Codelco - Corporación Nacional del Cobre de Chile

Spatial and temporal changes in water chemistry were evaluated using surface water extracted from a Mediterranean river basin, i.e., The Mataquito River, central Chile. The processes that control water chemistry dynamics in the basin were determined by assessing the relationship between hydrologic events (rainfall, river flow, runoff rates), physical-chemistry properties, and major ion concentrations/distributions along the river. During the rainy period, major ion levels were controlled predominantly by weathering (rainfall). During the dry period, seawater intrusion was the main factor controlling water chemistry. Unusually high chlorine and sulfate concentrations suggested anthropogenic sources of the ions entering the basin. Thus, pollution from industrial and agricultural activities in the basin might be quantitatively important and should be considered in future studies of this area.

Background: IgG4-related disease (IgG4 RD) is an immune-mediated fibro-inflammatory disorder, with tissue infiltration of IgG4+ plasma cells. It causes pseudotumors, tumors, and a wide spectrum of clinical manifestations. Aim: To report the clinical, laboratory, histopathological and treatment characteristics of a group of Chilean patients with IgG4 RD. Material and Methods: Review of medical records of 52 patients aged 18 to 76 years with IgG4 RD seen at six medical centers. Results: Elevated IgG4 serum levels (> 135 mg/dl) were found in 18 of 44 (41%) patients. There was histological confirmation of the disease in 46 patients. The most common sites of involvement were lungs, eyes and kidneys. Eighteen (35%) patients had only one organ involved, 34 (65%) patients had two organs and 13 (25%) patients had three or more organs. The involvement of two organs was significantly more common in men (p < 0.05). In patients with only one organ involvement, the most frequent location was orbital and meningeal. All patients with kidney or lung disease had multiorgan involvement. All patients received corticosteroid therapy, 67% synthetic immunosuppressants, and 16% rituximab. Conclusions: ER-IgG4 can affect any tissue. Multiorgan involvement was more common in this series, with preference for lungs, eyes and kidneys. An excellent response to steroids is characteristic of the disease, but with a high relapse rate that requires additional immunosuppression.

Nevado de Longaví volcano (NLV), in the Southern-Central Chilean Andes, has erupted during the Holocene magmas with compositions that are in several ways atypical for the region. These characteristics include elevated La/Yb ratios in evolved magmas, in an area of only moderately thick crust, coupled with low concentrations of K, Th, and other incompatible elements and elevated ratios of fluid-mobile (B, Cs, Li, Sb) to fluid-immobile elements. Samples have an unusual mafic mineralogy dominated by amphibole. The petrology of the Holocene products of NLV have been related to the influence of an oceanic transform fault (Mocha Fracture Zone; MFZ) that supplies the mantle wedge with unusually high amounts of fluids via dehydration of serpentinite bodies hosted by the subducted oceanic lithosphere. Because the trace of this transform fault is oblique to the convergence vector, its position along the arc has varied through time, as has the magnitude of its influence on the nature of the magmas erupted at NLV. The whole-rock and mineral chemistry of volcanic products from NLV, tied to a simplified stratigraphy, documents the secular changes in the magmatic system as the oceanic fault approached its current position. Magmas erupted ∼1–0.6 Ma are relatively low in water (as inferred from mineralogy and chemical proxies) and reduced (NNO-1 to NNO+0.5), and are similar to compositions found in neighboring volcanoes. From 0.25 Ma to the present, magmas are water-rich and oxidized (NNO-0.5 to NNO+1.7). In the intervening 0.6–0.25 Ma, mafic magmatism acquired a transient crustal component, which we identify as subducted sediment melts, on the basis of radiogenic isotopes and Pb, Th, and U abundances. Fluids released from serpentinite in the fracture zone were rich in Li, B, Sb, Cs and Ba, but not in K, Th, U and Sr. The fluid addition led to enhanced melting, particularly hydrous magmas that stabilized amphibole early during fractionation, higher oxygen fugacities, and distinctive chemical compositions. Open access article: https://doi.org/10.3389/feart.2022.846997

