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By E. Goris Cervantes

"A theoretical framework based on a detailed analysis of mine operations data from an oil sands mine in northern Alberta and the static simulation of truck cycle times are developed, verified, and validated in this paper. Implementation of this framework provides better results than existing tools that rely solely on manufacturer data. This, therefore, aids in efficient equipment planning for the life of the mine. The use of this framework to modify existing productivity curve estimation methods currently in use at the mine site is also proposed. This method replaces “loaded flat haul” with “loaded effective flat haul” in the productivity estimation. Validation of the model results in a 4% overestimation of productivity, versus an underestimation of more than 10% when using the existing in-house method. ¦ KEYWORDS Equipment planning, Life-of-mine (LOM) planning, Oil sands, Productivity, Truck cycle times RÉSUMÉ Un cadre théorique fondé sur une analyse détaillée des données relatives aux activités minières d’une exploitation de sables bitumineux dans le nord de l’Alberta et la simulation statique des temps de cycle des camions sont développés, vérifiés et validés dans cet article. La mise en oeuvre de ce cadre offre de meilleurs résultats que ce que proposent les outils existants, lesquels se basent uniquement sur des données des constructeurs. Ceci contribue donc à une planification efficace de l’équipement pour des projets relatifs à la durée de vie de la mine. On propose également de se servir de ce cadre pour modifier les méthodes d’estimation de la courbe de productivité actuellement utilisées sur le site minier. Cette méthode remplace le concept de loaded flat haul (la distance parcourue par des camions avec un chargement du point de collecte jusqu’au point de déchargement des résidus miniers) par celui d’effective loaded flat haul (la distance relative parcourue par des camions avec un chargement du point de collecte jusqu’au point de déchargement des résidus miniers) dans l’estimation de la production. La validation du modèle résulte en une surestimation de 4 % de la productivité, par rapport à une sous-estimation de plus de 10 % avec la méthode actuellement utilisée en interne. ¦ MOTS CLÉS planification de la durée de vie de la mine, planification de l’équipement, productivité, sables bitumineux, temps de cycle d’un camionINTRODUCTION One aspect that differentiates oil sands mines in northern Alberta from conventional hard-rock mining is the environment in which they operate. Due to ground characteristics, producers in the region experience roads with very high rolling resistance (RR) that, in turn, negatively affect haul-truck performance and greatly increase fuel consumption and emissions. Oil sands mining companies use some of the largest haul trucks in the world. In addition, oil sands mines cover more extensive areas than hard-rock pits, resulting in longer haul distances on roads made of comparatively more viscous material."

Jan 1, 2019

By N. Voennann

Stillwater Mining Company operates an electric furnace at its smelter in Columbus, Montana to treat a Ni-Cu-platinum group metal concentrate along with secondary PGM bearing materials. Hatch Associates has designed several improvements to this furnace, which was originally built by others. Implementation of these relatively low cost improvements has resulted in substantial increases in furnace availability and capacity, along with reduced unit costs. ? The improvements included: ? Installation of water-cooled copper cooling elements to stabilize refractory wear and increase furnace life.- ? Improved furnace 'bindings, to enhance the furnace's structural integrity by improving the contact between the refractory and cooling elements, and by promoting tight brick joints resistant to matte or slag leaks. ? Adjustment of the electrode regulator to allow higher furnace power levels. ? Installation of an automated air-slide (aeration conveyor) feed system to evenly distribute the furnace feed in an insulating layer on the bath surface. This "black-top" practice reduces unit energy costs and makes available additional smelting capacity.- ? Electrode seals to reduce ingress of air that absorbs heat before exiting the furnace in the off-gas stream. The saved energy can be used to smelt additional concentrate. This paper describes the above furnace modifications, and the benefits derived from their implementation.

