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By Dave Capstick, Ken Garner, Jim Porter

Technologies and systems used in the management of energy consumption in the mining and metal processing industry are well understood and documented from the supply side of the business. It is our contention that in many instances, through a more complete understanding of the demand side of the business, based on the detail of the operations plan, will provide greater lead time in terms of the design, implementation and utilisation of power supply infrastructure. Thus, optimal management of demand in a proactive manner, based on production requirements, will ensure both security of supply as well as continuity of operations. This paper describes the technology and methodology that is being developed to enable the above statement to be achieved. We use a case study to demonstrate the ability of the tools and methodology and conclude by outlining the business benefits achievable as well as the future developments emanating from this initiative.

Jan 1, 2005

By D. Whittles, C. J. Lea, T. X. Ren, A. Kelsey

A methodology for the simulation of methane drainage combining geotechnical modelling and computational fluid dynamics (CFD) will be described. Geotechnical modelling was used to predict the development of stress and strain due to mining. The results from the geotechnical modelling were combined with empirical expressions for the variation in permeability with stress of coal measure rocks and assumptions on fracture behaviour. This allowed the permeability, as affected by mining, to be specified in CFD simulations. Flow of methane through strata, with and without methane drainage, was then simulated to examine the effects of methane drainage.

Jan 1, 2003

By J. Stacey

This study was undertaken to generate a locally relevant guideline for the socio-economic aspects of mine closure for South African closure practitioners and decision makers. It should also represent a resource for interested and involved stakeholders. Mine closure, and its related post-closure social, environmental and economic characteristics, is part of the lifecycle of mining operations, given the finite nature of the ore resource. Many coal mines are anticipated to close in the next ten to fifteen years in Mpumalanga, as the epicentre of the industry shifts towards the Waterberg. Social aspects of mine closure have been historically underplayed, and under researched. Coaltech thus commissioned two studies, the first of which examined the closure dynamics of 36 mines in Mpumalanga and KwaZulu-Natal in 2006. A follow-up study (July 2007) focusing on Mpumalanga3,4 confirmed some of the results of the first study. It also contained broad guidelines for mine closure covering social and labour planning, job creation, the use of mine infrastructure, developmental incentives, and environmental rehabilitation.

Jan 1, 2010

By J. N. Van der Merwe

In the process of pillar extraction, pillars are seldom if ever extracted completely. The pillar remnants, or snooks, play an important role in the extraction process. At the working face, they need to be stable to provide a measure of support in the immediate area. Further back, they have to fail in a controlled manner to prevent undue load build-up on the pillars that have not yet been extracted. The stability condition at the working area is the result of interaction between the stability of the pillar and that of the roof rock. It is shown that the primary mode of roof layer failure is by bending induced tension. Direct tension can be excluded in most practical conditions, and only in exceptional cases will the first failure be in shear mode. Panel spans required to cause the first goaf to be formed, predicted using analytical considerations, are of the same order as has been observed in practice. Once the first goaf has formed, the horizontal stress is reduced and failure will occur at more frequent intervals. It is shown that bending induced tension is the most likely mode of failure in an unjointed roof layer. In roof layers with a high frequency of weak or uncemented jointing, failure can be expected to occur at spans equal to the joint spacing. In this context, failure will occur at the smallest of the spans required to induce tensile roof failure and the joint spacing. A fundamental procedure to evaluate the likely roof layer failure in a stacked beam system is developed. This can to be used to estimate the loading condition on snooks. It is shown that snooks assist in stabilizing the immediate roof beam. The sizes and positions of the snooks relative to the position of the next pillar to be stooped, control the magnitude of the contribution to stability. The further the snook is from the next pillar, and the larger it is, the greater the contribution to the stability of the immediate roof. Under the condition of loading by the immediate, continuous roof beam, the position and size of a single snook controls the load acting on it. The closer it is to the nearest solid, provided that the roof overhang extends beyond the snook, the greater the load on it. However, once the immediate roof beam fails, the loading conditions change. The snook is then loaded by the tributary area load. A procedure is developed to assess the condition of snooks for different situations. Using the fundamental considerations developed in this paper, snooks can be designed to be stable during the active mining phase in their immediate vicinity, but to fail once the next line of pillars has been extracted.

