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By J. B. Newkirk

Results of a Debye-Scherrer X-ray investigation are given which show that the order-disorder transformation is a first-order or heterogeneous reaction in Cu-AU alloys with compositions near CuAu. Evidence was found for conventional tie-line segregation across a usual type of two-phase field separating the ordered and disordered fields in the Cu-Au equilibrium phase diagram. The horizontal and vertical widths of the two-phase fields are about 3 atomic pct and 20°C, respectively, at 43 and 54 atomic pct Au. No evidence for the existence of an ordered structure based on a stoichiometric composition of Cu3Au2 could be found. ALTHOUGH the modern theories relating the de-Agree of order of binary alloys to temperature and composition have met with considerable success, the nature of the transformation from the disordered state to the ordered state and vice versa has never been well understood. It has been assumed by some' that this is a second-order transformation, that is, a homogeneous change of state. Others2 hold that the transformation is first-order and that the effects characteristic of heterogeneous phase transformation apply. Since this subject is discussed in detail in a recent paper,' the arguments will not be repeated here. The present paper summarizes an experiment which was designed to distinguish between these two viewpoints for the case of Cu-Au alloys near the composition CuAu. The Cu-Au system is an important one because it furnishes prototype alloys, the behavior of which has formed the basis of much of the present-day order-disorder theory. It has recently been shown- hat in alloys near Cu3Au there is a temperature range within which the ordered and disordered states coexist in equilibrium and are distinguishable as separate phases. Therefore, the transformation must be first-order for these alloys. A similar demonstration for alloys near CuAu, however, has been lacking. Experimental Method Essentially the experiment consisted of equilibrating Cu-Au samples at various temperatures, quenching them in water to retain the high temperature states, and then examining them at room temperature for the coexistence of the ordered and disordered structures. The thermal gradient method of heat treatment- as used because it was important that all temperatures over the transformation range should be represented in the test. Briefly, this method consisted of holding a wire of the desired composition, sealed under vacuum in Pyrex, in a known temperature gradient for a long enough time to allow each part of the wire to assume the crystal structure characteristic of the temperature at which it was held. The temperature gradient was produced by inserting into an ordinary wire-wound cylindrical laboratory furnace, an 18 in. length of 1/8 in. ID ceramic tube which was heavily wrapped with asbestos. The furnace power was controlled by a Tag-liabue Celectray controller and a chromel-alumel thermocouple with the junction located on the heating elements. During the equilibrating treatment the widest variation of temperature within the gradient tube was approximately 4°C at the highest temperature. The temperature at various places within the tube was determined, before inserting

Jan 1, 1954

By R. E. Hurst, D. E. Ramsey, J. M. Moore

The "frac" method of well stimulation has been applied successfully to all producing formations in the Permian Basin area. During the five years since its development, many changes and improvements have been made in treating materials. procedures, and equipie11t. A number of fluid carrying agents, having different physica1 and chemical properties, have been developed to meet variorus well requirements. The current trend is toward larger gallonage treatments, employing higher injection rates. The use of "down-the-casing" techniques has greatly reduced high surface working pressures, attributable to friction losses resulting from injection throrugh tubing. Petrographic studies of various Permian Basin formations, coordinated with laboratory and well log data, have been found a valuable guide in planning frac treat111o1t.s. A knowledge of the extent (and orientation of naturally occurring fractures and planes of weakness in the formation, aid in predicting the ultimate drainage pattern resulting from the frac treatment. INTRODUCTION The South Permian Basin covers an area in Wcst Texas and New Mexico about onc-half the size of the state of Texas, This vast region has been called the "Permian Basin" for so long that the term will he used here. It includes an area south of the Matador Arch. approximately 250 miles wide and 300 miles long. Structural features of importance within the basin are the Northwest Shelf, Eastern Platform, Midland Basin, Central Basin Platform, and Delaware Basin. The principal producing formations include sand, limestone and dolo-mite, with lesser amounts of shale, anhydrite. chert. and various silicates. All of the producing formations in the Permian Basin have responded to some type of frac treatment. Essentially, a frac treatment may be defined as the injection, into a formation. of a fluid carrying agent containing a particulated solid (usually sand), for the purpose of increasing production. The application of this method of well stimulation to many differing Permian Basin reservoirs has necessitated numerous changes and improvements in carrying agents, solids, service equipment. well equipment. and treating techniques. CARRYING AGENTS A number of different types of fluid carrying agents have been developed since the introduction of the frac method of well stimulation. These agents have different physical and chemical properties, and in many cases the extent of production increase derived from the frac treatment depends on the choice of fluid carrier. Unfortunately, due to many different systems of nomenclature used in the oil field, these differences are not always recognized by the oil Operator. In general, carving agents may he divided into the following broad classi-