Background: The presence of multiple lymphadenopathies can be a diagnostic challenge. Aim: To describe the clinical, laboratory and imaging characteristics of 19 patients with lymphadenopathies of rheumatologic origin. Material and Methods: Review of medical records of 19 patients aged 16 to 72 years (68%) with lymphadenopathies presumably secondary to a rheumatic disease. Results: Six patients had systemic lupus erythematosus, six had Sjogren's disease, three had sarcoidosis, two had rheumatoid arthritis, one had IgG4 related disease and one had mixed connective tissue disease. A lymph node biopsy was performed in 11 patients and in eight a lymphoid follicular hyperplasia was found. Systemic symptoms were reported by 68% of patients. Blood lactate dehydrogenase was elevated only in cases associated with hemolytic anemia. There was no specific or predictable localization of the lymphadenopathies in imaging studies, except in the cases of sarcoidosis. The average size of the lymphadenopathies was 13.5 mm in diameter in short axis and there was no presence of necrosis, calcification, or conglomerate formation. Only one case presented splenomegaly. All patients responded favorably to corticosteroids. Conclusions: Lymphadenopathies associated with rheumatologic diseases can occur in a wide variety of diseases, especially systemic lupus erythematosus and Sjögren's disease. The absence of LDH elevation and splenomegaly and the absence of imaging findings such as conglomerates can orient to a rheumatologic origin.

Discrete event simulation (DES) is a suitable framework to evaluate and optimise the dynamics of sulphide smelters. In particular, iron–nickel–copper–cobalt sulphides undergo continual oxidation within a roasting or smelting operation, followed by batch oxidation within the converting operation, thus producing iron-free Bessemer matte (or blister copper, in the case of copper smelters); this semi-finished product undergoes further processing to produce nickel, copper and cobalt products, and to recover precious metals. The juncture between continuous smelting and batch converting is often an appropriate focus for the earliest phases of DES development, since it is typically a major bottleneck within nickel and copper smelters; later phases may include increasing levels of detail for auxiliary unit operations, as well as plant logistics. Moreover, DES can support matte-slag chemistry, including Gibbs free energy balances to determine the iron speciation within the slag. DES is therefore capable of linking the fundamentals of oxidation reactions to the intricacies of plant dynamics.

Background: MicroRNAs (miRNAs) are a novel class of endogenous, non-coding, single-stranded RNAs capable of regulating gene expression by suppressing translation or degrading mRNAs. Single nucleotide polymorphisms (SNP) can alter miRNA expression, resulting in diverse functional consequences. Previous studies have examined the association of miRNA SNPs with breast cancer (BC) susceptibility. The contribution of miRNA gene variants to BC susceptibility in South American women had been unexplored. Our study evaluated the association of the SNPs rs895819 in pre-miR27a, rs11614913 in pre-miR-196a2, rs6505162 in pre-miR-423, rs4919510 in miR-608, and rs2682818 in pre-mir-618 with familial BC and early-onset non-familial BC in non-carriers of BRCA1/2 mutations from a South American population. Results: We evaluated the association of five SNPs with BC risk in 440 cases and 807 controls. Our data do not support an association of rs11614913:C > T and rs4919510:C > G with BC risk. The rs6505162:C > A was significantly associated with increased risk of familial BC in persons with a strong family history of BC (OR = 1.7 [95 % CI 1.0-2.0] p = 0.05). The rs2682818:C > A genotype C/A is associated with an increased BC risk in non-familial early-onset BC. For the rs895819:A > G polymorphism, the genotype G/G is significantly associated with reduced BC risk in families with a moderate history of BC (OR = 0.3 [95 % CI 0.1-0.8] p = 0.01). Conclusions: The contribution of variant miRNA genes to BC in South American women had been unexplored. Our findings support the following conclusions: a) rs6505162:C > A in pre-miR-423 increases risk of familial BC in families with a strong history of BC; b) the C/A genotype at rs2682818:C > A (pre-miR-618) increases BC risk in non-familial early-onset BC; and c) the G/G genotype at rs895819:A > G (miR-27a) reduces BC risk in families with a moderate history of BC.

