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By Peter Maltby

A $20M pressure oxidation facility is under construction at the Nerco Con Mine, Yellowknife. Plant commissioning will start in the third quarter of 1992. Roasting of arsenical auriferous concentrates prior to 1970 left 45,000 tons each of highly toxic gold-bearing arsenic trioxide sludge and roaster calcine at the minesite. Safe disposal of these wastes has been a high priority. In 1983 an arsenic trioxide plant was built by the former owner to re-treat the sludge and to sell the product. Due to a poor market and high operating losses, the plant was closed by Nerco in 1989. Mine production in the future will revert increasingly to refractory ore as a replacement for free-milling ore which has been the mill feed since the roaster was shut down. With this fact in mind, Nerco management saw the potential of a proven process to recover the gold from a combined feedstock of refractory flotation concentrate, sludge, and calcine waste. A further requirement was the stabilization of all the arsenic as an insoluble ferric arsenate. By the end of 1989, after the completion of a literature search and a study of process economics, pressure oxidation was selected. Extensive bench and pilot plant work was completed in 1990 and early 1991 to develop the process parameters and to complete environmental testing of the autoclave products. Management approval for construction of a pressure oxidation facility was made in December 1990. Plant capacity is 96 tpd requiring a 40 tpd VSA oxygen plant on site. Detailed engineering began in March 1991. The pressure oxidation building was completed by the end of 1991. The autoclave arrived on site and was mounted on its foundation in December 1991.

Jan 1, 1992

By William J. Maloney

OVERVIEW Blind drilled shafts are becoming increasingly popular, particularly in the Appalachian coalfields, as a secondary and sometimes primary means of ventilation. The reasons for the rebirth of the blind shaft are mainly due to it's economics, timeliness, safety characteristics and inherent independence from underground operations. Historically blind drilling has been used to a limited degree in hard rock and tunneling ventilation. With the recent advances in cutters, bit design, equipment and lining systems, particularly in the Appalachian coalfields, blind drilled shafts are once again the shaft construction technique of choice to the educated ventilation specialist. [ ] HISTORY OF BLIND DRILLING Blind drilling has it's roots in numerous places, including the Nevada Test site, the coalfields of Appalachia and Germany along with the uranium mines of Arizona. Early technology was developed using a variety of equipment mainly of oilfield origin with oilfield drillers entering the industry on a project basis only to "pull in their horns" and return to the oil patch. Shafts completed by oilfield equipment range from the shallow 5' and 6' lined shafts on the Nevada test site to two (2) 10' lined, 730' deep shafts in Alberta for heavy oil development. Several of these shafts were completed to extraordinary depths with the record being a 90" diameter, 6,150' deep shaft being completed in the Aleutian Islands of Alaska in 1969. EQUIPMENT Oilfield equipment is still being used on the Nevada test site but elsewhere specialized blind hole equipment has been developed to enhance the efficiency of particular applications. Where steel liners are required the A-leg derrick with a simple hoist and rotary system is used. The largest user of this type equipment in the world is the former USSR where blind drilling for mine ventilation is the norm. On applications where trip time and cutter changeout are a priority, top drive hydraulic rigs have been developed which are highly automated, efficient and mobile. These rigs are particularly well suited for tunneling applications where shafts are shallow and sites are usually tight.

