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By W. A. Anderson, F. N. Rhines, W. A. Johnson

The rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish- able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1942

By J. H. Hollomon, J. C. Fisher

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

By H. L. Sauder, J. L. Newman, C. Waddell

An instrument capable of measuring subsurface flow rates is described. The instrument is self-contained and may be run on piano wire line. It detects flow by means of an impeller suspended between two torsion wires. The force of the well fluid striking the impeller causes the impeller to rotate, exerting a torsional force to the wires. This force is determined by recording the angle of rotation of the impeller on film using a battery-driven, clock-controlled camera. The impeller is sensitive to flow in either direction and the same instrument can be used to measure injection as well as production rates. Changes in direction of flow, such as might be caused by thief zones, are measurable and are indicated by a reversal of the direction of rotation of the impeller. Adjustment of the sensitivity of the instrument to measure a wide range of flow rates is accomplished by the use of different size torsion wires. An umbrella-type fluid trap, which contacts the casing or wellbore, diverts the flow through the flow tube. The fluid trap remains closed while rurrning in the hole and can be opened at any point in the well. The instrument with the trap closed is 1 3/4 in. OD and may be run through 2 in. tubing. Successful flow profiles have been made on wells with flow rates ranging from 60 BID to 4,000 B/D at surface pressure up to 4,500 psi. The instrument is designed for high-pressure and high-temperature operations. INTRODUCTION The need for an instrument that will measure flow rates in a wellbore is as old as reservoir engineering itself. A number of such devices have been designed within the past few years. Some of these have been described in the literature1,2,3,4,5,6 One of these devices1. a hot-wire anemometer type, made many successful jobs in dry gas producing areas. Difficulty was encountered when this flowmeter was used in wells producing liquids and development work was initiated to overcome this difficulty. The present flowmeter is the result of this work and provides an instrument with a wider range of application in the industry. Consider- able development work has been done on the tool involving many changes in the mechanics of recording the flow readings, however, the basic principle of flow detection has remained the same since its inception. PRINCIPLE OF OPERATION The basic principle of operation of the flowmeter is the utilization of a portion of the kinetic energy of flowing well fluid to impart a rotational force to an impeller suspended between two torsion wires. This impeller, Fig. 1, is a screw-type propeller with the blades having a pitch angle of 40. As the well fluid passes through the instrument it strikes the impeller. The resulting force rotates the impeller and twist\ the torsion wires to a balance point at which the torque imparted to the wires balances the force required for the impeller to deflect the well fluid. The impeller is symmetrical and a change in direction of the flow results in a reversal of the direction in which the impeller is deflected. Thus the direction of the flow as well as its velocity is indicated. A dial is attached to the impeller by means of a hollow tube through which the upper torsion wire extends. The angular position of the impeller is recorded by photographing the dial at frequent intervals. In any given set of torsion wires the modulus of shear and polar moment of inertia remain constant and the deflection varies directly with the applied torque. The deflection imparted to the torsion wires also varies as the square of the fluid velocity. Further, the velocities represented by any two given deflections hear the following relationships: and Where V = velocity of flow stream and O ;= deflection. This is the basic relationship which is used to calculate the relative velocities represented by a given set of deflections where the velocity represented by any one of the deflection readings is a known quantity. For a given torque, the deflection of the torsion wire varies inversely as the fourth power of the wire diameter. Wire sizes ranging from ,005 in. in diameter to .022 in. in diameter can be used. The range of

