smelting industry achieved dramatic expansion corresponding to the vast growth of global economy. This was largely due to innovations in pyro-metallurgical processes, such as autogenous smelting and continuous smelting and converting technologies. However, as copper production capacity increased, its impact on the environment also could not be ignored, and thus with increasing global environmental awareness, many smelting operations either had to renew or rebuild their facilities. In addition to these changes, in places like Japan and Europe, with scarce primary resources, the treatment and recovery of metals from a variety of items such as car shredder dust, used electrical appliances and electronic devices, on top of scraps traditionally treated, is having a profound effect on the reduction of waste and the preservation of primary resources. Thus compared to the days when copper smelting focused on the environmental control in order to break with "Smoke Stack Industry", copper smelting today is making an important contribution to the sustainable development of human society.

Jan 1, 2003

By de Vaux. Deryck, Natalie J. Shackleton, Vratislav Malysiak Cyril T. O. Connor

"The major losses of PGM and base metals in the beneficiation of platinum group deposits occur during the separation of gangue from the value minerals by selective flotation. A number of studies have shown that this negative impact on flotation is due to surface passivation, caused by various ions that may originate from the external water supply or, as is likely in the majority of cases, from the oxidation of the mineral surfaces and the grinding media. This investigation aimed at reducing surface passivation of pentlandite and inadvertent activation of pyroxene, thereby improving ultimate valuable mineral recovery and selectivity. Both synthetic minerals and plant ores were studied in order to determine the effect surface passivation and inadvertent activation have on mineral surface alteration and floatability. Zeta potential determinations, microflotation, ToF-SIMS (Time of Flight Secondary Ion Mass Spectrometry) analyses, laboratory batch flotation tests and continuous flotation testwork were used as tools to study the surface alteration and/or floatability.Zeta potential determinations and ToF-SIMS analyses showed that copper adsorption is non-selective. Both pentlandite and pyroxene become copper (II)-activated in the presence of copper sulphate and subsequently, in the presence of xanthate, adsorption of the collector will occur onto copper activated mineral surfaces. Zeta potential determinations also showed an alteration of the surface charge in the presence of polyphosphate, thereby inhibiting surface passivation of sulphides by slime coatings due to surface repulsion.The addition of diethylenetriamine (DETA) reduces the copper concentration on both minerals, predominantly on the pyroxene surfaces and polyphosphate further enhances the selectivity at pH 6.The microflotation and batch flotation data obtained has shown a significant improvement in the ultimate flotation response of valuable mineral recovery and concentrate grade compared to the standard reagent regime, while the continuous flotation results significantly improved the selectivity, however, at a similar ultimate recovery."

Jan 1, 2003

By Grant C. Lukey, Jannie S. J. van Deventer

"The environmental effects of the mining and mineral industry include destruction of natural habitats, changes in river regimes and water tables, and other serious ecological impacts. In this century, it is likely that water will become a critical resource, and in most countries the mining industry competes for a share of this resource. The Kyoto Protocol may at first seem only relevant to the coal mining and power industry, however, it should not be forgotten that the mining and mineral industry is a significant consumer of power. Therefore the ratification of the Kyoto Protocol by most developed countries and the introduction of a carbon credit trading scheme will impact on the industry by potentially increased costs in utilities and waste discharges. It is clear therefore that the mining industry faces many challenges in the coming years. The mining industry?s commitment to sustainable development needs to continue to evolve, in order to meet these challenges effectively. With the advent of globalisation of the industry, it is now an opportune time for the industry to gain international agreement on how they want the industry to achieve sustainability in future years; such a progressive approach is necessary, otherwise government will force the industry to change, which may not necessarily be the best outcome for the industry.INTRODUCTIONThe Earth Summit in Rio de Janeiro in 1992 was an opportunity for world leaders to assemble and discuss strategies and initiatives that provide for further industrial growth without adverse effects on the environment. The World Summit on Sustainable Development held last year in Johannesburg, South Africa, was an opportunity to evaluate those initiatives implemented over the past 10 years, and to set a new and sustainable direction for the future. It is clear that industrial and technology development will continue at a rapid pace in order to serve the needs of a growing world population, but it is essential that the course of this development is well planned, well executed, and that it is sustainable. In reality, while government officials and politicians continue to debate policy and international protocols, the environment continues to suffer and the effects of climate change and global-warming become more real each day."

