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By H. D. Merchant

NUMEROUS publications have examined hot hardness of metals and alloys. Some have studied creep in long-time hardness tests, few of which, however, were tested under a spherical indentor. 1-3 The results of Mulhearn and Tabor' indicate a parabolic-type creep for indium and lead, whereas Moore and Tabor2 how a logarithmic-type creep for indium. Similar semilog relationships between hardness and time have been found by Goffard and wheeler3 for magnesium, aluminum, and their alloys. In this note, the elevated-temperature hardness of some complex alloys, shown in Table I, was examined to discover whether any basic information about the deformation behavior of the alloys could be obtained. One of the alloys, H-13 alloy steel, was tested for short-time creep tests to examine the hardness-time relationship at various temperatures. A standard Brinell Hardness Tester, mounted with an appropriate furnace and 99 pct A12O3 poly-crystalline indentor, was employed for the purpose. The alloys were tested at temperatures from room to 1400°F for 30 sec under 1500-kg load. The creep studies were conducted for about 8500 sec at 7l°, 500°, 1000°, and 1200°F. For constants A and B, a relationship of the type H = Aexp(-BT) [ll was obtained for all alloys between hardness, H, and temperature, T. In the semilogarithmic plot, the data points for each alloy were arranged into two groups, each group on a straight line with a specific set of A and B values. These results are in agreement with many such observations on hot hardness, notably those of Westbrook for pure metals,4 The thermal softening coefficient, B, and transition temperature, Tt, for various alloys are shown in Table I. The change in slope around the transition temperature suggests an apparent change in the mechanism of deformation, probably from the shear (below Tt) to the diffusion type of mechanism. At the temperatures above Tt, for constants A' and B, a relationship of the type was obtained between H and T, Fig. 1. The nature of the equation, where R is gas constant, suggests the possibility of a thermally activated mechanism of deformation above Tt. The constant B' may hence be defined as the apparent activation energy of indentation. The B' values of various alloys are shown in Table I. A plot of B vs B' gives a curvilinear relation shown in Fig. 2. The indentation-creep data for H-13 alloy steel is shown in Fig. 3. At 71" and 500°F, the creep initially follows the logarithmic time law. However, the indentation size stabilizes after 7 sec at 71°F, and after 10 sec at 500°F. Further increase in loading time has no effect on indentation size. The creep of 1000° and 1200°F follows the logarithmic time law for the first 1000 sec, after which the

Jan 1, 1964

By Z. T. Bieniawski

The importance of understanding the phenomena associated with rock fracture has long been fully appreciated in rock mechanics. This is clearly apparent from the special attention paid to rock fracture in the comprehensive papers published within the past four years.l-5 These papers present a picture of how the knowledge of brittle fracture of rock was gradually enriched and also show that what was often taken for granted three or four years ago is no longer considered as valid today. The Griffith hypothesis,6 thought in the past to predict the strength of rock, is now known to be applicable to fracture initiation only. The knowledge of a failure criterion for fracture initiation is not sufficient, however, as after fracture initiation the rock is still a useful material even possessing increasing load-bearing ability. The importance of the fracture propagation process, subsequent to fracture initiation, is thus obvious. Yet, relatively little attention has so far been paid to brittle fracture propagation in rock. As it is now realized that understanding of this process is a prerequisite for practical rock mechanics applications, studies of propagation of brittle fracture in rock constitute an important aspect of rock mechanics research. It has been pointed out 4 that it is essential that the failure mechanism is fully understood before a failure criterion is postulated. Many failure criteria have been propounded in the past on the basis of theoretical reasoning alone and could not be verified by experimental evidence. Recently, a hypothesis for the mechanism of brittle fracture of rock was propounded, 4 describing the events taking place in the rock from the initial application of gradually increased load to complete disintegration of the material.