Jan 1, 1957

By J. S. Miller

This paper describes the method of mining a steeply pitching anthracite seam on a heavy pitch in the Orchard vein in No. 1 Tunnel of the Lehigh Coal and Navigation Co. The Orchard vein in the Neaquehoning district has a thickness of about 15 ft. on the level of the gangway, which is sufficient thickness for the gangway to be driven full width in coal. Above the gangway, the vein becomes thinner and near the surface is about 8 it. thick. The coal is of good hard quality and carries a fairly good roof. The pitch of the vein is between 65" and 70". Usually the breast-and-pillar method has been employed in the mining of the steeply pitching veins in this section. This method produced good results as far as the mining of the breast was concerned but the recovery of the pillar was difficult as to full extraction and expensive as regards costs. To recover these pillars after the breasts were driven, three methods were commonly employed; they were known as the pillar-breast method, pillar-skipping method, and pillar-chute method. The pillar-breast method consisted in putting a battery in one corner of the pillar (Fig. I), coupling the manways A and B of the two adjacent breasts for two or three lengths ahead of the working face of the pillar being cut, and working the pillar as a breast. This method was used by the more skilled miners of the earlier days but has practically been abandoned. A slight variation of this method is used to some extent. In this case, the pillars are left wider than ordinarily and of sufficient width for the full-width breast to be driven in and a small pillar left on each side of the pillar breast between it and the regular breasts. With the completion of the "pillar breast," the ribs are drilled full of holes, loaded, and fired. In the pillar-skipping method (Fig. 2), the middle breast of three is not driven through and is drawn empty while the outside and inside breasts are kept full. At the corners of the two pillars standing, batteries are put in and a skip of the two pillars started; the coal in the two pillars is blasted over into the empty breast. A small pillar is kept along the

Jan 1, 1925

By Michael Shaughnessy, O&apos

The outstanding features of the Coloinbian situation for the year 1929 were legal and political. The passage of Law 84 and the promulgation of the Regulatory Decree 150 were recounted in the review for 1928, as was also the Presidential proclamation suspending this law and its accompanying decree until decision could be reached in the suits filed against them before the Supreme Court and the Council of State. Early this year the Minister of Industries, Jose Antonio Montalvo, announced the appointment of a commission of foreign experts to aid in drafting a new petroleum law. He requested all of the foreign experts employed not to consult with the oil company representatives in Bogota, and these experts were therefore shut off from receiving any suggestions from those who had actually operated in the country and knew the conditions under which operations would take place. It was to be expected that the provisions of a law suggested under such circumstances would not meet operating conditions satisfactorily. The specific objections are stated in O'Shaughnessy's South American Oil Reports (April, 1929). An especially qualified commentator observes that one of the curious provisions of the proposed law was the high royalty on gas—5c. per 1000 cu. ft. of gas produced. There was also a provision requiring 20 per cent. of the stock of the company operating in Colombia to be offered for sale to Colombians. The bill failed to pass Congress in the closing hours of the session. The Supreme Court, in the meantime, handed down its decision on Law 84 of the previous year and Regulation 150 covering the enforcement of that law. Contrary to expectation, the majority opinion of the Court practically affirmed the constitutionality of both the law and the regulatory decree, with the exception of Article 20 and parts of Article 21 of the decree which referred specifically to the registration of private properties. At the time the suit was filed against Law 84 and Decree 150 the operation of these measures was suspended by the Executive. Law 84 and its Regulatory Decree 150 still remain suspended as the Council of State has not yet brought in a decision upon the questions raised in the suits instituted by the various companies against the law and decree, and at the moment of this writing it appears unlikely that such a decision will be reached by that body.