Jan 1, 2003

By U. M. J. Boin, E. V. Verhoef

Pyrometallurgical reactors constitute a key processing component in the total primary and industrial/recycling resource cycle, being involved both in primary smelting, converting and extraction, as well as the reprocessing of scrap, from aluminium cans to end-of-life automobiles. Therefore the pyrometallurgical reactor?s role in achieving sustainability is the central theme discussed in this paper since optimising their operation minimises waste, residue and offgas (NOx, dioxin, CO2) and maximises product quality and therefore efficiency. To effectively control the overall resource cycle, one needs to take a systems modelling approach of the whole cycle, seeking to also understand the dynamic process behaviour of the individual components of the cycle, and then especially the part that contributes most to the chemical conversion, namely the pyrometallurgical reactor. This paper highlights the role of pyrometallurgical thermodynamics in the whole resource cycle and specifically places equilibrium thermochemistry in the context of process dynamics where large, variable inventories are recycled or maintained within the system. This paper will therefore review the semi-empirical dynamic modelling tools, which are used to model complex systems with the specific goal of developing dynamic predictive models, which also include slag-alloy chemistry, towards controlling the recycling in a feed forward manner. To illustrate the primary production of metals, high carbon ferrochrome and Ni-Cu-matte smelting will be presented as a brief case study. Also fundamental studies in blast furnace and waste incineration kilns will be given. It also will show how the distributed nature of the chemistry of melts in the case of primary extraction, and industrial (recycling) materials such as recycled end-of-life vehicles, have a significant impact on the process outcomes and model predictions. It is therefore argued that the fundamental thermodynamics and kinetics in metallurgical reactors play a final crucial role in modelling the closed material cycle, but only when it is used in conjunction with process systems theory based on reconciled data for parameter estimation and model calibration. System models for aluminium and car recycling will be given as well as a dynamical system model that describes the interconnected material flows for Ag, Au, Bi, Cu, Fe, Ni, Pb, PGM, Sn and Zn for a study on lead-free solder.

Jan 1, 2003

By E. V. Verhoej

The proposed EU directive on the restriction of the use of certain hazardous substances in electrical and electronic equipment promotes the substitution of lead in consumer electronics to reduce emissions from lead in the end of life phase. In this paper, the consequences of substituting lead in solders is assessed using the Eco-Indicator-99 method for the examples. The base metal production system is considered as an interconnected network modeled dynamically in Simulink 4 and Matlab 6 (Mathworks Inc 2000), where the recovery and production of metal components of the assessed product partially overlap. This approach requires global modeling of metal production processes and mass balances and resulting allocation choices. It also reveals the susceptibility of LCA scores to different choices in the modeling and data availability and uncertainty. Besides the comparison between lead-free and lead-containing solders, other side effects are revealed. Lead is carrier material for the recycling and production of many co-elements in the interconnected production and recovery system. Substitution may have adverse effects such as temporary shortages of other connected metals that are often not considered in normal LCA assessments, thus leading to erroneous results. The suggested approach provides directions for including these extemal effects and for further assessment of the environmental effects of substituting lead. This paper shows that in order to assess the environmental aspects of metallurgy, dynamic modeling of the total system is required based on the fundamental thermodynamics in each metallurgical reactor, the basis of this dynamic model. With this the true environmental impact of metallurgy can be explained. In the case of lead free solder, it is shown that the mining of substitutes has a very much larger impact.

Jan 1, 2003

By Richard K. Komarek, Antonios Zavaliangos, Roman T. Dec

Roller presses are widely utilized in mineral industry for fine milling and compaction. Recently used models are providing only limited information about the material behavior in the roll bite. This paper introduces a 2-dimensional finite element model for analyzing those two basic processes. A pressure-dependent plasticity model with linear elasticity was used as a constitutive model for the particular material. Coulomb friction law was used to describe phenomena on the material/roller surface interface. Two basic roller geometries are considered: smooth (used for milling and compaction) and with cavities, commonly used for briquetting. Comparison of the results obtained from the model with experiment indicates that they are following the general trends of experimental values recorded with laboratory roller presses. It is shown, that the model is suitable to analyze material behavior through all stages of the rolling process: feeding zone, nip region, neutral plane and release section. It can predict pressure, shear stress, slip of the material over the roller surface, material velocity field, failure of the compact during release and the course of other important process variables. This allows the process engineer to gain an improved understanding, leading to a better process and equipment design and control.

