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By Y. Oka, H. Majima

When a rock particle is subjected to an external force, internal stresses and deformations are experienced by the particle. Assuming that the breakage of a rock is mainly due to tensile stresses generated by the action of a pair of concentrated loads, F, directed in compression towards the loading points at the shortest distance, as illustrated in Fig. 1, the stress and deformation experienced by a particle of irregular shape can be determined with the aid of the theory of elasticity. According to the photoelastic experiments made by one of the present authors,' the stress states in a rock particle of irregular shape are quite similar to that of an inscribed sphere of diameter x, as indicated in Fig. 1, but accompanied by the faint stresses, in the vicinity of the particle outside of the inscribed sphere. Therefore, the stress components in an irregularly shaped particle can be estimated by referring to stress components in a sphere. Applying polar spherical coordinates to an elastic spherical body, as shown in Fig. 1, the stress components are all expressed as multiples of F /x2 and more or less influenced by the loading angle and Poisson's number m. In general, the energy w, acting on a rock particle is defined as the product of loading compression F

Jan 1, 1970

By A. A. Stripling

The Cretaceous limestone wells of the Mara/Maru-caibo Dist. of Venezuela are extremely prolific producers. To maintain production on cessation of natural flow, large scale gas-lift operations were commenced involving high production rates on caring Flow. For the design of these gas-lift installations it was essential to have some knowledge of the pressure gradients involved in casing flow, so that the required injection pressures, optimum gas injection raws, etc., could be forecast. This paper presents a method of calculating these annular pressure gradients. Basically the method makes use of an energy balance equation coupled with an empirical energy loss factor derived from field data. The calculations have been put in a form suitable for "punch card-type" calculating machines. A set of gradient curves for Mara/Maracaibo conditions covering flow rates up to 12,000 B/D, and GOR's of 500 to 2,000 cu fd/bbl is presented. From these curves the flowing BHP can be predicted from surface data and the vertical pow performance under varying conditions of gas injection can be estimated. The method has been applied to La Paz and Mam gas-lift operations for over three years and has given consistently accurate results. INTRODUCTION The Cretaceous limestone fields of the Mara/Maracaibo area in Venezuela are characterized by the presence of widely distributed fissure systems. Under these conditions individual wells frequently have extremely high potentials and such wells are generally flowed on the casing-tubing annulus in order to reduce the pressure loss in vertical flow. To maintain production on cessation of natural flow, an extensive gas-lift system was planned. As a first approach to this gas-lift design problem, an attempt was made to construct a set of empirical flowing gradient curves from the available subsurface pressure data. Such a method has been used successfully for tubing-flow conditions in California by Gilbert'. Unfortunately, the empirical construction of casing-flow gradient curves presents additional difficulties, as pres- sure bombs cannot bc run in the casing-tubing annulus against high rates of flow. Thus, the Full flowing gradients cannot be defined by actual measurement and the best that can be done is to obtain spot pressures at the tubing shoe. Under these conditions a vast accumulation of BHP data is required to construct a set of gradients. To the La Paz and Mara fields the majority of the available flowing pressure measurements fall into a relatively narrow GOR range, in the neighborhood of the solution ratio. While there appeared to be reasonable prospects of constructing gradient curves for this limited range, measurements at higher GOR's, which were of major interest for gas-lift operations, were relatively few and the prospects of constructing empirical curves cor~spondingly remote. As an alternative approach, the possibilities of a mathematical analysis of vertical flow conditions were investigated. May and Laird2fV n 1934 presented an excellent analysis of the vertical-flow conditions in the Anglo-Iranian Oil Co.'s fields. Their analysis was based on an energy-balance equation and calculated the losses due to kinetic energy, friction and slippage separately. By combining these losses with the total calculated available energy, the required depth-pressure traverse could be deduced. On applying the method to La Paz conditions, good results were obtained for tubing flow at high tubing-head pressures. However, for lower wellhead pressures (300 psi and under) the discrepancy between calculated and measured values increased appreciably. It was considered that this was probably due to energy losses caused by slippage or liquid hang-up in a continuous gas phase, for which it was difficult to visualize any analytical approach. In 1952 Poettmann and Carpenter4 presented a method of pressure gradient calculation which, while based on an energy-balance equation similar to that employed by May and Laird, made no attempt to evaluate the various components making up the total energy loss resulting from irreversibilities of flowing fluids. Instead, they proposed a method of analysis which assumed that all significant losses for multiphase flow could be correlated in a form similar to that of the Fanning equation for frictional losses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The total available