Jan 1, 1930

By Stanley C. Herold

A few hates on the occurrence and significance of mud volcanoes in Colombia may be of interest at the present time, owing to the renewed activity in geological exploration of the coastal regions bordering the Caribbean Sea. The best-known volcanoes are found a few miles from the seacoast. One is situated to the south of Puerto Colombia; the second, to the east of Cartagena near the village of Turbaco; and the third, near the village of Puerto Escondido south of the Sinu River. Others are reported in more inaccessible localities. Usually they stand 2 1/2 or 3 ft. (0.762 or 0.914 m.) above the surrounding ground at the crater, though several craters from 10 to 20 ft. -(3.04 to 6.09 m.) "apart will often build up an extensive mound at low gradient. The shallow mound may cover 1/2 or 3/4 acre (0.2 to 0.3 ha.) with an elevation of 12 or 15 ft. (3.65 or 4.57 m.) at the, center. The craters are formed of hardened blue clay; the inside diameters vary from 14 to 24 in. (35.56 to 60.96 cm.). The rim is continuous, except on one side where there is usually a cut 3 or 4 in. deep, thus allowing an overflow. The craters are filled to the' rim-cut with a thick mixture of blue clay mud and water, which is kept in agitation by escaping gas. Fig. 1 shows the bubble in the act of bursting and Fig. 2 the appearance of the surface of the viscous fluid a second or so later. The frequency of the explosions is determined by the weight of the column of fluid in the neck of the volcano, consequently, such explosions are not synchronous in a group of craters. Ordinarily, there arc two or three explosions in about 3 minutes. The supply of gas is small but steady and sufficient pressure must accumulate before the bubble can enter the column of fluid. The water is derived from the surface and enters the scdirnentary strata not far distant from the volcano. During long dry seasons, as the supply of water fails the volcano dries and geyser action ceases. The temperature of the muddy fluid is normal; the gas is dry and inflammable. - No petroleum products come with the gas. On the surface of the fluid, there is sometimes a dark brown streaky scum, which

Jan 1, 1920

By R. E. H. Pomeroy

The statistical data given in this paper are taken from the actual performance of the No. 2 reverberatory furnace of the Nevada Consolidated Copper Co., Mc Gill, Nev., for a period of four months, from April to July, 1914. The principal furnace dimensions are: Length, 132 ft. % in. at the skim-line level; average width, 18 ft., 10 in. at the skim-line level. The roof is 7 ft. above the skim-line level at the firing end. The average area in the uptake flue is 36 sq. ft., and the area above the skim line under the vulcatory arch is 24.3 sq. ft. Fig. 1 shows a diagrammatic plan and sectional elevation of this furnace. The furnace is equipped with two 400-b.h.p. Stirling waste-heat boilers set in parallel. California crude petroleum is used for fuel and has a specific gravity of 16.5" B., flashing in open test at 199" F. The oil is heated to about 200" F. in a steam heater before going to the burners, requiring about 9 b.h.p. per furnace day to heat it from the line temperature to the burning temperature. Measurement is made by oil meter, checked daily by reservoir readings. The oil is fed by gravity (34 Ib. static pressure) to seven low-pressure blast burners of the Steptoe type (Fig. 2). The blast for these burners is supplied at about 40-08. pressure by a motor-driven Connersville blower of 42 cu. ft. capacity per revolution. The air supplied by the blower through the burners for atomizing the oil amounts to about 10 per cent. of the theoretical air necessary for complete combustion of the oil. The remainder of the necessary air enters the furnace through the burner openings in the firing wall. No checker holes are provided, and the charge holes in the roof are equipped with slide gates and " dog houses" to minimize air leakages. The combustion of the fuel, as shown by gas analysis at the front of the furnace, is practically complete, the carbon monoxide in the gases being less than 0.5 per cent. The draft at the firing end of the furnace is 0.18 in. of water. At the throat or in the uptake above the "verb" the draft is about 1 in.

