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By A. S. Doty, E. I. Larsen, F. R. Hensel

The alloy under discussion is a Pig. I shows results of heat-treating tests nickel-silicon bronze and is one of many on two typical nickel-silicon bronze castings age-hardening or precipitation-hardening of the type on which the observations were copper-base alloys. The hardening constituent is a nickel-silicon compound.l The quenching temperature necessary to produce hardening by a subsequent aging treatment is a function of the composition and extends from about 700°C. to 950°C.; the aging temperature range extends from 4000 to 600°C. The work carried out by the authors of this paper was confined to cast alloys having compositions within the ranges of: 1.5 to 3.00 per cent Ni; 0.4 to 0.75 per cent Sj: balance. comer. made. A quenching temperature of 750°C. produces almost as high a hardness on subsequent aging as do quenching temperatures of 850' and 900°C. Several foundries have spent years of active and intelligent effort in trying to control the casting and heat-treating variables of nickel-silicon bronzes and finally gave up the attempts because of the inconsistencies of results.2 This undesirable characteristic was not manifest in the ultimate hardness or conductivity but primarily in tensile strength and ductility, as shown in Table I. The variation in tensile properties was often much greater than that existing on the alloys

Jan 1, 1941

By Waldemar Gooskov

IN his well-known work,1 published in 1867, P. Ritter von Rittinger gives the following formula for the velocity of a particle settling in still water: v=C/D(a -1) and for average grains he assigns to the constant C a value of 2.44. As is well known, the value of C depends on the shape of the grains resulting from crushing, and it is obvious that values obtained for coal particles will not only be very different from those for ore particles but will even be characteristic of coal from a certain seam. The only way of finding an accurate value of C, applicable to conditions in Russia, where all coal-washing plants are built on German principles, is to conduct a series of tests of which the results will determine what value of C is to be used. In the investigation outlined in this paper the theories of Prof. Robert H. Richards2 were taken as the basis of the tests; the slimes were removed from the charges to eliminate the trouble of handling them; and to obtain accurate results free from errors inevitably resulting from human observation, photographic apparatus was used and a series of pictures taken which form the basis for constructing a suitable diagram of velocity vs. time.3

Jan 1, 1928

By C. Chu

An investigation has been made of the radial heat-wave process using a mathematical model in two-dimensional cylindrical coordinates. This model considers combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. From a study of the general features of the process, an important phenomenon has been revealed, namely, the feedback of heat into the reservoir on the trailing edge of the heat wave. The effects of various process variables on the performance characteristics of the process have also been investigated. It was found that up to the time when the combustion front reaches a given point, the per cent heat loss, provided it is not higher than 40 per cent, is approximately directly proportional to the square root of thermal conductivity arid fuel content, but inversely proportional to the square root of gas-injection rate and oxygen concentration. The effecr of reservoir thickness is more pronounced, since halving the thickness doubles the per cent heat loss. The most decisive factor in determining the center-plane peak temperature is the fuel content of the reservoir. Within the temperature range investigated, doubling the fuel content doubles the peak temperature in the early stage, but the rate of decline of the peak temperature is high. Reservoir thickness is also a very influential factor. The peak temperature is lowered when the thickness is reduced; however, the effect of thickness becomes less pronounced when the thickness is high. Reduction of oxygen concentration increases the peak temperature in the early stage but lowers it afterwards because of the higher rate of decline of the peak temperature. Increase in gas injection rate or decredse in thermal conductivity geives a higher peak temperature which stays high for a longer period. The propagation range of the heat wave is chiefly governed by the fuel content of the reservoir. An increase of 0.2 1b/cu ft in the fuel content increases the propagation range by 100 per cent. The propagation range is more than doubled by doubling the gas injection rate, or reservoir thickness, or by reducing the thermal conductivity by 50 per cent. Comparatively, oxygen concentration has less effect on the propagation range. INTRODUCTION Several investigators have conducted theoretical studies of a radial heat wave. Vogel and Krueger1 studied a system with a moving cylindrical heat source of constant temper- ature, considering conduction in the radial direction only. Ramey2 included conduction in the vertical direction in his studies. Bailey and Larkin2 attacked a more general problem where initial well heating, vertical heat losses and arbitrary frontal velocities were included. In all these studies, however, conduction was considered to be the only means of heat transfer. Bailey and Larkin in a later paper included the effects of convection in a study involving both linear and radial geometries. Vertical heat losses were neglected in the radial case. Katz5 studied a similar problem in a one-dimensional radial model, using a heat-loss coefficient to account for vertical heat losses. Selig and Couch6 mployed a cylindrical model and investigated two limiting cases. In one case they considered no heat loss from the reservoir whereas in the other they assumed a constant temperature at the interface between the reservoir and its bounding formations. Thomas' studied a more general case but assumed a permeable bounding formation so that the convection effect is not confined to the reservoir. In the present work a more realistic and more generalized model is used. It involves a two-dimensional cylindrical system with combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. The purpose is to establish the temperature distribution both inside and outside the reservoir, to study the general features of the radial heat wave process, and to investigate the effects of various process variables on the performance characteristics of the process. THEORY We fist consider a circular porous reservoir of thickness H extending vertically from y = — H/2 to y = + H/2. The reservoir extends from a well bore radius r, to an external radius re. A stream of oxygen-containing gas is introduced into the reservoir through the wellbore. The oxygen-containing gas reacts with the fuel contained in the reservoir and forms a combustion front wherever the prevailing temperature can support the combustion. It is here assumed that this combustion front constitutes a cylindrical surface source of heat having an infinitesimal thickness in the radial direction and extending vertically throughout the whole thickness H. This is designated as Region I. We next consider a Region II corresponding to the upper and lower formations bounding the reservoir, extending from y = — - to y = — H/2 and from y = + H/2 to y = + m. Since r, is very small, we may assume that the two bounding formations have the same dimensions, symmetric with respect to the center plane of the reservoir. In this way, we may take the upper half of the system alone into consideration. In contrast with