Jan 1, 1993

By Bryan Morris

Quebrada Blanca (QB) is a copper project located in the semi-arid Andean highlands of northern Chile. The operation is situated 170 km ( 105 miles) southeast of the port of Iquique and 30 km (18 miles) west of the border with Bolivia, at an altitude of about 4300 m (14,000 ft) (Fig. 1). The QB ore body is a secondarily enriched porphyry copper deposit containing reserves of 85 Mt (93 million st) grading 1.3% copper. Underlying the enriched zone is a significant primary ore zone containing several hundred million tons grading about 0.5% copper. In the late 1970s and early 1980s Falconbridge and its affiliates spent $20- $30 million exploring the deposit and conducting feasibility studies. Falconbridge, however, decided not to develop the property. It was returned to its owners, Empresa National de Mineria (ENAMI), a Chilean state mining corporation. In 1988, ENAMI announced its intention to privatize the property through public bidding. Cominco Resources, then 61% owned by Cominco Ltd., examined the property and the extensive data base developed by Falconbridge. In conjunction with its parent company, Cominco Resources submitted a proposal to ENAMI to construct an open- pit mine, with heap leaching and solvent extraction/electrowinning (SX-EW) processing facilities. The plan would use patented heap leaching technology developed by Sociedad MineraPudahuel (SMP), a privately owned Chilean mining company. At that time, a $150-million project that would produce about 45 kt/a (50,000 stpy) of cathode copper was envisaged.

Jan 1, 1993

By Frank W. Pereira

The Montana Talc ore body was discovered in 1983 in Montana's Gravelly Range, about 40 km (25 miles) south of Ennis. Initial drilling indicated a 910-kt (1-million st) ore body of high purity talc. Preliminary analyses on ore cuttings included chemical analysis, brightness measurements, and microscopic evaluations of the structure of the talc. Results indicated it was similar to talc currently being marketed from Montana and it would probably have good commercial value. Based on the positive test results, a test pit was made and a 180-t (200-st) sample of ore was mined. A portion of the ore was ground to various particle sizes and evaluated to determine its strengths, weaknesses, and other characteristics. The deposit is located close to the Cyprus Yellowstone deposit. It was therefore believed that Montana Talc ore may possess many of the same characteristics. Testing and analyses showed the talc to have a high purity and an extremely large surface area, even for Montanatype tales. The ore was also situated in a massive deposit, indicating low cost mining. While the lab analyses were encouraging, the true evidence would be obtained from commercial tests in the marketplace. About 91 t (100 st) of ore were ground to product specifications for pitch control, paint filler, and plastics filler. Consumers were contacted and requested to evaluate the sample talc products. A major trial for the talc as a pitch control agent was arranged at a Northeast paper mill. The trial indicated the new Montana Talc product performed as well or better than the current standard in the industry. In fact, due to a minor modification in the compaction process to make the transport of the talc easier, the product had substantially less dust than the currently used product. The operating people at the paper mill requested that management purchase this talc. Trials were also run at paint plants for use as a pigment filler. And the talc was fabricated into a number of plastics compounds. The initial product tests were largely positive and provided encouragement to proceed with the project. Different grinding mills were used and their performance evaluated. Significant data were generated by the custom grinders. They indicated how the Montana Talc ore ground and the particle size distributions produced at different grinding settings. Encouraged by the positive marketing tests, a prefeasibility study was commissioned. A talc grinding plant and mine plans were designed and capital and operating costs estimated. Initial economics showed an attractive return. The operating costs were among the lowest in the industry. The positive economics, along with the excellent results by the products in the marketing tests to the paper, paint, and plastics industries, led to the recommendation to proceed with the project. Plant construction began in June of 1985. The Montana Talc Co. (MTC) analyzed the data from the commercial tests. Based on the product's outstanding performance and the uniqueness of its high purity and platy structure, a strategy was developed to position the company as a premium talc supplier.

Jan 1, 1989

By Robert E. Goodwin

There are four main requirements which must be considered when selecting a wire rope for the best serviceability. A proper choice is made by correctly estimating the relative importance of each of these requirements and selecting s rope which has those qualities best suited to withstand the combination of destructive forces expected under continued service. A wire rope should possess: 1. Strength sufficient to support the maximum load expected and with s proper safety factor. 2. Ability to withstand bending and to resist bending fatigue without failure of the wires. 3. Ability to withstand surface abuse such so abrasive wear, pounding, and wire scrubbing. 4. Ability to withstand abuse such as crushing and distortion.