Jan 1, 2003

By Gerke Gilian, Pretz Thomas, Pehlken Alexandra

"The evaluation of health hazards within the treatment of mineral and waste materials is gaining more and more importance in industrial countries. The need to control occupational health and safety has been recognised, and regulations which describe general protective measurements for personnel provide a tool to protect their health. It is the aim of the paper to give an outlook for practical approaches to risk assessment and to present measures for exposure reduction in accordance with the state of the art in Germany.Both the treatment of minerals and of waste materials are described in relation to the risk assessment. The method of evaluating health hazards in the two industries is similar and therefore both examples are presented next to each other.The example presented in the paper is the German “Biostoffverordnung” (the regulation for biological materials) which is important for the waste treatment industry. All kinds of waste treatment facilities (like composting facilities, waste dumps, sorting facilities for packaging materials) are obliged to carry out an assessment of health hazards for a variety of working areas and working places. The possible safety requirements deriving from this regulation are presented and discussed under the aspect of biological hazards."

Jan 1, 2003

By James Y. Oldshue

"Very seldom is it possible when contacting a gas with a slurry to measure the dissolved gas concentration in the slurry, and even where possible, equilibrium data with a suitable Henry.s law constant are seldom available.In general, by assuming a reasonable value for the dissolved gas concentration in the slurry and a corresponding equilibrium gas partial pressure P*, KGa values can be calculated for the pilot plant and then scaled up. Then, with the same P* value at various reaction conditions, a mixer can be designed which is quite satisfactory, having a reasonable design factor for full-scale performance."

Jan 1, 2003

By Lawrence Devon Smith

"This paper examines the impact of the various assumptions that go into an economic evaluation, and shows how these can be combined to show an exciting result that may not really exist. An example of an embellished case (the kind that one frequently sees when projects are being promoted) is developed and the cumulative impact is analysed to show the actual project underneath. The paper also points out some areas to watch for overly optimistic assumptions such as prices, inflation, and debt. The concept of a ""bare bones"" base case is proposed (constant metal prices, constant dollars, no inflation, no debt, no interest, on a project basis, after tax) as a common reference point.As well, the discount rate is examined as a fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed, and a methodology for the analysis of risk levels is proposed that assesses the constituent components of the discount rate: real interest, mineral project risks, and country risk.INTRODUCTIONOften, the first time that all of the technical and economic data for a mineral project comes together in one place is when the economic evaluation is developed. This typically happens when work on the project has progressed to a sufficient level of detail that the effort to produce a year-by-year cash flow is justified, usually at the pre-feasibility or feasibility study stage. The data involved will include:• production; tonnes waste and ore mined, ore grade, mining recovery, metallurgical recovery, metal sold• revenue; metal price, smelting & refining charges, marketing costs• operating Costs; mining, milling, administration, fees, royalties• capital Costs; exploration, development, construction, indirect costs (engineering, management), contingencies, start-up, inventories, working capital, replacement and sustaining capital, closure costs• taxes and royalties• exclusions; depreciation (this is not a cash item), sunk costs (only costs going forward)."

Jan 1, 2003

By C. Gomez, J. Finch, R. Dalhke, J. Torrealba-Vargas

The velocity of gas passing through a flotation cell can be estimated by collecting bubbles by natural buoyancy in a closed tube and measuring the rate of pressure increase. The governing equation is derived and verified. Single- and two-tube gas velocity sensors are described. The latter design permits a correction for bulk density and level change during signal collection.

Jan 1, 2003

By P. Huang, D. W. Fuerstenau

Various factors that control the natural flotability of talc, including differences due to crystal face and edge effects, were delineated. For study of talc depression phenomena, dextrin was used as a model depressant. For the enhancement of talc flotation, dodecylammonium acetate (DDAA) was used as the collector. The interaction of DDAA with talc was assessed by flotation experiments and electrokinetic (zeta potential) measurements, from which the role of hydrophobic bonding can be demonstrated. The results presented in this paper provide useful information on how the crystal chemistry and surface chemistry control the electrical double layer, adsorption phenomena, wettability, and flotation behavior of talc in aqueous media.

