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By Walter W. Lilly, Issa S. Oweis

Application of rock engineering in geotechnial consulting practice considered herein is in areas of: (a) bedrock verification for foundation support, (b) bearing capacity and settlements, and (c) excavations. A routine geotechnical investigation usually provides data on depth to rock, rock classification, and rock quality. In cases of rock outcrop, such outcrops are mapped for geologic structures and rock mass description. In addition, the regional geology and the general aspects of the groundwater regime are usually known from either published literature or previous experience. The predominant technique for ground and site investigation are usually drilling and geologic reconnaissance. Other techniques involving seismic and geophysical soundings, borehole camera, and oriented cores are used by by no means routine. Performing laboratory strength and compressibility tests is often made to be considered as routine. The use of the point load test is gaining increasing use in the United States and would, perhaps, become a routine field or laboratory test due to its simplicity and, more importantly, its relatively low cost. The purpose of this paper is to describe cases where mostly routine investigation and testing were used to arrive at engineering decisions. Bearing Capacity and Settlements The allowable bearing values for foundation support on rock is usually dictated by local building codes which presumably should reflect local experience. The interpretation of the code, however, can present a problem, especially if the interpretation is made by a designer under the delusion of knowledge in rock engineering. For

Jan 1, 1982

By John Reynders

Our entry into the World War suddenly brought home to us in a startling way the vital importance of manganese. Since the war, much has been written and said upon the subject of manganese and a great deal of time and money have been spent in attempts to find an adequate substitute for this metal in the manufacture of steel; none has been found. It is true that ways are known by which it is possible to make small amounts of good steel without manganese; but taking into consideration the diminishing quality of iron ores and fuels. as' well as the increasing exaction of specifications for finished products, it may safely be assumed that high-grade manganese ore will be more and. more a necessity in the production of steel as time goes on. Taking world resources as a whole it may be well to point out that the problem of obtaining needed supplies of manganese from a strictly commercial viewpoint is now less serious than it was before the war. Formerly it was feared that world resources of high-grade manganese ore might be exhausted in a relatively short time, but, largely as a result of the stress laid upon the importance of manganese during the war, the world's available supply of high-grade manganese ore has been greatly augmented by new discoveries and fuller development of previously known deposits.

Jan 5, 1927

By R. E. Cech

Particles -3 to 30 µ diam of a 29.5 pet Ni, 70.5 pet Fe alloy after being melted and solidified while falling through a hydrogen atmosphere were found to contain a distortion-free body-centered-cubic phase. In most particles, the amount of body-centered-cubic phase approaches or equals 100 pet. It was shown by a series of experiments that this phase forms directly from the liquid. It is pointed out that a mechanism previously suggested in recent papers on the theory of the liquid-solid transformation can account for the solidification of body-centered-cubic phase in a temperature range where face-centered-cubic is the stable phase. IN the course of an operation to produce powders for a study of the martensitic transformation in Fe-Ni alloys, an unexpected phenomenon was observed. Powders of a 29.5 pet Ni alloy, which has a subzero M, temperature, were found to contain considerable amounts of a body-centered-cubic phase at room temperature. The experiments to be described were designed to elucidate the mode of formation of this unexpected phase. Experiments and Discussion An alloy containing 29.5 wt pet Ni, balance iron, was vacuum melted from high purity electrolytic iron and carbonyl nickel shot and solidified in the crucible. The metal was converted to oxide, ground to 100 pet <37µ, pressed to a cake, and homogenized 20 hr at 1350°C. To insure homogeneity the grinding, pressing, and homogenizing heat treatment was repeated a second time. The oxide was then ground to 100 pct <37µ and hydrogen reduced at 500°C. The reduced powder was given a spheroidizing treatment to produce spherical cast particles. The treatment consisted of dispersing the particles in hydrogen and allowing them to drop through a vertical hydrogen furnace set to a temperature higher than the liquidus of the alloy. This operation, commonly known as shotting, has been described more fully elsewhere.&apos; The powder produced by this method was found to contain approximately equal parts of body-centered-cubic and face-centered-cubic phases. A magnetic separation technique, previously described,&apos; was applied, and it was found that particles were either completely face-centered-cubic or nearly completely body-centered-cubic. The microstruc-