Jan 1, 1956

By Frederik W. de Klerk

INTRODUCTION During the past 40 years, there has been in the United States of America and other industrialised Western countries a distinct displacement in the procurement of minerals from domestic sources towards an increased dependence on imported minerals. This was caused in part by one or each of the following: a lack of local supply of particular minerals, domestic source depletion or exhaustion and the relative ease and inexpensiveness of obtaining minerals from comparatively unexploited sources in underdeveloped and some developing countries, notably in the Middle East, South America, Southern Africa, and Australasia. Governments of the industrialised nations, concerned about the reliance of their economies on imported raw minerals examined both the degree of reliability and the extent of mineral resources in the countries and regions supplying the essential minerals. This brought a painful awareness of the vulnerability of industrialised countries as a result of the possible interruption of their mineral imports. In this regard, the United States of America may be quoted as a case in point: a report by a House of Representatives Subcommittee on Mines and Mining (Santini Subcommittee)1 revealed that the United States in 1980 was dependent on foreign sources for more than 50 per cent for 24 of the 32 minerals essential for national survival. The Subcommittee also acknowledged that although the United States may develop its own alternative energy sources, there are in many cases no substitutes for the strategic + minerals imported from foreign sources, from countries which are often unstable at best, hostile at worst. This resulted in various policy responses as well as contingency measures, amongst other, renewed emphasis on the utilisation of domestic mineral resources, an intensified search for substitutes of critical minerals and increased stockpiling programmes. Increased attention was devoted to analyses of the political and economic conditions prevailing in the regions from which strategic and other minerals are exported to the industrialised countries, and the formulation of policy measures vis-a-vis those regions. One region which attracted a considerable degree of attention has been Southern Africa, and in particular South Africa.2 The Santini Subcommittee affirmed that while the bulk of the minerals imported by the United States is supplied by a number of source countries, a host of critical[t] minerals vital to the well-being of that country (and this includes all the Western industrialised countries) originates from Southern Africa, a region, deservedly referred to as the "Persian Gulf of Minerals". Apart from the Republic of South Africa the mineral-rich countries concerned are Angola (diamonds, iron ore, oil), Botswana (diamonds, coal), South West Africa/Namibia (diamonds, uranium), Zambia (copper, cobalt), Zaire (industrial diamonds, copper, cobalt) and Zimbabwe (gold, nickel, chromium, asbestos). The Subcommittee however noted that, with the exception of cobalt, the greatest portion of the reserves of the critical minerals listed, lies within the borders of South Africa. SOUTH AFRICA A RELIABLE PURVEYOR OF MINERALS In view of the continual instability and political risk, along with the nationalisation of mineral industries in third world countries, importing industrialised nations have in recent years become more and more concerned about security of long-term supply, and have in consequence begun to diversify their mineral enquiries to areas where the following conditions prevail: • Long-standing record of consistency of supply; • An economic system of private enterprise; • Political stability; • A well integrated infrastructure, with a maintenance of transportation and development costs at realistic levels, and • Attractive investment opportunities, with security of the return of profits.

