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The new saw mill at Cache Bay of the Geo. Gordon & Co., Ltd., a subsidiary of International Nickel Co., of Canada, is equipped with the first fully electric saw carriage drives in Ontario. It has a capacity of 120,000 ft of lumber in an 8-hr shift. About half of the mill's production is high grade white pine lumber which is shipped to the general market. The other half, red pine is used in the mining operations of International Nickel in the Sudbury district, 55 miles west of Cache Bay. [ ] Inco with a potential need of 77 million board ft a year, gets only part of its supply from the new mill. The milling firm became an Inco subsidiary Jan. 1, 1948.

Jan 1, 1952

By Walter E. Lewis, Robert L. Marovelli

Underground support has a long history as evidenced by Agricola's general description in Dc Re Metallica:1 "The timbering of these openings is done as follows: stulls are set at intervals into hitches in the hanging and footwall, and upon them smooth poles are laid continuously; and that they may be able to bear the weight, the stulls are generally a foot and a half thick. After the ore has been taken out and the mining of the vein is being done elsewhere, the rock then broken, especially if it cannot be taken away without great difficulty, is thrown into these openings among the timbers, and the carriers of the ore are saved toil, and the owners save half the expense. This, then, generally speaking, is the method by which everything related to the timbering of shafts, tunnels, and drifts is carried out."

Jan 1, 1971

By Ronald A. Murdock

INTRODUCTION Exxon's Highland Uranium Operations in eastern Wyoming consists of an open pit, an underground mine and a mill complex. The geology of the deposit is reviewed in this paper, and an overview of the mining operations at both the surface and underground mines is presented. Topics discussed include geology, stripping of overburden and mining of ore in the open pit, and underground development and stoping methods. GEOLOGY The Highland uranium deposit was discovered in 1968 by Exxon Minerals Company, U.S.A., in Converse County, Wyoming, 35 miles north of Douglas. The mine is located at an elevation of about 5,200 ft in a high-plains, sagebrush-covered prairie typical of eastern Wyoming. The deposit is near the southern edge of the Powder River Basin in the Paleocene Fort Union Formation. The Fort Union Formation consists of 1,900 to 3,200 ft of sandstone, siltstone, mudstone, claystone and coal beds. Siltstone, mudstone and claystone are collectively referred to as "shale" at Highland. There are many alternating layers of shale and sandstone in the Fort Union Formation; but in the Highland area, there are only three principal sandstones, known as the Highland Sand Group, which host the uranium. The combined sand thickness is about 150 ft.

Jan 1, 1983

By Philip B. Dettmer

Up to now we have spoken optimistically of the many potential savings in capital and operating costs to be obtained from the selection of larger diameter and horsepower grinding mills. Such mills may well be the correct choice for one grinding plant but could be absolutely wrong for another plant. It is emphasized here that many significant factors other than the capital cost, labor, grinding media and power savings are involved in the sizing and selection of the optimum grinding circuit. The following discussion covers some of these factors and their relationship to larger mill design. The first consideration is: What is the grinding circuit supposed to do? In most instances it is one or both of the following: 1. Grind the feed material fine enough to liberate the desired minerals but with a minimum of over- grinding. Examples are preparation of ore for flotation, gravity separation, etc. 2. Grind to some pre-specified particle size or particle surface area. Examples of this are cement manufacture or the preparation of feed material for pelletizing; other examples are preparation for chemical reactions or ceramic manufacture.

Jan 5, 1965

By Eckley B. Coxe

At the first meeting of the Institute, a paper was read by Mr. Rothwell, calling attention to the importance of at once considering the great waste of anthracite coal under the present system of mining and preparing that fuel for market, and a committee was appointed to examine and report upon the method now in use. About the time the committee were selected, a general resumption of work, after the long strike, took place in the coal regions, and the members of the committee have not in consequence had as much leisure to devote to the study of the question as its importance demands. In the present preliminary report we shall merely sketch out the . plan which we propose to pursue in our investigations, so that when our fellow-members are called upon to assist us in our work by furnishing statistics, etc., they may understand more clearly for what object our inquiries will be made. As one of the most practicable methods of obtaining the information requisite for an intelligent consideration of our subject, we propose to send, from time to time, to members and others interested in the mining of anthracite coal, printed sets of questions relating to points under consideration. We would here impress upon our fellow members the importance of filling up these papers as far as they can from their own knowledge. We would, of course, wish each question to be answered as fully as possible, but we do not expect every one to answer them all. One question well answered would be of more use to us than the whole paper filled up with answers, many of

