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By L. Albert, A. M. Cameron, J. W. Gullick

International Nickel has 15 operating mines in Canada, and. 3 mines which are being maintained on a standby basis. Annual production is about 20 million dry short tons of ore, most of which is from underground mines, the remainder from open pit mines. Although some of the underground mines are served by ramps for trackless vehicles, most men, materials and ore are hoisted in vertical shafts. In addition to shafts and raises for ventilation and service purposes which are not equipped with hoisting plants, there are now 28 vertical shafts at Inco mines served by 47 hoists. Of these, 22 shafts and 36 hoists are located in the Sudbury District of Ontario, one shaft and two hoists are at the Shebandowan mine in Western Ontario, and 5 shafts with 9 hoists are located near Thompson, Manitoba. This paper describes the components of Inco hoisting plants-which have been applied at different times and under different conditions, and indicates the rationale for the various designs. Some engineering and maintenance practices, considered advantageous, are also described. MINE SHAFTS Many of the shafts sunk in the early days of the Sudbury District, on what are now Inco properties, were inclined shafts. Of the identifiable shafts sunk between 1885 and 1920, thirteen were inclined and at least four were vertical. Since 1920, thirty vertical and two inclined shafts have been sunk. All of the inclined shafts have been abandoned for hoisting purposes but the majority are still in use as service or ventilation ways. Shafts at Thompson- and Shebandowan are all vertical. The vertical shafts range from 2 or 3 compartment exploration and development shafts to 6 compartment shafts for ore, man and material hoisting. They vary in depth from 1,050 to 7,137 feet and in addition to hoisting compartments all contain manway and service compartments. Prior to 1948, unlined rectangular shafts with timber sets and guides were used. The rectangular cross-section was favoured since the rock is competent, the shape compatible with timber set framing, and since available shaft space could be used efficiently. Resistance to air flow was not of prime importance. Concrete linings were introduced for the first time at the Creighton No. 7 Shaft which was collared in 1948. All major shafts since that date have been concrete lined. Vertical set intervals were increased in steps, with the introduction of structural steel sets secured to the concrete linings. Whereas 7 foot set intervals were used with timber framing, this increased to 10 feet 6 inches with steel sets and more recently to 15 feet with steel and steel backed wood guides. With the advent of deeper shafts, or shafts which are expected to be deepened, the trend is to circular concrete lined shafts. The majority of shaft guides in service are of select Douglas Fir. This practice commenced as a component of timbered shaft design but continued as a

Jan 1, 1975

By Hsun Hu

Direct observations were made on the recrystalli-zntion of a cold-rolled (110) [001] crystal of 3 pct Si-Fe by annealing thin sections of the specimen inside the electron microscope during examination. Subgrain formation, presumably by polygonization, occurs rapidly, followed by a slow increase in the subgrain size before recrystallization can be detected. No migration of the subgrain boundaries was observed, and the formation of recrystallization nuclei by coalescence of subgrains is suggested. Re-c~ystallization characteristics of various texture components were individually examined. AS reported in a previous paper: orientations of the various deformation texture components in a 70 pct cold-rolled (110) [0011 crystal of 3 pct Si-Fe were completely confirmed by transmission electron diffraction patterns taken at various areas of the specimen. These orientations can be summarized as follows: Over most areas of the deformed crystal (111) planes are parallel to the surface. These areas correspond to either $- the two main defor: mation textures, the (111) [112] or the (111) [112].2-5 Within a few areas, (100) planes parallel to the surface are frequently found. These areas represent the minor deformation texture component, the (100) [Oll] type, which is derived from rotated Neumann bands.2'4'5 Only in very rare instances are (110) planes found parallel to the surface. This orientation corresponds to the very weak texture component of the (110) [001] type. In a pole figure, this (110) [0011 orientation is located within the orientation spread between the two main (111) [1121 type textures. Usually the electron diffraction patterns taken at various areas of the specimen are very simple ones, i.e., for any one area the pattern consists only of sharply defined spots of a single orientation. In some areas, however, more or less continuous rings of weaker intensities are superimposed on a simple pattern, indicating the presence of a wide range of additional orientations. In order to understand in detail the recrystallization of this cold-worked crystal, the recrywtallization characteristics of each of the various deformation texture components must be examined. This can best be done by using a high-temperature stage and transmission electron microscopy techniques, whereby small areas corresponding to the various texture components can be selected individually for examination. The present paper presents results obtained by this method. MATERIAL AND METHOD Specimens were prepared from a previously studied1 single crystal of a commercial grade 3 pct Si-Fe alloy with an initial orientation (110) [00l], cold-rolled 70 pct from 0.014 in. to 0.004 in. in thickness. Thin foils were prepared by electrolytic polishing as described in the earlier paper.' Specimens of this thin foil were then mounted in a high temperature stage similar to the one designed by Whelan.6 A direct current was used as the heating source. The temperature of the heating grid was calibrated by means of a Pt vs Pt-10 pct Rh thermocouple in a vacuum chamber (0.01 to 0.02µHg). Maximum variation within the temperature range of 250o to 000°C was about ± 25°C. After the desired areas were selected for examination, the specimen was heated to a low temperature for some time while the selected area was constantly watched. When no further change in structure and orientation could be observed, a higher temperature was applied. Photomicrographs and diffraction patterns were taken from time to time during examination, with the heater temporarily turned off* while the photographs were