By AIME AIME

In the present number of Mining and Metallurgy, issued on the fiftieth anniversary of the founding of the Institute, it appears appropriate to chronicle a few of the interesting incidents respecting its early life. We are fortunate in being able to cull the following notes from unpublished manuscripts of Doctor Raymond and Doctor Drinker, than whom no other members could have written with greater exactness and fidelity. THE seventh decade of the 19th century may be said to have marked an. era in the history of the world. Industrially and .commercially it was marked by the wide application and utilization of discoveries already made, which came to their full effect at this period in steamships, railways, telegraph and cable lines; the standardization of parts in machines, from watches to locomotives; the use of 'dynamite, antiseptic surgery, the open-hearth steel process, the compressed-air rock-drill, the electric generator, and the Gatling gun. Through the opening of the Suez canal in 1870 the maritime trade of the world was revolutionized, sailing vessels were supplanted by steamers, while ocean cables and ocean "tramps" brought about far more rapid movement of commerce than had before been experienced. Politically, this period was marked by the sudden birth of the German empire and the beginning of that intensive internal development of the national resources of that empire in preparation for colonial extension and war, the amazing result of which has been made evident by the recent world conflict. In the United States, the significance of this decade was peculiarly important. The re-admission to the union of Virginia, Mississippi, Texas and Georgia in

Jan 1, 1921

By J. M. Silliman

Several years ago, having occasion to determine the amount of some very slight atmospheric depressions, I devised and had constructed by a skilful tinsmith the manometer shown in the accompanying drawing. It consists of a cylindrical vessel of tin, 6.6 inches in diameter, through the sides of which, at a distance of about six inches from the top, passes an air-tube D, its upper extremity terminating 3.5 inches from the top. Within the vessel is a combined cylipdrical

Jan 1, 1889

By AIME AIME

WEST TEXAS, New Mexico and Northern Mexico form one of the most interesting regions in America for geologists and mining men and are full of points of historical and human interest for others. Including as the region does, a representative portion of the high plateau of Mexico, the front range of the Rocky Mountains and the great down-dropping plains of Texas, there is variety as well as interest in the geological and mining problems there to be studied. Gold and silver mining were the pioneer industries and are yet of high rank in importance. Among the papers to be presented at the El Paso meeting of the Institute this month will be two dealing with silver mining and ore treatment at the Shafter mine in Texas, that most un- usual property which has for so many years been the largest mining enterprise in its region. West Texas is now better known for its petroleum and gas, and in another paper will be described the problems involved in uding natural gas for smelting at the well-known El Paso smelter of the American Smelting and Refining Co. In still other papers, presented at the session sponsored by the West Texas Geological Society and cooperating organizations, the general geology of the region, the potash and the sulfur deposits will be de- scribed. At El Paso the refineries of the great com- panics will be available for visits.