Jan 1, 1972

By J. C. Jaeger, G. A. Wiebols, N. G. W. Cook

It is usual practice in engineering to design a stable structure by ensuring that the stresses in the elements of the structure are always less than their strength, which may be defined as the yield stress, the ultimate stress, or the fatigue stress, according to the type of the load. Such restrictive design is not practical in the design of underground excavations since the rock surrounding such structures is usually failed, but only occasionally does this give rise to instability of the structure. Thus, while the usual criterion for the design of a stable structure is certainly sufficient, it is not necessary for underground excavations. A proper understanding of the conditions necessary for stability is vital to the useful application of rock mechanics knowledge to the design of underground structures. Most tests on the properties and strength of brittle rocks are disrupted at or near maximum load by the rapid release into the specimen of energy stored in the resilience of the testing machine. This is in contrast with a phenomenon, which may be observed frequently, where the rock immediately surrounding an excavation is both failed and subject to stress. By postulating a complete stress-strain curve for rock, it can be shown that failure is unstable or stable, depending upon whether the stress-strain curve of the rock lies inside or outside the stress-strain characteristics of the applied stress. Stability is, therefore, a function of the stiffness of the system applying the stress relative to that of the failing rock. Many workers have established that the strength of rock specimens under a lateral hydrostatic confining stress varies linearly with confining stress, in a way which may be expressed by the equation CT=Co+K[o]3

Jan 1, 1972

By D. M. Dunbar

LONG before Columbus discovered America the original inhabitants toiled in the copper workings of the Andean Cordillera. Their best diggings appear to have been at Chuquicamata, site of the huge present-day open pit owned by the Chile Exploration Co., subsidiary of Anaconda Copper Mining Co. Located in Antofagasta Province of northern Chile, Chuquicamata is in the Atacama desert, high on the western slope of the Andes at 9500-ft elevation. In the Chuquicamata area the Atacama desert merges into the Cordillera. The climate is extremely arid and precipitation, either in the form of rain or snow, is very infrequent. The temperature varies from 50° to 85°F during the day, and drops to 20° to 40° at night. The Antofagasta and Bolivia Railroad, which connects the Chilean Port of Antofagasta with La Paz, Bolivia, passes within approximately 6 miles of the plant. A branch from the main line to Chuquicamata serves the property for outgoing copper and incoming freight. The distance to Antofagasta by rail is 163 miles. Previous to the Inca conquest, this region was inhabited by the Chuco Indians, a small tribe, descendants of the Aymaras and Quechuas. The Incas, whose capital was located in Cuzco, Peru, gradually extended their empire to the south, reaching at one time to what is now central Chile. It is believed that they built crude primitive furnaces on the banks of the Rio Salado where on a small scale they smelted copper ore from Chuquicamata. At the time of the subsequent Spanish conquest, legend has it that Diego de Almagro, on his return to Cuzco in 1536 after his invasion of Chile, obtained from these furnaces metallic copper for horseshoes. During the period from 1560 to 1879 the high grade veins of the Chuquicamata deposit were worked superficially by the Spaniards and Bolivians. The treaty signed after the war of 1879 recognized the sovereignty of Chile over this territory and Chile, realizing the importance of the district, started to develop it in an orderly manner, although only high grade veins were worked. New Process Is Key Reports on the deposit were brought to the attention of Albert C. Burrage, a Boston lawyer and financier, in 1910. Chuquicamata was described as a huge deposit of ore that was not amenable to the usual treatment by concentrating and smelting since much of the copper occurred as oxides. He had been working on a process for the recovery of copper from sulphide ore which involved a sulphating roast, leaching of the roasted product, and pre-