Jan 1, 1968

By Brian W. Mackenzie

The mine development decision is made on completion of exploration to determine whether or not a mineral deposit should be developed to production and, if so, how. This involves the selection of an optimum mine development alternative from a number of technically feasible alternatives and the comparison of this optimum with those of other available investment opportunities. If the optimum is sufficiently attractive, the deposit is developed to production. The selection process is carried out within a framework of corporate objectives and resources. The mine development decision is based on the balancing of two parameters - - rate of production as reflected in plant capacity and cut-off grade. On the basis of available information and experience, detailed revenue and cost 'estimates are made for each feasible combination of plant capacity and cut-off grade. What economic evaluation techniques should be applied to these estimates to reduce each alternative to economic indicators that will enable meaningful comparisons and an informed investment decision? This is the essence of the paper. The determination of optimum plant capacity and cut-off grade has been the subject of intensive research efforts by economists and mining engineers (1-7). Their studies are based on marginal analysis and assume that, at the time of decision, certainty conditions prevail with respect to ore reserves, mining costs and mineral markets. The optimum mine development alternative is defined as that which maximizes profitability.

Jan 1, 1969

By Walter H. Schwedes

Ore grinding mills are really just slowly rotating barrels, but barrels that are growing in size so fast that the application of electric drives for them is rapidly approaching a technology like that for wind tunnels or pumped storage drives. This application is particularly worthy of care because some 40% of the 75 megawatts of power used by a large copper ore concentrator, or some 60% of the 200 megawatts supplied to a large iron ore concentrator, are for grinding. These ore plants are located where the ore is, not where a utility happens to be. So, the challenge is not only to choose a drive and .power transmission for reasonable cost, high performance, reliability and minimum maintenance, but to afford the interface between mill drive and power distribution and source systems to minimize the whole ore plant's monthly power bill, or costs of self generation. Conclusions can be reached in optimizing a drive selection only for each particular ore plant's set of parameters, but by identifying the criteria for selection and then weighting each type of drive per criteria, yardsticks for final choice become apparent. This is the purpose of this paper. Grinding action takes place inside the barrel, where the ore charge is ground with the aid of balls, or mill length rods, or large chunks of ore as in autogenous grinding.

Jan 1, 1972

By R. C. Gilmore, A. Juganda, Jr. Bogin, S. Saki, S. A. Lolon, J. F. Brune, Jr. Zipf, J. W. Grubb

"Methane-air mixtures form explosive gas zones (EGZs) in underground longwall coal mine gob ventilation systems. Such EGZs have caused a number of fatal mine explosions, including the 2010 disaster at the Upper Big Branch mine, where 29 miners lost their lives. Researchers at the Colorado School of Mines use Computational Fluid Dynamics (CFD) modeling to predict EGZ locations. In this paper, a model of a bleeder-ventilated gob system includes two adjacent panels, an active longwall and a mined-out gob. Boundary conditions for the simulations match statutory ventilation conditions for methane concentrations and air flow rates at common measurement points throughout the mine. The modeling results predict the persistence of EGZs in the gob that may compromise the effectiveness of the bleeder ventilation system. INTRODUCTION Mine operators must maintain statutory air flow and air quality requirements at various locations throughout the mine ventilation network. U.S. regulations generally require mine operators to establish bleeder ventilation systems surrounding longwall gob areas (30 CFR §75.334.) Gilmore et al. (2015) documented that explosive gas zones (EGZs) exist within bleeder-ventilated gobs and may extend into the bleeder entries that must be examined weekly, presenting an immediate fire and explosion hazard to mine examiners. In a project funded by the National Institute for Occupational Safety and Health (NIOSH) under contract 200-2009-31409, researchers at Colorado School of Mines have developed a tool for modeling gob air quality using Computational Fluid Dynamics (CFD). This CFD model is capable of examining a wide range of longwall mine ventilation systems. Marts et al. (2014a, 2015) studied progressively sealed gobs with U-type ventilation and using a back return. Saki et al. (2015) examined the impact of gob ventilation boreholes and face air quantity effects on tailgate methane concentrations. Gilmore et al. (2014) modeled bleeder-ventilated gobs and Gilmore et al. (2015) studied the effects of bleeder regulator settings on EGZ volume and locations in the gob. CFD studies for progressively sealed gobs were generally carried out using 5000 ft (1500 m) panels because the gob atmosphere remains largely unchanged from about 500 m (1,500 ft) inby the face. A modular meshing methodology (Gilmore, 2015) permitted researchers to extend bleeder models to 10,000 ft (3050 m) to include the full extent of bleeder entries. This paper further expands the bleeder CFD model to study the gob atmospheres of two adjacent longwall panels, each 10,200 ft (3100 m) in length, with the active face located 6,700 ft (2040 m) from the startup room."