By Edward Estabrook

THIS paper gives a brief account of the geologic and production problems encountered in the Grass Creek oil field, the methods used in their solution, and the beneficial results obtained from the work. The author wishes to acknowledge the assistance received from J. H. Pearson and Miss Ninettta A. Davis in the collection of the data and the preparation of the cross-sections. Permission for its publication was given by the officials of the Midwest Refining Co. and the Ohio Oil Co. The Grass Creek oil field is located in Ts. 98-99 W., R. 46 N., Hot Springs County, Wyo. The productive area includes about 2 1/2 mi. (4 km.) on the apex of a great anticlinal fold occupying more than 150 sq. mi. Fig. 1 shows the structural contours of the field. Oil was dicovered in the field in June, 1914; development proceeded rapidly and production rose to a maximum in 1918. The marketed production has been approximately as follows: BARRELS BARRELS 1915 94,073.5 1918 2,946,774.27 1916 1,404,183.97 1919 2,000,584.84 1917 2,780,697.51 1920 1,485,080.94 About 350 wells, 800 to 1500 ft. (243 to 457 m.) deep have been drilled to reach the upper oil sands; two companies, the Ohio Oil Co. and the Midwest Refining Co., operate the entire field.

Jan 2, 1922

By Daniel L. Murphy

The iron ore province of Quebec and Baffin Island trends from the southern shore of Baffin Island northeasterly through the Labrador Trough to Matonipi Lake, approximately 185 miles northwest of Seven Islands, but future geologic field studies will very likely extend the limits of the province to include the ferruginous and associated rocks of the Lake Mistassini area. Recent improvements in the beneficiation of low-grade iron ore have stimulated widespread exploration for deposits amenable to concentration, particularly along the southwest extension of the Trough. GENERAL LITHOLOGY Pleistocene and recent deposits of clay, sand, gravel and erratic boulders cover roughly 60% of the land surface. All of the bedrock is of Precambrian age (Table I). Paragneisses and paraschists together with metasedimentary iron-formation, marble and quartzite are abundant and, for the most part, appear to be metamorphic equivalents of the relatively unmetamorphosed rocks of the Labrador Trough to the north beyond the "Grenville Front." Bodies of amphibolite are widely scattered. A large portion of the metamorphic rock shows some degree of permeation by granite material as well as alteration by hydrothermal solutions. The youngest bedrock consists of a complex containing slightly altered ultramafic to monozonitic intrusives.

Jan 9, 1962

By E. Werchowsky

FOR over four years, since the revolution of 1917, Russia has been cut off from the Western world. Political and general economical reforms have attracted the attention of the public and business world, but mining men have had no information as to the situation in their branch of industry, as various articles which have appeared in the European and American press gave little information as to actual conditions in our country. When the Soviet system of government was estab-lished and private ownership abolished, it affected the FIG. 1.-ORGANIZATION OF THE COUNCIL OF MINES. mining industry very little at first. The power of the Soviets did not affect the Ural provinces nor Ukraine or Asiatic Russia (Siberia, Turkestan, etc.) during 1918 and 1919, and, as is well known, the mineral wealth of the republic lies within those boundaries. In the Ural Mountains are copper, gold, and platinum; in Siberia, silver, lead, zinc, and gold, and the coal deposits in Koushetz district; in Ukraine, there are the coal fields of Donetz and the iron mines of Krivvy Rog, and silver, lead, zinc, copper, oil, etc. in the Cauca-sus. The mineral resources of Central Russia are the coal fields of Moscow (low-grade and brown coal), turf deposits, iron mines in Tula and Kalonga provinces, and quarries of granite and other building materials.

