GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using Monte Carlo methods. We present a model for preferential sampling, and demonstrate through simulated examples that ignoring preferential sampling can lead to seriously misleading inferences. We describe an application of the model to a set of bio-monitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the inferences.

Heat transfer in microwave heating

Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.

Paleomagnetic Study of the Portage Lake Volcanics exposed in the Quincy Mine

A detailed paleomagnetic and rock-magnetic investigation was conducted on thirty six basaltic flows of the ~1095 Ma Portage Lake Volcanics. The flows were sampled along the East Adit of the Quincy Mine (Hancock, MI). Thirty two flows yielded well-defined primary magnetization directions carried by magnetite. A secondary magnetization component carried by hematite was also found in twenty nine flows. After correction for serial correlation between the flows, nineteen independent mean directions were calculated. The corresponding paleomagnetic pole is located at 25.5 °N, 182.1 °W (A95 = 3.5°). The new pole overlaps with the pole from the ~1087 Ma Lake Shore Traps suggesting a standstill of the North American plate during that time period. The low angular dispersion of virtual geomagnetic poles (S = 7.9°) suggests that the flows were erupted within a short time period, or that the strength of geomagnetic secular variation was lower than that of the recent field.

BENEFICIATION OF HIGH-MgO SEDIMENTARY PHOSPHATE ORES

Dolomite [CaMg(CO3)2] is an intolerable impurity in phosphate ores due to its MgO content. Traditionally, the Florida phosphate industry has avoided mining high-MgO phosphate reserves due to the lack of an economically viable process for removal of dolomite. However, as the high grade phosphate reserves become depleted, more emphasis is being put on the development of a cost effective method for separating dolomite from high-MgO phosphate ores. In general, the phosphate industry demands a phosphate concentrate containing less than 1%MgO. Dolomite impurities have mineralogical properties that are very similar to the desired phosphate minerals (francolite), making the separation of the two minerals very difficult. Magnesium is primarily found as distinct dolomite-rich pebbles, very fine dolomite inclusions in predominately francolite pebbles, and magnesium substituted into the francolite structure. Jigging is a gravity separation process that attempts to take advantage of the density difference between the dolomite and francolite pebbles. A unique laboratory scale jig was designed and built at Michigan Tech for this study. Through a series of tests it was found that a pulsation rate of 200 pulse/minute, a stroke length of 1 inch, a water addition rate of 0.5gpm, and alumina ragging balls were optimum for this study. To investigate the feasibility of jigging for the removal of dolomite from phosphate ore, two high-MgO phosphate ores were tested using optimized jigging parameters: (1) Plant #1 was sized to 4.00x0.85mm and contained 1.55%MgO; (2) Plant #2 was sized to 3.40mmx0.85mm and contained 3.07% MgO. A sample from each plant was visually separated by hand into dolomite and francolite rich fractions, which were then analyzed to determine the minimum achievable MgO levels. For Plant #1 phosphate ore, a concentrate containing 0.89%MgO was achieved at a recovery of 32.0%BPL. For Plant #2, a phosphate concentrate containing 1.38%MgO was achieved at a recovery of 74.7%BPL. Minimum achievable MgO levels were determined to be 0.53%MgO for Plant #1 and 1.15%MgO for Plant #2.

INVESTIGATION OF AIR JIGGING AND AIR CLASSIFICATION TO RECOVER METALLIC PARTICLES FROM ANALYTICAL SAMPLES

Analyzing “nuggety” gold samples commonly produces erratic fire assay results, due to random inclusion or exclusion of coarse gold in analytical samples. Preconcentrating gold samples might allow the nuggets to be concentrated and fire assayed separately. In this investigation synthetic gold samples were made using similar density tungsten powder and silica, and were preconcentrated using two approaches: an air jig and an air classifier. Current analytical gold sampling method is time and labor intensive and our aim is to design a set-up for rapid testing. It was observed that the preliminary air classifier design showed more promise than the air jig in terms of control over mineral recovery and preconcentrating bulk ore sub-samples. Hence the air classifier was modified with the goal of producing 10-30 grams samples aiming to capture all of the high density metallic particles, tungsten in this case. Effects of air velocity and feed rate on the recovery of tungsten from synthetic tungsten-silica mixtures were studied. The air classifier achieved optimal high density metal recovery of 97.7% at an air velocity of 0.72 m/s and feed rate of 160 g/min. Effects of density on classification were investigated by using iron as the dense metal instead of tungsten and the recovery was seen to drop from 96.13% to 20.82%. Preliminary investigations suggest that preconcentration of gold samples is feasible using the laboratory designed air classifier.

Preliminary Construction of a Photo-Electric Cell Concentrator

The separation of the valuable portion from the waste portion of an ore is an individual problem for every ore. However, the various methods for accomplishing this end, more or less classify themselves by the physical properties of the constituents of the ore. Most of the properties of minerals have been utilized in some way or other to affect the separation of the valuable from the invaluable parts. Practically nothing has been done so far with color and luster to attain this purpose. It is believed that the photo—electric cell could also be used in concentrating a certain class of ores which are not well suited to other methods.

Joint Planes in the Rhyolites of the Butte District, Montana

The problem herein discussed deals with the pointing planes found in the area of rhyolite located in the northwestern portion of the Butte District. The question to be determined was whether or not the pointing planes in the rhyolites could be class­ified with the Butte Ore fissure systems.

The Recovery of Copper in Sulphide Ores by Roasting, Leaching, and Electrolysis

Sulphide ores of copper are insoluble in dilute sulphuric acid leaching solutions, but a very high extraction can be obtained if the copper ore is in the oxidized condition. The problem is to convert the sulphide into the oxide form. This can be done by giving the sulphide ore an oxidizing-sulphatizing roast. Copper sulphate is soluble in water, so acid will be saved in the leaching process if copper sulphate is present. The iron in the copper sulphide ores is present as pyrite, or in combinations as bornite, or chalcopyrite.

Some Notes on the Composition of "Copper Pitch"

A supply of so-called "copper pitch" ore was received by the Montana Bureau of Mines and Geology in response to a request by them from a resident of Kalispell, who had previously sent a specimen to the Bureau for a mineralogical analysis. Since this material was little known and had apparently received but little study under a reflec­ting microscope, it was thought that such a study might throw some light on the mineralogical and chemical composition of the material.

Leaching Copper Minerals in the Butte District

The history of mining in Butte is woven about three of our principal metals. The gold placers first attracted the attention of miners in 1863, and reached their peak production in 1867. Silver was the second metal mined, and this operation required the erection of large mills with a consequent increase in mining activity that made the district a prominent producer. Although the presence of copper in the silver ore had been known, the credit for the first development of the copper veins is due Senator W. A. Clark. The original Colusa, Mining Chief, and Gambetta claims were developed to 1872. The ore was freighted by wagon trains 400 miles to Corrine, Utah, thence by rail eastward, some of it going to Swansea, Wales. The cooper production of the "richest hill on earth" has mounted to ten billion pounds.