Jan 1, 2005

By H. Ogasawara

To study the preparation process of an earthquake, we should get closer to the hypocentre. In co-operation with ISS International, we had an experimental field (~200 m x~200 m) without dykes and faults in a South African deep gold mine. We have monitored more than 20,000 seismic events (M<2) with borehole tri-axial accelerometers. We used a data acquisition system with 15 kHz sampling and 120-dB dynamic range. In a remnant area at a distance of 100?200 m, an earthquake sequence associated with an M~2 event occurred. Significant changes in seismic parameters such as stress drop, b-value, energy index were observed associated with the sequence. We installed Ishii?s borehole strain meters and could monitor as large a strain change as 10-4associated with mining. However, sampling was only 4 times per hour and 12 bit A/D. A distance from the M2 sequence was ~100 m, being not close enough. Therefore, we found another field with several crosscut tunnels excavated across a fault where an M=2-3 event is expected. We installed the strain meter within several metres of the fault to monitor both shear and normal strains on the fault. The strains are continuously digitized with a 24-bit 25-Hz A/D conversion. The Earth Tide (10-8)is clearly detected. Seismicity induced by longwall mining can be compared to earthquake swarm induced by fluid intrusion to vertical dykes. We also found a decrease in energy index in the source area of M>5events a few days before the major events. Keywords: seismic monitoring, strain monitoring, seismic parameters, preparation process of an earthquake, South African gold mine.

Jan 1, 2002

By N. Z. Jovanovic

Irrigation of agricultural crops may be a cost-effective option for the utilization of gypsiferous minewater as it may also create an opportunity to produce crops during the dry winter season on farm sin South Africa, such as in Mpumalanga. In this study, intensive field monitoring systems were developed and implemented to assess the feasibility and sustainability of irrigation with gypsiferous mine water. Soil water and salt balance components, as well as crop yields, were monitored in field trials carried out at Kleinkopjé and New Vaal Collieries (Anglo Coal), and at Syferfontein (Sasol). Field measurements indicated that high crop and pasture yields can be obtained, provided fertilization and irrigation water management are appropriate. Soil water and salt balances indicated that considerable amounts of minewater can be used and considerable masses of salts can be removed through precipitation of gypsum in the soil profile. With appropriate management, water and salt runoff and salt leaching can be intercepted, thereby minimizing the impact on groundwater. The SWB model is being validated through on-going monitoring. This will allow the use of the SWB model at other sites to predict the long-term impact of irrigation with mine water on soil and groundwater, as well as to run scenario simulations in order to recommend sustainable management of irrigation with minewater.

Jan 1, 2004

By I. Alp

Application of magnetic separation was investigated for the enrichment of colemanite ores by removing the magnetic gangue fraction. The detailed XRD analysis of the ore has indicated that the gangue fraction is composed predominantly of the iron-bearing silicates such as smectite and, to a lesser extent, illite. Magnetic susceptibility measurements of the colemanite and gangue samples have proved that colemanite is diamagnetic in character whereas gangue fraction is weakly paramagnetic to allow the removal of this fraction by magnetic separation. Magnetic separation of the crushed and sized ore samples (-5 mm +75 µm) was performed using a high intensity permanent magnetic separator. Under the test conditions a colemanite concentrate (41.29 wt.% B2O3) was found to be produced from the crushed ore (30.76 wt.% B2O3) at a recovery of 96.76%. These findings suggest that magnetic separation has great potential as an alternative process for the production of a concentrate of commercially sufficient grade.