Jan 1, 1962

By James A. Brierley, Corale L. Brierley

Microorganisms have been considered as agents which may be of importance in catalyzing hydrometallurgical processes for the extraction of metals from low-grade ore minerals. Various microorganisms and their role in bacterial leaching are described. Bacterial leaching as applied to copper, uranium, zinc, lead, and coal is discussed.

Jan 1, 1981

By James R. Piper

Jan 1, 1985

By William H. Callahan

"For his exceptionally successful career as a geological mentor, for his ore-finding skills, and particularly the discovery of the Central Tennessee Zinc District and for his lecture, 'Prospecting in the USA-Promise and Problems.' " Recipient of the 1982 D.C. Jackling Award

Jan 1, 1983

By A. O. Bartell

The rich Columbia River Basin is producing a long list of minerals useful in ceramics, farming, construction, power, metallurgy, and other industries.

Jan 4, 1951

By D. A. Thomas, M. F. Comerford

Poly crystalline wires of Fe-3.2 wt pct Si were cold-drawn to 31, 66, and 87 pct reductions of area. Mechanical properties and tnicrostructures were studied after recovery and re crystallization. An initial increase in strength during recovery was ascribed to strain aging, and subsequent softening was largely due to polygonization rather than re-crystallization. No unique actioation energies could be determined for the recovery process. Rather, activation energies ranged from 60,600 cal per mole at 10 pct recovery to 83,200 cal per mole when recovery was 50 pct complete. Sites for the nucleation of recrystallization were found to depend on time and temperature. In the early stages of re-crystallization, nucleation occurred in deformation hands. Later, or at high temperatures, recrystal-lized grains were nucleated primarily al grain boundaries. Polygonized structures did not seem to be preferred sites for nucleation. MUCH of the research on deformation, recovery, and recrystallization processes in bcc materials has been performed on single crystals or lightly worked polycrystals. Little study has been devoted to the relation of mechanical properties to micro-structure in polycrystals after severe deformation and subsequent annealing. This paper presents the results of a study of the tensile properties and microstructures of Fe-Si wires drawn varying amounts and annealed at a series of temperatures. EXPERIMENTAL PROCEDURE The experiments were carried out on an alloy of the following composition: 3.2 wt pct Si, 0.08 Mn, 0.016 C, 0.005 0, 0.0002 N, 0.0001 H, 0.008 P, 0.034 S. The material was received as l-in.-sq bars cut longitudinally from a hot-rolled slab provided by the Armco Steel Corp. The bars were forged to 3/8-in. rounds, centerless-ground to 0.250 in., and swaged to '0.108 in. All subsequent reductions were performed by room-temperature wire drawing at the rate of 2 in. per min. Each preliminary draft gave approximately 30 pct reduction of area and was followed by a l-hr anneal at 1010°C in dry hydrogen. Three lots of wire were made with ultimate cold reductions of 31, 66, and 87 pct reduc-