Jan 1, 1915

By Arthur S. Dwight

We author of this historical chapter will perhaps be criticized for limiting his subject to the history of the blast furnace in lead smelting, and especially to the part it played in the great custom ore-smelting business which for three decades or more was the means of opening up vast mineral treasures and practically dominated the mining industry in the Rocky Mountain region of the United States, in Mexico and in Canada. The men of that era shared the romance and the thrills of mining, and bore their part as pioneers in the building of the great West. The present writer was too young to participate in the first of the three decades mentioned, but immediately thereafter came under the apprenticeship of some of the men who had worked out the early metallurgical problems of the industry, became personally acquainted with most of the others of that group, heard the tales of early experiences, successes and failures, the gossip of the frontier and mining camps, from all of which there remain embedded in his mind clear impressions of the outstanding personalities of that time. That is the background against which the fifty years of intimate contact with the mining and smelting business and his own experiences as metallurgist stand out in his memory, and it is hoped that the gentle reader may understand and approve his desire to rescue from comparative oblivion the fundamentally valuable results accomplished by these fathers of the industry. It will be the purpose of this chapter first to narrate the general history of the growth of the industry; second, to pay tribute to some of the pioneer metallurgists, and third, to discuss some of the salient points of the metallurgical practice at different periods, to illustrate the technical progress of the art. The series of eight Annual Reports of Rossiter W. Raymondl,† U. S. Commissioner of Mining Statistics from 1869 to 1876, contain most of the available information about the early smelting operations in the Rocky Mountain region, and much is in the early volumes of the Transactions of the American Institute of Mining Engineers. The monograph by S. F. Emmons2 though not published until 1886, contained an elaborate description of the smelting works operating in 1879. Otto H. Hahn3 wrote a valuable paper in 1883, on smelting prac-

Jan 1, 1937

By P. W. Rainier

The Chivor emerald field is situated on the eastern slope of the Andes in the Department of Boyach, at an elevation of about 8000 ft. above sea level. It overlooks the Llanos (plains) of the Orinoco and is watered by many streams flowing into the Rio Meta, the Orinoco's largest tributary. The Rio Meta is navigable from the Orinoco to a point within about 50 miles of the Chivor district and may eventually prove to be the reasonable outlet for the future development of this part of the country. The topography of the district is extremely rugged and mountainous (Fig. I), the difference in elevation between two points on a mining claim 1 km. square being sometimes as much as 4000 ft. The ground is covered with dense forest growth and the available timber is suitable and sufficient for mining purposes, but it is becoming gradually depleted by Indian clearings as the country around the mines becomes settled. The many streams combined with the rough topography give good possibilities for hydroelectric power. The center of population nearest to Chivor is Bogoth, the capital of the republic and a city of some 300,000 inhabitants; the distance is two and one-half days' travel. The first stage of the journey from BogotB is accomplished by rail to Choconta, some 4 hr. travel. From Choconth the journey is made in the saddle, one night being spent in Guateque. The latter is a small town and the nearest post office to the mines, being some 10 hr. ride distant. The roads are mere bridle paths, in parts hazardous and almost impassable in the wet season. All supplies brought to the mines, other than those produced locally, are carried by pack mule; mule freight from Choconth costs 3 centavos1 per pound. The climate of the Chivor district is healthful and bracing. The wet season begins in March and concludes in November, the remaining months being dry. The annual precipitation is about 130 in. The temperature throughout the year is nearly constant, varying from about 45" F. to about 65" F. shade temperature. The rains are cold and unpleasant, and for the greater part of each day in the wet season the country is shrouded in dense mist. A fire can with comfort be kept burning in a living room all the year round. There are a few slight

Jan 1, 1931

By J. J. Rutledge

On Sept. 4, 1914, Mine No. 1 of the Union Coal Co., Adamson, Oklahoma, suddenly caved, entombing thirteen miners whose bodies were never recovered. The seam of coal mined, the Lower Hartshorne, averaged 5 ft. in thickness and dipped at an angle varying from 22" to 30n. The strata overlying the coal seam were sandstones and shales. The mine was worked by the pillar-and-room method, the rooms being driven directly up the dip of the seam. All coal was blasted off the solid. Rooms were turned on short centers and room pillars were thin and irregular, as shown in Fig. 1. Fig. 2 is a cross-section of the form; showing the mine workings. Some cracks had been observed on the surface, it is said, at least a month before the squeeze occurred, but the collapse of the mine workings came very suddenly. As is usual when squeezes occur on such steep dips and the pillars fail, the crush progressed rapidly down the dip until it reached solid coal; there was a line of break, or draw, over in the solid coal. Several well-defined cracks appeared on the surface, after the mine had squeezed, but there was no appreciable subsidence of the surface, the weight seemed to be thrown entirely to the dip. About one year after the squeeze, and after the workings of the adjoining mine, NO. 4, had been retimbered and made safe, the writer inspected the tenth north (right) entry, or lift, off of No. 4 slope, which was below and fairly near the lowest caved portion of mine No. 1. The roof shale was composed of thin layers, which had been bent in somewhat the same manner as the leaves of a book having flexible covers are bent when the book is folded or rolled up in the hands. Though the mine workings are immediately beneath the streets and buildings of the mining town of Adamson, business was not disturbed by the squeeze, so far as any subsidence of the surface was concerned. No surface monuments were available and no elevations were taken, but the mine workings had been accurately surveyed and traversed, and the streets of the town overlying the mine workings had been carefully platted on the mine map, so that it was possible to locate accurately the cracks on the surface.