By D. H. Gurinsky, D. G. Schweitzer

The empirical equilibrium constantsd the heat of reaction for the reduction have been determined from 300° to 500°C. The mechanisms of the oxidation of uranium and magnesium from dilute bismuth solutions have been investigated. The kinetics of some of the reactions were affected by air adsorbed on the uranium oxides. THE Liquid Metal Fuel Reactor studied at Brook-haven National Laboratory uses a solution of uranium in bismuth as the fuel. Corrosion and stability problems require that the fuel solution contain corrosion inhibitors and deoxidants. Of the additives tested, magnesium has been found to be the best deoxidant and zirconium the best corrosion inhibitor in bismuth. Some experiments1 indicate that magnesium may play a secondary role in increasing the effectiveness of zirconium in inhibiting corrosion. The work reported here was intended to determine the relative concentrations of Mg and U required to prevent oxidation of the uranium fuel in the event of an air leak. In addition, an attempt was made to identify some of the mechanisms of the oxidation and reduction reactions occurring in the liquid bismuth solutions. EXPERIMENTAL Apparatus and Procedure—The equipment shown in Fig. 1 was designed so that the reaction kinetics could be studied as functions of temperature, melt composition, pressure, and flow rate. At the start of a run, the 10-liter bell jar (F) is removed by opening the bottom Dresser fitting (L), and the bismuth and additives are placed in a pyrex crystallizing dish (I). The bell jar is replaced, the system is evacuated to 10-5 to 10-6 mm Hg and then the heater (J) is turned on. When the selected temperature is reached, the oxidizing gas is admitted to the system to the desired pressure as read on the manometer (D). Gas is introduced through the slide tube (Q) which has a pyrex frit (R) sealed to its bottom. Stirring is accomplished by immersing the end of the tube in the melt. To maintain a constant pressure under flow the input and evacuation rates must be equalized. To obtain this condition stopcock (C) is closed and flowmeters (B) are matched. The reaction is "stopped" by closing the inlet flowmeter and quickly evacuating the system. To obtain a liquid metal sample, the system is evacuated with the sampler positioned near the surface of the liquid. The sampler, Fig. 2, is then immersed until its thermocouple reading matches thermocouple (G) Fig. 1. The system is then pressurized with helium which forces the solution through the frit. Twenty to 30 min elapsed between the time the system was evacuated and sampled. During evacuation and pressurization of the system, the temperature variations did not exceed ± 5°C. While bubbling occurred the temperature remained constant to within 1/2 oC. The volume of the equipment was determined by adding a known volume of air at atmospheric pressure to the evacuated system and noting the resulting pressure.

Jan 1, 1962

By B. S. Gottfried

This paper is concerned with possible transport mechanisms which occur during segregated burning (i.e., burning in an oil reservoir in which the oil-bearing formation is overlain by a "clean" porous zone containing only gas). ,Two analytical models are presented. In the first, burning is assumed to occur at the gas-oil interface, and the dominant mechanism is taken to be the rate at which oxygen diffuses to the interface. The second model assumes that combustion occurs within the clean zone, with the dominant mechanism being the mechanism of fuel deposition from the oil-bearing formation to the clean zone. ,Comparison of the results of the analyses with limited experimental data indicates that the latter mechanism is much more plausible. Both models are idealized representations of the actual process and are somewhat conjectural, however, owing to the lack of more definitive laboratory or field data. INTRODUCTION In recent years there has been considerable theoretical and experimental research directed toward understanding the recovery of crude oil by underground combustion. Although two different recovery schemes have been proposed, known as forward and reverse combustion, it is only forward combustion that shows promise of becoming a practical recovery technique.17 Most of the analyses of the forward combustion process have considered it to be pistonlike; i.e., oil is displaced by a vertical combustion zone which, with its ensuing gases, pushes die oil forward as the flame front is propagated through the reservoir.l-8,ll,l2,14-16 However, information gained in field pilot studies indicates that, at least to a certain extent, forward combustion proceeds in a segregated manner in oil reservoirs.10 An ideal segregated system is one in which the oil-bearing formation is overlain by a "clean" porous zone containing only gas. The location of the combustion zone in such a system is not immediately evident, although combustion is believed to occur either at the gas-oil interface or within the clean zone. In either case, the combustion zone may be horizontal and it moves in parallel rather than in series with the produced oil. The purpose of this paper is to explore the likely mechanisms by which segregated burning can occur, and to determine the sensitivity of the resulting models to changes in various physical parameters. Two governing mechanisms are considered: the case of a horizontal combustion zone at the gas-oil interface with the rate of combustion governed by the rate at which oxygen diffuses to the interface, and the case of combustion within the clean zone with the combustion process controlled by the transport of fuel from the oil-bearing formation to the clean zone. Both models are somewhat hypothetical and involve considerable simplification of the actual process. However, the results allow some preliminary understanding of segregated burning which is useful in the absence of more definitive laboratory or field pilot data.