Jan 1, 1952

By Earl S. Greiner, Eric R. Jette

ALTHOUGH the mechanical and chemical characteristics of certain iron-nickel-silicon alloys have been investigated,1 the available literature shows no results of a systematic investigation of the constitution of this system. This paper describes the results of an X-ray investigation of the constitution of the iron-rich iron-nickel-silicon alloys at 600°C. Data on the constitution of the included binary systems obtained in other investigations have been correlated with the structure of the ternary alloys. Jette and Foote2 have presented a tentative constitutional diagram of the iron-nickel system following X-ray studies on quenched specimens. This diagram shows that the alloys at 600°C. containing from zero to approximately 4 atomic per cent nickel consist of a body-centered cubic (alpha) phase, the alloys containing 4 to 24 atomic per cent nickel consist of body-centered cubic (alpha) and face- centered cubic (gamma) phases, and the alloys containing from 24 to 100 atomic per cent nickel consist of a face-centered cubic (gamma) phase. These investigators recognized that it was not possible to retain the gamma phase in equilibrium by quenching alloys containing less than approximately 25 atomic per cent nickel and that high-temperature X-ray methods were desirable to determine the gamma-phase solubility limit. In a later investigation of the iron-nickel alloys, Owen and Sulley3 determined the alpha-phase solid solubility limit to be 3.5 atomic per cent nickel at 600°C. High-temperature X-ray methods showed the solid solubility limit of the gamma phase to be 14 atomic per cent nickel at 600°C. Since the high-temperature X-ray method should reveal equilibrium conditions in these alloys better than the quench method of other investigators, the results of Owen and Sulley pertaining to the gamma-phase boundary are to be preferred. As the result of an X-ray investigation of quenched iron-silicon alloys, Greiner and Jette4 have shown these materials to consist of a body-centered cubic (alpha) phase containing from o to 26.4 atomic per cent silicon at 600°C. The alloys containing from 26.4 to approximately 50 atomic per cent silicon consist of two phases at 600°C.; namely, alpha and eta. The eta phase corresponds to the stoichiometrical formula FeSi (33.4 wt. per cent Si).* The literature pertaining to the constitution of the nickel-silicon alloys has been reviewed by Ackerman,5 who found disagreements in the results of various investigators on several parts of the system. Subsequent data on the constitution of the nickel-silicon alloys were reported by Osawa and Okamoto.6

Jan 1, 1943

By N. W. Wickersham, Ward B. Blodget, Roberts R. Boyd

The year 1926 has seen few radical changes or developments in methods of drilling and handling oil wells, but it has been a year of steady progress and development in deep drilling and production methods. Probably the outstanding development of the year was recognition by the directors of the American Petroleum Institute of the importance of natural gas in the production of oil, and the Institute directors' resolutions in December, 1926, regarding regulation of gas production with oil by state legislation. This matter is extremely important and will receive the attention of the industry in 1927. Advances in Drilling Equipment The history of the progress of deep well drilling is the solution of problems as they have confronted the operator. As the prospects for deeper production have become apparent, methods of penetrating the earth to greater depths have been devised. Rotary Equipment Improvements in the construction and in the methods of operation of rotary drilling equipment have practically caused elimination of cable tools in California for all but shallow work. The rotary drill, from 1910 when it began to be a practical factor in California, has been making steady advances, first displacing cable tools for drilling to the oil sands in proved fields and later displacing the cable-tool outfit entirely. With the perfection of machinery for taking core samples of the formation penetrated, the rotary drill has become generally used for wildcat work, continuous coring being practiced when desirable. Deep Holes The use of the rotary drill has made commercially feasible the opening of oil fields at greater depths than was considered possible with cable tools. Heavier equipment has been promptly supplied as occasion has

Jan 1, 1927

By Hermann Wedding

I ASK your permission to speak about a matter which is not of a specifically scientific nature, but more of a general-I might even say of an international-nature, and the international character which this city now presents must be my justification for introducing it. The Germans, very often, are thought to be an exceedingly warlike people, but I come to-day in the capacity of a peacemaker. Our German language is an original language; it is, therefore, a language in which it is impossible to change the meaning of a word at will. It may be, perhaps, easier in a combined language, as the English, to associate and to exchange meanings. Now, a word which we hear a great deal at the present day, is "Stahl," in English, "steel." This word means, in the German language, a substance which can be hardened. As the German literature, in relation to metallurgy, is the oldest of the modern world, this circumstance may give the German a right to ask for consideration. But I think, now, when the four languages, German, Swedish, French, and English, compete in rich metallurgical literature, it is very necessary to have uniformity in the nomenclature of iron, which would prove not only useful for science, but equally so for trade. For that purpose I propose to make the divisions of iron so that the word steel shall comprise a subdivision and not a primary division as formerly. Nature furnishes us iron mostly in the state of oxides, and if in any other condition, we must convert the ore into oxide before we can make iron. The oxides are always mixed with certain earthy substances called rock or gangue. The extraction of iron involves, therefore, the twofold process of the reduction of the iron, and im¬parting to it the amount of carbon necessary for technical purposes, and the separation of the reduced and carburized iron from the gangue. The reduction is always effected by carbon or carbonaceous substances (coke, anthracite, carbonic oxide, etc.), and the result is, according to the degree of heat employed, either malleable iron or a non-malleable iron. The process of making malleable iron in this way is called, generally, the direct process-in German, Rennarbeil. It produces the iron in a solid state with a fluid cinder. By this process our ancestors made all their iron, and it has been revived in various ways in modern times up to the process of Mr. Blair, so far as I know, always without commercial success. The