Jan 1, 1957

By Robert Maddin, Neng-Kuan Chen

THE (001) planes have been reported as the cleavage planes in body-centered cubic metals such as alpha-iron and tungsten.&apos; However, in molybdenum, which is also body-centered cubic, experimental X-ray evidence indicating a similar cleavage plane still seems lacking. Tsien and Chow" observed microscopically in the extension at around 1000°C of molybdenum single crystalline wires 0.25 mm in diam that the fracture plane seemed to be parallel to the operative slip plane, which appeared to be (110) at that temperature. Zapffe&apos; pointed out from fractographic study of polycrystalline molybdenum that "although the transgranular pattern is characteristically non-crystallographic, patterns occasionally reveal {100} cleavage." This has been generally assumed to be the case at ordinary temperatures. In the present experiments, a single crystal of Fansteel molybdenum, Vs in. diam x 2 in. long, prepared by the methods described by Chen, Maddin, and Pond" was fractured at room temperature by bending. The fracture surface appeared to be quite similar to the cleavage surface of zinc and was crys-tallographic. A back-reflection Laue photogram was made using 35 kv copper white radiation; the X-ray

Jan 1, 1952

By James R. Grage

The lead deposits of Missouri may be divided into three districts, the southwest, middle, and southeast. As too much time would be required to devote a detailed account to each district, only a description of the modes of occurrence of the lead ores in the southeast district will be given. The lead mining region proper of Southeast Missouri is embraced in an area of about twenty-five miles in width by about one hundred in length. The country embraced in this district is very broken, and traversed by ridges from one hundred to three hundred feet; in height, with an occasional knob rising higher. Porphyry forms almost the entire substructure of the region, with here and there outcrops of granite. The crystalline rocks were eroded into ridges and valleys before the deposition of the limestone took place. These porphyries are older than the Silurian limestones, and " belong (according to Pumpelly) to the Archaean (Azoic) formation, of which they may be the youngest member in Missouri. They are the near equivalents, in point of age, to the great iron-bearing rocks of Lake Superior, New Jersey, and Sweden."

By Arthur Wilson, Frederick Carr

INTRODUCTION 1. The application of retreat longwall mining to the North American coal mining conditions is becoming more advantageous as more experience is gained. The productivity results being achieved and potential possible illustrates that this system can be keystone of future underground coal production. 2. In the American coal fields multi-entry is normally practiced as this allows profitable longwall development with existing equipment and systems. Difficulties are being experienced however in the longwall retreat phase by the collapse of multi-entry roadways and excessive use of supplemental support in the following panel tailgates. In some instances the headgate of an operating face can also be in difficulty. 3. Jim Walter Resources Mining Division is developed on a mining plan that calls for three retreat longwalls at each of its four deep mines which have varying depths of cover and immediate roof and floor conditions. The 63 Mine has experienced longwall entry difficulty and there were differing viewpoints with respect to the best development systems to adopt particularily regarding the number of entries and pillar sizes. In an attempt to reconcile these different points of view J.W.R. asked Dr. Wilson to examine the problem and this paper outlines the new approach developed.

Jan 1, 1983

By Stanley W. Sundeen

2.3-1. Introduction. The subject-"Preliminary Evaluation of Coal, Metallic and Industrial Mineral Deposits for Surface Mining&apos;-seems at first glance to be definitive and not likely to be misinterpreted. Nevertheless, there are widely divergent opinions as to what is meant by "preliminary" and even as to what is meant by "evaluation." Some definition and qualification is necessary in order to provide a readily recognized basis for discussion. Evaluation evokes the idea of organizing extant data and judging its significance especially in the economic sense. It also may evoke the concept of the physical processes of acquiring the data that will characterize the deposit such as the geologic mapping, drilling, etc. Castle (5) considers that evaluation may embrace psychological aspects wherein human traits as, for example, over optimism might cause the evaluator to overlook obvious project weaknesses. In this chapter, evaluation is discussed primarily from the viewpoint of economically appraising a project from data available at a given point in time. The qualifying adjective "preliminary" is not easily defineable. In fact, some kind of evaluation proceeds, if not continuously, intermittently over the full span of exploration and early stages of development of a deposit. Bailly (1) comments: "Sometimes, before starting exploration in new areas or countries for a given commodity, we establish models to define what minimum combinations of re- coverable grade and tonnage are needed to give the minimum acceptable rate of return established by corporate policy. Then, before starting physical exploration in any target area we try and guesstimate optimistically what best &apos;geometry-grade-tonnage&apos; can be expected. If these are acceptable in light of above minimum combinations, exploration is started as soon as funds are appropriated for the target area.&apos;&apos;