Jan 1, 1967

[Executive J. V. W. REYNDERS, Chairman WILLIAM H. BASSETT E. DEGOLYER I-I. C. BELLINGER RICHARD PETERS, JR. Finance GEORGE OTIS SMITH, Chairman H. A. GUESS F. JULIUS FOHS Admissions GEORGE D. BARRON, Chairman DAVID LEVINGER P. A. MOSMAN H. K. MASTERS J. A, SINGMASTER Alternates F. G. BREYER C. W. HAMILTON F. E. PIERCE]

Jan 1, 1928

By Robert B. Fulton

The use of industrial minerals by the chemical industry as raw materials for manufacturing and in processing spans a wide assortment of minerals. This chapter aims to supplement rather than duplicate the commodity chapters. Its objective, to describe the uses of industrial minerals in the manufacture of chemicals, is attained by considering minerals used by the chemical industry in terms of the chemical element required and by giving particular emphasis to market factors. The mineral aspect, which is covered in the commodity chapters, is subordinated and attention is focused on the chemical and market aspects. Condensing this broad subject into a few pages permits treating only the most important elements derived from industrial minerals. The elements derived from petroleum, hydrogen and carbon, which quantitatively dominate as raw materials for the chemical industry, are omitted, as are the metallic elements and the minerals covered in other "use" chapters such as phosphorous, potash, and nitrogen for fertilizers and titanium dioxide for pigments. After eliminating on this basis, our definition leaves six elements of major importance: boron, bromine, chlorine, fluorine, sodium, and sulfur. These elements are treated individually under separate headings. Salt brines have particular importance as raw material sources for the chemical industry as shown in Table 1 "Salt Brine Derivatives" (Anon., 1967), which charts the chemical compounds derived from four types of brines: (1) Owens Lake type brines which are sources of boron and sodium compounds; (2) Midland type brines from which bromine, iodine, and chlorides of calcium, magnesium, potassium, and sodium are derived; (3) Searles Lake type yielding boron, bromine, lithium, magnesium, potassium, and sodium compounds; and (4) Silver Peak type produced mainly for lithium. Table 2 (Jones, 1973) affords an overview of the chief industrial minerals, the chemical products derived from them, and end uses of the products.

Jan 1, 1975

By R. J. Colony

DEPOSITS of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residua] limonite at the west end of the island near Mayaguez1-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7-9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugues, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By G. T. Engel, W. G. Gruzensky

Jan 1, 1960

This discussion was prepared by members of the Phelps Dodge Corpn. staff who were designated to review the minutes. It is confidential but permission has been granted to distribute copies among those who attended the Conference. The minutes of the above conference contain numerous references to the plants and practices of Phelps Dodge Corporation. As many of these references are inaccurate, the following notes are made covering such points: Construction Magnesite Brick in Reverb. Arch (1) An.18" arch, 20 feet long, was built on one furnace with 5 feet on each side of magnesite brick, the center portion .being of silica brick. The furnace was put in operation February 13, 1930 and on April 23rd after 68.8 days' operation it was replaced due to failure of the silica brick forming the center of the arch. At this time, while the silica brick had completely gone, there was 14" of magnesite left. Bridgewall Tapping (2) Tapping matte through the burner wall was first tried at the Copper Queen Smelter in April, 1925. At that time, a copper casting with 1 ½ extra heavy pipes for water cooling cast in it, and having one taphole block was used. Later, on the other (old) furnaces, similar castings, but equipped with two tapholes, were used. We found with these furnaces that we could tap through the burner wall at the beginning of a campaign, but would subsequently have to go back to side wall tapping. This was the case until sometime in 1926. The new furnaces, that went in operation at the beginning of 1927, each had water. cooled castings with two tapholes. These have been used entirely and have been quite successful. Sometime after the furnaces were put into operation sidewall tapholes were put in, simply for the removal of any accumulation of matte that might be temporarily retained at the front end by bridges or dams in the furnace formed by overcharging locally.