Jan 8, 1922

By Jouko O. Kallioinen

The control of zinc flotation at Outokumpu Oy's Pyhasalmi and Vihanti mines is described. At Pyhäsalmi the zinc flotation circuit is partially open. Zinc and other metal assays of pulp flows are measured and direct assay control of concentrates in various flotation steps is adopted. Assay control is carried out by adjusting flotation air and pulp levels. Optimization with copper sulphate ensures high Zn- recovery and minimum copper sulphate consumption. A froth depth monitor is used to measure froth quality. At Vihanti the zinc flotation takes place in closed circuit. The most important control loop is the Zn-assay control of rougher concentrate by adjusting flotation air. The quality of froth is measured indirectly and thus copper sulphate consumption is altered. The circulating load is controlled also by flotation air in the three cleaning steps. The comparison of the control strategies shows that a more sophisticated control is adopted at Pyhäsalmi because the selective flotation of this massive sulphide ore is considered to be difficult. The control strategy includes numerous tests performed by the computer and control algorithms developed for the case. The control targets of the two zinc flotations described are also different: At Pyhäsalmi Zn-assay control of final concentrate including copper sulphate optimizing, at Vihanti the control of circulating load and Zn-assay of rougher concentrate.

Jan 1, 1984

Carlisle: This is August 1960 and I am sitting across the table from Henry DeWitt Smith. We both took the mining course at Yale the same year; and here we are, over fifty years later, at Nantucket Island where we have spent quite a number of summers together. Now, let's start the questions with something about the center of your career. Let's say Tsumeb; not about the mine itself which people know, but some of the details on how you happened to take it over for Newmont. Mr. Smith: I first heard of Tsumeb, a famous German mine, through our own associates O'okiep Copper Co. From 1935 on, the local management at O'okiep, being reasonably close, kept the New York office informed. It served as a listening post for new mine development, as well as being a highly profitable copper mine in the northwest Cape Colony. We had all known of a famous German mine in South West Africa called Tsumeb. But it had a reputation for not welcoming visiting engineers. One engineer who went to this property for the Ministry of Supply in 1943, '44 and '45 was Arthur Storke. He was much impressed with possibilities of profitable operation. This mine had been operated by a German company since 1910. It was finally taken over by the Custodian of Enemy Property for the Union of South Africa.

Jan 11, 1963

By Z. T. Bieniawski, E. Unal, H. Reginald Hardy

INTRODUCTION Rock bolts are a major means of support in underground coal mines in the United States. However, two of the most crucial problems facing the mining engineer today are that of finding a well defined and standard method for testing the anchoring ability of rock bolts, and of selecting the most suitable type of rock bolt and bolting pattern for a particular mine or specific mine section (Anon., 1982). Such selection requires not only an understanding of the behavior of the rock mass and the rock-bolt unit itself, but also a knowledge of the basic mechanisms by which rock bolts provide support while they interact with the rock mass during various field loading conditions. A recent study in this area has shown the inadequacy of present methods used in selecting and testing of rock bolts and the lack of clearly defined guidelines for safe and economical design of bolting patterns (Bieniawski, et al., 1980). The present paper describes a research study aimed at developing laboratory instrumentation and associated techniques for the evaluation of bolt-rock interaction. The instrumentation system developed, procedures followed during various experiments, and typical results from a series of studies carried out on mechanical bolts are presented. DEVELOPMENT OF THE ROCK BOLT TESTING FACILITY General A block diagram of the experimental facilities are shown in Fig. 1. The system consists of three main sections. The first

Jan 1, 1982

By E. C. Harder

SINCE early in 1916, when it became apparent that the steel industry of the United States could not depend, for the duration of the war, on several important foreign sources of manganese and might have to depend entirely on domestic ores, the U. S. Geological Survey, with the assistance f several cooperating organizations, has made a comprehensive investigation of domestic manganese resources. The work has included field studies in a number of states as well as annual, quarterly, and monthly canvasses among operators concerning current and future production. In order that the interested public might have access to the important results of the studies, preliminary reports concerning the field work as well as periodic summaries of production were issued as promptly as possible. Although large deposits of rich manganese oxides appear to be lacking in the United States, small deposits of high-grade material are numerous and widely distributed and large low-grade deposits are found in several places. The principal districts in which high-grade manganese ore is mined, in the order of their importance as recent sources of production, are: Philipsburg district, Mont.; Butte district, Mont.; Southern Nevada region; Central California region; Bisbee district, Ariz.; Appalachian region of Virginia; Batesville district, Ark.; Tintic district, Utah; and Cartersville district, Ga. Scattered deposits of some importance are found in western Arizona, southern California, eastern Tennessee, southern Oregon, and central Utah. The formation of many manganese oxide deposits appears to be related to the physiographic histories of the regions in which they occur.