Jan 1, 1982

By H. F. Seifert

THE classification and preparation of non-ferrous scrap metals is a subject of interest to every individual and corporation that employs in its processes of manufacture non-ferrous metals and alloys and accumulates in such manufacture scrap from these materials for disposition in the form of turnings, borings, short ends, punchings, clippings, grindings, washings, etc. All too frequently the disposition of such scrap is left to individuals who have no knowledge of the subject either from a metallurgical or a commercial standpoint, or both. Much money is thus lost which with a little more intelligent effort might be saved, and in this day of fierce competition and small profits such an opportunity cannot be ignored. The Mineral Resources of the United States for the year 1925, the latest issue available (Part 1, page 221), gives the secondary non-ferrous metals of certain classes recovered in the United States for the year 1924 to 1925 as shown in Table 1. The figures are tabulated simply to give the reader some idea of the scope of the secondary non-ferrous metal industry. Approximately 900,000 tons of an annual value of $244,000,000 were recovered in the year cited. In 1916 (again using the Mineral Resources of the United States as authority) the tonnage reclaimed was approximately 632,000 tons and the value, because of the high prices for metals prevailing at that time, amounted to $265,000,000. It is not the purpose of this paper to discuss smelting and refining operations or the feasibility of an organization, primarily engaged in some other activity, conducting smelting and refining operations to convert its own non-ferrous scrap metals and alloys. The classification and preparation of these non-ferrous materials is a preliminary step, regardless of what subsequent operations the material may pass through or where these operations may be conducted. For that reason the subject can be readily discussed without any reference to subsequent activities. Space must be provided, with suitable handling facilities, scales and the necessary storage bins where the material may be accumulated. The scope of the activity, the nature of the industry and the tonnage handled will determine, in a large measure, what preparation, if any, it may be desirable to give these scrap materials to put them in the best marketable condition. By preparation is meant largely what, for the want of a

Jan 1, 1928

By H. F. Seifert

The classification and preparation of non-ferrous scrap mctals is a subject of interest to every individual and corporation that employs in its processes of manufacture non-ferrous metals and alloys and accurnulates in such manufacture scrap from these materials for disposition in the form of turnings, borings, short ends, punchings, clippings, grindings, washings, etc. All too frequently the disposition of such scrap is left to indivitluals who have no knowledge of the subject either from a metallurgical or a commercial standpoint, or both. Much money is thus lost whicli with a little more intelligent effort might be saved, and in this day of fierce competition and small profits such an opportunity cannot be ignored. The Mineral Resources of the United States for the year 1925, the latest issue available (Part 1, page 221), gives the secondary non-ferrous metals of certain classes recovered in the United States for the year 1924 to 1925 as shown in Table 1. The figures are tabulated simply to give the reader some idea of the scope of the secondary non-ferrous metal industry. Approximately 900,000 tons of an annual value of $244,000,000 were recovered in the year cited. In 1916 (again using thc Mineral Resources of the United States as authority) the tonnage reclaimed was approximately 632,000 tons and the value, because of the high prices for metals prevailing at that time, amounted to $265,000,000. It is not the purpose of this paper to discuss smelting and refining operations or the feasibility of an organization, primarily engaged in some other activity, conducting smelting and refining operations to convert its own non-ferrous scrap metals and alloys. The classification and preparation of these non-ferrous materials is a preliminary step, regardless of what subsequent operations the material may pass through or where these operations may be conducted. For that reason the subject can he readily discussed without any reference to subsequent activities. Space must be provided, with suitable handling facilities, scales and the necessary storage bins where the material may be accumulated. The scope of the activity, the nature of the industry and the tonnage handled will determine, in a large measure, what preparation, if any, it rrlay he desirable to give these scrap materials to put them in the best niarketable condition. By preparation is rneant largely what, for the want of a

By Robert F. Mehl

Jan 1, 1944

By Robert F. Mehl

Jan 1, 1944

By Charles E. W. Bateson

The Mojave mining district is situated in a group of small hills centering around Soledad peak, in the Mojave desert, Kern county, Cal. These hills are about 4.5 miles SSW. of Mojave, a railroad town at the junction of the Santa Fé and Southern Pacific railroads. The town of Mojave is about 50 miles north of Los Angeles, to which it is connected both by telegraph and by rail. The distance on the Southern Pacific railroad is 102 miles, covered in 3 hr. and 45 min. by express train. A sketch-map of this region is shown in Fig. 1. The Mojave district is relatively isolated. The only other mining towns in this section of California are Randsburg and Johannesburg, in a district (containing the well-known Yellow Aster mine) at the northern end of a low range of hills, which begins about 20 miles NE. of Mojave, runs nearly N. for 35 miles, and varies in width between 3 and 6 miles. As will be seen later, the origin and formation of these hills are not the same as those of Soledad peak. II. Climate and VEgetation. The climate and vegetation of the Mojave district are typical of the arid regions of the southwestern United States. During the winter and spring there is some rainfall, and the tempera ture is generally from 60" to 70" F. in the day-time. The rainfall in the spring is often very considerable for short spaces of time, and cloud-bursts are not infrequent. In summer there is continual sunshine, with temperatures, as a rule, exceeding 100" F. in the day-time, while 115" F. in the shade of a house is not at all unusual; but at night the temperature falls considerably. No rain falls during the summer. The vegetation

Jan 1, 1907

By Larry Dale

An approach for predicting the development of mineral resources on public lands has been developed as an aid to resource agencies. It consists of new techniques for evaluating the economic potential of the resource, the uncertainty about mine cost estimates, and the uncertainty about the occurrance of mineral deposits. New mineral sup- plies from inferred and hypothetical resources can be predicted by using these techniques. A case study illustrates their application in predicting development of copper resources in western Montana.