Jan 1, 1930

By James J. Halbouty, Michel T. Halbouty

Drilling activity in the South Texas area, which includes the South Corpus Christi and Laredo districts, showed a marked decline during 1941 from that of the preceding year. The rate of new discoveries, however, 'compared favorably with exploratory results of 1940 because of the many new productive sands opened in existing fields. South Texas completions for 1941 were about 12.3 per cent below the 1940 figure, compared with an increase of approximately 5.5 per cent in the total number of completions in the United States during 1941 over the 1940 total. During the year, 1452 wells were drilled in this area; of these, 1205 were drilled in or as extensions to the proven fields, and 247 were rank wildcats drilled in search of new producing pools. The comparable 1940 figures were: 1320 field or extension wells and 336 rank wildcats, a total of 1656 completions. This represents a decline in 1941 of approximately 8.7 per cent in proven-area wells, and of about 26.5 per cent in rank wildcats. It must be stressed that wells that were considered rank wildcats at the beginning of operations, but which opened production later classified as additions to existing fields, are not regarded as rank wildcats in this and previous annual reports on this same area. These wells are classified as semiwildcats (Table 2). There were 13 new oil or distillate fields and 4 new gas areas opened during the year, as listed in the next column. This listing represents a decline of 32 per cent from the 25 new areas found during the previous year, and to a great extent can be attributed to the 26.5 per cent decline in wildcatting. The rate of new discoveries based on the 247 wildcats was 14.5 to I, which compares somewhat unfavorably with the 13.4 to I ratio obtained in 1940 (Table 5). Dry wildcats totaled 230. The proof of the prolific character of the South Texas area as a source of petroleum reservoirs is to be found in the fact that of the 1205 field or extension (semiwildcat) wells completed during the past year 61 opened production from new sands or found crude in formerly distillate-producing sands. The 1940 total of 1320 such wells accounted for 50 horizons that provided either new production or crude in distillate sands, and in this respect the 1941 rate of discovery shows to greater advantage, the ratios for new sands being 19.7 to I for 1941 and 26.4 to I for 1940. The 1205 field or semiwildcat wells completed in 1941 resulted in 926 oil or dis-

Jan 1, 1942

By James J. Halbouty, Michel T. Halbouty

Drilling activity in the South Texas area, which includes the South Corpus Christi and Laredo districts, showed a marked decline during 1941 from that of the preceding year. The rate of new discoveries, however, 'compared favorably with exploratory results of 1940 because of the many new productive sands opened in existing fields. South Texas completions for 1941 were about 12.3 per cent below the 1940 figure, compared with an increase of approximately 5.5 per cent in the total number of completions in the United States during 1941 over the 1940 total. During the year, 1452 wells were drilled in this area; of these, 1205 were drilled in or as extensions to the proven fields, and 247 were rank wildcats drilled in search of new producing pools. The comparable 1940 figures were: 1320 field or extension wells and 336 rank wildcats, a total of 1656 completions. This represents a decline in 1941 of approximately 8.7 per cent in proven-area wells, and of about 26.5 per cent in rank wildcats. It must be stressed that wells that were considered rank wildcats at the beginning of operations, but which opened production later classified as additions to existing fields, are not regarded as rank wildcats in this and previous annual reports on this same area. These wells are classified as semiwildcats (Table 2). There were 13 new oil or distillate fields and 4 new gas areas opened during the year, as listed in the next column. This listing represents a decline of 32 per cent from the 25 new areas found during the previous year, and to a great extent can be attributed to the 26.5 per cent decline in wildcatting. The rate of new discoveries based on the 247 wildcats was 14.5 to I, which compares somewhat unfavorably with the 13.4 to I ratio obtained in 1940 (Table 5). Dry wildcats totaled 230. The proof of the prolific character of the South Texas area as a source of petroleum reservoirs is to be found in the fact that of the 1205 field or extension (semiwildcat) wells completed during the past year 61 opened production from new sands or found crude in formerly distillate-producing sands. The 1940 total of 1320 such wells accounted for 50 horizons that provided either new production or crude in distillate sands, and in this respect the 1941 rate of discovery shows to greater advantage, the ratios for new sands being 19.7 to I for 1941 and 26.4 to I for 1940. The 1205 field or semiwildcat wells completed in 1941 resulted in 926 oil or dis-