Jan 1, 2009

By R. Dippenaar

Traditionally, iron ore has been reduced with coke in a blast furnace and the hot-metal product of the blast furnace containing carbon, manganese, silicon, sulphur and phosphorous, was subsequently refined in a steelmaking furnace. During iron making as well as during steelmaking, significant amounts of slag are produced. Two decades ago, more than 13 m tonne of blast furnace slag and 4 m tonne of steelmaking slag per annum were produced in the USA alone. It is, therefore, not surprising that many attempts have been made to re-use iron and steelmaking slags. However, these slags are not merely metallurgical waste products but, on the contrary, their compositions and physical properties are judiciously designed to optimize the operations in the respective metallurgical reactors. The variation in composition and properties of blast furnaces lags are largely determined by the gangue in the ore and ash in the coke and much progress has been made in the re-use of such slag. With respect to steelmaking slag, emphasis has in recent years been placed on hot-metal treatment before refining and ladle treatment after decarburization. The bulk removal of silicon, phosphorous and sulphur from the hot-metal product of the blast furnace by specially designed slags prior to refining in a basic oxygen furnace, has reduced tap-to-tap time, lowered cost and produced steel of much higher quality. The use of synthetic slags in ladle refining techniques subsequent to decarburization in the basic oxygen furnace has resulted in reduced hydrogen and nitrogen contents and reduced solute impurities. Moreover, inclusion shape and composition control, again by the use of specially designed slags has led to the achievement of much improved mechanical properties of the steel. In these revised process routes, slag of different compositions are produced in the variety of unit processes and hence the re-use of steelmaking slags has become much more complex. Clearly, a thorough understanding of the design and use of these different slags is a pre-requisite to the development of re-use strategies. Japanese steelmakers have spearheaded attempts to reduce slag volumes in the individual unit processes and to strive towards ‘slagless steelmaking’ by recycling slags internally. Steelmaking slag volumes have been reduced on commercial scale from about 140 kg/tonne steel to 60kg/tonne steel. Moreover, model predictions have shown that, in principle, all slag can be recycled and the phosphorous extracted to produce fertilizer. This development is of particular significance since the supply of low-phosphorous iron ores is diminishing at an ever increasing rate. Keywords: slag, environment, iron, steel,

Jan 1, 2004

By G. Vouille, P. Bérest

Residual stresses observed in rocks often result from non-compatible initial strains. These stresses can be determined when the incompatibility tensor associated with the initial strain tensor is known. The residual stresses in a cylindrical rock sample can be computed the sample is considered small enough for its incompatibility tensor to be constant. Les contraintes résiduelles, dont on observe couramment les manifestations dans les roches, résultent souvent de l’existence de déformations initiales non-compatibles. Ces contraintes peuvent être calculées lorsque le tenseur d’incompatibilité associé aux déformations initiales est connu. Les contraintes résiduelles dans une éprouvette cylindrique sont données dans le cas où le tenseur d’incompatibilité est constant. Eigenspannungen, die man haeufig in Steinen beobachtet, sind oft Ergebnis einer inkompatiblen Deformation des Anfangszustandes. Diese Spannungen koennen berechnet werden, wenn der Inkompatibilitaets-Tensor der Anfangsdeformation bekannt ist. Die Eigenspannungen einer zylindrischen Probe werden fuer Fall eines konstanten Inkompatibilitaets-Tensor bestimmt.

Jan 1, 2003

By Nobuzwe Makhotla, Sasha Boskovic, Steve Hearn

"Mineral separation efficiency in flotation depends, to an extent, on the type of frother used. Huntsman develops and manufactures unique frothers which are suited for mineral processing applications. This paper discusses the Huntsman approach to understanding the industry’s flotation frother requirements to optimise frother selection and introduce the Huntsman’s POLYFROTH® frother range. Specific case studies where the frothers are used are discussed. INTRODUCTION Froth flotation is a process of using bubbles to separate minerals based on their relative affinity for water. Bubbles are induced in the slurry through aeration. Chemistry is used to aid the flotation process and chemical reagents are added to enhance the separation process. The flotation reagents include frothers, collectors, surface modifiers and pH regulators that control physical and chemical conditions of solid, air and liquid phases, respectively. As described by Harris (1976), the key effect is that of bubble size control by way of preservation of the generated bubble size, which is attributed to the coalescence inhibition by the presence of the frother on the bubble surface. Following this, the frother must stabilize the froth phase. Frothers are also added to create optimal conditions for bubble creation and stability by decreasing the surface tension of the water. Depressants may be added, depending on the ore treated, to assist the hydrophilic particles to stay in the water phase. Clay particles may need to be dispersed to prevent them from attaching to the bubbles. Hydrophobic particles attach to the bubbles and are carried to the surface of the slurry where froth is formed. It is important for these bubbles to have the mobility to carry the mineral to the launder where the concentrate is collected. Types of Frothers There are generally three main groups of frothers used in froth flotation. Alcohol Type These frothers have a molecular structure that usually includes 5 to 8 carbon atoms in a hydrocarbon chain and their solubility in water is limited. Methyl isobutyl carbinol (MIBC) belongs to this category and is widely used in the industry. The weaker alcohol-type frothers are more selective and typically suited to finer particles. There are three sub-categories under this group: aliphatic, cyclic and aromatic alcohols."