Jan 1, 1930

By Elmer A. Jones

Development work in mines of St. Joseph Lead Co., Southeast Missouri, using trackless loading equipment shows definite advantages: Speed of cleaning, ability to work on steep grades and sharp crosscuts, good later tracking conditions, and possibility of wasting rock in old abandoned stopes.

Jan 1, 1950

By F. C. Schora, H. P. Meissner

Iron ore from Cerro Bolivar, Segre', and Sierre Grande was reduced in fluid beds at about SOOT, using gas analyzing 20.5 pct CO, 41 pct Hz, and 38.5 pct N2. Except in the early stages of reduction, the rate of oxygen loss from the bed was directly proportional to the oxygen concentration in the bed, independent of gas composition as long as the gas was reducing, and little affected by temperature. The percentage reduction of the bed solids at any time was independent of particle size. I HE reduction of spheres or cubes of dense iron ore in a slowly moving stream of either pure H, or pure CO has been found to take place at distinct interfaces between well defined layers of iron and the iron oxides.'y4 These interfaces generally penetrate the ore lump in topochemical fashion, remaining parallel to the original contours of the specimen. Thus in the earlier stages of reducing hematite, the specimen's core is Fe,O, surrounded by successive shells of the lower oxides, and finally by an exterior shell of iron. McKewan5 assumed that the rate limiting step occurred at the Fe-FeO interface, with reducing gas penetrating up to this interface through the external porous iron shell, and reduction of the higher oxides within the ore lump occurring by diffusion of iron through the dense FeO shell. He developed an analytical expression based on this model relating the amount of oxygen removed from

Jan 1, 1962

By C. K. Leith, W. J. NEAD

(Glen Summit Meeting, June, 1911.) . ONE Of the most significant developments in the iron industry in recent years has been the discovery and opening of enormous reserves of low-grade ore in eastern and northeastern Cuba. The two principal fields are the Mayari and the Moa, situated on Nipe bay, in the Province of Oriente. A less well-known district of the same type is that of Baracoa, at the east of the island, and another is in Camaguey province in central Cuba. In the comprehensive estimates of the iron-ore reserves of the world, published during the summer of 1910 by the International Geological Congress in Sweden,' these Cuban deposits are estimated at about 2,000,000,000 tons. Certain it is that the reserve is a large one. The Spanish-American Iron Co., the Juragua Iron Co. (Bethlehem Steel Co.), the U. S. Steel Corporation, and others have been active in this exploration.. The Spanish-American Iron Co. has established a port for the handling of these ores at Felton, has built a railway 16 miles to the ore-fields, and has opened up deposits for steam-shovel mining. Its expenditures have reached an aggregate of about $6,000,000 in preparation for the handling of these ores. Shipment of the ore to Sparrow's Point, Md., has begun and may be expected to rise to a considerable amount in the near future. The ore reaches this point at a cost per unit of iron considerably lower than Lake Superior ores, and the presence of a low percentage of nickel gives a desirable steel. It is not the purpose of this article to consider these ores from a commercial stand-point, but rather to discuss their-origin. If our conclusions are correct, they throw light on the character of the deposits which should have some commercial significance. 1 The Iron Ore Resources of the World, an inquiry made upon the initiative of the Executive Committee of the Eleventh International Geological Congress, Stockholm, vol. ii., p. 795 (1910).