Jan 1, 1923

By J. J. Rutledge

On Sept. 4, 1914, Mine No. 1 of the Union Coal Co., Adamson, Oklahoma, suddenly caved, entombing thirteen miners whose bodies were never recovered. The seam of coal mined, the Lower Hartshorne, averaged 5 ft. in thickness and dipped at an angle varying from 22" to 30n. The strata overlying the coal seam were sandstones and shales. The mine was worked by the pillar-and-room method, the rooms being driven directly up the dip of the seam. All coal was blasted off the solid. Rooms were turned on short centers and room pillars were thin and irregular, as shown in Fig. 1. Fig. 2 is a cross-section of the form; showing the mine workings. Some cracks had been observed on the surface, it is said, at least a month before the squeeze occurred, but the collapse of the mine workings came very suddenly. As is usual when squeezes occur on such steep dips and the pillars fail, the crush progressed rapidly down the dip until it reached solid coal; there was a line of break, or draw, over in the solid coal. Several well-defined cracks appeared on the surface, after the mine had squeezed, but there was no appreciable subsidence of the surface, the weight seemed to be thrown entirely to the dip. About one year after the squeeze, and after the workings of the adjoining mine, NO. 4, had been retimbered and made safe, the writer inspected the tenth north (right) entry, or lift, off of No. 4 slope, which was below and fairly near the lowest caved portion of mine No. 1. The roof shale was composed of thin layers, which had been bent in somewhat the same manner as the leaves of a book having flexible covers are bent when the book is folded or rolled up in the hands. Though the mine workings are immediately beneath the streets and buildings of the mining town of Adamson, business was not disturbed by the squeeze, so far as any subsidence of the surface was concerned. No surface monuments were available and no elevations were taken, but the mine workings had been accurately surveyed and traversed, and the streets of the town overlying the mine workings had been carefully platted on the mine map, so that it was possible to locate accurately the cracks on the surface.