The Sierra Baguales, situated north of the Torres Del Paine National Park in the Magallanes region of southern Chile, shows a well-exposed stratigraphic sequence ranging from the Late Cretaceous to late Pliocene, which presents a unique opportunity to study the evolution of sedimentological styles and trends, palaeoclimate changes, and tectonic events during this period. The depositional environment changed from a continental slope and shelf during the Cenomanian-Campanian (Tres Pasos Formation) to deltaic between the Campanian-Maastrichtian (Dorotea Formation) and estuarine in the Lutetian-Bartonian (Man Aike Formation). During the Rupelian, a continental environment with meandering rivers and overbank marshes was established (Río Leona Formation). This area was flooded in the early Burdigalian (Estancia 25 de Mayo Formation) during the Patagonian Transgression, but emerged again during the late Burdigalian (Santa Cruz Formation). Measured palaeocurrent directions in this Mesozoic-Cenozoic succession indicate source areas situated between the northeast and east-southeast during the Late Cretaceous, east-southeast during the middle Eocene, and southwest during the early Oligocene to early Miocene. This is confirmed by detrital zircon age populations in the different units, which can be linked to probable sources of similar ages in these areas. The east-southeastern provenance is here identified as the Antarctic Peninsula or its northeastern extension, which is postulated to have been attached to Fuegian Patagonia during the Eocene. The southwestern and western sources were exhumed during gradual uplift of the Southern Patagonian Andes, coinciding with a change from marine to continental conditions in the Magallanes-Austral Basin, as well as a decrease in mean annual temperature and precipitation indicated by fossil leaves in the Río Leona Formation. The rain shadow to the east of the Andes thus started to develop here during the late Eocene-early Oligocene (~ 34 Ma), long before the “Quechua Phase” of Andean tectonics (19–18 Ma) that is generally invoked for its evolution at lower latitudes.

Rising costs in the mining industry have necessitated a search for alternative methods for the recovery of metals from deposits that are no longer economically or environmentally exploitable by conventional mining. These alternative methods include in situ mining. A laboratory model was developed and an experimental programme undertaken to determine the effect of temperature, aeration, material compression, and material extraction on copper recovery by in situ leaching using H2SO4 and Fe³⁺. Recovery was estimated using the shrinking core model. Based on the experimental results and recovery estimations, an economic evaluation was completed comparing in situ mining with conventional mining methods. © 2016 The Southern African Institute of Mining and Metallurgy.

The stratigraphy of the Bahía Inglesa Formation in the Caldera Basin west of Copiapó, (north-central Chile) is revised, based on hitherto unpublished stratigraphic sections and 87Sr/86Sr dating. The depositional environment varied from a rocky shoreline to the upper continental slope, with sea-level oscillations and tectonic movements causing numerous local unconformities as well as lateral and vertical facies changes. Geohistory and sedimentological analyses show that the area was close to the concurrent sea level at about 15.3 Ma, but at the same time being elevated about 100 m above the present sea level. Although the basin then subsided at least 350 m until around 6 Ma, marine deposition was only recorded after 10.4 Ma. This suggests that the sea level initially dropped faster than the rate of subsidence so that subaerial erosion occurred. The period of subaerial exposure before 10.4 Ma can be attributed to the presence of a NE-trending branch of the Juan Fernández Ridge below the continental crust at this time, whereas the ensuing subsidence was due to subduction erosion and crustal accommodation in its wake as it migrated south along the South American coastline. The subsequent uplift of at least 250 m can be explained by an acceleration in plate expansion and isostatic rebound of the continental crust after being partially submerged in the upper mantle. The uplift–subsidence–uplift pattern mirrors those recorded around the Nazca Ridge in Peru, as well as in similar basins to the south of Caldera. However, a higher southward migration rate of the Juan Fernández Ridge against the edge of the South American Plate and less intense uplift–subsidence–uplift cycles are recorded in the latter basins. This can possibly be attributed to oroclinal bending of the ridge due to friction with the overlying continental plate, which diminished the angle of incidence and the intensity of the stress field, but increased the migration velocity of the ridge relative to the coastline.

Even though block caving mining method is already the most economical underground mining method for large massive ore bodies, it requires further technical advancements to also become a practical method for deep deposits with low grade and high stressed zones. Continuous Mining System is a material handling approach introduced by Codelco, Chile. This system is recognized as an alternative approach in future block caving operation due to its high extraction rate and productivity and improved safety. This paper describes the research undertaken at the University of Chile, Block Caving Laboratory to understand the operational characteristics and automation potentials of Continuous Mining System. The main objective of the R&D was to establish the short-term extraction planning fundamentals for the system and to lay the basis for its potential automation. Various pilot tests were conducted using a representative scaled physical model. The implementation of an automation system shows higher productivity due to the higher extraction rate and better utilization of the material transport system.