Jan 1, 1965

By W. H. McFarland

The mechanical properties have been determined for a large number of alloy-free martensitic steels with carbon contents ranging from 0.08 to 0.20 pct and with manganese contents of about 0.4 to 0.5 pet. These steels were tested 1) as water-quenched, 2) after quenching, temper rolling, and tinning, and 3) after tempering treatments which involved temperatures from 400o to 1300oF and times from 1 min to 8 hr. The majority of these tests represent steel from commercial-size coils, i.e., strip 32 in. wide, coil weights up to 20,000 16, and steel thicknesses from 0.0055 to 0.024 in. As a result of these treatments, it has been shown that as-quenched low-carbon alloy-free steels can be produced with tensile strengths ranging from 140,000 to 220,000 psi and tensile elongations from 3.0 to 4.0 pet in 2 in. The tensile strength of the as-quenched martensites can be represented by the equation, tensile strength (ksi) = 119 + 560 (wt pet C). The response to tempering of these steels is related to previous work by Muir, Averbach, and Cohen and by Grange and Baughman. Strain aging of low-carbon martensite has also been investigated. If low-carbon steels are defined as those steels with a maximum carbon content of 0.2 pet, it is found that the literature on low-carbon, alloy-free martensites contains little data on the mechanical properties of these steels. However, the following facts concerning low-carbon alloy-free martensites seem firmly established:'-' 1) The major factors in controlling the strength of the martensite appear to be a) fine structure, b) the internal strain resulting from the transformation, and, particularly, c) the amount of carbon in solid solution. 2) In low-carbon steels, the martensite is auto-tempered and is in the form of needles with only minor amounts of internal twinning, whereas the martensite in high-carbon steels forms as plates which are internally twinned on a fine scale. 3) Care must be taken in comparing the results of work that has been done on low-carbon steels with varying amounts of alloying elements to data on plain carbon steels. As has been noted by Irvine, Pickering, and Garstone,6 alloying elements generally lower the martensite start temperature and, thereby, decrease the amount of auto tempering obtained during the quench. This makes it difficult to

Jan 1, 1965

By C. H. Lee, R. Maddin

The diffusion rates of Ag110 in cylindrical single crystals of 99.99 pct pure silver, which were twisted to a total surface strain of 0.91 during the diffusion anneal at temperatures of 700°, 750°, and 800°C, were measured by sectioning and counting as a function of the strain rates. The ratio of the diffusivities while strain ing occurred (Ds) to those of the unstrained specimens varies linearly with the rate of twisting and attains values of near 100 for some of the rates used. The enhancement of diffusion by straining is inversely proportional to the temperature at which diffusion occurs. The activation energy for diffusion determined from the data plotted as a function of the rate of twisting decreases from 44,090 cal per mole for zero strain, to an asymptotic value of 21,000 cal per mole for the strain rates of 22 x it)"5 see-l. Qualitative explanation for the observations based on the generation of nonequilibrium number of defects by plastic deformation will be discussed. The initial research of Buffington and cohen1 on self-diffusion in a iron under compressive stresses contributed the first quantitative information concerning the effect of applied stresses on diffusion. These results were obtained from radioactive Fe55 plated on one of the horizontal surfaces and compressing the large-grained specimens while the diffusion-anneal was occurring. Enhancement of diffusion of a maximum of seventeen times was observed provided the strain was in the tertiary stage of creep and the rates of straining were at least as fast as rates used in the normal creep test. On the other hand, Darby, Tomizuka, and Balluffi,2 extending silver single crystals up to 30 pct elongation at rates of straining about equal to those used by Buffington and Cohen observed no effect. For the past two and a half years at the University of Pennsylvania, we have been investigating the effect or torsional strains on self-diffusion in silver single crystals. If enhancement is observed as has been reported1 a possible explanation may be based upon the generation of fairly large numbers of point defects and their role in the diffusion process. Hence, since torsion should produce an abundance3 of point defects, an increase in the diffusivity while the crystal is being twisted should easily be measured. EXPERIMENTAL PROCEDURE Our research uses single crystals of silver prepared from 99.99 Ag by the Bridgman method in a dynamic vacuum of less than 25 µ. As grown, they are about 25 cm long by 1.3 cm in diam. The crystals are cut into 7.5 cm lengths with a jeweler's saw and machined to the shape shown in Fig. 1. The test length of the crystal is machined to a 0.6 cm diam after which the ends are masked and the test section etched heavily in HNO3, and KCN:(NH4),S2Os , solution to remove the effects of machining. The specimen is then annealed in vacuum for 8 to 12 hr at 800°C to remove any residual stresses and also to recrystallize the end sections. The recrystallized ends are necessary since experiments showed that single-crystalline end sections are too soft to transmit the desired torque. Occasionally, recrystalliza-