Jan 1, 1968

By Arthur Knapp

NEARLY every technical man is called upon at some time in his life to deliver a paper before a technical audience or to write a technical paper for publication. It is not necessary to be an accomplished public speaker to deliver a technical paper successfully; it is only necessary to bear in mind a few obvious points. Poorly presented papers are nearly always the result of a few errors of deportment, but they are vital and at the same time so obvious that they are often overlooked. Experience is a good teacher but a little study and careful preparation will moderate the suffering of both an amateur speaker and his audience. An author&apos;s paper suffers, through poor delivery, in direct proportion to the suffering of his audience. The best test of a paper is to have it read aloud to the author. This will bring out faults not apparent when read silently by the author. Some of the things which will probably need correcting are improper phrasing, noneuphonic sequences, and long or involved sentences. Frequently authors write their papers in short crisp sentences for oral presentation, then rewrite them for publication.

Jan 1, 1942

By Henry Howland

INTRODUCTION DURING the last decade no topic has created more interest or received more thought among blast-furnace men than colic. One reason for this is, undoubtedly, the remarkable increase in the use of byproduct coke. Formerly our coke was made at a distance from the furnaces and by a distinct organization. There was little cooperation or development possible under these conditions. Today the situation is greatly changed. Much of our coke is made by the organization operating the furnaces and the coke oven is operated with the primary object of obtaining the best results in the blast furnace. The effect of changing the method of coke manufacture, even in some minor detail, is often felt almost immediately at the blast furnace. There naturally results one of the most valuable assets of the byproduct coke oven, -i.e., the possibility of increased blast-furnace efficiency clue to close observance and correct operation of the ovens. The results are evident, but it often is difficult correctly to account for them. In attacking the solution of a problem of as much importance as why one coke is better than another, there are facts which should be kept clearly in mind The author hopes, in this paper, to bring out some points relative to the use of carbon in the blast furnace which will be of value in solving this question.

Jan 3, 1916

By Leonard Obert

Before 1957 a number of investigators reported stress determinations made on or near the surface of underground excavations. The usual procedure was to measure surface strains and to calculate the stresses using laboratory-determined values of the elastic constants of the rock. In some instances strain gages were stress-relieved so that the measured stress was absolute. Also, several investigators reported near-surface absolute stress determinations made by the flat-jack procedure. In 1958, Hast1 described a procedure for making absolute stress determinations within a body of rock. In this procedure a diametral deformation gage was placed in a borehole and then the borehole was overcored to produce stress relief. The secondary principal stresses in the plane normal to the axis of the borehole were calculated from measured deformations and the elastic constants of the rock. During the past nine years a number of investigations have been reported1-20 in which this technique, or modifications of it, have been reported. Both the stress distribution in the walls of underground openings and the stress field at points as great as 200 ft from these openings have been determined. Considered collectively, these reports shed some light on the nature of the stress distributions in the proximity of underground openings and on the stress field, that is, the state of stress outside of the zone of influence created by openings. To summarize these findings first consider the stress distribution in the wall and structural components of openings. Fig. 1 (a) shows a typical theoretical stress distribution curve in a linear-elastic, isotropic, homogeneous material. Fig. 1 (b) is an idealized measured stress distribution curve for the same opening in a relatively unfractured uniform, but brittle,

Jan 1, 1967

By W. P. Blake

Forty-five years have passed since I discovered the extensive and remarkable diatom-earth beds at Monterey, California., and now I have the satisfaction of bringing to notice still another wonderful deposit in the heart of Arizona. The Monterey beds mere described at the Philadelphia Academy,* and specimens were sent to Prof. J. W. Bailey, West Point, N. Y., at that time the leading American authority upon such microscopic relics of organic life. The earth from both localities is snow-white and pulverulent. It rubs off&apos; like soft chalk upon the fingers when handled, and has the general appearance of chalk. But, unlike the Monterey beds, these newly-discovered deposits consist largely of volcanic ash, through which the siliceous shells of the diatoms are distributed. These deposits are in the central portion of the San Pedro valley,† in the southeastern corner of Pinal county. The region of their greatest development is a few miles south of the mining town of Mammoth, on the east bank of the stream, and near Redington, some 40 m. N. of Benson, on the Southern Pacific railway. The altitude is about 2600 ft. above tide. This portion of the San Pedro valley lies between the high Catalina and Rincon ranges on the west and the Galiuro mts. on the east. The Catalinas are composed chiefly of crystalline DIRECTOR OF THE ARIZONA SCHOOL OF WINES,