Jan 1, 1942

By Charles Hart

In this paper it is the author's intention to show the extent and character of foreign ores now known to be available; these deposits may be in active production or held in reserve until economic conditions may make them active. He hopes to show the relation existing between these ores and the American supply, and which of the former are now producing or will in turn come into production when our better ores have been exhausted. This phase of this discussion must of necessity include some data as to the present rate of consumption and a study of the changes we may expect here and abroad in the general steel trade and its sources of supply in raw materials. It is obvious that the occurrence of coal, ore and limestone in relation to one another and the proximity of a market are the elements in control of this feature of the problem. If the foregoing situation is favorable, all the other questions may be solved, for it is clear that with proper basic conditions finance, labor and operations will fall in line. We present a short outline of the present methods of carrying on the foreign iron ore trade, believing that it is of general interest in comparison with our own highly specialized methods, and that with the exhaustion of our better ores we will be compelled to seek a part of our supply abroad. A partial list of iron ores, with incomplete analyses (Table I), is added, to give a better understanding of the general situation and explain to some extent the reason for things being as they are in the iron and steel trade of the world and to help in bringing this paper to an informing conclusion. The question of the world supply of iron ores has been a subject for study on the part of geologists and engineers for many years, and found its best results in the Eleventh International Geological Congress, appropriately held at Stockholm, Sweden, in 1910. The proceedings are published in two volumes and are undoubtedly the best records available on this subject at the date of publication. It should be borne in mind, however, that much has happened in the 20 years since these figures were assembled. There is just as much known ore at present as at that time, minus the quantity consumed, plus newly discovered reserves. The World War had great effect upon this situation; during that time explorations were greatly reduced and the settlements after the

Jan 1, 1929

By W. H. Yarroll Discussion by W. A. Griffith

W. A. Griffith (Head, Research Department, Phelps Dodge Corp., Morenci, Ariz.) - It is gratifying to see the increasingly common use of classical statistical procedures by metallurgical researchers. Mr. Yarroll has given excellent illustrations of the utility of multiple correlation analysis of complex metallurgical data. Our experience in applying these procedures to historical plant operating data has differed, however, from that which he suggests. The uninitiated frequently assume that the volumi-

Jan 1, 1969

By C. F. Cornell, R. C. Emmett, D. A. Dahlstrom

FOR many years the disk-type and cloth-covered drum filters have found widest application in liquid-solids separation, which uses continuous filters. The disk type is less expensive, occupies less floor space per square foot of filtration area, and requires negligible down time for filter media changing. However, because filter cloth is billowed out by the blowback in the cake discharge, it is very short-lived if the scraper blades are set too close. Consequently cake weight is very important in assisting cake discharge, which normally necessitates a minimum cake thickness of 3/8 to ½ in. Also, the vertical position of the disks eliminates the possibility of efficient cake washing for removal of soluble values. The disk-type filter is generally limited, therefore, to applications that require no cake washing and form relatively thick cakes within the normal range of filter cycle times. The conventional cloth-covered drum filter is a more flexible unit, permitting wider variation in the percentage of cycle time devoted to cake formation, dewatering, or washing, as required by the application. Thinner filter cakes can be discharged because a horizontal line across the filter medium at the location of the scraper blade is equidistant from the edge of the blade at all points. The scraper blade therefore may be set a short distance from the filter medium or, where wire winding is not used, a floating scraper can be utilized so that the contour of the cloth can be followed. The drum filter is generally employed when there are difficult filtering slurries with resultant thin cakes or when cake washing to recover soluble values must be practiced. Difficulties sometimes encountered in continuous filter operation can be summarized in the following four categories: 1) Low filtration and/or washing rates due to blinding of the filter medium. 2) Poor cake discharge resulting from sticky cakes, filter medium blinding, or too thin a cake for the particular type of filter. 3) High filter media costs caused by short life and frequent down times for cloth changing. This results from blinding or from abrasion by the scraper blade when cakes are thin. 4) Blowback of filtrate at cake discharge because not enough air passes through the cake to purge the drainage area and filtrate lines during dewatering. To reduce or eliminate blinding tendencies several modifications have been tried, for example, cover-cleaning showers, blowback under the feed slurry, and snap-blow cake discharge. In many cases, however, this simply retards the rate of blinding, since the filter medium is kept clean at its outer surface only by these methods. As blinding usually occurs within or on the back of the medium, the operator is finally forced either to remove the cloth and scrub the medium intensively with a cleaning solution or acid-rinse it on the filter—all resulting in down time, short cloth life, and additional costs.

