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By H. R. Pierce

A gas well has a certain definite capacity to deliver gas from the gas sand through the producing string of pipe. This capacity depends upon the pressures in the sand; that is, a well will deliver gas at a rate of flow which is determined by the formation or "shut-inn pressure in the sand and the back pressure at the face of the sand in the well. The three factors, rate of flow, formation or "shut-in" pressure, and the back pressure, for a given well, can be written into a fundamental relation which is strictly applicable only to that well. This relation can be used to determine the capacity of the well to deliver gas from any formation pressure against any back pressure held at the f ace of the sand in the well. Studies have been made of the deliveries of 400 gas wells operating under different conditions of pressure, Most of the wells which have been studied are in Osage County, Okla.; however, several representative studies have been made on wells in southern Louisiana, southern Texas, the Texas Panhandle, and West Virginia.

Jan 1, 1929

By S. Jennings

The Red Dog zinc-lead-silver deposit is located in the DeLong Mountains of the western Brooks Range in northwest Alaska. The region is located 145 km(90 miles) north of the village of Kotzebue (Fig. 1).Red Dog’s current resource base is 143 Mt (157 million st) averaging 16.1% zinc, 4.3% lead and 83g/t (2.4 oz/st) silver. It is contained in four structurally separate deposits— the Hilltop, Main Deposit, Aqqaluk and the newly discovered Paalaaq deposit. Recent exploration for the Aqqaluk and the Paalaaq deposits has contributed to Cominco American’s understanding of the detailed structural geology of the district and its role in the placement of individual ore bodies.

Jan 1, 1999

By F. Hassani, D. O’Donnell, M. Momayez, P. Guevremont

Shotcrete is a practical and economical support system in many Canadian underground mines. Although shotcrete technology has gained acceptance in the mining industry, there are some problems that have emerged with respect to quality assessment and thickness measurement of the liner. This paper presents recent tests performed with miniature seismic reflection technology (MSR) developed and patented at McGill University primarily for thickness measurement of this heterogeneous liner. MSR is also capable of providing information regarding the quality of shotcrete in terms of its mechanical properties such as modulus of elasticity and Poisson’s ratio. Work was performed on site in an underground mine in Ontario, Canada. This paper also presents the results from laboratory tests performed on fiber-reinforced and non-reinforced shotcrete panels that were used to assess the P-wave velocity in both materials. The results of these tests were used in a second site investigation. The NDT thickness measurements showed good agreement with direct thickness measurement such as coring. In addition, the MSR technology has the advantage of being more accurate and more affordable compared to other non-destructive testing (NDT) systems in the market.

Jan 1, 2002

By G. A. Kosick, G. S. Dobby

"This paper presents the principles and application of a recently developed control system for flotation columns and column circuits. The control system uses triple pressure sensors to directly sense zone densities and level, and to help in characterizing the operating behaviour of individual columns. A complete expert system development tool is incorporated within the system to provide the facility for full operator training, an on-line help facility, and a means for incorporating the column behavioural patterns into decision making rules. The system is configurable to any number of columns and can be run in either supervisory mode or direct control through Minnovex PIO software. Additional process signals can be interfaced with the system if desired. Operating experience with the control system on the Minnovex column flotation pilot plant is described.I: INTRODUCTIONColumn flotation cells have been more difficult to control and are more sensitive to circuit changes than conventional mechanical flotation cells. This susceptibility encouraged investigation into various types of control strategies ranging from inexpensive single pressure measurements for level control, to highly instrumented and expensive systems using a variety of control methods.Flotation operators, in many cases, do not understand the column control philosophy or have not been trained to deal with this new type of cell. Some operators have subsequently absolved themselves of the column operating responsibility. Some column cells, for example, have run for hours with slurry pouring over the top or no froth coming off at all.ColumnEX is a column flotation control system which was developed from the viewpoint of an operating shift foreman who wishes to:1. control the column or column circuit through a genuine understanding of what is happening inside the columns, and2. to share this knowledge with his flotation operators and be available to guide them through times of circuit upsets."