Jan 1, 1923

By Tomek Ulatowski

This presentation discusses the necessary ingredients for the creation of an acceptable credit structure, i.e., the structure that enables the borrower to attract the funding from different groups of lenders. As the amount of debt in the capitalization of new projects increases, it becomes quite critical that the mining venture sponsors obtain funding in a manner which maximizes the project economics. Attention normally is focused on the inherent operating cost characteristics of a venture such as the cost of mining, milling, transportation, smelting, and refining. The projected costs are derived from lengthy feasibility studies often taking millions of dollars and years to prepare. For a variety of reasons as the amount of equity directly provided by the sponsors declines, the balance must be made up from external credit sources. As a result, once the project becomes operational, debt service requirements assume crucial importance. For most new ventures, in the early years of production, the total amount of periodic debt amortization charges together with the projected interest expenses equals or exceeds the total operating cost. Utmost care must be taken, therefore, to reducing these costs which will then increase the chances for the implementation of the project. Project sponsors must carefully evaluate different funding sources in terms of their potential economic impact and, concurrently, evaluate alternative credit structures in order to be able to attract the selected funding vehicles. In this presentation I will discuss credit sources in the order of their relative appeal; i.e., from the standpoint of maximizing rates of return to the project owners. The tenor of the credit, that is the period from signing a loan agreement to the time of last repayment under the loan agreement, is undoubtedly the most important variable in evaluating the attractiveness of debt sources. Therefore, I will begin by discussing debt sources with the longest maturities and will end with a description of credits with relatively shorter tenors. The availability of different funding possibilities will naturally depend on the geographic location of the proposed venture, the creditworthiness of the borrower and the sponsors, the project economics, and finally the actual liquidity conditions in the capital markets at the time that the funds are committed. U.S. LONG-TERM DEBT MARKET - PUBLIC OFFERINGS AND PRIVATE PLACEMENTS The long-lived nature of most mining projects dictates that the majority of the mine financing be raised from long-term sources. In today's world capital markets U.S. debt issues probably carry the longest maturities available. The maturities can range from 5 to 40 years. Various types of long-term corporate debt instruments can be differentiated from one another by their terms, seniority as to claims against the assets of the issuer, legal form, and whether issued privately or through a public offering. The terms of these debt issues vary widely. For example, the interest rate which is typically fixed at the time of issuance, is determined by the credit quality of the issuer, the maturity, the average life, the seniority of the debt, the quality of control covenants or type of assets pledged as security, and other exogenous factors such as: economic policy, general level of interest rates and cur-rent level of financing activity. The entire principal amount of the debt may be due and payable at maturity (known as a "bullet" maturity) or, more typically, through periodic repayments in equal or staggered amounts. Almost all such debt issues allow for prepayment at the option of the issuer, but require varying amounts of repayment penalties. Disbursements are made over a relatively short period after signing of the debt documentation which may not coincide with the actual funding needs of the project. Financial covenants can be quite stringent, covering areas such as the issuer's financial leverage, working capital, payment of dividends and other distributions, merger and acquisition activities, and limitations on the disposition of property. Long-term debt issues may also be distinguished by the seniority of their claims against

Jan 1, 1985

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By W. A. Tiller

The unidirectional freezing of a semiinfinite liquid from one end has been treated by calculating the solute and temperature distributions in the liquid and solid phases with time, when the solid-liquid interface advances at a rate proportional to (time)lt2. The nucleation probability for new grain formation is calculated as a function of the constitutional and thermal properties of the alloy, the pouring conditions and the catalytic efficiency of the nucleating agents. The transition from columnar crystal formation to equiaxed crystal formation is assumed to occur at a critical nucleation frequency for a particular alloy and the quantitative dependence of the ratio (columnar zone length/equiaxed zone length) upon the freezing conditions has been predicted. The effects of (i) fluid flow in the liquid, (ii) heat transfer through a mold wall, and (iii) a finite ingot length, have been explicitly tveated as departures from ideality. These departures from ideality are found to have very important consequences on the ingot stmcture. In Part I&apos; of this series, a qualitative description of the general ingot structure was developed. The factors that determine i) the ratio of the equiaxed zone length to columnar zone length and ii) the grain sizes in these zones, were discussed. In the present paper, topic (i) will be treated quantitatively, and it is intended that topic (ii) will be treated quantitatively in Part 111. The complete treatment has been split in this manner for ease of development and coherency of presentation. The treatments are quite mathematical in nature and, although some of the conclusions to Part 11 depend upon the treatment presented in Part 111, it was felt that the intended audience would find the material more readable and more useful in its present form. To this same end, it seems worthwhile to reiterate some of the qualitative aspects of grain nucleation during ingot solidification before embarking on the mathematical description. QUALITATIVE ANALYSIS In the conventional method of casting, a liquid alloy with a certain degree of superheat is poured into a mold. The outer rim of liquid metal cools rapidly to the liquidus temperature of the alloy and begins to undercool. As the degree of undercooling increases, nuclei of solid begin to form in this chill layer, this nucleation being catalyzed by certain heterogeneous particles in the liquid. The grains in the chill layer which are generally of random orientation, begin to grow inwards because of heat conduction through the mold. The grains usually develop a columnar shape since the frequency of nucleation of new grains in the liquid ahead of the advancing interface is generally insufficient to seriously impede the growth of the original grains. Due to the slow diffusion rate of solute in the liquid, a solute distribution is formed in the liquid adjacent to the interface which is either an excess or a depletion if the partition coefficient, ko, of the solute is < 1 or > 1, respectively. Thus, the liquidus temperature of the liquid adjacent to the interface is a function of position. The actual temperature in the liquid is also a function of position and the temperature gradient at the interface decreases as the interface moves away from the mold wall. Since the rate of advance of the interface decreases with time, the equilibrium temperature distributions and the actual temperature distributions as a function of interface position, X, can be illustrated as in Fig. 1. Thus, a region of liquid may exist in which the actual temperature is below the liquidus temperature. This liquid is contitutionally supercooled and therefore unstable with respect to the nucleation of new grains. Now, since the supercooling in Fig. 1 increases as the interface moves further away from the mold wall, the nucleation rate of new grains will increase. When the nuclea-