Jan 1, 1982

To Install Waste Heat Boiler at White Pine White Pine Copper Co.'s smelter 18 miles southwest of Ontonagon, Mich., will have a six story high boiler utilizing what otherwise would be waste heat from a copper reverberatory furnace. Designed and under construction by the Babcock & Wilcox Co., the boiler will supply steam to a turbo-generator furnishing power for the projected development. The boiler will be in line with and following the reverberatory furnace. Using waste heat from the furnace in place of fuel for steam generation, about 50 pct of heat in the fuel originally supplied to the furnace will be recovered by the waste heat boiler. Exploration conducted over the past 15 years at White Pine, wholly owned subsidiary of Copper Range Co., has disclosed reserves of 309 million tons averaging 21.3 lb of copper per ton. Ore mineral is chiefly chalcocite (Cu2s).

Jan 5, 1953

By B. J. Nelson, F. N. Rhinos

Studies upon the rates of oxidation of copper alloys containing small quantities of the alloying elementsl,2 have shown that steady growth of the scales at predictable rates is limited to a small concentration range and to oxidation at temperatures above 600°C., whereas unpredictable and erratic oxidation behavior is found with alloys containing larger additions and at low temperatures. The latter effect appears to be associated with modifications in the geometric disposition of the oxides. At low concentrations of the baser elements in copper, simple oxidation behavior is typified by the formation of two distinguishable zones of oxidation: (I) a subscale composed of discrete particles of the oxide of the alloying element embedded in substantially pure copper and (2) an external scale composed of cuprous oxide (with a very thin layer of cupric oxide on the outside) containing particles of the alloying element distributed throughout, but most profusely near the metal surface (see Fig. 2, top). Where this type of structure obtains, the process of oxidation is believed to be implemented, and its rate controlled, by the diffusion of the reacting elements through a' continuous matrix phase; i.e., through the alpha (metallic) phase of the subscale and alloy and through the cuprous oxide of the external scale. Copper is presumed to diffuse outward through the cuprous oxide layer to the external surface, where it reacts to form more cuprous oxide.3 Oxygen is delivered at the oxide-metal interface in the form of cuprous oxide, which may either react with the alloying element to deposit its oxide at the inner limit of the external scale or dissolve in the pure copper that remains at the surface of the metal after it has become depleted in its oxidiza-ble alloying elements. Both oxygen and the alloying element are pictured as diffusing through the metal, the oxygen inward and the alloying element outward. Where the two diffusion streams meet in sufficient concentration the oxide of the subscale is precipitated. If the oxygen pressure in the surrounding atmosphere is just below the pressure necessary to maintain cuprous oxide undecomposed, no cuprous oxide can be formed; some of the oxide of the alloying element may form upon the external surface, if its decomposition pressure is below that of cuprous oxide, and a normal sub-scale appears. This condition is achieved experimentally by enclosing the alloy with cuprous oxide together with an excess of copper. At temperatures from 600°C. downward, the precipitated oxides tend to accumulate at the grain boundaries of the alpha phase where a relatively small volume establishes a partial barrier to the diffusion of the reactants- Similarly, large volumes of Precipitated oxides tend to deposit in various patterns that may be expected to