Jan 1, 2016

Gaby Copper Mining?s Gabriela Mistral property is located in the Antofagasta region of northern Chile, at an altitude of 2,660 m (8,727 ft) above sea level. The reserve contains an estimated 562 Mt (620 million st) of oxide ore with an average grade of 0.41 percent total copper. The mine went into production in 2008. Gaby Copper faced the problem of having no reliable way to measure the solids level. This is a challenge that exists throughout the mining industry, where dust in the air and accumulation of solids on a sensor make accurate measurements difficult in areas such as transfer chutes, the rock box underneath crushers, silos and anywhere else that information is needed on the level of solids. The next-generation technology in the Sitrans LR560 radar from Siemens addresses this challenge. With a frequency of 78 GHz ? higher than previous generations of radar ? it provides a more robust signal for measuring in areas where there are high levels of dust accumulation. The Sitrans LR560 provides a signal beam angle of four degrees, significantly narrower than any other product on the market can offer.

Jan 1, 2014

In addition to capital and operating costs, the accurate estimation of ore reserves is a key component to the successful outcome of any feasibility study. In recent years, there have been many project failures caused by the improper estimation of ore reserves. The accurate estimation of an ore reserve relies heavily on an understanding of the geology and the underlying assumptions unique to the estimation techniques being used. These assumptions are reviewed, and the shortcomings of the estimation techniques and their possible impact on a given project's economics are discussed. The latest developments in geostatistics in overcoming existing reserve-estimation problems are presented.

Jan 1, 1998

By Corneille S. Ek

Flotation of several copper and lead-zinc ores has been carried out with mercaptobenzothiazole (MBT) as promoter. The results of laboratgory batch flotation tests have been compared with those obtained when using more common collectors like xanthates or dithiophosphates. It generally appears that MBT is an effective collector of all the sulfides, including pyrite, but that high selectivity is rather difficult to attain, except for gangue drop-out. Some kinetic tests have been performed to check the froth production rate by MBT as compared to other collectors.

Jan 1, 1995

By J. Launay

In order to control and dispatch the sewage water coming from 3 tunnels toward 2 downstream sewage tunnels, a large cavern has been excavated in a suburb of PARIS. Located at a depth of 47,00 m, it has been excavated using the NATM procedure through swelling clay, weathered sandstone, and marl and chalk. It is 16,50 m high, 12,40 m wide and 60, 00 m long, with an elliptical cross-section and its two ends are egg-shapped. The final lining of the cavern is composed of 30 to 40 cm of shotcrete, steel ribs and passive anchor bars. The excavation stages and related movements were surveyed by extensometers, pressure cells and convergence devices. The design, method of construction of the cavern and the results of the measurements made are commented.

Jan 1, 1989

By S. S. Peng

Hydraulic powered supports have been employed in the U. S. longwall mining for the last two' decades. Yet the sciences of roof control at the powered supported faces remain largely unknown. Many questions remain unanswered. To address the problems, field investigations were conducted from 1980 to 1984 in seven longwall faces (1-10)(Table 1). Some of the findings have been reported by Peng and Chiang (11). The basic geological conditions of these panels are listed in Table 2. The mining equipment used in these longwall panels are listed in Table 3. Instrumentation and Observation Programs Two events were generally instrumented: one was the hydraulic leg pressures of the powered supports, and the other was the canopy and base plate load distributions.