Jan 5, 1919

By Daniel L. Noble

Riparian communities are those related to, or near a natural watercourse (or sometimes of a lake, impoundment, or tidewater). Generally, riparian communities contrast sharply with the dominant vegetation type in an area, for example, the willow-birch-aspen- dominated watercourse in the Black Hills with its associated beaver- muskrat-trout habitat as compared to the dominant monotype ponderosa pine forest on either side of the drainage. Riparian ecosystems are valuable for the aesthetics, namely, varied landscape; photography and art; human awareness; diversity of plant and animal life, some of which may be unique to that habitat; cover, food, and water for associated wildlife and domestic animals; for recreation; for domestic water supply; and as natural outdoor laboratories. One major negative impact on riparian communities is hazardous chemicals from effluents from agricultural, industrial, and mining- metallurgical processes. One such chemical is cyanide, long used in the processing of gold and silver, and discharged previously directly into some of our natural ecosystems. With present environmental awareness, industry and government are attempting to minimize or eliminate this contamination. Homestake Mining Company began processing gold ore in the Lead- Deadwood area of South Dakota in 1878 and has remained in production at variable activity levels to the present time. The amount of cyanide (and heavy metals) entering the ecosystem during this time can only be crudely estimated, in part because of the variability in activity and the lack of understanding and concern about environmental pollution until the 1960's. Whitewood Creek, a tributary of the Belle Fourche River which flows into the Cheyenne River and

Jan 1, 1983

By Leonard Waldo

The recent and rapid development of the physics of engineering materials at temperatures as low as that of liquid air and as high as that of the electric are, has drawn renewed attention to the absence of tables, properly printed and spaced, for the convenient and accurate translation of temperature from centigrade to Fahrenheit scales and vice versa. It is to be noted that the Fahrenheit scale is the almost universal usage in foundries and shops in the United States, though the laboratories of the same works employ the centigrade notation. The growing use of the electric furnace in Germany and France calls for much American citation all in centigrade high temperatures, and while the arithmetical calculation is simple, it becomes burdensome when often repeated. I have been surprised at the numerous reprints of Table I. from centigrade to Fahrenheit degrees, first privately printed for personal use, which have been made by works, blue-prints, text-books, and technical journals, and I hope that Table II., from Fahrenheit to centigrade degrees, will be equally useful. For mental calculation the easiest rule to convert centigrade into Fahrenheit is to add 32° to twice the centigrade reading less one-tenth of this product: Thus 1000' C. = 2000" — 200" + 32" = 1832" F., and to convert Fahrenheit to centigrade, subtract 32" from the Fahrenheit reading, multiply by 10 and divide by 2 and 9 successively : Thus 1000° F. = 1000° — 32° = 968° X 10 = 9680° - 2 = 4840° - 9 = 537.77° C. Another and often very convenient method is by 'use of a graphic construction as follows :