Jan 1, 1960

By E. F. Johnson, F. H. Brinkman, H. J. Welge, S. P. Ewing

This paper presents a method for predicting the manrler in which oil will be displaced from a porous body by enriched gas. The calculations apply to a gas rich enough to give a partially, but not a completely, misci-ble displacement. The method — a three-component, two-phase analysis — takes into account condensation of some of the intermediate hydrocarbons from the injected gas into the oil, as well as enhanced volatility of heavier hydrocarbons at elevated pressures and temperatures. The condensation swells the oil and decreases its viscosity, thus aiding in its recovery. The calculations have been extended to apply to actual crude oil-natural gas systems by arranging the components into three groups according to their volatility. As an approximation, each group is then treated as a single component in the analysis. The influence of an angle of dip for an inclined displacement is also taken into account. The recovery predictions are corroborated by experiments which used both consolidated sand cores and un-consolidated glass beads. In some of these tests, actual live crude oil was displaced by a multicomponent gas typical of enriched gases used in oil fields. INTRODUCTION This paper presents a method for predicting the amount of oil that can be displaced from a homogeneous, linear, porous body at various stages during the injection of enriched, or "wet", gas. The porous body can be in either a horizontal or an inclined position. 'This type of displacement is sometimes known as condensing gas drive The method is developed especially for the case in which the injected gas is enriched enough to be partially, but not completely, miscible with the reservoir oil. The need for a calcula-tive procedure for this type of operation is emphasized by the number of field projects where completely miscible drives are not practical, but where near-miscible conditions are feasible. The factors taken into account in the predictive calculations include: (1) the condensation of gas components into the oil, with a resulting increase in oil volume; (2) the lowering of oil viscosity by the addition of lighter ends from the gas; (3) the increase in oil volatility at high temperatures and pressures; and (4) the physical displacement of the oil by the gas. The techniques developed in the paper can be extended to other nonequilibrium displacement processes. Other such processes that we have analyzed include a displacement by lean gas which stripped intermediates from the oil, and a water flood in which the water con. tained in solution a substance somewhat soluble in the oil. ANALYSIS OF ENRICHED-GAS DRIVE GENERAL PRINCIPLES Our method for predicting the amount of oil that can be displaced by an enriched gas uses an analogy between a three-component and a multicomponent system.' The predictive method is based on these assumptions: (1) constant, or nearly constant, pressure; (2) complete equilibrium by diffusion perpendicular to the main direction of flow, but no significant mixing along the direction of flow; (3) constant injection velocity; and (4) flow in a linear porous body. The composition of a liquid or a vapor with respect to three components can be plotted on a three-component, or ternary, diagram like that in Fig. 1. Let Point A represent the composition of the oil originally in place. In this case, Oil A is undersaturated with gas. If Point A lay on the equilibrium Curve BF, the oil would be saturated. In the extreme case where the original oil contained no intermediates or dissolved gas, Point A would lie at the lower left-hand corner of the ternary diagram. In a displacement of Oil A by Gas D, there will be a progressive change in the composition of the oil phase as more and more gas is brought into equilibrium with the oil. The end result of this progressive change is an oil having the composition represented by Point F. This oil is richer in intermediate hydrocarbon and methane than the original oil and, therefore, has a greater forma-

By N. T. Burdine

Procurement of uranium is vital to the future of the Nation. Its utilization for atomic energy can destroy mankind or raise an unsurpassable civilization-the problem of the statesmen. Uranium poses a challenge to the mining profession. Evanescent in occurrence, its discovery and mining can mean substantial profits, plus safeguarding the future of the Nation.