Mar 1, 1911

By Elton A., Youngberg

The Holden mine operated by the Chelan Division of the Howe Sound Co. is on the east slope of the Cascade Range in north central Washington on the south slope of Railroad Creek valley at an elevation of 3500 ft. The mine may be reached by a 40 mile boat trip from the town of Chelan which is at the southern tip of Lake Chelan, to Lucerne at the mouth of Railroad Creek and an 11 mile bus ride up Railroad Creek to Holden. All freight and concentrate is moved over this route to Chelan Falls on the Columbia River which is on the railroad four miles below the town of Chelan. The mine is now producing 2000 tons of gold, copper, and zinc ore per day which is treated in the Holden mill. Gold-copper and zinc concentrates are made, the first of which is shipped to Tacoma, Wash., and the latter to Kellogg, Idaho, for smelting.

Jan 1, 1949

By F. F. Aplan, P. H. de Bruyn

The adsorption density of hexyl mercaptan was measured at the gold-solution and the gold-vapor interfaces. This collector is strongly adsorbed at low concentrations, a monomolecular layer being formed at the gold-solution interface at concentrations as low as 2 x 10'6 moles per liter. A maximum contact angle of 83 ± 3° is observed. From a thermodynamic analysis of the experimental data the changes in surface tension at the gold-gas and gold-solution interface are calculated. The data also suggest that the adsorption density of mercaptan at the gold-gas interface exceeds that at the gold-solution interface. In the equilibrium state, a simple flotation system consists of three phases, the solid to be floated, air, and an aqueous solution in stable contact along a line. During the process leading to this final state, a solid-gas interface is created at the expense of a portion of the liquid-gas and solid-liquid interfaces. This change of state is achieved by addition of a collector and, if necessary, suitable modifying agents to the system. By a combined application of the Gibbs Adsorption and the Young Equations, de Bruyn, Overbeek and Schuhmannl were able to show theoretically that the equilibrium distribution of the collector at all three interfaces determines the magnitude of the contact angle. Their analysis led them to conclude that the equilibrium adsorption density of the collector at the solid-gas interface exceeds its density at the solid- liquid interface. This paper succeeded in focussing attention on the neglected role of the solid-gas interface in flotation. In recent years the application of radiotracer, infrared, electrochemical and electro-kinetic techniques to studies of the solid-liquid interface2-5 enhanced our understanding of adsorption processes at this interface. Except for the measurement of contact angles, the solid-gas interface received no attention in fundamental flotation studies. In an attempt to apply the analysis of de Bruyn, Overbeek and Schuhmann to a simple flotation system, an investigation of the adsorption of hexyl mercaptan onto gold was undertaken. Gold was chosen as the solid phase in order to keep the number of dissolved chemical species in the solution phase to a minimum. Hexyl mercaptan (1 - hexanethiol) was selected as collector because its relatively high vapor pressure at room temperature makes it possible to obtain adsorption measurements at the solid-gas interface. This flotation system consists, therefore, of a pure solid phase (gold), an aqueous solution of a weakly dissociated collector (1 -hexanethiol), and a gaseous phase, nitrogen saturated with respect to both water vapor and mercaptan vapor. EXPERIMENTAL MATERIALS AND METHODS Materials: Liquid 1-hexanethiol (C6H13SH) was obtained from Distillation Products Industries and was further purified by double distillation. The purity of the final product was established by boiling point and refractive index measurements. For the adsorption studies from aqueous solution, the radiotracer element, sulfur-35, (half life 87.1 days, 0.169 Mev beta ray) was synthesized into the mercaptan by Tracerlab Inc., Boston, Mass. A close boiling fraction of the synthesized compound was used in the adsorption studies. The specific activity of the radioactive compound was 10 millicuries per gram.