Jan 1, 1990

By Luciano Gianizeli Rodrigues

Este trabalho estuda a obtenção da fase S livre de precipitados, a partir da nitretação a plasma de pós de aço inoxidável austenítico 316, e analisa a variação do parâmetro de rede (aS) em função das diferentes condições de tempo e temperatura de tratamento. Os pós com granulometria entre 38 e 54 ?m foram nitretados em reator a plasma pulsado DC, sob atmosferas de 80%N2 e 20%H2, pressões de 400 Pa, por tempos de 1 a 9 h, e temperaturas de 420, 450 e 470ºC. Os resultados mostram que para a temperatura de 420ºC o parâmetro de rede (aS) aumenta continuamente com o tempo de tratamento, atingindo a máxima expansão (8,5%). Com o aumento da temperatura e do tempo de tratamento, verificou-se um recuo em aS associado à perda de nitrogênio e conseqüente formação de nitretos. É possível obter na temperatura 420ºC após 9 h cerca de 37% de fase S livre de precipitados, o que mostra a necessidade de realização de experimentos adicionais ou do desenvolvimento de métodos de separação das partículas nitretadas das não nitretadas.

Aug 8, 2018

By B. Genc

"The risk of spontaneous combustion is well known in the South African coal mining industry. In the coming years it is very possible that the incidence of spontaneous combustion will increase from current levels, due to factors such as an increased rate of mining, re-working of previously mined seams, more stooping and total extraction for underground mines, and higher stripping ratios for surface mines, leading to more spoils. It is also fairly certain that coal mining will face tougher environmental emissions legislation in the near future. To determine the areas where the risks of spontaneous combustion are high, it is necessary to improve on our current laboratory procedures for testing and evaluating coal samples, combining the results with site and field data, and if necessary revising the laboratory rating system to refine our understanding of South African conditions.Currently, laboratory tests are conducted in order to determine both the Wits-EHAC index and the crossing-point temperature which, when combined, give an indication of the spontaneous combustion propensities of the coal samples. This procedure has enabled the establishment of a database of results to review and evaluate South African coal seams. Using this database, the high-risk areas in terms of spontaneous combustion are identified. Tests have been undertaken for five consecutive years, between 2008 and 2012. In total, 119 coal samples from different coal seams and production coalfields have been analysed and classified through a series of laboratory tests. A comprehensive database of these results is available, and is continually being updated as new test results are added. This database will continue to expand, and to provide the basis for an improved risk evaluation methodology for spontaneous combustion"

Jan 1, 2015

As it is probable that a large proportion of the members of the Institute attending this meeting are connected with the metalliferous side of mining, the writer thought that, as coal and coke are required for various purposes in considerable quantities by their companies, some particulars of the coal industry might be of interest, especially when visiting such an important coal-mining centre as Newcastle. It is proposed to deal with the matter from the mining and economic point of view, as the geology has been so well and exhaustively dealt with in various publications referred to in the bibliography at the end of this paper. In the immediate vicinity of the city of Newcastle the collieries are gradually being abandoned, and during the past few years the Wickham and Bullock Island, Stockton, Hetton, Newcastle Coal Mining Company's "B," and the Australian Agricultural Co's Sea pit, have disappeared from the coal-producing list of collieries. AIl of these collieries worked the Borehole seam, from which, up to date, the largest quantity of coal has been produced in the northern district.It is the bottom seam of any present commercial value in the Upper or Newcastle coal-measures, and although the coal-in this seam has not been entirely 'exhausted in the collieries referred to, they have been abandoned for various reasons. For example, although about 60% of the seam (18 to 20 ft. thick) was left in the workings in the form of rectangular pillars under the city of Newcastle, this was not sufficient to 1?revent'the subsidence which took place about twelve years ago.Again, large quantities of coal in the Borehole seam have been left to protect the shipping arrangements at the Dyke, and other...