Jan 1, 1959

By M. Prats

Most of the information available on the heat efficiency of hot fluid injection processes, both water and steam, has been obtained from calculated temperature distributions in the pay zone and adjacent formations. The usual approach has been to write the heat balance equations in terms of the temperatures, and then to introduce whatever simplifications are necessary to help obtain an analytical or a numerical solution. In either case, the assumption has often been made that the vertical thermal conductivity in the flooded interval is infinite, so that the temperatures within the flooded interval are then independent of vertical position. Because it was first made by Lauwerier,l and has been used extensively since, this assumption will be referred to as the Lauwerier assumption. Excellent reviews of the literature on the heat efficiency of hot fluid injection processes have been given by Spillette,2 Flock et al.,3 and Ramney.4 Of course, the most significant contributions take into account the effect of a finite vertical thermal conductivity on the vertical temperature profile. The most general analytic expression for the heat efficiency of a hot fluid injection process is that of Antimirov5 who considers injection of a heated incompressible fluid into a reservoir through an arbitrary number of wells. The rate of heat injection into the reservoir, as well as the injection temperature, is an arbitrary function of time. The geometry of the horizontal flow is arbitrary, although the reservoir is considered to be of uniform thickness and properties and to be of infinite areal extent. Heat transfer within the reservoir is by horizontal convection and conduc- tion, and by vertical conduction. In the formations adjacent to the flooded interval, heat transfer is by conduction in any direction. Thus, the available expression for the heat efficiency due to hot water injection has been developed for rather general conditions. This degree of applicability has not been obtained for other thermal recovery processes. By making the Lauwerier assumption we have been able to obtain expressions for the heat efficiency that are essentially independent of the thermal recovery process, be it steam, hot-water, or underground combustion. Clearly, then, the approach followed here is more restrictive than that of Antimirov5 in that it uses the Lauwerier assumption. At the same time less restrictive assumptions are made about the horizontal heat transfer mechanisms, either in the flooded interval or in the formations adjacent to it. The main difference between our approach and that of other investigators is that the heat balance in the pay zone is expressed for the pay zone as a whole rather than for a volume element within it. The Lauwerier assumption is introduced after the problem is developed along these lines as far as possible. The details of the development of the heat efficiency are given in the Appendix, while the main features of the model are discussed in the next section. Results and their implications are discussed later in a separate section. The Model Certain assumptions have been made to determine

Jan 1, 1970

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

By C. C. Harris, A. Jowett, S. K. Ghosh

An equation derived from first-order kinetics and accounting for return from froth to pulp has correlated continuous flotation data. The concentration of floatable material in the pulp can be altered either by changing the feed concentration or the feed rate. The latter does not affect the flotation rate constant, the froth to pulp return constant, and the concentration of non-floatable material in both the pulp and concentrate. Both the return constant and the concentration of non-floatable material in the pulp are directly proportional to the feed concentration, while the concentration of non-floatable material in the concentrate is related to the feed concentration. The investigation of the froth flotation process by continuous test methods, previously used by Brown and smith,1 Jowett and Safvi2 and Jowett and West,3 is being continued. Recent tests, primarily concerned with flotation cell design, have yielded kinetic data suitable for testing an equation proposed by Arbiter and Harris4 which postulates that a flotation process is defined by two rate constants: 1) the rate constant for mass transfer from pulp to froth. Previous workers have regarded this as the flotation rate constant. 2) the rate constant for mass transfer from froth to pulp, which has previously been ignored. THEORY Under continuous flow conditions at the steady state in Fig. 1 the equation developed4 is Symbols are defined in Table I. The air-liquid ratio terms4 have been omitted, since they are substantially constant for a given set of conditions. Also, for a system operating at the steady state Vf and V, remain constant and Eq. 1 can be written: Cp/Cc=b'/a,+Qc/a' [2]