Jan 1, 1962

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system&apos;s behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell&apos; have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine&apos; have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.&apos; A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz&apos;s model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965

By D. O. LIVINGTON

(Presented by invitation at a meeting of the Spokane Local Section of the institute, Feb. 17, 1912.) THE Pilares de Nacozari mine is located in Sonora, 75 miles south of Douglas, Ariz. The town of Douglas is on the International Boundary and is the place at which the ores from the Bisbee mines are smelted. The Moctezuma Copper Co. owns the mines at Nacozari, and the copper-concentrates shipped to the Copper Queen smelter, at Douglas, make a good smelting-mixture with the Bisbee ores. The Moctezuma Copper Co. and the Copper Queen smelter at Douglas, as well as the railroad from Douglas to Nacozari, are owned by the Phelps Dodge Co. The ore-deposit occurs in the form of a large ellipse with a major axis of approximately 2,000 ft. and a minor axis of about 600 ft., the major axis bearing about 90 W. of N. The whole of this ellipse is more or less mineralized; the surface being principally an iron gossan with some occasional copper-stains. Below the oxidized zone, which is not more than 50 ft. deep, the minerals are pyrite and chalcopyrite, with occasional seams of chalcocite, the latter being rare. There appears to be no well-marked zone of secondary enrichment, the oxidized gossan over the greater part of the deposit changing suddenly to what is apparently the original unaltered ore. The copper-values are concentrated around the perimeter of the ellipse, and it is principally around this perimeter that the mining is done. The ore mined averages a little more than 3 per cent. of copper, with a small amount of silver, less than an ounce per ton. Some ore of considerably higher grade than this has been shipped, however, but the above average is of the mill-run. The ore is wider near the two ends of the ellipse than along the sides, and is mined in some cases to a width exceeding 200 ft. The country-rock for the first vertical 500 ft is a volcanic acid breccia, probably rhyolitic; below

Sep 1, 1912

By N. H. Emmons

THE work of a consulting engineer or manager, when controlling mining-operations, requires that he have all the information concerning the mine in as concise a form as possible, and as the ore-reserves and their depletion and enlargement are the vital points to be studied, it is well to have them kept up to date and in some convenient form. The present paper describes a method adopted by me, which shows in a very clear manner the ore-reserves in a mine. The case illustrated is that of a vein near enough to the vertical for the vertical elevation of the mine to be the main working-map. A flat ore-body would be represented on a similar plat, but instead of the horizontal thickness of the vein being shown in the circles, the vertical thickness would be inserted. Fig. 1 represents an ideal longitudinal elevation of a mine, plotted in the ordinary way, using 100-ft. blocks and section-lines. In a mine where the block-numbers are posted by the engineer underground, the system of keeping the ore-tonnages extracted from the different blocks is easily maintained, and the actual tonnages of ore extracted can be kept so that the surveyor can have a check on his estimate from time to time. The ore-reserve sheet, Fig. 2, should be the same size as the map it is to accompany. Each square is used for the description of the ore-reserve in the block it corresponds to on the elevation. Where the section-lines cross the levels a circle is drawn, in which are written the widths of ore at that point, these widths being used in the calculations of each block cornering in the circle. It has been found convenient to show the figures in black in the lower half of the circle when the actual widths of ore are known, and when it is necessary to make up the figures of probable ore, as at the time of making