Jan 1, 1918

By P. Wittke-Gatterman

ABSTRACT: A three dimensional constitutive law for swelling rock is presented. It can be applied to the osmotic swelling of mudstone as well as to the swelling of rocks containing anhydrite. It describes the development of time-dependent strains and stresses due to swelling considering elastic and viskoplastic behaviour. Furthermore an anisotropic swelling behaviour can be considered. This constitutive model was implemented within a numerical computation program according to the finite element method and calibrated on the basis of the results of measurements in the investigation drift of the Freudenstein tunnel which is completely located in the unleached Gypsum Keuper. A parameter combination could be found which results in a good agreement between numerical solutions and results of measurements. Therewith an analysis procedure which enables the design of tunnels in swelling rock is available. ZUSAMMENFASSUNG: Im vorliegenden Beitrag wird ein dreidimensionales Quellgesetz vorgestellt, das nach derzeitigem Kenntnisstand sowohl auf das osmotische Quellen von Tonsteinen als auch auf das Quellen anhydrithaltiger Ton- beziehungsweise Schluffsteine anwendbar ist. Das Stoffgesetz wurde in ein Finite-Elemente-Programm implementiert und anhand von Meßergebnissen des im unausgelaugten Gipskeuper liegenden Untersuchungsstollens des Freudensteintunnels kalibriert. Es ist gelungen, eine Kennwertkombination zu finden, mit der alle Meßergebnisse gut beschrieben werden können. Damit steht ein Bemessungsverfahren für Tunnel in quellfähigem Gebirge zur Verfügung. RÉSUMÉ: Dans l'article présent un loi de gonflement à trois dimensions est présenté, qui peut être appliqué aussi bien au gonflement osmotique de l'argile compactée q'au gonflement de l'argile compactée ou du limon compacté contenant de l'anhydrite. Le loi de comportement était implémenté dans un programme numérique d'éléments finis et calibré avec des résultats de mesures de la galerie de recherche du tunnel de Freudenstein, situé dans le Keuper de gypse non lessivé. On est réussi à trouver une combinaison de paramètres avec laquelle tous les résultats de mesures peuvent être bien décrits. Par ce moyen, une méthode de dimensionnement existe pour des tunnels dans de la roche capable de gonfler.

Jan 1, 2003

By Robert C. Dyni

This report details the investigation of multiple-seam longwall subsidence conducted by the U.S. Bureau of Mines from 1978 to 1989. A field investigation monitored ground surface movements over four upper-seam longwall panels and six lower-seam panels. The characteristics of the subsidence occurring as a result of mining these panels are examined; in particular, the angle of draw, subsidence development, total magnitude and areal extent, and critical width are evaluated and discussed. Comparisons are also made between the characteristics of multiple-seam longwall subsidence and single-seam longwall subsidence that occurred at the same site.

Jan 1, 1991

By Robert C. Horton

The Getchell Mine is located on the east flank of the Osgood Mountain Range in the Potosi Mining District, Humboldt County, NV. Mining in the area first began in 1883 for copper, lead and silver in skarn-related deposits. Tungsten was discovered in the skarns in 1916 and was mined sporadically until 1957. The first major discovery was made in 1933 when two Winnemucca prospectors, Edward Knight and Emmett Chase, found gold at the present site of the Getchell gold mine. In 1934, after a small amount of preliminary prospecting, the claims were purchased by Noble H. Getchell of Midas, NV. The Getchell Mine Inc. was organized and exploration and development work began on a broad scale. Major funding was provided by George Wingfield and investors he assembled. Laxalt described Wingfield’s immediate history prior to his financing of Getchell as follows.