Jan 1, 2003

By K. W. Stöckelhuber, A. Wenger, H. J. Schulze

"An important elementary step of the flotation process is the forming, drainage and rupture of a thin intervening liquid film between bubble and mineral particle.After the encounter of the bubble with the solid surface a wetting film is formed. The initial thinning of this film is driven by the capillary pressure inside the bubble. When the film has reached a certain thickness rupture can take place.There are two possible mechanisms describing this process:-, Growing fluctuation waves (spinodal dewetting) on fluid interfaces under the influence of any kind of attractive forces (electrostatic, van der Waals). -, Nucleation inside the film.Metastable wetting films on negatively charged, hydrophobic glass surfaces (gaseous phase methylated), or on hydrophilic, positively charged glass surfaces (with Al3+ ions), have been analysed by means of the kinetics of film thinning according to the Reynolds law. These experiments demonstrate that both mechanisms can be responsible for the rupture of a thin wetting film. In the case of hydrophobic surfaces the nucleation mechanism is preferred; in the case of opposite charged silica surface the capillary waves mechanism due to an attractive electrostatic double layer force between silica and air bubble takes place.Hereby the existence of a long range hydrophobic force. on a hydrophobic surface can be excluded. The apparent interaction can be explained by the presence of gas nuclei formed on heterogeneous surface sites. The results provide deeper insight into the mechanisms of wetting film stability, adhesion process in flotation and droplet coalescence."

Jan 1, 2003

By P. Harris, D Bradshaw

"Comparison of the two most commonly used classes of depressant in the South African platinum industry is complicated by the fact that these polymers induce different effects on the surfaces onto which they adsorb. The use of carboxymethyl cellulose (CMC), which is ionically charged in solution, can lead to increased particle dispersion in addition to the effect of reduced surface hydrophobicity (depression). Guar is typically only slightly charged in solution. Comparison of these two depressants is complicated since it is uncertain whether differences in their action is a result of either depression of dispersion effects.This work investigates the role of dispersion independently to that of depression in the batch flotation of a platinum bearing ore. An inorganic dispersant, sodium hexametaphosphate (NaHMP) was added in parallel to the uncharged guar depressant to simulate the action of depressants with varying degrees of dispersion. By distinguishing between the material recovered by entrainment and the floatable gangue and by including the effects of froth stability it was possible to decouple the effects of dispersion and depression.The results show that both dispersion and depression led to increased grade of the sulphide minerals. Depression leads to a decreased recovery of floatable gangue minerals. Dispersion leads to an increased recovery rate of these minerals and an accompanying decrease in froth stability."

Jan 1, 2003

By R. L. Pascual, W. J. Whiten

"The froth flotation process is not well understood. Both flotation models, and the parameters used to describe the stream flows are not well defined. They in fact vary considerably in different applications. This creates difficulties is designing a simulation program suitable for use by plant personnel, consultants, and researchers. In addition to simulation, an effective simulation program can be expected to provide a range of other services.This paper shows how a process circuit simulator can be designed with sufficient flexibility to satisfy these needs, and discusses some of the additional services."

Jan 1, 2003

By Juan B. Yianatos

"After almost 100 years, since the first commercial application began in Australia, flotation has shown an extraordinary growth and nearly 2 billion tons of ore per year are presently treated by flotation processes. During this time flotation has promoted a wide scope of research activities ranging from fundamental chemistry and hydrodynamic studies to studies of industrial operations. In general, fundamental studies have been mainly related to ideal situations. In recent years, however, large efforts have been focusing on achieving a better insight into the actual sub-processes provided by the development of new and more sophisticated instrumentation. Since the massive incorporation of flotation columns, around 15 years ago, a renewed interest in flotation fundamental studies, process modelling and new cell designs have been observed worldwide. The key role of the froth has been recognized as an independent and sometimes rate limiting process step. Thus, separation of pulp and froth process stages seems the most appropriate in terms of process modelling, diagnostic, design and scale-up purposes.In relation to flotation equipment development, until the middle of the 1970?s, only the sub-aeration mechanical cells were dominant. Since the 1980?s, the use of pneumatic cells and forced air mechanical cells has emerged strongly. Also, in the last decade, flotation equipment has shown a dramatic increase in size, reaching values of 200m3 in unitary mechanical cells and more than 300m3 in columns. The general feeling, however, is that, despite the great advance observed in terms of process knowledge, the mechanisms and principles of industrial flotation cells design and scale-up are still not fully understood.Advances in process instrumentation and control now in use allow for more efficient operations, both in metallurgical performance and savings in operating costs.INTRODUCTIONFlotation is a widely used process within the minerals processing industry, as well as being used for water treatment and de-inking of recycled paper. Froth flotation started in Australia at the beginning of the 20th century and since then flotation technology has made significant advances. Flotation was firstly applied to sulfide ores. The largest tonnages treated by flotation are copper and copper/molybdenum ores, handling about 50% of the total ore processed. Also significant are phosphate, iron ore and coal treatments. At present, Chile is the foremost copper producer in the world with around 35% of the world?s production. Figure 1(a) shows the evolution of copper production in Chile over the last decade. The total amount of fine copper produced in year 2001 was 4.7 million tons, from which 3.2 million tons was processed by flotation while 1.5 million tons went through LIX-SX-EW processes, which also showed significant development during the same period (Anon, 2001). The total flotation treatment of copper ores in Chile is about 325 million tons per year (Anon, 2002), so the world treatment of copper ore by flotation can be estimated at about 1 billion tons per year. Consequently a total of nearly 2 billion tons of ore per year is presently processed worldwide by flotation (Fuerstenau, 2001). In order to handle the higher tonnage of low-grade ore, a worldwide trend towards the development and use of larger flotation machines began in the 1960?s. Figure 1(b) shows that the trend became extremely marked from the beginning of the 1990?s, which is consistent with the strong increase in copper production during the same period."