Jan 1, 1877

By Hermann Wedding

I ask your permission to speak about a matter which is not of a specifically scientific nature, but more of a general—I might even say of an international—nature, and the international character which this city now presents must be my justification for introducing it. The Germans, very often, are thought to be an exceedingly warlike people, but I come to-day in the capacity of a peacemaker. Our German language is an original language; it is, therefore, a language in which it is impossible to change the meaning of a word at will. It may be, perhaps, easier in a combined language, as the English, to associate and to exchange meanings. Now, a word which we hear a great deal at the present day, is "Stahl," in English, "steel." This word means, in the German language, a substance which can be hardened. As the German literature, in relation to metallurgy, is the oldest of the modern world, this circumstance may give the German a right to ask for consideration. But I think, now, when the four languages, German, Swedish, French, and English, compete in rich metallurgical literature, it is very necessary to have uniformity in the nomenclature of iron, which would prove not only useful for science, but equally so for trade. For that purpose I propose to make the divisions of iron so that the word steel shall comprise a subdivision and not a primary division as formerly. Nature furnishes us iron mostly in the state of oxides, and if in any other condition, we must convert the ore into oxide before we can make iron. The oxides are always mixed with certain earthy substances called rock or gangue. The extraction of iron involves, therefore, the twofold process of the reduction of the iron, and imparting to it the amount of carbon necessary for technical purposes, and the separation of the reduced and carburized iron from the gangue. The reduction is always effected by carbon or carbonaceous substances (coke, anthracite, carbonic oxide, etc.), and the result is, according to the degree of heat employed, either malleable iron or a non-malleable iron. The process of malting malleable iron in this way is called, generally, the direct process—in German, Rennarbeit. It produces the iron in a solid state with a fluid cinder. By this process our ancestors made all their iron, and it has been revived in various ways in modern times up to the process of Mr. Blair, so far as I know, always without commercial success. The

By L. G. Jones

The objective of this paper is to present a better method for determining reservoir reserves of gas from extended drawdown test data. Means are proposed for conducting the test with or without the requirement of prior build-up to a static reservoir pressure. The test is based upon solutions to unsteady-state gas flow developed in an earlier paper and is believed to be superior to previous methods for determining reserves from flow-test data. The limitatiom of such tests are discussed, with emphasis on the subject of test duration. The test can supply useful information if the mechanics and limitations of it are understood. This type of information can be particularly valuable in deciding whether or not to drill offsets to producing wells. INTRODUCTION In the life of any gas or oil field, the engineer in charge must decide if certain wells need stimulation and whether or not to drill more wells in the field. Well production tests can aid in making these decisions. For instance, the value of stimulation can be estimated by determining formation permeability and the amount of well damage from drawdown or build-up tests. These tests are freely used in the oil industry. A less well-known type of analysis uses data from extended drawdown tests for determining reservoir reserves. Into this category fits the "reservoir limit test" of Jones,'-3 and the "reservoir reserve test" presented in this paper. The chief value of these tests is their ability to "see" reservoir boundaries and thus prevent costly dry holes. Methods for determining reserves of both gas and oil reservoirs were proposed in the work of Jones. His proposals appear sound for single-phase liquid flow. The generality of his work on gas flow is open to question, however, since the analysis is based upon solutions to liquid-flow equations. The test for gas reserves presented here is derived from unsteady-state gas-flow solutions presented in a previous paper.' In deriving this reservoir reserve test, it has been assumed that all of the reservoir energy is provided by expansion of the reservoir fluid and that the reservoir is radially symmetrical. No mention has been made of the effects of deviations from Darcy's law such as quadratic (turbulent) flow and well damage. Since the terms representing these effects are function of rate only, since the rate is constant and since the data are plotted in a differential form, it seems reasonable that these terms will not affect the test results in any way. No attempt has been made to estimate the effects of water drive, faults, or other departures from an idealized and isolated reservoir. For a qualitative discussion of some of these effects, the reader is referred to a paper by Jones3