Jan 1, 1999

By Sergio Burelli, Darren C. Megaw

"Operational challenges associated with solvent extraction (SX) plants include the effective on-line management of solids introduced from a variety of process streams. Solids are carried over from leaching circuits due to incomplete solid–liquid separation, may be formed as a result of chemical precipitation within the SX circuits, or introduced from downstream electrowinning operations. Solids in SX settlers result in operational challenges that impact plant availability and reduce optimized name-plate design capacity operation. Most available SX crud and bottom solids removal systems are limited in their effectiveness to handle high total suspended solids in SX circuits. Operations are often forced to take settlers off-line for complete removal of contained solids. These cleaning operations are hazardous, high risk, labour-intensive and costly in terms of production down-time and organic extractant and diluent reagent losses. Production pressure results in operations being reluctant to take SX settler units off-line for solids clean-out, resulting in continued operation of the SX, at reduced levels of mass transfer performance. Crud ForxTM is an SX solids removal system, for the on-line removal of interfacial and bottom solids associated with hydrometallurgical SX processes. A case study conducted at Glencore’s Mutanda Mining copper and cobalt operation in the Democratic Republic of Congo demonstrated the effectiveness of the Crud Forx. Benefits identified were an overall improvement in SX fire risk reduction, SX occupational health and safety and an improvement in copper mass transfer. INTRODUCTION Hydrometallurgical copper extraction and purification processes are often associated with ultra-fine solids distribution profiles throughout the process flowsheet (Virnig et al., 1999). The level and impact of the undesired deportment of solids to process streams varies from operation to operation, but the common denominator for all operations that employ solvent extraction (SX) as a copper upgrading and purification step is that, at some stage, they will have to manage solids (crud) within the SX circuit. Available crud removal systems in the industry have had limited success in continuous, effective interfacial crud and bottom solids removal from SX settlers. Most operations use basic removal methodologies which, at best, only result in delaying the requirement for taking the affected SX settler stages off-line for complete clean-out. This operational methodology results in production loss, increased SX organic extractant consumption and adds occupational health and safety risk to SX operations. The integrated Crud ForxTM/Crud FrogzTM SX solids management system assists operations in on-line SX solids management. The system has been proven to significantly reduce the requirement for off-line cleaning of settlers."

Jan 1, 2015

By M. P. Brandt, T. P. Knoetze, I. I. M. Kessler

It has generally been accepted that the volatile mater in a coal is the factor that determines whether or not a specific coal dust is an explosion risk. This paper presents the results of an attempt to relate the explosibility index (Kex) of South African coals, as determined in a AD-litre explosion vessel, to the volatile mater content of the coal and the calorific value of the volatiles. A good relationship between the calorific value of the volatiles and the explosibility index was established, which makes it possible to calculate the violence of an explosion, as expressed by Kex, for South African coals. The Kex value is but one of a number of parameters that influence the explosion hazard in a specific colliery and cannot be used as the sole predictor of the propagation of an explosion underground. Other parameters include the ignitability of the coal, temperature, humidity, dispersibility of the dust, methane concentration, amount of incombustibles present, and ventilation.

Jan 1, 1993

By P. Tsang

The mechanisms and functions of yield pillar are analyzed by employing finite element method that takes time dependent and plastic failure of rock into consideration. The design criteria for different geological conditions are discussed. The results provide further evidences that yield pillar design will improve floor or roof condition, especially when the floor and/or roof strata are weaker than the coal. Based on this study, the yield pillar size is determined for one cod1 mine located in southern West Virginia.

Jan 1, 1989

By J. P. Gous, J. J. Sutherland

"Transalloys is a silicomanganese (SiMn) producer located in South Africa, and uses only local manganese ores to produce SiMn alloy. The plant operates five open submerged arc furnaces (SAFs) with an annual capacity of 180 000 t of saleable SiMn.Maintaining tap-holes is critical for effective furnace operation, allowing proper drainage of the furnace with minimal operator interference. Using a claygun and drill arrangement installed at each furnace, tapping occurs every four hours. Tap-holes are maintained through mickey replacement and brick repairs. Three furnaces have SiC tap-holes and two have graphite tap-holes.This paper gives a review of SAF operation, furnace and tap-hole design, daily tapping operation, and maintenance practices for repairing tap-holes.IntroductionDefining tap-hole life cycle, Steenkamp et al., (2016) highlighted four main steps: installation during furnace relines, day-to-day operations, tap-hole maintenance, and tap-hole repair. The authors argued that the design of the tap-hole area should allow for all four stages in the tap-hole life-cycle. Design principles for each stage were presented using silicomanganese (SiMn) production as a case study. Here we present a further analysis of the case study by providing practical examples of how the tap-hole life-cycle is managed at Transalloys during the design, operation, and maintenance of submerged arc furnaces (SAFs) applied in the production of SiMn.BackgroundTransalloys is the largest producer of SiMn in Africa. Its smelter complex is based outside the town of eMalahleni, in the Mpumalanga Province of South Africa. Transalloys was commissioned in the mid- 1960s as a high- and low-carbon ferrochromium plant based on the Perrin process. In 1967 the plant was converted to SiMn production because of constraints in the ferrochrome market (Basson, Curr, and Gericke, 2007; Bezemer, 1995). Today, the installed production capacity is 180 000 t of SiMn annually. Plant operations consists of five SAFs (see ratings in Table I), operating 24 hours a day, 365 days a year (including maintenance), involving 280 permanent employees, with up to 120 contract employees on site at any given time."