Jan 9, 1951

By Conrad E. Hesse

To increase the durability of paint exposed to the weather, it is necessary to protect the oil with a substance that is itself unaffected by the elements. The so-called " metallic " paints, containing ochre,

Jan 1, 1891

By W. C. Maurer

A study of bit-tooth penetration, or crater forniation. under simulated borehole condirions has been made. Pressure conditions existing when drilling with air, water and mud have been sirnulated for depths of 0 to 20.000 ft. These crater tests showed that a threshold bit-tooth force must he exceeded before a crater is .formed. This thresh old force increased with both tooth dullness and diflerenrial pressure between the borehole and formalion fluids. At low differential pressures, the craters formed in a brittle manner and the cuttings were easily removed. At high differenlial pressures, the cunings were firmly held in the craters and the craters were formed by a pseudoplas-tic mechanism. With constant farce of 6,500 16 applied to the bit reeth, an increase in differential pressure (sitnulated mud drilling) from 0 to 5,000 psi reduced the crater volumes by 90 per cent. A comparable increase in hydrostatic fluid pressure (simulated water drilling) produced only a 50 per cent decrease in volutne while changes in overburden pressure (simulated air drilling) had no detectable effect on crater volume. Crater tests in unconsolidated sand subjected to differential pressure showed that high friction was present in the sand at high pressures. Similar friction belween the cuttings in craters produces the transition from brittle to pseudo plastic craters. INTRODUCTION The number of wells drilled below 15,000 ft increased from 5 in 1950 to 308 in 1964. Associated with these deep wells are low drilling rates and high costs. High bottom-hole pressures produce low drilling rates by increasing rock strength and by creating bottom-hole cleaning problems. This paper describes an experimental investigation of crater formation under bottom-hole conditions simulating air, water and mud drilling. Although numerous investigators have studied bit-tooth penetration (cratering) at atmospheric pressure conditions, only limited work has been done on cratering in rocks subjected to pressures existing in oil wells. Payne and Chippendale2 have studied cratering in rocks subjected to hydrostatic pressure using spherical penetrators. Garner et aLJ conducted crater tests in dry limestone by varying overburden pressure and borehole fluid pressure independently and using atmospheric formation-fluid pressure Gnirk and Cheathem4,5 have studied crater formation in several dry rocks subjected to equal overburden and borehole pressure and atmospheric formotion pressure. Podio and Gray studied the effect of pore fluid viscosity on crater formation using atmospheric borehole and formation-fluid pressurc and varying overburden pressure. Although these studies have provided useful information on crater formation under pressure, they were limited in that the three bottom-hole pressures could not be varied independently and, therefore, that many drilling conditions could not be simulated. The prersure chamber used in this study allowed visual observation of the cratering mechanism and independent control of the borehole, formation and confining pressures. By using different fluids in the chamber, pressure conditions existing in air, water and mud drilling to depths of 20,000 ft were simulated. The mechanisms involved in cratering at these different pressure conditions were studied for teeth of varying dullness and at different loadins rates. High-speed movies (8,000 frames/sec) and closed-circuit television were used to visually study the crater mechanism under pressure. EXPERIMENTAT PROCEDURE PRESSURE CHAMBER The Pressure chamber in Fig. I was used to simulate bottom-hole pressure conditions. This chamber has been pressure-tested to 22,500 psi and is normally operated at pressures up to 15,000 psi. The chamber contains four lucite windows' used for illuminating and observing the crater mechanism under pressurc. A closed-circuit television and a Fastax camera (8,000 frames/sec) have been used in these studies. Cylindrical rock specimens (8-in. diameter X 6-in. long) were subjected to three independently controlled pressures simulating overburden, borehole fluid and formation-fluid pressures. Overburden pressure, which corresponds to the stress induced by the overlying earth mass, was applied by exerting fluid pressure against a rubber sleeve surrounding the rock. Borehole pressure, which is the pressure exerted by the column of mud in the wellbore, was simulated by applying pressure to the fluid overlying the rock in the chamber. Formation pressure was simulated by applying pressure to the water saturating the rock. The borehole and formation pressures were equal except when mud was used in the chamber, in which case the differential pressure between these fluids acted across the mud filter cake.