Jan 1, 2015

By K. Schwerdtfeger

Data are presented on the effect of iron oxide on the electrical conductivity of CaO-SiO2-FeO-Fe2O3melts, and on limiting current and impedance in direct current or alternating current charge transfer at iron electrodes. The strong influence of iron oxide content can be utilized for in situ determination of total iron oxide content and Fe3+/Fe2+ratio. The possible probe designs are presented and the principles and procedures of the measurements are explained. Keywords: in situ probe for iron oxide determination in steelmaking slags, electrical conductivity of CaO-SiO2-FeO-Fe2O3slags, direct current over voltage and alternating current impedance at iron/slag electrodes.

Jan 1, 2004

By K. Drescher

Excavations in deep level hard rock mines show rheological or time-dependent deformation responses to mining-induced stresses. These are generally not as dramatic as those seen in soft rock environments, such as potash and salt mines, but these deformations can nevertheless become substantial in time. It is usual to see total excavation closure at a much earlier stage than predicted by numerical models, and real-time measurements underground have confirmed that closure takes place on a more-or-less continuous basis, with highest closure rates observed after a blast and then slowly diminishing with passing time. This paper describes laboratory tests to determine the time-dependent response of hard rocks to loading, the results of the tests, and then quantifies these effects to explain the time-dependent phenomena observed underground. The primary intention of this work is to help explain the various time-dependent deformation processes around typical deep level hard rock tabular excavations. Three mechanisms were investigated in two typical hard rock types present in the deep level gold mines in South Africa, namely Ventersdorp Lava and Elsburg Quartzite. Uniaxial compression creep studies were done as the first part of the study followed by shear creep studies on discontinuities where crushed lava and crushed quartzite as well as a natural gouge were used as infilling. The last part of the study consisted of triaxial post-failure relaxation tests. The compression creep tests and the triaxial post-failure relaxation tests showed that the amount of energy dissipated by the lava is significantly less than for quartzite. For mines operating at depths greater than 2000 m the implication is that the lava must show a greater rockburst-proneness than the quartzite. Since the lava shows a lower post-failure stress relaxation, it can store sufficient energy for multiple rockbursts, which is seen in the clustering of multiple seismic events in the deep level mines. This study provides the first data available for energy change calculations in fractured rock masses, and provides the first general indications for rockburst intensities ahead of active mining faces.

Jan 1, 2003

A comprehensive review of ore pass records, from ten Quebec underground mines, indicated some of the limitations of available design tools to predict the occurrence of ore pass interlocking hang-ups in metal mines. The Distinct Element Method was used to perform a series of numerical experiments in order to investigate the influence of ore pass geometry, rock fragments shape and size distribution on material flow in an ore pass. Guidelines have been developed to help limit the occurrence of interlocking hang-ups in an ore pass. The proposed guidelines were evaluated with respect to field observations. Ein kompletter Bericht der Erzrollezeichnungen, von 10 Quebec unterirdischen Gruben, hat einige der Beschränkungen der vorhandenen Designwerkzeuge angezeigt, um das Auftreten Erzrolle der blockierenhang-ups in den Metallgruben genau vorauszusagen. Eine Reihe numerische Experimente mit der eindeutigen Element-Methode, wurden aufgenommen, um den Einfluss von Erzrollegeometrie, Partikelform nachzuforschen und Felsenkorngrößenverteilungen auf Materialfluss in ein Erz überschreiten. Dieses hat zu die Entwicklung der Richtlinien geführt deren Implementierung das Auftreten der blockierenhang-ups in eine Erzrolle begrenzen sollte. Die vorgeschlagenen Richtlinien wurden in Bezug auf Labor- und Feldbeobachtungen ausgewertet. Une revue de la performance actuelle des cheminées à minerai dans 10 mines souterraines du Québec a indiqué les limites des outils de conception servant à dimensionner les cheminées pour minimiser le nombre d’accrochages par enchevêtrement rocheux. Des séries de modélisations numériques, utilisant la méthode des éléments distincts, ont été réalisées afin d’évaluer l’influence de la géométrie des cheminées, de la forme des fragments rocheux et de la distribution granulométrique sur l’écoulement du matériel dans les cheminées. Cet exercice a permis de développer des lignes directrices pour le dimensionnement des cheminées afin de limiter l’occurrence d’accrochage par enchevêtrement rocheux. Les lignes directrices proposées ont été évaluées en fonction des observations effectuées sur le terrain.