Jan 1, 1998

By J. P. A. Hortley

In conventional electrolytic copper production, looped copper starter sheets, on which the copper is deposited, are supported by hard-drawn copper bars. These bars have cross-sectional areas of between 1 and 1.4 in2. The suspension bars serve two purposes: firstly to support the cathode, which can weigh up to 150 kg, and secondly to introduce the electric current. IYI examined these two requirements in detail to see whether a better design could be achieved. Considering firstly the current carrying requirement, it wee noted that under normal refinery conditions, each cathode carries between 400 and soak. If one applies the generally accepted rule that 1 in of copper can carry 1000A4 a suspension bar need theoretically contain only 1/2 in2 of copper. This contention is supported by the fact that the 500A current passed through the cathode also appears to pass quite satisfactorily through the two support loops, which have a cross-sectional area of approximately 0.35 in 2. Turning now to the strength requirements, the cross-section of hard-drawn copper bar required to support a 150 kg cathode is relatively small, and easily met by the present designs. It is not, however, the static load applied by the 150 kg cathode immersed in the electrolyte which causes the damage to the hard-drawn copper, or even the increased static load of a 100 kg man standing on one foot in the centre of the bar; the damage is actually caused by the dynamic loads applied to the bare when they are dropped, thrown into containers, lowered too rapidly into the cell, or otherwise mistreated. The important requirement is therefore that the bar does not permanently bend. Its proof stress of limit of proportionality, rather than the amount that it deflects under static loading, should be the strength criterion. With the hard-drawn copper normally used for the manufacture of suspension bars, it has been observed that the copper becomes annealed during use, particularly at the end of the bar where the current is introduced. Thus, after a relatively short time, the cathodes are in effect being supported by annealed copper bars.

Jan 1, 1978

By Tomoya Kawasaki, Tatsuya Motomura, Yutaka Yasuda

Saganoseki Smelter, one of the largest copper producers in Japan, currently operates a single flash smelting furnace to produce 450,000 tons of new copper annually. The smelter used to employ two flash furnaces, and integrated the two into one in 1996. Since then, various improvements to its facilities and technologies have been made to increase productivity. To upgrade the operation efficiency, "stability" was considered a key issue, and the measures were taken to increase the operation and facility reliability. Currently, the furnace is running at a feed rate of 215 DMT/h, while the furnace utilization has been maintained at 97%. This paper outlines recent improvements that have made to increase furnace productivity and efficiency.

Jan 1, 2014

Nowadays, the more successful plants are those who have adopted effective and efficient strategies to optimise their plant operation. As the ?heart of the plant? could be viewed as the mil-ling/grinding area, one of the key steps in plant optimisation is, therefore, ensuring the mill is operating properly. In the past, when primary, secondary and tertiary crushers fed material directly to large ball mills, the energy efficiency of the concentrator was determined for the most part by the ball mill operation, whereas now the energy efficiency of a plant often rests largely on the semiau-togenous grinding (SAG) mill operation. As a result, mines have shifted their emphasis in optimization from ball mills to SAG mills. The grinding mill?s energy efficiency essentially depends on ore characteristics and the discharge rate of broken particles, which in turn depends on how efficiently the discharge pump (grate and pulp lifters) operates. The essential function of pulp lifter being to transport the broken material and slurry out of the mill, its design optimization therefore affects the discharge capacity (or mill throughput) of AG and SAG grinding mills. This paper will discuss how the optimised design of the pulp lifter/ discharger has helped to eliminate material transport issues such as flow-back and carry-over of slurry and pebbles to in-crease the energy efficiency of SAG mill using the actual operational data.

Jan 1, 2014

By F. Henríquez

Traditionally, the implementation of an automated control for a ball mill has been a challenging one. First, it must be capable of processing a variable SAG mill feed while at the same time avoiding to become a process bottle neck. Second thing is, it must deliver an adequate quality product (P80) to the process downstream. Then the ball mill itself and its associated classification equipment has problems of its own: it must maintain adequate control of cyclone?s pressure, density and pump-box level with often, less manipulated variables than needed, namely, variable pump speed and the opening/closing of cyclones. Thus, it becomes a non-linear multi-variable type of process with often too multiple and contradictory control objectives to satisfy simultaneously. On top of that, to extend cyclones availability and yet, maintaining their performance, is must both for process and maintenance purposes. Trying to solve the puzzle, Minera Los Pelambres implemented a novel and successful combination of MPC (Multivariable Predictive Control) and advanced control in two of its newest ball mills, reducing considerably process variability while maintaining high throughput and keeping the process well within constraints limits. Because of their differences in processing capacity, size and topology, two different stabilizing-control strategies were developed, tested and tuned. Hence, for both control approaches their implementation process, main results, areas of applicability, limitations and their key performance indicators are discussed further. This paper also discusses the need of such advance control technologies in the mining industry, including the impact of these technologies on best practices for their implementation, operation and long term sustainability