By J. Koskinen, P. Vanninen, T. Leskinen, A. Leppala

Continuous and accurate analysis of slurries has become a critical requirement in mineral processing. With on-stream assay data, automation procedures can be employed to obtain higher recovery and improved control of production. The Courier system was developed by Outokumpu Oy, taking advantage of mineral processing know-how, to provide means for achieving these objectives in the company's ore concentrator operations. It became evident, based on early experience with on-stream analysis, that the Courier should be a complete system to fulfill all functions of the analysis operation. The system includes equipment and techniques for primary sampling, sample preparation for assaying, and processing of data for final assay results. In addition, the on-line X-ray spectrometer unit was developed specifically for industrial use, incorporating a number of technical advances. A new system for converting spectrometric data to assays is based on a physical model programmed on a digital computer. The Courier system is furnished on a turn-key installation basis incorporating all elements needed for operation including calibration. The experience to date with the Courier system at the Pyhäsalmi concentrator is summarized. Reference is also made to recent results with installations at the Outokumpu and Vihanti concentrators.

Jan 1, 1972

We did install one 100% brick bottom in our #33 furnace which is basically the same design as Inland's furnace. We had previously embarked on a program of replacing all bottoms in our 300 ton furnaces every 2nd campaign which would be about every 2000 - 2300 heats. This had been necessitated by the effect of our rather high oxygen blowing rates and our desire to maintain a minimum bottom interval level. This meant that we were able to compare bottom performance of various types of materials on a realistic bas is. Since furnace availability is critical to our operation, we are organized to employ every piece of equipment and all the necessary man power to complete a rebuild in the shortest possible time. A 300 ton furnace requires 7.5 days to rebuild. If a new bottom is to be installed an additional 2.5 days is added - 24 hours for tear out and 36 hours for bricklaying - making a total of 10 days.

Jan 1, 1972

By J. Donald Graham, John G. Kuhn

The goal of any development drilling program is the drilling of the exact number of holes necessary to adequately determine grade and dimensions of an ore body, no more and no less. Any technique which eliminates unnecessary drilling costs produces beneficial results, both to the company and to the person who can claim the savings. The method for controlling development drilling programs to be described was developed during the latter part of a major development drilling project at the Christmas mine of Inspiration Consolidated Copper Co. in Gila County, Arizona. It was used to test the need for drilling individual holes but could be expanded to control an entire project. Application of this method involves an evaluation of geological conditions present and a good bit of common sense. Projects involving large disseminated, rather homogeneous ore bodies of the porphyry-copper type would be the most likely candidates for application of the technique. Discontinuous ore bodies would not be amenable. The method is based on the measurement of the linear correlation between the spatial distribution of two sets