Jan 1, 1944

By F. N. Rhinos, B. J. Nelson

Studies upon the rates of oxidation of copper alloys containing small quantities of the alloying elementsl,2 have shown that steady growth of the scales at predictable rates is limited to a small concentration range and to oxidation at temperatures above 600°C., whereas unpredictable and erratic oxidation behavior is found with alloys containing larger additions and at low temperatures. The latter effect appears to be associated with modifications in the geometric disposition of the oxides. At low concentrations of the baser elements in copper, simple oxidation behavior is typified by the formation of two distinguishable zones of oxidation: (I) a subscale composed of discrete particles of the oxide of the alloying element embedded in substantially pure copper and (2) an external scale composed of cuprous oxide (with a very thin layer of cupric oxide on the outside) containing particles of the alloying element distributed throughout, but most profusely near the metal surface (see Fig. 2, top). Where this type of structure obtains, the process of oxidation is believed to be implemented, and its rate controlled, by the diffusion of the reacting elements through a' continuous matrix phase; i.e., through the alpha (metallic) phase of the subscale and alloy and through the cuprous oxide of the external scale. Copper is presumed to diffuse outward through the cuprous oxide layer to the external surface, where it reacts to form more cuprous oxide.3 Oxygen is delivered at the oxide-metal interface in the form of cuprous oxide, which may either react with the alloying element to deposit its oxide at the inner limit of the external scale or dissolve in the pure copper that remains at the surface of the metal after it has become depleted in its oxidiza-ble alloying elements. Both oxygen and the alloying element are pictured as diffusing through the metal, the oxygen inward and the alloying element outward. Where the two diffusion streams meet in sufficient concentration the oxide of the subscale is precipitated. If the oxygen pressure in the surrounding atmosphere is just below the pressure necessary to maintain cuprous oxide undecomposed, no cuprous oxide can be formed; some of the oxide of the alloying element may form upon the external surface, if its decomposition pressure is below that of cuprous oxide, and a normal sub-scale appears. This condition is achieved experimentally by enclosing the alloy with cuprous oxide together with an excess of copper. At temperatures from 600°C. downward, the precipitated oxides tend to accumulate at the grain boundaries of the alpha phase where a relatively small volume establishes a partial barrier to the diffusion of the reactants- Similarly, large volumes of Precipitated oxides tend to deposit in various patterns that may be expected to

Jan 1, 1944

Robert T. Hill, Washington, D. C.: Having studied very minutely the geology of the district referred to by Prof. Branner, I beg to state that his quotation of my classification of the Cretaceous deposits of Arkansas is not the one which I originally gave,* nor is it the one which has since been published and is now generally accepted.? I did not assign ally of the Cretaceous formations of Arkansas to the " middle Cretaceous,"

Jan 1, 1898

By WM. HUFF WAGNER

Computations and allowances for mine depletion for Federal income tax purposes depend upon the meaning of certain terms in the pertinent provisions of section 114(b) 4 of the Internal Revenue Code. Unfortunately, but one of these terms is defined in the Code. Congress left it to the Commissioner to define the other terms in the Regulations. Even though the Commissioner, through his staff, labored long and earnestly to draft these definitions they have not been satisfactory to the mining industry, because the definitions in the Regulations and the interpretation placed thereon by the Commissioner do not state what the industry believes to be the clear and obvious intent of Congress. Consequently serious and prolonged disputes, unduly delaying the settlement of Federal tax returns involving percentage depletion deductions are continually arising between taxpayers and the Commissioner.

Jan 1, 1949

Edward Halse, Puerto Berrio, Colombia, S. A. (communication to the Secretary): I have read with much pleasure the interesting and valuable paper by Mr. Kunz, and hope that the following brief notes, gathered a few years ago, while a resident in Mexico City, may help to elucidate the subjcct: Turquoise.—This was known to the Aztecs as Xihuitl. Santiago Ramirez states that they found it in the Cerro Xicohtzonc, close to Atzcapatzalco, a suburb of the City of Mexico (compare page 59). Opal.—This was known to the ancient Mexicans, for they named it mezcuitlatt (compare page 63). Jade.—Under this was iucluded a third mineral, prehnite, not mentioned by Mr. Kunz. According to James D. Dana, part of the "jade " of China is prehnite; and Humboldt informs us, in his work on New Spain, that the same species of jade is known in some parts of Mexico as mahagua (majagua ?). The same writer says, in his Views of the Cordilleras, that the Aztec name Tecpatl included flint, hornstone, and green jade; and finally, in his Travels in South America," he discusses the nature of the ancient amazon-stones, and declares them to have been made out of a jade resembling " compact feldspar," one of the constituents of the gabbro verde di Corsica. IIence those stones were probably composed of nephrite. According to Humboldt, the form given to them most frequently is that of the Babylomian cylinder, longitudinally perforated, and loaded with inscriptions and figures. They were also cut by the natives into very thin plates, perforated at the center, suspended by a thread, and worn as amulets. According to the historian Clavijero, the specific name given by the Aztecs to the nephritic stone (jadeite) was Quitzalitztli,