Sep 1, 2012

By Benoît Pinier, Jason Furtney, Gustavo Sampaio Lopes, Jorge Valencia, Johan Hawinkel

This paper describes a numerical modeling study on the effect of airdecking on vibrations, fragmentation, and movement in mining-related rock blasting. Practice has shown that air gaps reduce blast vibrations and damage while maintaining the required fragmentation and movement, yielding similar blast outcomes with less explosive mass per hole. Given that the premise of “replacing explosives with air” for better blast results is counterintuitive, this paper aims to shed light on the physical mechanisms and processes occurring in a blast with airdecks. It is hypothesized that airdecks are effective and beneficial because they load the rock at pressures lower than what is required to crush the rock. In the airdeck, the explosive gasses directly fracture rock and avoid energy loss due to crushing. In essence, the airgap allows similar outcomes in fragmentation and throw with less total explosive product, as the lower pressure gasses in the airdeck are still effective at breaking and moving the rock. This is distinct from only having less explosive and more stemming, as the stemming reduces the pressure more than an airdeck at the same position. This study uses the blastFoam software (for modeling of single and multiphase flows) to accurately calculate the pressure history throughout a blasthole and air gap. The pressure and gas loading are coupled to numerical models of vibration, fragmentation, and blast movement. Using this modeling technique, a suite of blast scenarios for typical configurations in a range of commodities is assessed with and without airdecks. Rock blasting practitioners have a responsibility to protect communities, infrastructure, and heritage — demystifying airdecks through a better understanding of the physics provides another tool in the blasting engineering toolkit to serve this goal.

Jan 21, 2025

By John Floyd, Larry Wardrip

A series of tests were conducted to evaluate the performance of a high density, high velocity cartridged explosive. The tests included two production blasts in a limestone quarry and two production blasts in a granite quarry. To quantify blast and product performance, each blast was monitored with the following equipment: l Two (16mm (Lo Cam) high speed cameras (500 images per second) l Velocity of detonation recorder (I million samples per second) l Four face motion accelerometers (1 million samples per second) l Digital seismograph The fragmentation distribution produced by each blast was quantified with digital image analysis The benefits of the use of high velocity, high density toe loading was quantified in terms of: l Vibration reduction l Fragmentation improvement l Excavator performance In addition to the field tests, a comprehensive evaluation was performed to determine the cost/benefit relationship of the use of the toe load. This paper will include the findings of the study along with guidelines for use in other quarry operations.

Jan 1, 2002

By R Wedmaier

Henty Gold Mine is an underground operation producing 100 000 ounces of gold per annum. The original mining method used was flatbacking with paste fill. However, a non-entry method û uphole benching û was introduced in 1998 to recover the deteriorating crown pillars. Initial challenges were encountered, including poor drilling accuracy, difficulty in charging holes and poor rise performance. These challenges were overcome by a Continuous Improvement Team, consisting of mining engineers, supervisors and miners. Following this, the Team implemented further changes aimed at reducing ore loss and dilution. A second area addressed by the Team was development blasting, where innovative detonator technology known as the ExelTM DevelDetTM was introduced and rapidly accepted by the operators. Continued use of the ExelTM DevelDetTM resulted in a number of benefits, such as easier bogging, less perimeter damage, faster charging and hook-up and decreased wastage. Finally, improvements were made in the area of explosive handling, where competency-based training of operators was conducted and manual handling of ANFO has been significantly reduced by the introduction of the MiniMoverTM into the underground magazine.

Jan 1, 2001

By Khiva Haidar Shauma Tassno, Zulham Ahmad, Farhan Harist Maharesi, Abdullah Badawi Batubara