Jan 1, 1966

By Y. C. Liu, G. A. Alers

measurements of the anisotropy in Young's modulus produced in copper by rolling 95 pct reduction in thickness below room temperature have been carried out in order to study the dependence of the texture on rolling temperature. The results clearly show the transition from a copper-type texture to a brass-type texture as the temperature of rolling is lowered. The intermediate textures observed can be described very well as a simple mixture of the two terminal textures. These results cormbined with other texture measurements make possible afresh review of the experimental facts velating to rolling textures in fee metals and, as a consequence, a critical examination of the current theories is presented. PREVIOUS experiments have shown that the transition from the copper- to the brass-type rolling texture is clearly displayed and can be quantitatively analyzed by measurements of the anisotropy of Young's modulus.' Application of this method to the Cu-Zn alloy system showed that the description of the texture transition as a gradual rotation of the grains from the orientation characteristic of the copper texture to the {110}(112) texture of brass2 was inconsistent with the data. Instead, the data suggested that the texture within the transition region could be described as a simple mixture of the two terminal textures.5 Unfortunately, it was difficult to establish this point conclusively because of the inadequacy of corrections for the composition dependence of the single-crystal elastic constants. Since a rigorous establishment of the nature of this texture transition is essential to our understanding of the formation of rolling textures in fee metals, it is clearly important to undertake an investigation in which the composition dependence of the elastic constants would not enter. A suitable composition-independent texture transition is provided by the well-established variation in the rolling texture of copper with rolling temperature. This temperature-dependent texture transformation has been studied by smallman' in several fee alloys and by Müller5 and others"' in copper. They observed that the texture characteristic of copper rolled at room temperature changed to a brass-type texture when the rolling temperature was lowered to 77°K. Although it is not possible to decide unequivocally from the published pole figures whether or not the 77°K rolling texture of copper is entirely of the brass type,' this complication does not affect the main purpose of the present investigation. In addition to establishing the nature of the texture within the transition region, the modulus data should also provide a determination of the temperature at which the transition occurs as well as the temperature range over which the transition extends. This information when combined with the modulus data on Cu-Zn alloys would then provide a considerable body of new information on textures in fee metals. Since these modulus results and the data obtained from pole-figure studies must be internally consistent, it is appropriate to compile a brief summary of the experimental observations based on all available methods rather than on the pole-figure data alone as has been done in the past. The primary purpose of such a summary would be to yield a more precise definition of the experimental facts on the rolling textures of fee metals, and thus greatly facilitate our evaluation of various proposed theories in this field. The final section of this paper is devoted to this compilation of consistent, experimental facts and their application to the various theories. EXPERIMENTAL PROCEDURE Two 18-lb ingots of cathode copper of 99.99 pct purity were induction-melted under a nitrogen atmosphere in a graphite crucible and chill-cast into a steel mold. The ingots were repeatedly cold-rolled and annealed (I hr at 500°C) into slabs about 1 1/8 in. thick. Blocks 3 1/4 in. wide, 2 1/4 in. long, and 1.000 in. thick were machined from each slab. The rolling schedule used was the same as in the previous investigation1 and the final thickness of the sheet was 0.050 in. with a rolling reduction of thickness of 95 pct instead of 97.5 pct as in the previous work.' The compositions and temperatures of the cold baths used for the low-temperature rolling were as shown in Table I. After each pass the rolled strip was immediately immersed in the cold bath for about 1 min or until the bubbling of the bath had subsided. The modulus data were taken within 2 hr after the rolled strip was warmed to room temperature for the first time, so that effects due to recrystallization were minimized. The modulus specimens were in the shape of flat bars, 3 in. long, 4 in. wide, and 0.050 in. thick, cut with their long dimensions oriented at 15-deg intervals between the rolling direction and the transverse direction. The values of Young's modulus were deduced from measurements of the frequency at which these long narrow bars were set into longitudinal, resonant vibration as previously described.9 To excite the mechanical vibrations in the specimen, an electromagnetic drive similar to that employed by Thompson and lass" was used. The maximum in the amplitude of

Jan 1, 1968

By John D. Erickson

The concepts of long-range, open pit planning presented here are not new. The new idea is how the factors that control the location of the final pit limits can be considered altogether as one large, simultaneous equation. The X, or unknown quantity that is being solved for, is a long-range pit design that fulfills the desired objectives. The objectives of a final pit plan are determination of the extent and location of ore reserves, the allowable stripping necessary to uncover the ore, the final pit surface intercept, final pit topography and the contained metal values in both ore and waste.