Jun 1, 2019

By Donelson A. Robertson

Literature was searched and cases of alleged water well damage were investigated. Occurrence of ground water in Appalachia is primarily in low yield, fractured, water table aquifers. Four test sites were chosen based on geographic and geologic diversity. Test wells were drilled at each site and base line data on water quality, static water level, and drawdown characteristics were obtained before surface mining commenced. Blast induced ground vibrations were measured at the surface by the wells at levels up to 5.44 inches per second maximum resultant particle velocity. Measurements made at the bottom of wells indicated that vibrations were considerably attenuated at depths of 140 to 160 feet. No direct evidence of change in water quality or well performance was produced by blast vibrations, but removal of downslope support by excavation does cause lateral stress relief which permits the water-bearing fractures to become more open. This additional storage capacity causes the static water level to drop and for well-bore permeability to improve. Static water level recovers if sufficient recharge is available and well performance is

Jan 1, 1980

By R. C. Neavel

One of the most important requirements to be met by any coal producer is delivery of size consists tailored to specific applications. Generally these specifications include a minimum as well as a maximum size limit. The customers of a major Indiana coal producer noticed that some shipments of sized coal contained a large proportion of undersize pieces. Also, in these shipments, the pieces which remained within the specified limits were cracked and, when handled, crumbled readily. The producer, certain that these shipments had been properly sized at the tipple, suspected that degradation had occurred in transit. The Indiana Geological Survey was requested to examine the coal from one of these shipments to attempt to determine the cause of breakage. Two basic facts about coal and coal seams led to the employment of petrographic techniques in this investigation. First, all coal seams consist of accumulations of diverse organic and inorganic constituents; and second, most coal breakage, either desirable or undesirable, can be attributed to the inherent weakness of some of these constituents or to poor adhesion between certain constituents. Analyses of degraded coal Sampling: Samples were secured from 2 stock piles of 2-by 4-inch coal in a dealer's yard. The coal in both piles had received the same treatment from mining to storage, although it had been mined and shipped on two different days. The size consist of one pile, however, appeared smaller than that of the other. The sample from the degraded pile is referred to as the slack sample, and the other is called the unslack sample. Size analyses: In order to determine the actual size consist, the samples were screened, with a minimum of rough handling, on square 2-inch, 1-inch, 1/2-inch, and 12-mesh screens. It is assumed that 100 percent of the 2-by 4-inch coal is retained on a 2-inch round screen at the tipple. Analyses of several loads at the tipple indicate that approximately 26 percent of the 2- by 4-inch coal, 100 percent of which was assumed held on a 2-inch round screen, passed through a 2-inch square screen. Twenty-six percent may be taken as the normal difference between round and square screens. Results of the analyses of stockpile coal are shown in Table 1. Cumulative percent versus size are plotted on a Rosin-Rammler chart as Figure 1. Both samples approximately follow normal size distribution; this indicates that breakage is not size preferential and also that the samples are representative of the stockpiles. Although both samples exhibit the same general size distribution, the median size of the slack sample is considerably smaller than that of the unslack sample. Fifty-five percent of the unslack sample was undersize (29 percent greater than the normal 26 percent difference), and 83 percent of the slack sample was undersize (57 percent greater than the normal 26 percent difference). Both piles contained a greater percentage than normal of undersize coal; this indicates that they were both affected by degradation, but to a different degree. Bedding-plane analyses: Coal, because of its laminated nature, will break preferentially along bedding planes, especially where adjacent constituents are poorly cemented to each other. Subsequent breakage perpendicular to the