Blasting operations can use a bulk emulsion explosive (EE) with a formulation based on used oil as a replacement for refined fuel oil. The most commonly employed used oil for making EE is a mineral based used engine oil that passes an impurity content standard. It is known that not all types of used oil are easily incorporated into EE formulations. Impurities in used oil can disturb EE stability resulting in crystallization and phase separation and consequently led to poor detonation quality. In 2024, a poor blast result occurred at an Indonesian mine due to utilization of used oil that was not within specification. A research project conducted from February to April 2025 found that used transmission oil differs from used engine oil in hydrocarbon composition. Transmission oil contains more additives that affect EE stability due to polarity differences and the disruption of colloidal state stability. Lab tests including stress testing and crystal growth observation aided the development of a stable EE formulation based on used oil and used transmission oil. In mid-April 2025, blast evaluations were conducted using the EE that was formulated using used engine oil and used transmission oil. Measurements of velocity of detonation, fragmentation, and digging time, demonstrated high quality EE was produced. Application of used oil in EE revolutionized the capability of mining operations to improve blast sustainability and cleanliness. Through comprehensive research, robust testing, and effective supply chain management, it is possible to replace some portion of refined fuel oil with used oil without compromising blasting performance. The inclusion of used transmission oil broadens the overall used oil specification and increases the volume of recycled used oil available for blasting. The increased volume of used oil available can reduce the amount of waste generated by mining projects while maintaining operational efficiency.

Jan 26, 2026

By A Campbell

Trials of different tapping operations at Olympic Dam have been carried out with the aim of improving the safety of tapping and improving the integrity and lifetime of the taphole. This has involved trialling the use of a mudgun and drill on one of the tapholes of the electric furnace in place of the normal manual tapping procedures. The blister copper tapholes are currently closed using a conical clay plug formed around a steel bar. The plug is pushed into the taphole by hand to stop the flow, and the cooling on the outer part of the taphole freezes the blister copper in the tapping channel. The hole is burnt open using consumable oxygen lances. This puts the furnace technicians in close proximity to molten metal and heat û which is reflected in the safety incidents reported by these operators. By moving to a mudgun and drill operation, the furnace technicians will be moved away from the taphole area improving their safety. Additional benefits include: improved tapping cycles; extended taphole refractory lifecycles; and improved furnace integrity around the taphole, hopefully extending the campaign. This paper outlines the trials that have shown that it is possible to plug and drill blister copper (not matte) tapholes using a mudgun and drill.

Jan 1, 2005

By A D. Campbell, G R. Power

Many caving mines use numerical flow models to simulate mine production, forecast recovered ore grades and optimise the draw strategy. In sublevel caving (SLC) mines, the effects of blasting and fragmentation at an individual ring scale generally cannot be included in these models. Previous attempts to use results from marker recovery trials to calibrate numerical flow models have been limited due to difficulties in accounting for blasting effects at a ring scale. This paper outlines how an empirical criterion for blasting and fragmentation was used to attribute variable flow properties into a numerical flow model based on the blast design and modelled fragmentation. The flow model was then validated using data from a number of full scale marker recovery experiments. The result of this approach was a significant improvement in forecast accuracy when compared against the same modelled cave marker recovery without the inclusion of these blasting effects. Improvements in the flow model are currently being adopted within the mine scale model to further improve the accuracy of grade forecasting, optimise the draw strategy and increase net present value. The integrated modelling approach is also being used to simulate the effects of different drill and blast designs on cave recovery. It is suggested that, if implemented, the technique would lead to improved blast designs in other SLC mines, increase the value of marker trial data and reduce costs associated with large scale blast design trials.CITATION:Campbell, A D and Power, G R, 2017. Improving calibration of flow models against SLC marker trials by linking blasting effects to particle mobility, in Proceedings 13th AusIMM Underground Operators’ Conference 2017, pp 11–22 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Oct 16, 2017

By M. Shapiro, L. A. le Grange, B. Henning

A paper was presented by Bateman Minerals and Metals at INFACONX (2004) describing a simplified Computational Fluid Dynamics (CFD) Model for predicting the temperature and velocity distributions in all the fluid zones of a single electrode DC Furnace simultaneously with the temperature distributions in the refractory lining of the vessel. The boundary conditions imposed on the model consisted of the arc current, external surface film coefficients and ambient temperatures. The temperature and velocity distributions in the free-board, slag and metal were solved simultaneously by coupling across the interfaces between the fluids and transportation phenomena developing in the plasma arc. A simplified model was used to describe the ex-change of energy by radiation between the arc and surfaces enclosing the freeboard region. The strengths of this model were reported as being the ability to: ?Solve the different zones and transportation phenomena simultaneously without the need to transfer partial numerical results between different numerical analysis applications. ?Solve velocity and temperature distributions without assumptions regarding internal film coefficients and additional internal temperature boundary conditions. One of the disadvantages of the model was that the energy absorbed by the process was not modelled, resulting in vessel performance predictions under heat loss conditions only. Whilst this allowed potential problem areas such as localized refractory heating to be identified, the model was only capable of predicting how these could be improved by varying the overall geometry and materials of construction. This paper presents improvements in the application software and user defined subroutines of the model as follows: ?Incorporation of surface to gas, gas to gas and gas to surface radiation models to improve the accuracy of radiative heat transfer mechanisms within the freeboard. ?Incorporation of a process energy absorption model based on a theoretical temperature dependant enthalpy curve which incorporates melting, smelting and superheating in selected areas of the bath. This enables the effect of feed distribution and power to feed ratio changes to be estimated. The effects of a commercial arc at full power on the freeboard and slag can now be simulated with increased accuracy.