El Teniente Mine, with 2,400 km of tunnels excavated since the beginning of the last Century is the largest underground copper mine in the world. El Teniente Mine production plan has a thin overlap between the exhaustion of the current production level and the activation of the New Mine Level, located at almost 1,000 m depth, planned for 2017. The infrastructure system involves the construction of 24 km of access tunnels, consisting of two adits, a tunnel for vehicular access of personnel and a twin conveyor tunnel for the transport of the ore. The definition of geological and geomechanical scenarios, as predicted on the basis of the reference models, and the related hazards identification and mitigation (following a risk analysis based design), are cornerstones along the production chain. Tunnel alignment intersects a complex geological environment characterized by rock variability: from igneous (effusive and intrusive) to sedimentary volcanoclastic rocks, with sectors of intense hydrothermal alteration. Due to high overburden and variability of rock mass properties, geomechanical hazards such as squeezing and rockburst are expected, together with caving and flowing-ground conditions crossing fault sectors associated with high hydraulic pressures. This paper synthesizes the design methodology, focused on risk management (Risk Analysis-driven Design, Geodata 2009). The construction of the tunnel is actually in process and then also a preliminary comparison “predicted versus observed” is anticipated.

Two different pre-conditioning techniques have been applied at the Sur Andes mine sector (SuaPi) of the El Teniente mine in order to improve caving performance of the primary copper ore, which can be considered as a typical heavily veined massive, competent and unfractured rock masses. Hydraulic fracturing (HF) and blasting under confined conditions (BUCC) have been applied to a significant portion of the ore column to be mined. Both techniques introduce new open fractures into the massive rock mass with the aim of improving fragmentation performance at the draw points. A range of rock mass characterisation activities were undertaken before and after pre-conditioning took place in order to evaluate any change in rock mass condition. These geotechnical campaigns included both drill core logging and borehole camera (BHC) inspection and mapping. Mapping of the borehole walls allow the identification of the massive rock mass including the healed veins, the sub-horizontal HF fractures and also the sub-vertical (both radial and concentric to the blast hole) BUCC fractures. Using these rock mass characterisation properties, a Discrete Fracture Network (DFN) model was developed for both HF and BUCC fractures in order to quantify the occurrence of new open fractures within the primary ore. The DFN models allow the estimation of in situ fragmentation following preconditioning and these data were compared with fragmentation performance measured at the draw points in the SuaPi mine Sector. This paper presents the results of the pre-conditioning on the rock mass, the DFN modelling procedure undertaken (particularly the BUCC fractures), the characterisation of the preconditioning intensity and how it is related to the fragmentation performance at the SuaPi mine sector. © 2015 Institute of Materials, Minerals and Mining and The AusIMM.

One of the main problems related to mining investment decisions is the use of accurate prediction models. Metallurgical recovery is a major source of variability, and in this regard, the Chuquicamata processing plant recovery was modelled as a function of geomining-metallurgical data and ore characteristics obtained from a historical database. In particular, the data-set gathered contains information related to feed grades, ore hardness, particle size, mineralogy, pH, and flotation reagents. A systemic approach was applied to fit a multivariate regression model representing the copper recovery in the plant. The systemic approach consists of an initial projection of the characteristic grinding product size (P80), based upon energy consumption at the particle size reduction step, followed by a flotation recovery model. The model allows for an improvement in the investment decision process by predicting performance and risk. The final geometallurgical model uses eight operational variables and is a significant improvement over conventional prediction models. A validation was performed using a recent data-set, and this showed a high correlation coefficient with a low mean absolute error, which reveals that the geomet-allurgical model is able to predict, with acceptable accuracy, the actual copper recovery in the plant. © The Southern African Institute of Mining and Metallurgy, 2015.