Jan 1, 2003

By Hamid-Reza Manouchehri

"The triboelectric charge attributes of feldspar, quartz and wollastonite minerals, after contacting different triboecharging medium made of different materials, were considered. Their charge acquisitions by different size fractions of minerals were monitored and accordingly their energetic work function values were estimated. Moreover the separation behaviours of these minerals through the electric field of a laboratory free falling separator were determined and the effects of some chemical reagents on separation their separation characteristics were studied.Finally an attempt was made to translate the findings from single mineral systems to a complex silicate ore, containing quartz, feldspars, wollastonite and some other silicates. The results show favourable prospect to apply the triboelectric separation technique for beneficiation such a complex raw material."

Jan 1, 2003

By Robin B. Batterham

"Since the 1970?s we have seen a marked corporate response in terms of the environment. In part this has come from regulation but it has largely come from stakeholders and the community. Rising expectations have in general been met. We now see a similar trend towards sustainability. At the same time, the importance of mining to the share market has decreased drastically and with that decrease has come the requirement for the mining sector to show returns similar in manner to other sectors. While rationalisation can achieve some progress towards these goals, the long-term requirement is for innovation, as it always has been. This paper looks to the logical goal of innovation within a sustainable mining framework and targets the removal of the desired metal values with minimal environmental footprint. It is suggested that broad ranging alliances will be necessary, particularly amongst the R&D suppliers, to achieve this goal. Industry will need to take an active role given the recent global restructuring.THE MARCH TO SUSTAINABILITYSince the 1970?s there has been an increasing corporate response on environmental matters. We have moved from matters environmental being issues relevant only to minority groups through a series of attitudinal changes by management. Whilst there have always been examples of excellent environmental performance, for many in the 70?s spending money on improving the environment beyond some minimal level was seen as a distraction from production or treated in a similar way to donations to the community. There is little of that attitude these days, as most mining companies have long since regarded the environment as a core business direction. Indeed, for some years one could note an escalation in matters of environmental reporting to the extent that the environmental performance of companies is now very public. In some cases, NGOs have even been invited to help certify and audit the reporting standards. Similarly with health & safety.There is now a rising expectation on the part of the community that social matters will also be given the same level of support as health, safety and the environment. This time around it would appear that the mining industry is at the leading edge of sustainability. The Global Mining Initiative (Global Mining, 2002) and the contributions to the Rio World Summit on Sustainable Development (Rio +10, 2002) suggest that sustainability is being taken very seriously by the mining industry. For sustainability it is convenient to use the Brundtland (1987) definition. This definition has widespread acceptance with governments, industry, environmental groups, financial institutions and individuals as a direction against which our activities and plans can be measured."

Jan 1, 2003

By Ray Everson, Henry Kasaini

"We carried out adsorption experiments in chloride media to study the adsorption characteristics of Pd (II) anions on the surface of activated carbon. Throughout the experiments, we used commercial activated carbon pellets (0.8 Norit). The adsorption process was interpreted by using the ionisation and adsorption model. This implies that palladium anions were adsorbed physically on a protonated surface of activated carbon either as anionic complex species (PdCl4 -2) or aqua chloro-complex species [PdCl3(H2O)-] in acidic media. Furthermore, we established that adsorption of Pd (II) species was reversible at high chloride [Cl-1] concentration. The maximum adsorption capacity (Qsat) of Pd (II) anions averaged 27 mg/g. The Toth adsorption isotherms fairly predicted the equilibrium adsorption of Pd (II) species and the associated surface coverage.The effect of temperature and acid strength of the feed solution on the adsorption of Pd (II) ions were quantified. The adsorption kinetics was limited by external mass transfer since the effect of pore diffusion on the overall rate constant was negligibly small. A pseudo first-order kinetics model was used to describe the adsorption kinetics."

Jan 1, 2003