Jan 1, 2007

By Patridge A. C

Hydrocyclones have widespread use as classifiers in applications such as mine fill preparation and coal preparation. A fundamental conflict often exists between recovery of all of the valuable material and maintaining the quality of the product. This conflict is a result of a portion of the feed material passing through the cyclone, effectively without undergoing any classification. This paper describes an investigation, undertaken as an undergraduate project in mining engineering at the University of NSW (Brook, 1994), into aspects of cyclones in which supplementary water injection is used in an attempt to reduce the amount of misplaced fine material reporting to the coarse product and hence improve the overall classification efficiency. In particular, the study concentrated on the effects of different modes of water injection. Two methods of introducing wash water into the cyclone body were investigated. A series of tests were performed on a laboratory hydrocyclone having provision for radial water injection at different levels through small orifices in the wall of the conical section, and a preliminary study was made of the performance of a novel cyclone in which the conical section had walls of a permeable polyethylene, permitting a uniform introduction of wash water over the entire surface.

Jan 1, 1995

By P Dowd, R Jeuken, C Xu

In Australian coalmines there are a number of coal quality parameters that are measured by analysing samples from boreholes. The data points are used to generate spatial models of these parameters, typically using inverse distance as an interpolation method. Numerous additional boreholes are drilled which have geophysical logs measured downhole but from which no coal quality samples are taken. Full suites of coal quality analyses are expensive and time consuming to drill and sample. If geophysical proxies for coal quality could be used, this would greatly improve the accuracy of the resource estimation without additional cost.This paper examines two of the most important coal quality parameters – ash and volatile matter – and assesses the results of a number of geostatistical interpolation methods. The aim is to improve the accuracy of the interpolated models. Auxiliary variables from geophysical logs are also trialled to improve the estimation.A multivariate analysis of ash, volatile matter and several auxiliary variables of a selected coal seam was undertaken in a spatial context, using variography. This was used to construct a model of co-regionalisation that relates all of the variables as manifestations of an underlying geological theme.The traditional inverse distance interpolation approach was compared to ordinary kriging, universal kriging, co-kriging, regression kriging and kriging with external drift approaches. The relative merits of the six interpolation methods were compared by removing all points, one at a time and estimating at the thus known location. The mean error and the root mean square error were evaluated as a measure of bias and precision.This paper demonstrates that there is significant opportunity to improve the estimations of coal quality when using kriging with external drift. For example, the results show that when using the depth of a sample as an external drift variable there is a significant improvement in the accuracy of estimation for volatile matter. Furthermore, when using borehole wireline density logs as an auxiliary variable for ash content, there is improvement in the estimation of the in situ ash. The underpinning reasons for this are discussed in the context of the underlying geology and the physical properties of the coal. These findings hold promise for utilising cheaper proxies for coal quality parameters to dramatically improve data density and the quality of estimations.CITATION:Jeuken, R, Xu, C and Dowd, P, 2017. Improving coal quality estimations using geostatistics and auxiliary variables, in Proceedings Tenth International Mining Geology Conference 2017, pp 157–168 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 20, 2017

Mineral flotation is effective over a relatively narrow particle size range of approximately 10 µm to 150 µm. If the upper particle size limit can be increased, however, a run-of-mine ore may be coarse ground, and only the middlings are ground further to achieve required grades. This will result in significant energy savings and increased throughput. In this communication, methods of increasing the upper particle size limit will be discussed on the basis of a flotation model that can predict flotation from both hydrodynamic and surface chemical parameters. An example of increasing flotation recovery by control of a chemistry parameter is given.