Jan 1, 1902

By P. E. Chapman, J. E. Worthington, I. T. Kiff

Increases in the price of gold starting about six years ago, and rapid fluctuations since then, have created a substantial popular interest in the noble metal. Gold prospecting had been at a low ebb since the end of World War II in most of the United States, except for a flurry of activity in Nevada after the Carlin and Cortez discoveries. The last few years, however, have seen a great awakening of interest in gold exploration as well as an opportunity for education for many explorationists in the geology and other vagaries of gold deposits. The writers have participated over the last few years in a search for gold deposits throughout the United States. This search was greatly influenced by the geologic studies of Dr. William Spence at the Haile gold mine in South Carolina, as reported in a companion paper. Spence's studies resulted in definition of a geologic model that has proven useful in a number of other geologic environments in the United States. These programs were all carried out under the auspices of Cyprus Mines Corp. and permission by Cyprus to present these results is gratefully acknowledged. The writers, however, reserve for themselves all responsibility for the results and conclusions. The exploration program to be described began in the southeastern United States. Spence's studies provided a reasonable basis for interpreting and understanding the geology of the Haile deposit, and also provided a means for predicting additional occurrences. This concept was then expanded to other gold occurrences in the Piedmont, and became an effective tool for evaluating other prospects. Finally, it became evident that the concept could be applied in some western gold districts. The following discussion will then include descriptions of other Piedmont examples and a few western districts that also appear to fit the pattern.

Jan 1, 1981

By AIME AIME

THE MILLING PROGRAM on Monday required a morning and afternoon session with a special luncheon of the Milling Committee in the Engineers Club at noon. Grinding and flotation were the main subjects of the papers which drew an attendance of fifty or more at each session. Under the direction of Chairman Arthur F. Taggart in the forenoon, all papers on flotation and general milling were considered, leaving the, after- noon free for crushing and grinding, with Dr. Galen H. Clevenger in the chair. The high spot was the first public presentation of the idea of size reduction of minerals by explosive shattering.

Jan 1, 1932

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

By A. STEPHENSON

EXPERIMENTAL work conducted at the Petroleum Engineering Laboratory of the University of California by L. C. Uren, J. Domercq, Jr., and J. Mejia has shown that small diameter wells offer tremendous resistance to the flow of fluids in their immediate vicinity. This resistance is due in part to the constriction of the area through which the fluids must pass as they approach the wall of the well, but is also accentuated by the increased volume which results from gas expansion. The latter in turn is a function of the deduction in pressure, the fundamental cause of fluid movement. If the diameter of the bore is enlarged several diameters, the capacity of the well, or the volume of fluid passing per unit drop in pressure per unit of time, is greatly increased without necessitating such high fluid velocities. The fundamental features which should be taken into consideration in the design of casing joints were stressed by J. B. Graham and E. E. Smith. These involved such points as correct thread design, high efficiency, and small diameter, together with the insurance that leakage will absolutely be prevented. The practical features of such design were ably discussed by engineers from leading steel manufacturers.

Jan 1, 1935

By M. Vallée

This case study compares the actual production figures for the No. I and No. 2 copper orebodies of the Société Miniére Louvem, Val d'Or, Quebec, with the preproduction estimates and a postmortem geostatistical estimation using kriging techniques. The deposits considered are small subvertical sulphide orebodies which were mined from August 1970 to April 1973, producing 648,000 tons at 2.04% Cu versus the 1968 computed reserves of 671,000 tons at 2.51% Cu (with 20% dilution), thus showing a 25% overestimation of the copper contained. The postmortem geostatistical estimation based on the same 44 D.D.H. intersections available in 1968, shows 2.24% Cu (no dilution), compared to 3.23% Cu (no dilution) given by the conventional section method. Block by block kriging techniques were used, but within the ore contours as determined by the geologist. In this case, Characterized like many sulphide deposits by highly dispersed sample values, geostatistical kriging techniques permit a more realistic estimation of the metal contained within a given volume, than the conventional methods which overestimate it. This study has been conducted by the Mineral Exploration Research institute (IREM-MERI) for SOQUEM, and is one of the few case studies released with all pertinent data. More postmortem of this kind are required for geologists and geostatisticians to improve their methods and their "batting average".

Jan 1, 1977