Jan 1, 1903

By J. C. Smock

THE magnetic iron ores of New Jersey are found in the northern part of the State, in the Highland Mountain range, which runs from the New York line on the northeast, to the Delaware River, near Easton, at the southwest. The same range continues across Orange County to the Hudson River, and towards the southwest it is known in Pennsylvania as the South Mountain. It is more properly an elevated table-land, quite deeply furrowed by several narrow, longitudinal valleys, and shorter cross-valleys or gaps. The ridges or lines of elevation, as well as the lower valleys, conform in their general direction very closely to the general trend of the whole belt or table-land, that is, from northeast to southwest. This also agrees with the prevailing strike of the rocks. This great uniformity in the altitudes of the hills and ridges, and the direction of the lines of depression corresponding to the strike of the strata, point to an original table-land, which, through the long action of denuding agents, has been quite deeply eroded, giving rise to the present surface configuration, so that some of the former and uniform features have been partially obliterated. The very few cross-valleys or depressions are much more irregular in their course, and serve as outlets through which the drainage is carried either into the Kittatinny Valley on the northwest, or to the broad, red shale and sandstone plane bounding the highlands on the southeast. The area of this highland

Jan 1, 1874

By J. D. Edwards

When Charles Martin Hall invented the electrolytic process for the production of aluminum, one basic requirement was a supply of pure alumina. Now, more than 50 years later, the same requirement still holds, and there are no technical straws in the wind to indicate that this situation is likely to change. Long ago, Aluminum Company of America took a number of steps to see that this country should not face shortages of alumina and aluminum in time of emergency. As one step to this end, the Company developed and used a supply of bauxite in South America in order to conserve dwindling Arkansas reserves. Another, and more a program than a step, was to investigate every type of process that might bear the possibility of utilizing the low-grade ores of aluminum that are more plentiful than bauxite. It is a long story, but the investigation included electric-furnace processes, acid extraction processes and alkaline extraction processes, with or without preliminary furnace and sinter treatments. Some of the processes developed were operated in commercial production. This work has been continuous since the first World War. The turn of the wheel came sooner than was expected when, in 1942, bauxite shipmerits through the caribbean became uncertain and hazardous through the operation of submarines. The tremendous requirements of aluminum for the war effort were consuming high-grade bauxite at an alarming rate and a national search for substitutes began. High-grade bauxites, for technical and economic reasons, have been defined as those containing about 7 per cent or less of silica. While bauxite of this grade was limited in amount in the United States, there was in sight a substantially greater volume of low-grade, high-silica bauxite not amenable to economic treatment by the Bayer process, but richer in alumina than the clays or other available low-grade ores. It was at this point, and after several years of intensive research on this particular phase of the problem, that Aluminum Research Laboratories brought to completion the invention of one of its research staff, which made practical the utilization of large reserves of low-grade bauxite in America. Bayer Process The Bayer process has been almost universally used for the production of alumina from bauxite. This process, in outline, comprises the digestion of hely ground bauxite in a solution of caustic soda (NaOH) under pressure and at an elevated temperature. Alumina in the bauxite goes into solution as sodium alumi-"ate and the impurities—oxides of iron, titanium and silicon—remain undissolved. The undissolved residue, known as "red mud,&apos;&apos; from its color, is separated and run to waste. AluKlinum hydrate (A12O3.3H2O) is precipitated from the solution of sodium aluminate, and the liquor containing the caustic soda and some alumina is returned to the Process for digesting more bauxite. The aluminum hydrate, after washing, is calcined at a high temperature to produce