Jan 1, 1963

By C. C. Clark, J. S. Iwanski

The purpose of this investigation was to study mi-crostructural changes that take place in a commercial nickel-chromium-iron alloy, such as Incoloy "901," over long periods of time at temperatures up to 13 50°F and to correlate such changes with creep-rupture properties. of the alloy. In the course of the investigation, some microstructural changes were observed which correspond to microstructural alterations found in previous studies of Inconel "X." Microstructural phases have been identified in both alloys with the aid of electron and X-ray diffraction and an electron probe microanalyzer. The materials used in this investigation were from commercial heats of the following chemical composition: Pct Cr Pct Ni Pct Mo Pct Fe Pct Cb Incoloy "901" 12.51 43.67 5.72 Bal. -Inconel "X" 14.61 73.44 - 6.61 1.02 Pct A1 Pct Ti Pct Mn Pct Si Pct C Incoloy "901" 0.10 2.46 0.46 0.24 0.05 Inconel "X" 0.70 2.43 0.51 0.36 0.04 Long-term creep-rupture tests were conducted on Incoloy "901" at temperatures of 1000°, 1200°1 and 1350°F. A summary of these results is shown in Table I along with the results of a long-term creep-rupture test conducted on Inconel "X" at 1500°F. The heat treatments given the specimens are also shown in Table I. When the creep-rupture results on Incoloy "901" are compared with shorter-tertn data, there is no evidence of any undue deterioration of the creep-rupture strength with time, nor is the elongation decreased more than would be expected from the influence of time alone. INCOLOY "901" PHASE IDENTIFICATION Microscopic examination of the Incoloy "901" specimens reveals a dark etching grain boundary constituent in the specimen which was under test for about 11,500 hr at 1000°F. This grain boundary constituent was seen to increase in size as the test temperature was increased to 1200" and 1350°F, Figs. 1, 2, and 3. Simultaneously, an acicular structure of definite crystallographic orientation appears within the grains of the 1350°F specimen, Fig. 3. Under examination with the electron microscope, a fine precipitate is observed in the 1200 °F specimen. Fig. 4. It becomes considerably larger in the 2850-hr 1350°F specimen, Fig. 5. In a few areas the precipitated particles have been replaced by, or transformed to, small needles or platelets. After 7380 hr at 1350°F, Figs. 3 and 6, the needles are much larger and have replaced nearly all of the fine precipitate. X-ray diffraction studies detected the presence of hexagonal Laves phase and hexagonal n phase (Ni,Ti) in the 1350°F specimens, Table 11. Only the Laves phase was detected by X-ray diffraction in the 1200°F specimen and none was detected in the 1000°F specimen. In this latter specimen, however, the small quantity of precipitate in the grain boundaries (presumed to be Laves phase) precludes its detection by X-ray diffraction. Composition of the hexagonal Laves phase is not yet known, although its diffraction

Jan 1, 1960

By E. A. Anderson

THIS seems to be the year for superlatives in A.I.M.E. meetings. The programs of the various Divisions and Institute committees offered an abundance of interesting and valuable information in the form of technical papers, symposia. and lectures to large and interested audiences. The Institute of Metals Division may hold up its head with pride for its own program. With six technical sessions, three full-day symposia, and the annual I.M.D. dinner, four meeting days were not enough and many simultaneous sessions were required. The quantity and quality of the paper were equaled by the numbers and interest of those attending.

Jan 1, 1944

By T. K. Prentice

ABSTRACTED AND REVIEWED BY E. W. DAVIS,* MEMBER A.I.M.E. THE January-February number of the Journal of the Chemical Metallurgical and Mining Society of South Africa is made up entirely of a discussion of Ball Wear in Cylindrical Mills. Following the principal paper by T. K. Prentice are several remarkably pertinent and carefully prepared discussions. Few persons in this country would be likely to see this publication, and since the information presented is new and of current interest, it seems desirable to abstract and review this publication for the benefit of the members of the A.I.M.E. The purpose of the investigation is stated in the first two paragraphs of Prentice's paper, as follows: Early in 1941, The Chamber of Mines Steel Products, Limited, initiated a series of tests under semi-working scale conditions to determine, if possible, those physical and chemical properties of a ball which make it resistant to wear when used in a cylindrical mill as a grinding medium, with the primary object of incorporating those beneficial qualities in the balls being produced at their works. This paper describes the tests carried out and discusses the results obtained. From these results it was possible to formulate a new theory relating to ball wear in cylindrical mills. This theory is presented in the second portion of this paper. PRACTICAL BALL-MILL TESTS IN A CYLINDRICAL MILL Part I of the paper begins with a discussion of the methods used for the manufacture of grinding balls in South Africa. The following paragraph is of particular interest. The cast steel ingots, 4 ¼ - in. square by 3 ft. 6 in. long, are re-heated in a gas-fired sloping stationary-hearth furnace and then rolled in a six-pass continuous mill into 2 5/8 in. round billets. Some of these billets are then removed and cut into suitable lengths for forging into 4 in., 3 ½ in., 3 in. or 2 ½ in. balls by means of three Drop and two Beché hammers, but the greater number, whilst still at about 1,000 ºC., pass directly into a set of scroll rolls which produce, in an ingenious manner, finished 3 in. balls direct from the 2 5/8 in. billets. Except in special cases, all balls are allowed to cool in the atmosphere and are not water quenched. Details of the Tests In order to enable the reader to evaluate properly the results and conclusions in the rest of the paper and in the discussions following the paper, most of the information presented by the author under this heading is quoted: ….. The testing unit was a nominal 30 in. diameter and 18 in. long centre discharge Denver Ball Mill. The ore pulp to the ball mill comprised a small portion of the normal feed to one of the fourteen City Deep 5 ft. 6 in. X 22 ft. tube mills, and the grinding media consisted of the balls under test plus other balls to give the desired load. The running time of the test-mill was divided into approximately equal periods of five days 13 ½ hours each. The usual procedure was to examine and make up the load