The Campanani, Casualidad and Inca de Oro prospects, owned by Codelco-Chile, are extensive areas covered by post-mineralization deposits. To assist the detection of potential exploration targets, we carried out basic soil gas sampling campaigns by means of the Ore Hound GOCC® passive collectors, which were buried on a regular grid at a depth of 30–40 cm. After 90–120 days, samples were retrieved, sealed, and adsorbent material was submitted to an acid elution and analysed by ICP-MS for a set of 72 elements. In this study, databases have been analysed and modelled by statistical and geostatistical methodologies, mainly by factorial kriging analysis (FK). In all cases, a systematic analytical error was detected, discriminated and filtered, allowing the definition of contrast anomalies at different scales of spatial variation, and the interpretation of evidence of secondary dispersion processes by which present time surface contrast anomalies have been developed. The interpretation of contrast anomalies and element associations allowed the recognition of structural influences as pathways for gaseous circulation at the Campanani and Casualidad prospects. Likewise, lithological controls were detected at the Campanani and Inca de Oro prospects. At the Casualidad Prospect, a Co-Sn-Cu association describes a prospective zone c. 2 km north of the Casualidad deposit. At the Inca de Oro prospect, a marked influence of groundwater flow and/or surface drainage has been recognized in the configuration of contrast anomalies.

The El Teniente Cu-Mo porphyry deposit, Chile, is one of the world's largest and most complex porphyry ore systems, containing an estimated premining resource of approximately 95 Mt Cu and 2.5 Mt Mo. Although Cu mineralization at the deposit is quite well studied, little work has focused specifically on the distribution and timing of Mo mineralization. Combined grade, vein, and breccia distribution analysis reveals that deposit-wide Mo grades of 0.01 to 0.06 wt % are strongly controlled by the abundance of main mineralization (type 6a) quartz ± molybdenite veins. These show a clear spatial relationship with several felsic-intermediate intrusions and appear to develop outward and upward into Cu-rich (type 6b-7b) quartz-chalcopyrite veins and (type 8) chalcopyrite-anhydrite ± bornite veins with sericitic alteration halos. High-precision Re-Os molybdenite dating reveals that these linked vein types did not develop in a single, deposit-wide evolution, but are diachronous, related to distinct episodes of hydrothermal activity associated with the emplacement of diorite finger porphyries and the composite Teniente Dacite Porphyry. These units acted as effective, short-lived (<100,000 years) conduits for pulses of Mo- and Cu-bearing hydrothermal fluids between 6.3 and 4.6 Ma. The rapid thermal contraction of each system during mineralization led to extensive overprinting of Mo-rich veins by their lower-temperature, Cu-rich equivalents. Separate pulses in magmatic-hydrothermal activity are separated by distinct gaps of up to 300,000 years, during which Mo-mineralizing activity appears to have gone into quiescence. Mo grades exceeding 0.06 wt % correspond to the presence of molybdenite-bearing, late mineralization-stage, tourmaline-cemented (type 9), and anhydrite-carbonate ± gypsum (type 10) veins and breccias. These are abundant at shallow mine levels and show a close spatial relationship with a series of concentric faults associated with the Braden Breccia Pipe. Mineralization in this paragenetic stage is relatively short-lived and occurs in all parts of the deposit between 4.80 and 4.58 Ma. The generally Cu poor nature of the late mineralization stage is attributed to the prior preferential extraction of Cu from the underlying magma chamber in earlier mineralizing events. This led to the late exsolution of oxidized, Mo-rich fluids that may have undergone further enrichment by remobilizing Mo from main mineralization-type veins associated with the Teniente Dacite Porphyry. The formation of the Braden Breccia Pipe is likely to have occurred in a single cataclysmic event at approximately 4.58 Ma, which cut the Mo-rich tourmaline breccias and created a distinct Mo-rich grade halo at shallow mine levels. With the exception of minor mineralization associated with small dacitic dikes at approximately 4.42 Ma, the Braden event marked the termination of Mo deposition.

The horizontal seismic loading coefficient is an essential input in evaluating the seismic adequacy of slopes, such as those in open-pit mines and natural slopes. In some cases the coefficient is established through dynamic finite element analyses, which are time-consuming and require a new analysis for each facility, including anew suite of accelerograms. Values of the coefficient are sometimes incorporated in design manuals, but the procedures for establishing the values are seldom transparent. The usual situation is that the values arise from consensus, experience, and previous practice. In this paper the Urzúa-Christian model for normalized sliding displacement has been extended to develop the critical acceleration value corresponding to the probability of observing prescribed amounts of sliding displacement. The method has been applied to two sets of data based on probabilistic seismic hazard analyses. The results show that, to satisfy the criterion that there must be 0.1 probability of the sliding displacement exceeding 100 cm if the Maximum Credible Earthquake (MCE) occurs, the critical acceleration must be approximately 0.16 g. This means that a slope with these parameters in this environment must be stable enough that a horizontal acceleration of 0.16 g is necessary to put it in a state of sliding motion. In the case of the Operational Basis Earthquake (OBE), which is a much smaller ground motion, the criterion of 0.1 probability of 100 cm of sliding is achieved for a slope with a critical acceleration of 0.05 g.