Jan 1, 1913

Jan 1, 1935

Jan 1, 1935

By J. L. Smith, A. L. Albee

This article presents a series of guidelines by which the geologist can evaluate the likelihood of surface faulting and its probable extent at any given site in Southern California and Nevada. The information is intended primarily for geologists concerned with establishing design criteria for proposed nuclear plants. The geologic problems involved in the location of a nuclear power plant are fundamentally no different from those for other types of installations. They fall into four main categories: foundation stability, landslides and slope stability, shaking due to earthquakes, and surface faulting. For problems in the first three categories the foundation engineer, the geologist, and the seismologist can provide criteria for plant location and design, and these problems can generally be economically handled by appropriate design measures for a project of the magnitude of a nuclear plant. However, problems in the last category — surface faulting — are more difficult to handle and require a unique evaluation. Accordingly, this paper will deal primarily with the problem of establishing design criteria for surface faulting, particularly as it affects nuclear facilities. A nuclear reactor is a power source that for greater safety is contained in a heavy, air-tight structure, just as gas, oil, water, and other power sources must be contained. Surface faulting is significant in that it may reduce the integrity of the containment by affecting critical exterior piping or by breaching of the containment. A similar significance exists relative to dams or tanks for the storage of water, gas, or oil, except that in these latter examples the breaching of the container automatically releases the fluids to do their damage. This is not necessarily the case with the rupture of a reactor containment structure because the function of the containment is totally protective, i.e., it is necessary only in the event that radioactive products are released from the reactor, and there are many other safeguards to pre- vent this release even if the containment is ruptured. At the present time, nuclear power plants must be located near large sources of water for cooling the steam generated. The construction of an industrial facility of any kind on the coast line is esthetically distasteful to most people since, unfortunately, there is not enough coast to fulfill all the needs and all the desires of all the people. In most cases where industrial facilities encroach on the lives of citizens, there is no mechanism other than zoning laws by which a person can effectively protest. But in the case of a nuclear facility, the public hearing required by the Atomic Energy Commission provides a forum for dissent, as in recent case histories, and the question of safety provides objectors with a weapon for fighting the construction of the plant. The nature of a public hearing for a nuclear plant is such that the prospective owner and operator must prove that there is no undue hazard, whereas the objectors need only demonstrate that there is a reasonable doubt. It is in this situation that geology becomes the Achilles Heel of nuclear power plant location. For his investigation, the geologist has natural exposures of rock at the ground surface and a limited number of trenches and drill holes to give him a fairly complete picture of the distribution of the various rock types. From the surficial data, he must infer three more dimensions — depth below the surface, past time, and future time. Unlike many problems faced by engineers, the geologist has only this one set of data from which to reach a conclusion — he is unable to reproduce the natural sequence of events in order to obtain another set of data for comparison. Hence, by the very deductive nature of a geologic conclusion, it is difficult to prove a geologic conclusion beyond a reasonable doubt even to other geologists — and perhaps one should say especially to other geologists because the experience and background of a geologist will strongly influence his conclusion, and no two geologists have exactly the same experience and training. The engineer and the public official would like the geologist to conclude that faulting cannot occur at a given site or to assign a numerical value to the probability of its occurrence — but no responsible geologist can do either of these things. Since government officials and others must make decisions that affect the public safety, it would seem that the geologic profession must attempt to establish criteria and

Jan 1, 1968

By D. A. Stevenson, R. A. Burmeister

Single-phase silver antimony telluride has been prepared by zone-melting techniques using initial compositions of A new phase appears upon prolonged annealing of this material, but the reaction does not appear to be a simple eutectoid decomposition. A complete analysis of the phase equilibria is complicated by the slow kinetics involved. The Hall coefficient, magneto -resistance, electrical resistivity, and Seebeck coefficient are all sensitive to the presence of second phases. The low Hall mobilities measured for single-phase material indicate that the usual band theory is inadequate to explain the observed transport properties in the system. Density anomalies of up to 2.5 pet between measured and theoretical density were observed but are not conclusive evidence for a defect structure. COMPOSITIONS in the Ag-Sb-Te system have been studied previously by several investigators.1"18 The interest in this system arises from potential thermoelectric applications of alloys on the Ag2Te-Sb2Tes vertical section. Although the composition corresponding to the formula AgSbTe, has received most attention, it has been found to consist of more than one phase.7'8 A thorough understanding of the properties of this heterogeneous material has been impeded by both lack of knowledge of the properties of the homogeneous phases comprising it and the problem of analysis of transport properties in an inhomogeneous system. The present work describes the preparation of the homogeneous ternary phase and the corresponding electrical properties of both homogeneous and heterogeneous material. MATERIAL PREPARATION Most specimens for this investigation were prepared by encapsulating the elements in evacuated quartz tubes after which they were melted and homogenized in the liquid state. The ambient temperature was then dropped to 500°C and the resulting ingot zone melted. The growth rate, width of zone, stoichiometry, and number of passes have an effect on the resultant microstructure. Grains several centimeters in length were easily produced by this method. Other solidification techniques were also used, including uniform slow cooling of the entire specimen and rapid freezing. The microstructures of specimens produced by these techniques frequently differed appreciably from similar compositions prepared by zoning. A variety of nonequilibrium microstructures characterized by long needlelike particles resulted from the rapid-freeze method. PHASE EQUILIBRIA The lack of information on phase equilibria is a major difficulty associated with a comprehensive study of the Ag-Sb-Te system. Considerable confusion has resulted from the use of the formula AgSbTe, to identify the cubic ternary intermediate phase even though it has been established that material of this stoichiometry normally contains AgzTe as a second phase.798 In this paper, silver antimony telluride will denote the cubic ternary intermediate phase comprising the major portion of AgSbTe,. The term "single phase" will denote material which consists of only the cubic phase (as evidenced by metallographic examination and X-ray diffraction) and the term heterogeneous will describe multiphase material containing AgzTe, SbzTe3, or other phases in addition to the cubic phase. The single-phase material may actually contain a variety of inhomogeneities—gradual changes in composition on a macroscopic scale, localized fluctuations in composition, clusters or other products of early stages of the precipitation process, and a variety of point and line defects—all of which will not be detected by the present techniques for determining homogeneity. Single-phase material has been prepared from compositions close to 59 mole pct SbzTe3 21 (this notation refers to the location on the Ag,Te-Sb2TeS vertical section). Zone widths of =2 cm and growth rates 51.2 cm per hr were used. The single-phase region at elevated temperatures extends off the vertical section to a composition which can be expressed approximately as Ag,,SbzgTes,.9 The latter two compositions as well as AgSbTe, are represented in the conventional Gibbs triangle in Fig. 1. It is not presently possible to ascribe exact values to the limits of the single-phase region on a given isotherm or vertical section due to the extremely