Jan 4, 1968

By T. K. Perkins, L. R. Kern

A study of fluid mechanics, rupture of brittle materials and the theory of elastic deformation of rocks shows that, for a given formation, crack width is essentially controlled by fluid pressure drop in the fracture. Operating conditions which cause high pressure drop along the crack (such as high injection rate and viscous fluids) will result in relatively wide cracks. Conversely, operating conditions which cause low pressure drop (low injection rates and thin fluids) will result in relatively narrow cracks. Charts and equations have been derived which permit the estimation of fracture widths for a variety of flow conditions and for both horizontal and vertical fractures. INTRODUCTION There has been considerable speculation concerning the geometry of hydraulically created fractures in the earth's crust. One of the questions of practical importance is the width of fractures under dynamic conditions, i.e., while the fracture is being created and extended. Such width information could be used, for instance, to help estimate the area of a fracture generated under various conditions. Also, there has been a recent trend toward the use of large propping partiles.13, 15 Therefore is is desirable to know what factors can be varied in order to assure entry of the large particles into the fracture. There has been some work on fracture widths reported in the literature. In particular, there have been several Russian publications dealing with this sub-jeCt.1.31,3 These papers have dealt principally with the elastic theory and the application of this theory to hydraulic fractures. These studies have not led to an engineering method for estimating fracture widths under dynamic conditions. A recent paper3 has reviewed and summarized the Russian concepts. An earlier paper- from our laboratories also discussed the application of the elastic theory to hydraulic fractures. This first approach, based largely on photoelastic studies, has proved to be too simplified to accurately describe the fracturing process. However, these early thoughts have served as a guide during the development of more exact concepts. We would like to present in this paper our current concepts regarding fracture widths and some estimates of hydraulic fracture widths for several conditions. We believe that it is now possible to predict with fair accuracy the factors influencing fracture widths. Furthermore, the method of prediction has been reduced to a simple and convenient graphical or numerical calculation. CRACKS IN A BRITTLE, ELASTIC MATERIAL Many investigators2, 4, 30 have shown that competent rocks behave elastically over some range of stresses. Of course, if the tensile stress imposed upon a rock exceeds some limiting value, then the rock will fail in tension. In similar manner, there are some limiting shear stresses that can be imposed upon rocks. Hubbert and Willis11 have discussed the shear conditions which will lead to failure. Under moderate stress conditions (such as those likely to be encountered when hydraulically fracturing) and when stresses are rapidly applied, relatively, most rocks will fail in a brittle manner. Hence, for this discussion of hydraulic fractures in the earth's crust, we assume the rocks behave as brittle, elastic materials. Let us develop the discussion in the following way. (The following thoughts are applicable only to brittle materials.) 1. First we consider a brittle, elastic system. An energy balance will show the minimum pressure necessary to fracture rock, and from this pressure we calculate the minimum crack width resulting from extension of a hydraulic fracture. 2. Then we will show that, under ordinary fracturing conditions, fracture widths are appreciably greater than the minimum widths of extending fractures. In fact, we will find that crack width is controlled by fluid pressure drop in the fracture. 3. We will discuss pressure drops in fractures and resulting crack widths for various operating conditions and both vertical and horizontal fractures. 4. Finally, we will discuss the significance of these concepts, their relationship to fracturing pressures, etc. First, consider minimum fracture extension pressures. We can shed some light on this question by considering the theory proposed by Griffith7, 8 Yo explain the rupture of brittle, elastic materials. Griffith recognized that solid materials exhibit a surface energy8 (similar to surface tension in a liquid). The fundamental concept of the Griffith theory is that, when cracks spread without the application of external work (in the interior of an elastic medium which is stressed

By G. S. Rice

Undoubtedly there is a serious problem through the juxtapostion of gas and oil wells and coal mines, not only at the present time, but possibly of far more serious import for the future.

Jan 1, 1915

By Tokio Yanagida

Major parameters relating to the operating of the conventional calcine-charged reverberatory f'ce process such as distribution coefficients of major elements among slag, matte, blister, and gases, temperatures and weights of intermediates, and heat losses of furnaces were measured and determined. A computer program to estimate heat and material balances at the process was prepared utilizing these data, showing a good agreement with actual results.

Jan 1, 1984