Jan 1, 1961

IF a straight line should be drawn on the map (See 1, page 96) through the northern half of the South Island of New Zealand, from Mt. Domett in the north to Arthur's Pass in the south, and another line drawn parallel to it and at a distance of ten miles to the west, according to the topographic scale, it will be found that within the belt thus drawn across the country all the most important mines, past and present, of the South Island are situated, with the exception of a few in Otago.The most important product of this tract being gold, and Reefton, the most important southern mining field, being situated at about its central portion, the zone may aptly be termed "The Great Reefton Gold Belt." The occurrence of so many gold mines along this particular strip of country is not at all a matter of chance, but is the outcome of cause and effect. Running along the eastern side of the gold belt are the Brunner and Victoria Ranges, which are chiefly composed of crystalline schists and metamorphic granite of probably Cambrian or Silurian age; between these and the gold-bearing series there are interposed at one or two places some beds of slates, limestones, and...

Jan 1, 1910

By Richard Kastner, Emilie Vanoudheusden, Fabrice Emeriault, Jacques Robert

INTRODUCTION The subway line B of Toulouse (France) has been realized with three different tunnel boring machines (TBM) techniques: Contracts 2 and 5 are excavated with earth-pressure balanced TBM, Contract 4 with a slurry shield TBM, and Contract 3 with a compressed-air TBM. The first three machines are around 7.7 m in diameter, while the last one is 5.3 m. Moreover, a small part of the line (50 m) has been excavated by a conventional method. The tunnels run through the Toulouse molasses, composed of hard sandy clay with pockets and lenses of dense sand. Geotechnical investigations have shown that in these formations, K0 is greater than 1, around 1.8 at a depth of 25 m (Serratrice,2005) and that geotechnical characteristics are homogenous on the whole layout (? =22 kN/m3, Su = 300 kPa, c' = 30 kPa, F' = 32°). The water table is found between 2 and4 m below ground level. As geology, stratigraphy and tunnel cover (between 10 and 20 m) are almost identical, a comparison of movements induced by the excavation by each of the four excavation techniques is possible. This paper presents the soil mass movement measures in the case of the conventional excavation method and in the case of TBM sections. It shows how tunneling parameters may explain the different surface movements observed during excavation. For the sake of simplicity, only the results of Contract 2 (earth pressure balanced TBM)will be presented. MONITORING Monitoring for the Conventional Method Section For the conventional method section (Vanoudheusden et al. 2005) the mass soil movements are measured with two inclinometers and one multi-point extensometer borehole with automatic data acquisition (Figure 1). The monitoring devices include

Jan 1, 2007

Stress induced, gravity-assisted failure processes typically dominate long before stress levels approach the strength of the intact rock (at approximately smax > 0.4UCS where smax = 3s1 ? s3 and UCS is the Unconfined Compressive Strength of the intact rock (Martin et al. 1999)). Under these conditions, discontinuities typically become clamped and the failure process becomes brittle. This brittle failure process is dominated by new stress induced fractures growing subparallel to the excavation boundary. While it is possible to identify areas with the potential for brittle failure, for example, using the general assumption that brittle failure will occur in areas at right angles to the major principal stress (Hoek et al., 1995), when the threshold smax > 0.4UCS is reached in areas around the tunnel boundary, or elastic modelling and the Hoek-Brown brittle parameters proposed by Martin et al., (1999) (i.e. m? 0 and s ? 0.11), amongst others, recent observations discussed by Everitt & Lajtai (2004), and Kaiser (2005; 2006) suggest that brittle failure processes are enhanced when structural features such as joints, weakness zones, bedding planes or foliations are preferentially orientated around the excavation boundary creating stress raisers which in turn facilitate the stress-driven rock mass disintegration process (e.g., as illustrated by Everitt & Lajtai (2004) on Figure 1b). Such weaknesses induce stress heterogeneities that thus promote tensile-spalling failure processes (Diederichs 2000). The observations suggest that stress induced damage can occur ?prematurely? depending on the orientation of micro and macro structures in situations where the known stress conditions should not yet initiate brittle failure processes. In general, when structural features (micro and/or macro), especially foliations, are present in a rock mass, the strength is effectively reduced, largely due to tensile strength heterogeneity in areas depending on the orientation of the structural features with respect to the excavation boundary. As a result, stress induced damage could occur in areas not normally considered due to the influence of anisotropy (Figure 1).

May 1, 2009

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970