Jan 1, 1944

ZAY JEFFRIES (author's reply to discussion *).-Messrs. Merica's and Humfrey's criticisms of some of my conclusions are rendered in the true scientific spirit by means of which differences of opinion are gradually smoothed out and all participants are benefited. It is true that the statement of generalizations on such a complex subject is hazardous, but I shall endeavor to point out the explanations for the discrepancies noted. Owing to the fact that I am now submitting a long paper on the same general subject to the Institute, my present remarks will be brief. Dr. Meric&s Assumptions' I agree with No. 1 and No. 2, with the modification that the A (amorphous) metal between grains of annealed metal has substantially the same properties as that at slip planes in deformed metal, but the two have different arrangements with reference to C (crystalline) metal and they may be in different conditions as regards internal stress, thickness, and nature of contact with C metal. Assumption 3.-I believe Fig. 1 is wrong. I know of no evidence to substantiate the curves. I believe cc (elongation of C phase) = 0 (approximately) at all temperatures and ?A (elongation of A phase) has finite values at elevated temperatures only; but these play no important direct role in the ordinary deformation of metals at low temperatures. I believe Ec (elastic limit of C phase) = Tc (tensile strength of C phase) because as soon as C metal begins to deform permanently it would rupture were it not for the A metal generated by its breakdown. We know that Ec = Tc in brittle crystals and a crystal cannot be permanently deformed without generation of A metal. Therefore Dr. Merica's

Jan 12, 1918

By K. L. Young

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection case. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. INTRODUCTION When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressures. The two methods are Cullender and Smith1-" (numerical integration), and average temperature and com-pressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correcton. The average temperature and compressibility method, in addition to neglecting kinetic energy change, asumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. l or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. where 111.1 qeC2/d p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation,

By J. E. Harris, J. A. Whiteman, A. G. Quarrell

The graphitizing reaction has been studied in a number of Fe-C-Si alloys in the temperature range 550° to 725°C. The TTT relationships exhibit "C" curve behavior except where nuclei, either foreign or graphite itself, are present before the start of the reaction. It is suggested that the rate -controlling process is diffusion of carbon through ferrite. For the reaction to proceed at the observed rate it is calculated that the matrix surrounding the particles must deform plastically; experimental evidence for this deformation is presented. It is well-established that the decomposition of austenite to pear lite occurs at a maximum rate at an intermediate temperature.l-5 This "C curve" be- havior, which has been reported in a number of other systems,5-10 is a consequence of the relatively low rate of nucleation of the pearlite at small degrees of undercooling of the austenite. The cemen-tite phase in the pearlite is, in turn, metastable with respect to graphite and if steels are held for prolonged periods at elevated temperatures decomposition of the pearlite occurs. It is difficult to predict the shape of the subcriti-cal graphitization TTT (time, temperature, transformation) diagram for, in this case, undercooling does not occur. However, the free-energy change for the reaction does decrease with increasing temperature" (Fig. 1) and it is thus anticipated that the rate of nucleation will fall as the temperature approaches that of the eutectoid. In addition, a decreasing growth rate with increasing temperature is predicted in some circumstances with pure Fe-C alloys. However, apparently similar conditions exist for first-stage graphitization in the austenite range (malleabilization) but no evidence for C curve behavior has been presented in the extensive liter-