Jan 1, 1986

By K. E. Laughery

The Nevada Barite industry has experienced a 277% growth over the last five years with a total production of 2,542,000 tons. Total production prior to 1970 approximates 2,700,000 tons dating back to 1907 Annual production, as can be seen in Table 1, has increased from 192,000 tons in 1971 to 723,000 tons in 1975. During this same period U.S production has increased from 825,000 tons to 1,056,000 tons. Nevada is now the leading producer with 69% of the market. The increase in the Nevada barite production is, of course, directly related to the increased demand for weight material coupled with the lack of other sources and the relative economic advantage of the Nevada barite, A significant tonnage of Nevada barite is utilized in the non-oil well market, principally at FMC's barite chemical plant at Modesto, California; however the growth has been in the oil well market.

Jan 1, 1976

By David Loomis

Unlike previous gold mining booms in Nevada's Great Basin, the current boom includes a serious commitment to mine reclamation. Many of the smaller mines began reclaiming in the late 1980s but met with limited success due in part to poor soil characteristics. Public land managers and the mining industry began looking for ways to improve reclamation success. One promising technique is suggested by an ongoing research project using sludge biosolids, the solid residue of municipal waste water treatment. During the 1980s, limited space in landfills led municipal governments to search for alternate ways to dispose of their biosolids. The cities of Reno and Sparks, NR and the US Bureau of Land Management (BLM) searched for ways to combine these needs to everyone's mutual benefit. Yet barriers remained. The federal government had major concerns about potential bioaccumulation of metals and contamination of drinking water from the land application of municipal biosolids. The barriers were lifted late in 1991 when an interagency task force led by the Environmental Protection Agency (EPA) issued a new federal policy on the use of biosolids on federal land. The policy encouraged biosolids as a soil amendment to reclaim degraded minelands and invited federal agencies to develop biosolid pilot projects. In response, BLM enlisted the help of American Resources Corp. (ARC) and the University of Nevada, Las Vegas for a pilot study at ARC'S' Butcher Boy Mine near Wadsworth, NR. Although biosolids have been used in mine land reclamation in the eastern United States for 20 years, before this pilot study, none had been used on public lands in the arid Great Basin. Land application of biosolids improves soil conditions by improving nutrient uptake, increasing water retention, permitting easier root penetration and enhancing soil fertility. Biosolids increase ecosystem productivity and can lead to significant improvements in the structure and diversity of plant and animal communities. Thus, land application of biosolids promotes biodiversity.

Jan 1, 1993

By Yu. A. Polozov, V. A. Lagunov, O. Yu. Lushinkova, Yu. I. Svirskiy, Eh. Ya. Kipko, Roy A. Williams