Jun 1, 1912

By Otto W. Nuttli

THE magnetic method of prospecting is well suited to determination of faulting in the basement rock. In addition to establishing the horizontal position of the fault, it often furnishes valuable information concerning the depth and amount of faulting. Consider a simple case of a vertical fault, represented in cross-section in Fig. 1. Let A A&apos; represent the plane of observation (ordinarily the surface of the earth), and BB&apos;B"B"&apos; the upper surface of the basement. Assume that the sedimentary rocks are nonmagnetic, so that the magnetic susceptibility of the material above the basement is zero. Let k indicate the susceptibility of the basement rock, c the density contrast between it and the neighboring sedimentary rocks, and the amount of vertical displacement. Fig. 1 shows the material, indicated by cross- hatching, which gives rise to the magnetic anomaly. In most cases it can be assumed that is small compared to the thickness of the sedimentary rocks. The semi-infinite, rectangular slab of rock of susceptibility k, density contrast , and thickness t may then be replaced by a semi-infinite sheet CC&apos; of mass t per unit area at depth 2 (the mean depth of the slab). Nettleton 1 states that this approximation results in an error of less than 2 pct for the computed gravitational field intensity when t is as great as 2/2 and decreases rapidly for smaller values of t. By a theorem of Poisson, the magnetic field intensity can be determined readily from the gravitational field. The theorem states that W = (I/) • (U/i) i1 [1] where W is the magnetic potential associated with the structure, I is the intensity of magnetization which is assumed to have the direction of the inducing field, ? is the constant of gravitation, the density contrast, U the gravitational potential associated with the structure, i the direction of the inducing magnetic field, and i1 a unit vector in that direction. The multiplication indicated in Eq. 1 is

Jan 1, 1956

IN describing the mining and treatment of ore at the Broken Hill Proprietary mine E. J. Horwood, superintendent of mines, gave the following account of the development of flotation there. It was in 1902 that the recovery of zinc from the ore by flotation was hit upon. The former general man-ager, Mr. Delprat, directed our then research officer, Mr. Carmichael, to try boiling the tailing with salt cake of which there was a considerable tonnage left over from the leaching process. The idea was the possibility of dissolving the zinc. Carmichael made the. Experi-ment, but, rather discouraged, took the glass beaker down to the general manager&apos;s office, remarking that he could not get the stuff to settle. On showing the beaker to Mr. Delprat, the latter recognized the marked distinction between the black scum on the surface and the rest of the tailings, and exclaimed: "Why, this is the very thing we are after; the zinc is floating!" Patents were applied for at once, but later on it was found that another investigator, Potter, had already hit upon the idea of flotation. His patents, however, were so involved with other operations that his process was impracticable. Litigation followed, but in the end the B. H. P. paid the Potter Company a substantial sum as settlement. In the case of Carmichael&apos;s beaker, the acid in the salt cake acted on the small amount of carbonate present in the ore, producing CO. bubbles. Owing to the aversion of sulfide crystals to being wetted, the gas as generated attached itself to the zinc in in-creasing quantities until there was sufficient to buoy the zinc particle to the surface. This action went The next problem was to apply the principle on a commercial scale, and this involved much experiment and developmental work. Various kinds of sloping copper pans with gas jets below to maintain the tem-perature were first tried, but were found too slow and too costly in operation.

Jan 6, 1928