Jan 1, 1965

By D. P. Harris

The construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area is postulated. The questions (1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and (2) can this geology be related mathematically to mineral wealth and probability are answered in a case study of 97,000 square miles in Arizona and New Mexico. Measurements on mineral wealth and geologic variables of 243 cells were made. The geologic variables, valued in counts, percentages and lengths, quantified the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. The cells of explored area must be allotted the value class indicated by their cumulative production and estimate reserves (given well-defined geological relationships in a mineral wealth area), and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. This determines whether high value cells can be distinguished from low value cells by their geology as well as indicating those cells misclassified by the model into a higher value group than warranted by their known mineral wealth. The second use of the model is for extrapolation. It is demonstrated how geologic information on an explored area can be utilized in guiding exploration in an unexplored area. Exploration decisions can be predicted on explicitly determined measures of uncertainty (the probabilities). SUMMARY This study postulates the construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area. Such a model will distinguish those cells deserving further exploration on the basis of their geology: The basic postulates of this study are as follows: v = Q(R,S,F,A) P(V) = G(R,S,F,A,V), where V = a measure of mineral wealth P(V) = the probability of occurrence of V R = age and type of rock F = rock fracturing A =age of igneous activity and contact relationships. There are really two questions to be answered: 1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and 2) can this geology be related mathematically to mineral wealth and probability? In order to answer these questions, an area of about 97,000 square miles situated chiefly in Arizona and New Mexico was selected as a case study. This case study area was divided into 243 cells, each 20 miles square, and measurements were made on mineral wealth and geologic variables. Crude geologic variables valued in counts, percentages and lengths are constructed to reflect the above postulated variables. These measurement variables thus provide quantified values defining the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and the multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. Given the availability of an area that is well explored and upon which the relationships of mineral wealth to geology can be adequately defined, there are two ways in which the analysis outlined in this paper can prove beneficial. First, the cells of the explored area must be allotted the value class indicated by their cumulative production and estimated reserves, and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. Such an analysis determines whether cells of high

Jan 1, 1967

By V. J. Kniazeff, S. A. Naville

The problem of unsteady-state condensate-gas flow through porous media leads to a set of second-order non-linear partial differential equations. Such a set of equations is numerically solved in the case of radial two-phase flow around a well, taking into consideration both the thermodynamical properties of the fluid and the mechanical properties of the reservoir. The fluid properties, reflecting the PVT relationship of the gaseous and liquid phases, are expressed by using the partial specific masses of the two main separator products in these phases. The flow properties of the reservoir rock are expressed by the generalized Darcy's law for the liquid phase and by a quadratic relationship between the rate of flow and the pressure gradient for the gaseous phase. The numerical solution of the equations for pressure and saturation US radius and time is worked out through programs written for a computer. The evolution of bottom-hole pressures, well productivities or- deliverabilities and effluent compositions with the depletion of the reservoir is easily derived. The application to the Saharian gas-condensate field Hassi R'Mel led to a better understanding of the drainage mechanism. A zone of fairly high liquid saturation develops around the wells, reducing the effective permeability, and represents a loss of condensible products in addition to the PVT-like retrograde condensation. lnside this zone, near the well, the deviation from Darcy's law for the flow of the gaseous phase governs the well deliver-ability. A back-pressure test has been computed and correlates with the field results. INTRODUCTION Two-phase flow of volatile hydrocarbons, like condensate gas or light crude oil, may be treated as the flow of a binary mixture by an arbitrary division of the chemical components into two groups. This is translated into two equations of mass continuity, which constitute a set of relation- ships for the pressure and the saturations vs the space coordinates and the time. The equations contain the laws governing the composition and the motion of the phases. The problem so defined is solved with the assumption that the compositions of the phases at any pressure are respectively the same as those observed in a PVT measuring cell under differential liberation. In a first series of computations, it was assumed that the flow obeys the generalized Darcy's law. A satisfactory representation of the retrograde condensation around the well was thus obtained. In addition, the trend toward decreasing effective permeabilities was obtained, and the computed composition of the effluent checked the laboratory values. However, it has not been possible within this basic assumption to represent the non-linear relationship between the production rate and the bottom-hole pressure drawdown as observed for gas wells in the field. Following the advice of A. Houpeurt it was decided to consider the relative permeability to gas as a function of the velocity of the gas Phase.1 The necessary physical determinations were made by E. COstaséque using a method devised by A. Houpeurt and R. Iffly. As numerical processing of the equations progressed, several difficulties were encountered which were overcome through collaboration with the computer manufacturer. This mathematical model of two-phase flow in porous media had been primarily intended for and extensively applied to the case of the Hassi R'Mel gas-condensate field, operated by SN Repal for SEHR, a joint subsidiary of SN Repal and CFP (A). The programs have also found their applications to forecast the behavior of several fields in the Sahara area containing light and volatile hydrocarbons. BASIC EQUATIONS We will consider a zone in the porous reservoir where the flow properties and the in situ composition of the fluids can be assumed to be uniform. A part of the equations of transient flow can be written with the specific gravity of the fluids being taken equal to the sum of the contributions due to the