Jan 1, 1973

By Ernest F. Burchard

PAGE. I. Introduction,........... 75 II. Outline of the Geology......... 76 1. Stratigraphy............ 76 A. Clinton Formation........ 77 2. Structure...........82 3. The Ore..........85 A. Character............ 85 B. Geographic Distribution....88 III. Local Descriptions........... 88 1. Birmingham District.......... 88 A. Topography and Its Relation to Industrial Development... 88 H. Distribution and Structure of Formations.... 89 C. Divisions of the Birmingham District. 95 Division A (Description of the Ore-Beds), . 95 Division B.........105 Division C.......... 106 Division D,..107 Division E,...........108 Division F........ 111 Division C.......... 112 D. Mining .Development.... 113 2. Northeast Alabama........114 IV. Possible Origin oF the Ore......... 119 V. Relation of Origin to Quality and Extent of Ore... 122 VI. Estimates of Ore-Reserves,......... 125 1. Method of Making Estimates......... 125 2. Data and Results....126 VII. Production and Consumption oF IRon-ORe,.... 132 I. Introduction. Brief and interrupted studies of the Alabama Clinton iron-ores have been made within the last four years by members of the IT. S. Geological Survey. Reports on the progress of this

Jan 1, 1910

By A. L. Field

WOOLSEY McA. JOHNSON, Hartford, Conn. (written discussion).¬When ;we regard the number of British thermal units running into the billions that-must be applied to metallurgical slags in the United States, we cannot but conclude that the physical chemistry of-slags is a very important subject when measured in dollars and cents. A further contemplation of the subject shows us that it has been hitherto treated in too purely a practical manner. It is needless to comment at length on the cost of these heat units and on the cost of fluxes to produce these metallurgical slags, for, it amounts to tens of millions of dollars annually. Accordingly, this research is of value to the country. But we must,all balance our results against our efforts. Therefore, while the speaker is unwilling to criticise unduly this meritorious research, lie does criticise it in the interest of the profession for the reason that it seems to him too highly theoretical. The article is much too, scientific to produce results at a minimum cost. Let us explain our meaning. It has been said that there are always two sides to a question. It may be further said that there are always three sides to a question, the two extremes and the middle ground. In any industrial research there are the highly theoretical side, the purely practical side, and the theoretico-practical side. To study a slag and be practical in the studying, there is something needed that represents in the laboratory (or in microcosm) what actually happens macrocosmically in the blast furnace. There is such a thing as the art of metallurgical research occupying the middle ground between theory and practice.

Jan 4, 1917

GENERAL GEOLOGIC DESCRIPTION The Escalante silver deposit located in southwestern Utah is an epithermal vein system consisting of a hanging wall and footwall vein, straight along strike and dipping about 1.2 rad (70°). The veins consist of banded quartz and calcite fissure fillings between volcanic wall rock that are silicified for some distance outward from the vein. The walls of the veins are sharp and the silver values are irratically distributed through the various bands within the vein. Only very low grade values are to be found in the wall rock on either side. The portion of the veins above the water table have been somewhat leached, with some secondary enrichment below. The mineralogical zonation is variable due to a fluctuating water table through geologic time. SAMPLE MANAGEMENT AND COMPOSITE ASSAYS Sample data for the deposit was obtained from over 50 diamond drill holes, from channel samples cut at intervals across a drift, and from scattered surface trenches along the out- crop of the hanging wall vein. Fig. 13-1 is a surface plan map showing the vein outcrop and some diamond drill locations. Two cross sections through the vein are shown in Figs. 1 3-2 and 13-3. Nearly all of the diamond drill core of vein material was assayed in 0.3-m (I-ft) lengths, from which weighted composite assays were manually calculated for the horizontal thickness of the vein. The centers of the composited samples were plotted in north and east coordinates and by elevation, and locations and assay

Jan 1, 1980

SEC. 1. The membership of the Institute shall comprise seven classes, namely: 1. Members; 2. Honorary Members; 3. Senior Members; 4. Associates; 5. Junior Members; 6. Rocky Mountain Members; 7. Junior Foreign Affiliates. All shall be equally entitled to the privileges of membership, excepting that no member of any class whose residence shall be outside of the United States of America, except those residing in Mexico and Canada, shall be entitled to vote. SEC. 2. Members: A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years' employment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. This shall not apply to Rocky Mountain Members.