4.1 THE GENERAL COMPOSITION AND PROPERTIES OF CLAY-BASED GROUTS Clay-based grouts are visco-plastic systems; they are made by adding structure-forming reagents to a clay mineral mortar. Small amounts of cement and various chemical ad¬ditives constitute the reagents. If necessary, fillers also are added. The distinguishing feature of clay-based grouts is that throughout their entire stabilization period they do not form a crystallized structure as does cement grout. The structure of stabilized clay-based grouts does not deteriorate during minor rock movement or upon the initiation of blast¬ing during the construction of a shaft or a drift. Because they can possess good rheological properties during the ini¬tial structure-forming period relative to cement grouts, clay¬based grouts are not easily eroded from large fractures and karstic cavities by flowing ground water. In addition, their finely dispersed clay particles facilitate a greater fracture penetration capacity, especially in dual porosity rocks. Numerous investigations of the structural-mechanical and rheological properties of clay-based grouts by STG have demonstrated that the most effective grouts for pre¬venting the inflow of ground water into underground work¬ings are grouts that have a cement content of 8 to 10% (90 to 120 kg/m3) of the clay grout by mass. The grout should have a density of 1.18 to 1.30 T/m3. Various additional substances and chemicals can be added as additional fillers and structure-forming reagents. In pure ground water at temperatures above freezing, sodium silicate in the amount of 0.8 to 1 % by mass normally is the only structure-forming reagent that is necessary if the proper clay is selected and if it is available. The production process for making clay-based grout is divided into two stages: 1) the production of an initial clay mortar with specified properties and 2) the production of a clay-cement additive grout mixture using the initial grout along with the structure-forming reagents, including the ce¬ment. The properties of clay-based grouts depend on the phys¬ical-mechanical properties of the initial clay mineral, the properties of the cement and the properties of the chemical reagents that are added. 4.1.1 TECHNOLOGICAL PROPERTIES OF CLAY-BASED GROUTS The dynamic shear stress' To, the viscosity 11, the static shear stress2 0, the maximum shear stress of the structured that the rheological and structural-mechanical prop¬erties of clay-based grouts must fall within the following limits: the dynamic shear stress To = 50 to 200 Pa; the viscosity -9 = 0.02 to 0.07 Pa sec; the static shear stress 0 = 150 to 600 Pa; the plasticity strength Pm of the structure one minute after preparation (according to P.A. Rebinder's method) equals 150 to 500 Pa. The plasticity strength 10 days after preparation is ? 0.15 MPa. The general relationship of the change in the structural strength of clay-based grouts relative to stabilization time is shown in Fig. 32. The figure shows that the structure-form¬ing process for clay-based grouts is characterized by three stages. These stages correspond to the time periods required for conducting the principal operations during the injection of the grout into a fractured aquifer as described below. Stage I, corresponding to the time period T1, reflects the small development of structural strength during early stabi¬lization. During this time, the structural strength must not preclude the capability to pump the grout. The time Tl must correspond to the length of pumping time from the moment water is shut off and mixing occurs until the pump stops forcing the grout through the manifold block and pipeline into the fractured rock as described subsequently herein. Stage II, corresponding to the time interval T2, reflects a sharp but controllable increase in the structural strength of the grout. The length of time period T2 is controlled by the addition of appropriate reagents. Stage III produces the final value of the structural strength. This final strength is used to design the dimensions of the isolation curtain. Consequently, the development of grouts is guided by two principal criteria: 1) the grout must develop the highest possible structural-mechanical properties and 2) it must be able to be pumped by a piston pump prior to final stabili¬zation. Successful grouting depends to a large extent on the correct design of a grout for each specific case. It is impor-

Jan 1, 1993

By J. S. Wozek

In metallurgical applications, coal fulfills dual roles as a chemical feed stock and as a fuel source. These applications range from cokemaking, ironrnaking (including pulverized coal injection), foundry, basic oxygen furnace / electric arc furnace coal additions, direct ironrnaking, Corex, and the futuristic direct steelmaking. In all steelmaking related processes, chemical reactions are simultaneously temperature and chemical dependent. Therefore, coals used in these processes must consistently comply with specific quality parameters in order to promote efficient operations. This paper limits discussion of Metallurgical Coal Quality to cokemaking and ironmaking applications. Its purpose is to present the customer's perspective on the control of critical coal and coke properties.

Jan 1, 1994

By Roy A. Grancher

CYCLING WITH CEMENT "THE WHEEL IS COME FULL CIRCLE" Shakespeare's King Lear Act V, Scene 3, Line 176 The time clock of the cement industry has been turned back to the early 1950s. After the trials and tribulations of the decade of the Sixties, the hands now stand where they did just over twenty years ago. Cement shipments have steadily increased, with a record 419 million barrel level (78.8 million tons) being reached last year. Plants are operating at average utilization rates in excess of 85 percent of rated capacity. The spread between supply and demand has narrowed to where a definite shortage of cement now exists within the industry. The notable and unfortunate difference between the two periods however is that, back then, cement's returns were a respectable 14 to 18 percent, whereas today they stand at less than half those levels. Insufficient return forms the present foundation of the U.S. cement industry. This lack is destined to have a cumulative effect. Just as the industry's balance between supply and demand is returning to favorable proportions, promising a period that has historically and now should generate those profit levels required to modernize and provide for capacity addition, cement instead finds itself frozen by federal price controls into the semi-depressed condition that has existed for over a decade and from which it was just starting to emerge. Capital is not attracted to continued low returns, and increasingly restrictive pollution control measures are necessitating great non-productive expenditures be made as definite costs to stay in business. Even a clouded crystal ball would reveal that additional cement plant closings can be expected.