Jan 1, 2014

By H. Do, R. Yoon

Mineral flotation is effective over a relatively narrow particle size range of approximately 10 to 100 µm. If the upper particle size limit can be increased, however, a run-of-mine ore may be coarse ground, and only the middlings are ground further to achieve required grades. This will result in significant energy savings and increased throughput. In this communication, methods of increasing the upper particle size limit will be discussed on the basis of a flotation model that can predict flotation from both hydrodynamic and surface chemical parameters. An example of increasing flotation recovery by control of a chemistry parameter is given.

Jan 1, 2007

By R A. Pakhomov, L V. Krupnov, P V. Malakhov, I M. Dymov

The article presents results of thermodynamic calculations and laboratory studies, focusing on the cobalt behaviour during oxidative smelting of copper-nickel mattes. The compositions of the studied solutions are related to the products formed during the second stage of the converting process of copper-nickel matte at the Nadezhdinsky Metallurgical Plant (NMP) of MMC Norilsk Nickel company. These sulfide products typically contain from 1.5 to 12 wt per cent of iron. The obtained experimental results and thermodynamic calculations indicate that adjusting the CaO ratio to increase the proportion of CaO or complete replacement of SiO2 with fluxes containing CaO leads to a significant increase in cobalt recovery rates in the matte phase (with an iron concentration of 2.5 wt per cent) raising them from 30 per cent to 45 per cent. Meanwhile, the recovery rates of copper and nickel remain constant.

Aug 21, 2024

By Jose R. Hernandez-Aguilar, Jeet Basi

"The study evaluated the impact on overall circuit metallurgy of improving the performance of the two flotation columns that make up the final Mo cleaning stage in the Cu/Mo separation circuit at Highland Valley Copper mine. The results showed that a key factor to improve the overall circuit metallurgy was to control the size of the bubbles generated in the columns. When a large proportion of small (< 1 mm) bubbles were generated, the production rate of solids-in-concentrate increased by a factor of 4-5 compared to typical production figures without compromising concentrate quality. This increase in concentrate production rate reduced the circulating load in the circuit causing a significant increase of Mo recovery. A statistical analysis of historical production data showed a strong relationship between final concentrate production rate and overall Mo recovery. This relationship along with the results from this study indicated an opportunity to increase the recovery of Mo from 90% (typical) to 94% without downgrading concentrate grade. This 4% increase represents about 14,000 lbs or $500,000 worth of Mo each month at current metal prices.To provide a rational interpretation of the results, this study also examined whether the model of Gorain et al. (1997; 1998; 1999) could explain the increase of Mo recovery seemingly resulting from the decrease of bubble size. The data showed that the model predictions did not agree with the experimental data, i.e., for a given change (decrease) of bubble size, the predictions underestimated significantly the observed recovery increase. An interpretation based on the fundamental analysis of Finch and Dobby (1990) and Hernandez-Aguilar et al. (2005) is proposed to explain the discrepancy between measurements and predictions obtained from Gorain et al.’s model.INTRODUCTIONIt is generally accepted that the size of the bubbles generated in a flotation cell – a concept usually referred to as “bubble size” – has a significant effect on metallurgical performance. However, a significant number of mineral processing practitioners often question, with valid reasons, the practical benefits of implementing process improvement strategies based on controlling bubble size. “Small” bubbles are often considered to be “favourable”, but how small they need to be for a particular case, or how to adjust operating conditions to control a target bubble size, or whether the bubbles need to be smaller in the first place are questions that usually remain unanswered. Two reasons explain this situation."

Jan 1, 2009

By J. Basi, J. A. Finch

ABSTRACT Testing the effects of bubble size (Db) in a Mo cleaning ?otation column at Highland Valley Copper mine indicated that increasing the proportion of small (< 1 mm) bubbles signi?cantly improved column metallurgical response, compared to typical operation. The results were a three- to four-fold Mo recovery increase and a 1 to 2% Mo (absolute) concentrate grade increase. The improvedcolumn operation produced a 4% Mo plant recovery increase. This study also showed that modelling the ?otation rate constant (k) as an inverse square function of Db was more accurate than considering k to be inversely proportional to Db.

Jan 1, 2010