Jan 1, 1946

SEC. 1. The membership of the Institute shall comprise seven classes, namely: 1. Members; 2. Honorary Members; 3. Senior Members; 4. Associates; 5. Junior Members; 6. Rocky Mountain Members; 7. Junior Foreign Affiliates. All shall be equally entitled to the privileges of membership, excepting that no member of any class whose residence shall be outside of the United States of America, except those residing in Mexico and Canada, shall be entitled to vote. SEC. 2. Members: A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years' employment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. This shall not apply to Rocky Mountain Members.

Jan 1, 1946

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By T. B. Counselman

AfteR several years study, the Universal Atlas Cement Co. decided to rebuild its plant at Leeds, Alabama. The entire old plant, which was to operate during the new construction, was then to be scrapped with the exception of two kilns. The quarry was to be mechanized, new and larger kilns installed, with the most modern type of equipment all through the plant. Raw grinding operations at all of the Universal Atlas plants were dry. However, the dust hazard of this operation and the growing emphasis on occupational diseases made wet grinding attractive. Coal at Leeds is cheap, so that a slightly higher coal practice was unimportant. Power was cheap, so that waste-heat boilers were not desirable. Since new kilns were to be installed, these could be made long enough to make filters unnecessary. Wet raw grinding could be either the old practice of open-circuit compartment mills or closed-circuit grinding in accordance with metal-lurgical practice. The latter saved power and steel wear and saved initial investment. This had been demonstrated in cement plants. Also, the elimination of tramp oversize was a most important advantage. Ease of chemical control was another factor. Blending in the thickener, with elimination of slurry mixers had been found practicable. Therefore, if wet raw grinding were used at all, the advantages were clearly in favor of closed-circuit grinding. Detailed layouts of the most modern possible closed-circuit dry-grinding plant and of a closed-circuit wet-grinding plant were prepared, and careful estimates were made of initial investment and operating costs. Full consideration of all the factors involved resulted in a decision to install wet closed-circuit grinding. The capacity of the new kilns was established at 4000 bbl. per day. Two new kilns were installed, each with a capacity of 80 bbl. per hour. Since 625 lb. of raw material is required to make a barrel of finished cement, the capacity of the grinding plant for the new kilns had to average only 1250 tons per day. Sufficient additional grinding capacity had to be provided for the two remaining old kilns, or their possible replacement by a third new kiln. The grinding rate, therefore, was set at 90 tons per

Jan 1, 1939

By T. B. Counselman

AfteR several years study, the Universal Atlas Cement Co. decided to rebuild its plant at Leeds, Alabama. The entire old plant, which was to operate during the new construction, was then to be scrapped with the exception of two kilns. The quarry was to be mechanized, new and larger kilns installed, with the most modern type of equipment all through the plant. Raw grinding operations at all of the Universal Atlas plants were dry. However, the dust hazard of this operation and the growing emphasis on occupational diseases made wet grinding attractive. Coal at Leeds is cheap, so that a slightly higher coal practice was unimportant. Power was cheap, so that waste-heat boilers were not desirable. Since new kilns were to be installed, these could be made long enough to make filters unnecessary. Wet raw grinding could be either the old practice of open-circuit compartment mills or closed-circuit grinding in accordance with metal-lurgical practice. The latter saved power and steel wear and saved initial investment. This had been demonstrated in cement plants. Also, the elimination of tramp oversize was a most important advantage. Ease of chemical control was another factor. Blending in the thickener, with elimination of slurry mixers had been found practicable. Therefore, if wet raw grinding were used at all, the advantages were clearly in favor of closed-circuit grinding. Detailed layouts of the most modern possible closed-circuit dry-grinding plant and of a closed-circuit wet-grinding plant were prepared, and careful estimates were made of initial investment and operating costs. Full consideration of all the factors involved resulted in a decision to install wet closed-circuit grinding. The capacity of the new kilns was established at 4000 bbl. per day. Two new kilns were installed, each with a capacity of 80 bbl. per hour. Since 625 lb. of raw material is required to make a barrel of finished cement, the capacity of the grinding plant for the new kilns had to average only 1250 tons per day. Sufficient additional grinding capacity had to be provided for the two remaining old kilns, or their possible replacement by a third new kiln. The grinding rate, therefore, was set at 90 tons per

Jan 1, 1939