Jan 1, 1949

By J. Eric Belford

The Kidd Creek orebody is a massive base metal sulphide deposit with surface dimensions of 168 m by 670 m. The steeply dipping ore- body has been evaluated to a depth of 1 524 m. To date, the mining of the orebody has been divided into three stages. The first stage of mining was an open pit operation which supplied ore from 1966 until 1977 when a depth of 219 m was reached at the widest or north end of the orebody. The second stage of mining, called No.1 Mine, was the development of an underground mine to replace the pit and recover the ore from the floor of the pit to a depth of 792 m. Development of the underground mine started in 1969. Full production of 273 000 tonnes per month was attained in 1977. The third stage of mining called No.2 Mine, was initiated to accommodate a production expansion and included the development of a second underground mining operation to recover the ore from the bottom of No.1 Mine, i.e. the 2600 level; to a depth as yet undetermined but most likely the 4600 foot level. Development of the No.2 Mine began in 1974. Full production of 91 000 tonnes per month will be achieved in 1982. The choice of the 2800 level as the partition between the two underground mines was based on the following factors: The 2600 level is the lowest level which can conveniently be mined through the No.1 Mine crusher on the 2800 level. Development and trial stoping methods for mining at depth could be evaluated in the 2600 to 2800 block utilizing the existing hoisting facilities of No.1 Mine. Early development of the ore in the 2600 to 2800 block would provide additional mill feed sooner than could be achieved by developing from No.2 Shaft. The underground mining plan then is to mine from the pit floor down to the 2600 foot level and at the same time mine from the 2800 level down to at least the 4600 foot level. PLANNING The Kidd Creek operations are designed to follow a logical mining sequence. The grade of ore supplied to the concentrator is the result of following the mining plan. The philosophy of mining has been to mine downward in horizontal slices. In the case of No.1 Mine the slices are 122 m thick while in No.2 Mine the slices will be 183 m thick. The point of this approach is to mine the pillars immediately after creating them rather than allowing them to stand, deteriorate and generate uncontrollable situations. Two types of ore are handled separately to optimize recoverable values in concentrates. The &apos;A&apos; type ore is a copper zinc ore with some silver and little lead. The &apos;C&apos; type ore is a zinc silver ore with some lead and copper

Jan 1, 1981

By L. D. Jaffe, D. C. Buffum

EARLY papers1-&apos; reported that temper brittleness is influenced by microstructure. This conclusion was based on room temperature impact tests, the inadequacy of which has been pointed out. Pellini and Queneau7 measured impact energy absorption at —80O to +25oC for several microstructures. On the basis of the shift, associated with temper brittleness, in the energy vs testing temperature curve they concluded that tempered martensite is somewhat more susceptible to temper brittleness than is tempered pearlite. The range of temperatures was insufficient to give complete curves covering the transition from tough to brittle behavior, so it is difficult to evaluate quantitatively the shift for the different microstructures. Also, the smaller shift of pearlite might be attributed to its already being temper embrittled at its temperature of formation. Accordingly, blanks 2 3/16 in. long were cut from a heat of SAE 3140 hot rolled steel barstock, 5/8 in. diameter, on which other work has been reported? A set of blanks was austenitized 1 hr at 900°c, water-quenched, tempered 16 hr at 675oC, and water-quenched, giving a microstructure of 100 pct