Jan 1, 1966

By J. L. Dumanoir, Maurice Martin

The induction-electrical log is a combination of a SP curve, a short normal curve, and an induction log; all three logs being recorded simultaneously in a single run. The spacing of the short normal is 16 in. The induction log is designated as 5FF40, which means that the sonde involves five coils and a focusing system, and that the distance between the main coils is 40 in. Examples of induction-electrical logs are shown in Figs. 13 and 15. The right-hand track contains the induction conductivity curve. The scale of this curve is linear with the units of conductivity, i.e., mhos/m or millimhos/m (mmhos/m), increasing from right to left. The same curve can be read in the reverse direction as a resistivity log, with a hyperbolic scale. In the middle track, the solid curve represents the short normal. (An amplified short normal is also shown in Fig. 15). The dotted curve is the resistivity curve of the induction log, i.e., the reciprocal of the conductivity curve, recorded with the same linear scale as the short normal. The SP is in the left-hand track. In this combination, the SP curve and the 16-in. normal are the essential correlation curves, as in the conventional electrical log. The induction log provides a more accurate and detailed record of formation boundaries than the conventional log, especially in hard rock territories. Furthermore, the induction-electrical log makes possible the determination of fluid content, particularly in thin beds—at least qualitatively and very often quantitatively. In such thin beds, because of the adverse effect of the adjacent formations, the responses of the conventional devices are generally doubtful and/or incom-plete. Another advantage of the new combination is that the induction log is little affected by the presence of thin hard streaks interbedded within the permeable sections, whereas such occurrences are the cause of serious distortions of the long normal and lateral curves. The evaluation of saturation from any resistivity log implies the knowledge of the true resistivity R, of the bed and of the resistivity R.. of the flushed zone, or at least of the ratio Rxo/Rc. With the induction-electrical log run in fresh mud, the 16-in. nor-mal has a smaller radius of investigation than the induction log, so that the former reads closer to R.. and the latter closer to Rt. Thus, it has been observed that the ratio of the 16-in. normal to the induction log readings can be used as a basis for the interpretation in terms of saturation, with the help of appropriate charts. The purpose of the present paper is essentially to explain this procedure and to provide the corresponding charts. On the other hand, when a formation is deeply invaded, the response of any log (in particular the induction log) depends upon the radial distribution of formation resistivities behind the wall of the hole, which itself is a function of the arrangement of the fluids saturating the formation pore spaces. This paper, accordingly, will begin with a schematic description of the distribution of fluids and resistivities in the invaded zone. Next, some essential characteristics of the induction log will be reviewed. Finally, the determination of the interpretation charts and their application will be explained. The discussion will be confined to the case of fresh muds, i.e., muds whose resistivity is at least five times as great as that of the formation waters. With the present equipment the induction log is not well adapted for logging in salty mud. The Laterolog and guard electrode log are at their best under conditions of low resistivity mud. Accordingly, when these tools were introduced a few years ago, the use of salty mud was recommended. Now, with the introduction of induction logging, spe-

Jan 1, 1958