Jan 1, 2003

By Jeffrey C. Hillman

The need to recruit locally produced engineers by the South African Mining Industry led to the Engineering Faculty at the University of the Witwatersrand developing a number of academic bridging initiatives for educationally disadvantaged students. The graduation rate achieved during the initial five years of operation by the most successful of these programmes has been on a par with that of al other students but the performance of subsequent intakes has declined to such an extent that the continuance of this scheme could now be at risk. One reason for this reduction in throughput is that many of the applicants for the increasing number of mining bursaries have been more interested in the bursary than the profession and have either failed or dropped out due to a lack of application and motivation. This will have serious consequences for both Wits and the Industry if it continues and some method of identifying unsuitable or suspect applicants needs to be introduced as a mater of urgency. It is recommended that an introductory course be set up at a working mine that would be run under the auspices of Wits, as a joint venture with industry, and include a level of academic input that would provide both bridging needs and certain first year credits. The final form of this course will require extensive consultation with al parties but needs to be completed before the end of 1996. It is further recommended that the advertising and promotion of mining careers be expanded and much improved.

Jan 1, 1996

By V. Labiouse, B. Heidenreich

The rebound phenomenon, which occurs during rockfalls when a rock block impacts with a slope surface, is influenced by several parameters related not only to the slope material but also to the block and the kinematics. The paper presents a small-scale testing campaign undertaken at the LMR (EPFL) to better understand and quantify the bouncing of blocks on granular slopes. The influence of some factors related to the ground material, the block and the kinematics is examined. Bei Steinschlägen wird die Flugbahn eines stürzenden Felsbrockens maßgeblich durch den Abprall vom Hang bestimmt. Der Rückprall hängt von verschiedenen Parametern ab, wobei nicht nur das Hangmaterial sondern auch Blockeigenschaften und Kinematik eine große Rolle spielen. Zum besseren Verständnis dieses Phänomens und seiner Quantifizierung werden am LMR (EPFL) kleinmaßstäbliche Versuchskampagnen auf granulären Materialien durchgeführt. Der vorliegende Artikel stellt die Versuche vor und untersucht den Einfluss verschiedener Boden-, Block- und kinematischer Parameter. Le phénomène de rebond qui se présente lors de l’impact d’un bloc rocheux sur la surface d’un versant dépend non seulement des caractéristiques du terrain, mais aussi de facteurs relatifs au bloc et à la cinématique. L’article présente une campagne d’essais sur modèle réduit entreprise au LMR (EPFL) afin de mieux comprendre et quantifier l’impact de blocs sur des matériaux granulaires. L’influence de divers paramètres relatifs au sol, au bloc et à la cinématique est mise en évidence.

Jan 1, 2003

By P. W. Lotz

Traditionally, bottle roll tests have been used to optimize the extraction process for best gold extraction and recovery. Such tests typically involve exposing the ore to defined reagent concentrations (lime, cyanide and sufficient oxygen) and balance the gold input with recoveries and losses. With mounting pressures to accommodate sustainability issues during development work, it became apparent that much more information would be required on the interactions and kinetic behaviour of solid and solution species during the entire leach process. This information is vital to enable proactive management of critical issues such as cyanide, arsenic, water and tailings management. Inadequate management of these aspects has led to temporary closures and, in cases of non-compliance, to the dynamically changing regulations. MINTEK?s advanced leach facility (ALF) is being developed with the aim of bridging the knowledge gap between the gold leach process and the predictable environmental impacts upon discharge. The facility aims to monitor all parameters of relevance such as pH, Eh, dissolved oxygen, metals, cyanide species, and viscosity during the entire process to enable more informed decisions on practical interventions. The presented set of data reflects first experiences gained from processing a refractory gold ore concentrate. Attempts at optimizing the process were limited due to the developmental nature of the work. Data relating to leaches with differing preoxidation conditions and cyanide staging is presented.