Jan 1, 1954

By Ralph M. Hunter

Until recent years, maintenance of surface coal handling facilities was a relatively simple task. Equipment consisted principally of conveyors, screens and crushers of comparatively simple construction. Electrical equipment consisted of motors and starters, with little, if any, interlocking. In most cases failure of any component affected only the grades of coal loaded so that even a prolonged breakdown did not affect mine operation materially. However, with the introduction of modern cleaning plants, the picture has changed. The equipment is much more complex and therefore more difficult to maintain. In many cases failure of any component of the plant prevents loading of coal. Even if provision is made to bypass, the quality of coal loaded is lowered, affecting markets. In the case of plants designed to permit full seam mining, marketable coal cannot be loaded without operation of the cleaning plant. Under these conditions it is apparent that considerable thought and effort toward better maintenance are justified. In order to assure continuous, efficient and economical operation, maintenance should receive consideration, not only after the plant is in operation, but while it is being designed. It is hardly necessary to say that the designer should strive for sturdi-ness and wearing qualities. It is sometimes not realized, however, that even the best parts will sooner or later require replacement or repair. The designer should, there- fore, give consideration to accessibility. Anyone who has had to do with cleaning plant maintenance is familiar with installations where several hours are required to get at a part that can be repaired or replaced in a few minutes, once it is accessible. As in most cases, experience is the best guide. The men who operate and maintain this equipment know the problems encountered. Whenever available, the opinions of these men should be sought and heeded. As an example, we might consider the refuse elevator on a Chance Cone. Our company is now operating three of these cones, the first of which was installed in 1941, and the latest in 1946. Exact records are not available, but well over 50 pct of delays charged to the Chance Cones have been caused by the refuse elevator. This elevator receives refuse from the cone and carries it to a point above the water level of the cone, discharging onto a dewatering and desanding screen. Since the elevator operates under water and necessarily has close clearances in the lower boot, it tends to jam on large pieces of refuse or tramp iron. The chain, buckets and boot are also subjected to the action of water, sand and refuse, which accelerate normal wear. In case of jamming or chain-breakage it is necessary to drain the elevator and the cone so that even a minor fault in the elevator causes a considerable loss of time for the cone. In our new plant, which will contain two Chance Cones, the refuse elevator has been eliminated. This was accomplished by raising the cone so that the refuse gates could discharge directly onto the dewater-

Jan 1, 1949

By L. G. Austin, R. R. Klimpel

This article demonstrates that the Gilvarry and Klimpel-Austin equations for the random fracture of solids are incorrect by deriving intuitively correct expressions for simple cases and showing that the foregoing equations do not reduce to right answers. It is the purpose of this article to point out serious errors in some existing treatments of the random fracture of solids. Gilvarry &apos; gives the equation where B(y,x) is the cumulative fraction by weight of particles which fall below size y when particles of size x are broken. The constants i, j, k contain shape factors and densities of flaws leading to propagating fracture surfaces. The authors believe this equation to be incorrect. Klimpel and usttin&apos; give where r~ is the number of fracture planes originating from edge flaws (per L where L is the edge length of the original particle), rs is the number of fracture planes originating from flaws on the particle surface (per S where S is the surface of the original particle) and rv is the number of fracture planes originating from flaws within the particle volume. This equation is also incorrect. The failures of these equations will be demonstrated by deriving intuitively correct expressions for simple cases and showing that the Eqs. 1 and 2 do not reduce to the correct answer. In this process, the flaws in statistical reasoning inherent in the derivations of Eqs. 1 and 2 become apparent. THE KLIMPEL-AUSTIN EQUATION Eq. 2 was derived by considering a set number of fracture planes occurring spatially at random within a given particle. This case will be treated here in its simplest form: a line with 1, 2, 3, etc., fractures occurring at random. This is illustrated in Fig. 1, with the original length of the line as Vo. The breakage of a long, thin, brittle fiber is a corresponding physical case, with the volume of a fragment proportional to its length. Assuming independence of the occurrence of the fractures, the probability of any one fracture occurring in length dV is dV/V0. The probability of the first fracture occurring at a length V to V + dV is dV/Vo. For the case of only one fracture per particle, formation of a number-size distribution of the left-

Jan 1, 1969

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,&apos; who first dealt with the coning problem; (2) Chaney, et al,&apos; who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.&apos; Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,&apos; and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy&apos;s law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry&apos;s law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2&apos;= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,&apos; using Laitinen and Liu&apos;s&apos; value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,&apos; and the equations of Wagner and Werner,&apos; the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O&apos; and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies&apos; have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By P. C. Upadhyay, J. G. Singh

Reissner&apos;s thick plate bending theory has been recast for rocks which exhibit the property of double elasticity: different Young&apos;s modulus and Poisson&apos;s ratio in compression and tension. The governing differential equation and other relevent expressions have been presented in a form compatible to the applied mechanics results so that they can readily be used. Effect of the ratio of Young&apos;s modulii in compression and tension, (Ec/Et), on the maximum plate deflection and the maximum bending moments has been evaluated over a wide range. It has been found that the inclusion of bi-modulus property through a parameter (ß = Ec/Et), changes the sheer deformation of the plate to such an extent that the bi-modular effect of rock cannot be overlooked in the thick plate analysis, especially when ß is expected to be greater than 2.

Jan 1, 1982