In an active tailings impoundment, we studied the evolution of freshly deposited tailings from alkaline, unoxidized to acidic, oxidized tailings tracing changes in pore water quality, mineralogy, and element pathways. The tailings originate from the giant porphyry copper deposit Chuquicamata (Chile), and were deposited in different basins with varying times of surface exposure (0 to five years) to the hyper-arid climate in the Atacama desert. Fresh alkaline tailings (pH 9.1) had high concentrations of dissolved Na (1773 mg/L), Ca (556 mg/L), SO4 (2496 mg/L) and Cl (1678 mg/L) due to dissolution of primary gypsum, and high dissolved element concentrations in the flotation process water due to recycling of water from the tailings impoundment. High As and Mo concentrations resulted from desorption processes during the flotation, with minor contributions from As-rich river water and recycled tailings water. After draining of free water in freshly deposited tailings, evaporation-driven capillary rise was the dominant water transport in the vadose zone. In younger tailings (up to three years), the pH decreased due to sulfide oxidation to circumneutral values (6.4 - 8.6). The capillary fringe reached 1 m depth, where ongoing evaporation enriched Na (up to 5483 mg/L), K (742 mg/L), and Cl (6892 mg/L). In the vadose zone above 1 m, the high daily temperature amplitude resulted in condensation of pore water in the uppermost 80 cm of sedimented tailings. Subsequent capillary rise depleted uppermost tailings in soluble phases and increase superficial salt precipitation (halite, gypsum and Na-K-Ca-Mg sulfates). After four years, a 13 cm thick oxidation zone with acidic pH (4.7) evolved. After five years, a well-defined oxidation zone (28 cm thickness) with low pH (3.8) and high mobility of heavy metals was found (e.g., 247 mg/L Fe, 177 mg/L Cu, 61.8 mg/L Zn). This mobility allowed transport and enrichment in the efflorescent salt crust (e.g., as Cu sulfates devilline, krohnkite and Cu-chlorides eriochalcite and atacamite), with SO4 dominantly from sulfide oxidation (5.9 - –1.0 ‰ δ34S, 4.4 - –1.0 ‰ δ18Osulfates). Stable isotope data suggest that capillary rise from the water table reached the surface, most probably due to the reduction of pore size by precipitating secondary minerals, decreased water loss by clogging of pores and heat isolation by the efflorescent salt crust. The cycles of surface exposure and new tailings deposition in the las decades resulted in buried former oxidation zones, which showed lesser K and Cu concentrations in Fe oxides than recent oxidized tailings, most probably due to transformation of jarosite and schwermannite to Fe(3 +) oxyhydroxides and dissolution of Cu sulfates. Pore water in the saturated deep tailings was highly dynamic and displayed influences of local groundwater, and mixing with acid rock drainage (ARD) and fresh tailings water, both infiltrating from the surface. At the tailings dam, seepage water varied in time between neutralized ARD and fresh tailings water with groundwater influence, due to the periodic shift of the deposition zone and the resulting shallow groundwater changes. Adjacent efflorescent salts include typical minerals found in secondary porphyry copper deposits in northern Chile (e.g., atacamite), displaying the similarity between geochemical processes in weathered tailings impoundments and secondary enrichment zones of ore bodies, like Exotica from the Chuquicamata mine.

Within the mining industry, a safe and economical mine ventilation system is an essential component of all underground mines. In recent years, research scientists and engineers have explored operations research methods to assist in the design and safe operation of primary mine ventilation systems. The main objective of these studies is to develop algorithms to identify the primary mine ventilation systems that minimize the fan power costs, including their working performance. The principal task is to identify the number, location, and duty of fans and regulators for installation within a defined ventilation network to distribute the required fresh airflow at minimum cost. The successful implementation of these methods may produce a computational design tool to aid mine planning and ventilation engineers. This paper presents a review of the results of a series of recent research studies that have explored the use of mathematical methods to determine the optimum design of primary mine ventilation systems relative to fan power costs.