Jan 1, 1963

Organization Place Date 1919 American Society of Civil Engineers..: Twin Cities, Minn. June 17-20 American Society of Mechanical Engineers Detroit, Mich. June 17-20 American Institute of Chemical Engineers Boston, Mass. June 18-21 American Drop. Forge Association Pittsburgh, Pa June 19-21 American Institute of Electrical Engineers Lake Placid, N. Y. June 24-27 American Society for Testing Materials Atlantic City, N. J. June 24-27 Society for Prom. of Engng. Education Baltimore, Md. June 25-28 American Chemical Society Philadelpia, Pa. Sept. 2-6 National Assn. of Stationary Engineers Huntington, W. Va. Sept. 8 American Peat Society.. Minneapolis, Minn. Sept. 22-24 American Iron; Steel Electrical Engineers St. Louis, Mo. Sept. 22-26 American Institute of Min. and Met. Engineers, Chicago, Ill. Sept. 22-27

Jan 6, 1919

By Ogden Malin

IN conducting the manufacture of extruded brass rods and brass forgings it has been noticed that there is considerable variation in the physical properties, particularly the machinability of different rods and forgings, even though the composition, working temperatures and method of manufacture remain the same. It is the purpose of this paper to attempt to establish the cause and extent of this variation, and also to determine whether variations in composition within certain defined limits influence hardness and machinability to any marked degree. The writer believes that this variation probably is due to the variation in grain size of the metal, therefore the microstructure of several compositions under various conditions of working were examined in an effort to establish this as a fact.

Jan 1, 1932

ONE DAY IN the mid-1880s, in a suburb 0f Pittsburgh, Pennsylvania, there dismounted from a train the two foremost leaders of the day in the coal and steel industries-Andrew Carnegie and H. C. Frick. Their attention was drawn to a well-loaded car of coke, which their experienced eyes recognized as a superior product. "I'll bet you that coke is from the H. C. Frick Coke Company," Mr. Frick challenged. "I'll bet it was shipped by my company." In a spirit of fun Mr. Carnegie accepted the wager. Mr. Frick lost the bet: the coke had come from M0rewood, one of three sites being operated under the direction of a young entrepreneur, Erskine Ramsay. If Mr. Frick's confidence was somewhat dented by this occurrence, the responsibility was his own. He himself had opened the way for Erskine Ramsay to become the youngest of mine superintendents; and he had dispersed all dissension regarding his choice with the words : "I'm not interested in his years, I'm interested in his record. He makes more coke in an oven than any other superintendent. And I'll take 'em out 0f the cradle if they can make coke... Suppose he is only twenty years old? ... The d --- kid is a genius, I tell you." Erskine Ramsay was to follow in the tradition of Carnegie and Frick. Not only was he ambitious and a worker his background had prepared him for it. Coal mining was in the Ramsay blood. His father, Robert Ramsay, of whom the son once stated that he had no superior as coal mining and mechanical engineer in this country, once accounted in these words for the phenomenal accomplishments which had attached to the name "It does no harm to belong to a family of mining engineers who are just as good as any in America-if it is myself that says it." Anyone acquainted with Robert Ramsay's character realized that he was not given to overstatement. And the above-mentioned Mr. Carnegie encountered young Ramsay again, a few years later in his career, and wrote of him to young Erskine's father, that he was "going to be a credit `tae us a' " (a quotation from Robert Burns.) Nor have Mr. Ramsay's achievements been identified exclusively with the industrial field in which he early asserted himself. He has been an inventor whose techniques in mining engineering have received international recognition. As an investor of foresight, he has benefitted others immeasurably, as well as himself, being an influential factor in the upbuilding of several communities in his chosen and well-loved adopted home state of Alabama since 1887. He is a philanthropist whose benefactions have run into millions, the chief beneficiaries being educational and charitable institutions. Amidst his accomplishments the lighter side of life has not been neglected and he is known for his hospitality, his

Jan 1, 1953