Jan 1, 1972

By B. Nyman

A lot of work is in progress to improve copper recovery by leaching-solvent extraction-electrowinning (L-SX-EW). At Outokumpu the focus of attention is on SX equipment development as a result of which a new mixing-settling technology, the Vertical Smooth Flow (VSF) has been introduced. Using helical stirrers in the VSF mixers a more gentle and uniform contacting can be obtained than in the mixing compartments of the low-profile design. The benefits of Outokumpu's new approach are an essential decrease in organic losses and in aqueous in organic entrainments. Separate pumping using a smoothly pre-contacting "Dispersion Overflow Pump" (DOP) is a key feature of the VSF design. The scale-up of this pump as well as the VSF mixers are shown to follow simple mathematical relationships which also have been confirmed by full scale experiments.

Jan 1, 1995

By R. K. Mehta, S. K. Dhar, R. R. Mallepali

Introduction The incentives for developing a distributed form of the comminution model include: • for describing the heterogeneous comminution behavior of multiphase mineral systems (i.e. realistic ore bodies, such as complex sulfide ores consisting of chalcopyrite, galena, sphalerite, pyrite and siliceous minerals) and •for generating, for various locked and free particles, in situ, microscopic, breakage behavior such as the mode of fracture (intergranular vs. transgranular), the relative rates of breakage and the breakage distribution. However, the computational difficulty and the effort made in estimating a large number of parameters (Andrews and Mika, 1975; Wiegel, 1976; Herbst et al., 1985, 1988) do not justify the utility of this approach. Also, obtaining the results experimentally is very tedious and time consuming if using this approach. Although recent work in this area (Choi, Adel and Yoon, 1987; Mehta, Adel and Yoon, 1989, 1990) showed good results for liberated particles, the quality of the estimation and prediction was poor for locked particles. Attributing this to the complex breakage behavior of locked particles, it was concluded that additional constraints, and possibly modification in the breakage distribution functional form for locked particles, were necessary. However, further mathematical analysis revealed that the method previously used was in error. The purpose of this technical note is to present the correct solution methodology used in solving the general model equations of a multicomponent mineral system containing multiple classes of locked particles. Previous work and connection The general form of the comprehensive, distributed-component comminution model has been described as (Herbst et al., 1985) [d (m (0) -[ I - B ] S_ m(t) = A m(t) (1)] where [A] is the fundamental matrix/state companion matrix, commonly referred to, in the comminution literature, as the "mill matrix." Note that for a distributed-component comminution model, this is a full, general, real matrix, unlike a lower triangular matrix for a simple grinding model or a lumped-binary grinding model with one locked-particle class (Herbst et al., 1985, 1988). Also note that all of the underlined letters refer to matrices. Herbst et al. addressed the difficulty in arriving at a closed form of the analytical solution of Eq. (1) via similarity transformation [IT J inv (T)]]. This difficulty occurs for several reasons: •[A], as a general real matrix, may have complex eigenvalues and complex eigenvectors. •More importantly, there is no guarantee that a set of eigenvectors of [A] will turn out to be independent. An attempt was made to solve this problem by implementing a decomposition method. With this technique, the mill matrix was decomposed into a sum of lower and upper triangular matrices [(i.e., A = L + U)]. Then the solution was obtained using similarity transformation (Mehta, Adel and Yoon, 1989, 1990). [e(At) = e(L+U)t = e(Lt).e(Ut) _ [ TL Jt- (t) inv(T_L)] [-Tu Ju (t) inv(Tu)]] [But, unfortunately, e 1+U = e t . eu is true only for scalars and not for matrices (i.e., eL+u# eL- eU) unless they commute. In other words. eAt = e(L+u)t= ekt - eU' if LU = UL. Hence, this decomposition scheme must be replaced by a mathematically acceptable method known as the "splitting method"]

Jan 1, 1994