Jan 1, 1964

By J. Washburn

Two simple types of dislocation distribution were introduced into zinc crystal specimens and the effect of each on the stress-strain curve was investigated. Quantitative results were obtained for simple edge dislocation arrays and for an array of screw dislocations lying in the slip plane. A CCORDING to present knowledge, the disloca-tions present in large annealed metal crystals can be divided into two somewhat arbitrary groups: 1—single dislocation lines distributed more or less at random or forming elements of a three-dimensional network in which the distance between adjacent dislocations is of the order of 10 2 to lo-' cm and 2— widely separated planar arrays of edge dislocations forming dislocation walls or small angle boundaries within which adjacent dislocation lines are spaced at much smaller distances (lo-' to 10- hm). The former can be considered as a dislocation interpretation of the mosaic crystal proposed by Darwin and Ewaldl, ' 40 years ago to account for anomalously high integrated intensities of X-ray diffraction maxima. Small angle boundaries, although now known to be present in most single crystals used for mechanical testing, were not generally recognized by the early workers. This was partly due to the fact that only recently have improved X-ray and metal-lographic techniques been available for checking the macroscopic perfection of crystals."" It has long been known that changes in growth conditions and in annealing procedure, which might logically be expected to cause variations in the structural details of both the dislocation network and of dislocation boundaries, produce marked variations in some mechanical properties such as yield strength." However, no quantitative experimental correlations between changes in dislocation distribution and changes in mechanical properties have yet been made. Such a correlation has been difficult to obtain because, even when great care is exercised to keep the histories of a number of single crystal specimens identical, it usually has not been possible to avoid considerable variation in macroscopic per- fection.' The number and orientation of dislocation boundaries vary from specimen to specimen. This has probably been an important contributing factor to the large scatter in the results of most mechanical measurements on pure single crystals. Some recent experiments"% ith single crystals of zinc have shown that the presence of dislocation boundaries in a specimen can increase its resistance to deformation by slip. With polycrystalline aluminum and nickel, there is also evidence that dislocation boundaries within the individual grains of the aggregate can increase the resistance of the material to plastic deformation, either as measured by tension tests at room temperature or by creep tests at higher temperatures.'" " Although the foregoing observations seem to have established the fact that substructure can have a strengthening effect, the test conditions were too complex to give much information concerning the mechanism. In the foregoing cases, a network of intersecting boundaries having various orientations and boundary angles were present. Before their apparent strengthening effect can be understood, it will be necessary to isolate and study separately the effect of a number of variables: 1—boundary angle, 2—boundary orientation with respect to the active slip direction, 3—number of boundaries, 4—intersections of boundaries, 5—detailed structure of the boundaries, and 6—interaction of impurity atoms with dislocations in boundaries. The object of the present work was to study the effect of dislocation boundaries on flow stress under the following simple experimental conditions: 1— substantially pure shear deformation and 2—boundaries of controlled angle, orientation, and number. In this way, it might be possible to distinguish the important variables from the relatively unimportant ones. Experimental Procedure Stress-strain curves of hexagonal metals are generally nearly linear even out to very large strains."

Jan 1, 1956

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-