Jan 1, 2009

By J. Betzhold

Knowing more about an orebody makes it easier to exploit it profitably. Many orebodies are made up of different rock types, alteration zones or mineralogical ensembles: oxides versus sulphides or facies with different metallurgical properties for example. Being able to model the spatial layout of these different facies is vital to good mine planning and management. Kriging cannot be used to generate numerical models of orebodies with complex geometric patterns because it gives too smooth an image. Over-smoothing has the meaning of changing the natural selectivity. Conditional simulations are required to do this kind of model respecting the natural variability: honouring the natural selectivity, dilution and ore loss. Standard geostatistical simulations cannot duplicate many of the complex spatial relationships seen in the earth sciences, such as differently orientated facies, sets of conjugate veins or ore types where certain facies cannot touch. After a presentation of the case study, it will be shown why traditional methods for simulating indicators like the sequential indicator simulations, or the truncated gaussian method, cannot be used to simulate it. Plurigaussian simulations are then introduced and shown to be more powerful than the previous methods in their range of application. This is confirmed by the case study treated; a Chilean copper deposit, for which the plurigaussian simulations are seen to respect the different orientations of the individual facies as well as honouring the facies seen in drill holes, and respecting the proportion of each facies even if this varies in space (e.g. increases or decreases with depth). Key words: geostatistics, indicators, conditional simulation, plurigaussian method, copper variability.

Jan 1, 2000

Changes in reductant and energy inputs which are required to adjust the slag composition in an ilmenite smelter to a higher or lower FeO content are calculated. The calculated changes are based on the assumption that solidification equilibrium with the freeze lining constrains the slag composition to follow a eutectic groove in the TiO2-FeO-TiO1.5phase diagram. Calculated equilibrium conditions along the eutectic groove are presented, and form the basis of the calculations. The inputs of energy and carbon need to deviate strongly from the steady-state values to adjust the slag composition. The inputs required at any given time depend on the desired rate of change of the slag composition, and the current slag composition. The steady-state relationship of a change in energy input of 5 kWh corresponding to a 1 kg change in carbon input also holds for the changed inputs during transient changes in FeO content. Keywords: Ilmenite smelting, freeze lining, solidification, eutectic

Jan 1, 2003

By O. Bazhko, F. D. L. Uahengo, Y. R. S. Hara

Although the conventional acid-reductive leaching method effectively extracts copper (Cu) and cobalt (Co) from Cu–Co oxide ores, efforts to enhance hydrometallurgical performance are ongoing. This study evaluates the influence of sulphuric acid (H2SO4) and sodium metabisulphite (Na2S2O5) on metal extraction from Zebesha Cu–Co oxide ore using ferrous sulphate heptahydrate (FeSO4·7H2O) and ferric sulphate (Fe2(SO4)3) as lixiviants. Ore samples (<150 μm) were leached at ambient temperature for two hours, and metal concentrations were determined via X-ray fluorescence analysis. In the FeSO4·7H2O system, Co, Mn, and Ni recoveries increased w=ith Na2S2O5 concentration, reaching a maximum of approximately 80% Co at 150 kg/t, while Cu recovery remained below 5%. Conversely, with Fe2(SO4)3, Cu recovery peaked at 88% at 50 kg/t Na2S2O5, then declined to 79% at 150 kg/t. The addition of H2SO4 improved metal recoveries in both systems. Notably, 60 kg/t H2SO4 yielded 92% Cu extraction in Fe2(SO4)3, while Co, Ni, and Mn remained below 40%. However, in FeSO4·7H2O, Co recovery improved from 40% to 84%. These findings suggest Na2S2O5 is more effective for cobalt extraction with FeSO4·7H2O, whereas H2SO4 enhances copper extraction in Fe2(SO4)3.

Oct 24, 2025

By E. V. Lilford

A number of countries have introduced codes governing the valuation of mineral assets and securities. The African continent will follow suit in due course considering the importance of the global minerals industry as it relates to the attraction of foreign investment. South Africa is to introduce the Petroleum and Minerals Development Bill legislating the involvement of previously disadvantaged individuals and communities in the country?s minerals industry. One of the challenges facing the successful implementation of such codes and bills lies with the abilities of independent valuators to value mineral properties and projects on a consistent basis. Certain valuation principles and methodologies are applicable in all jurisdictions in the minerals industry. These valuation tools and principles are considered and developed in this report. They have been discussed and developed to encourage minerals valuators to consider and consistently apply the most applicable valuation methodologies.

Jan 1, 2002