Search Documents

By Henry G. Granger

Repeated failures in attempts to work gold-bearing gravels by means of suction-dredges have created the impression that this method is impracticable. The suction-dredges have failed from three special causes: excessive wear and frequent breakage of pump-shell, runners and liners; inability to dredge compact gravel which would not readily move towards the intake; and, most important of all, closing of the suction-pipe by stones too large to enter it. In my opinion, all three causes of trouble may be remedied: the first, by making stronger the parts most liable to wear and breakage; the second, by means for loosening the gravel at the intake; and the third, by sufficiently increasing the diameter of the suction-pipe. In suction gold-dredges, this diameter has not usually exceeded 10 or 12 in.; whereas there are few profitable gold-fields which call be considered dredge-able, in which stones more than 12 in. in diameter are not frequently encountered. II. An Effective Suction-Dredge. In harbor-operations, much larger stones are handled by suction-dredges. The large dredge of the Henry Steers Contracting Co. worked for nearly four years at League Island, Philadelphia, where it sucked up, passed through the pump, and forced through 3,700 ft. of discharge-pipe, gravel containing boulders up to 200 lb. in weight. This was done with no bad breaks and few shut-downs. The cutter and liners were the only parts liable to damage, and these were easily replaced with brief interruption of work. The chrome-steel liners are said to have lasted from six to nine months. I am informed that this dredge worked continously for nine

Jan 1, 1910

By Andrew Button

INTRODUCTION This review deals with the controls exerted by unconformities on the stratigraphic and areal distribution of gold (and uranium) in Precambrian conglomerates. The relations described are drawn mainly from Precambrian basins in southern Africa, particularly the Witwatersrand Basin. The mining industry of South Africa started in earnest with the discovery of diamonds in 1866. Gold was first discovered in 1870, and in March of 1886, two out-of-luck prospectors stumbled across what was to become the world's greatest goldfield, in the vicinity of Johannesburg. George Harrison and George Walker sold their claims for a pittance and were heard of no more. The Witwatersrand goldfield has been in continuous operation since that time, some 150 mines having operated at one time or another. Deep mining technology developed here has allowed operations to proceed to depths approaching 13,000 feet. The Witwatersrand has produced some 55% of all the gold ever mined, and currently produces 60% of the world's supply, some 650,000 kg Au per year. To 1971, the Witwatersrand had produced some $32 billion of gold and $2 billion of uranium (when average prices were less than $35/oz. for Au and $10/lb. for U308). At present prices, the annual Witwatersrand production of close to 700,000 kg would be worth about $10 billion. Uranium was discovered in the Witwatersrand in 1923. In the $15-30/lb. bracket, the basin contains a reasonably assured plus

Jan 1, 1983

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By Henry Rawdon

ONE of the most vital problems in the manufacture of steel at present is the occurrence of the defects that have been popularly termed "snow flakes," "flakes," or "scabs." Particularly is this the problem of many manufacturers who during the past 2 yr. have undertaken large-scale production for the first time. A study of the microstructure of such defective material throws considerable light upon the nature of these defects and is essential before measures may be taken for the elimination of the defects. Flakes do not appear to be found in the plain carbon steels; they have been found, however, in abundance in some of the simple alloy steels that are being used in such vast quantities; viz., nickel steel of the approximate composition, 0.40 carbon and 3.5 per cent. nickel, and in the chrome-nickel type. The present article summarizes the characteristic features of defective steel of the flaky type as they have been found by laboratory study of numerous specimens, and it aims to show the conditions within the metal that are favorable to the occurrence of this type of defect without entering into the details of mill practice (size of ingot, design of molds, rate of cooling, distribution of cooling stresses, etc.), all of which conditions appear to play a role in the production of these defects.

Jan 2, 1919

By C. S. Matthews, H. C. Lefkovits

Drilling progress is often delayed by sticking of the drill string. The development of preventive and remedial methods has been hampered by incomplete understanding of the sticking mechanism. A recent lahorntory investigation hns indicated that one type of sticking may be attributed to the difference in pressure between the borehole and formation. This paper shows, by means of soil mechanics, that the primary cause for differential pressure sticking is cessation of pipe movement, whereas diflerential pressre and stanrtding time determine the severity of the sticking. The analysis stresses the importance of using low-weight muds with low solids content and low water loss to alleviate diflerential pressure sticking and describes why packed hole drilling, long strings of drill collars, and a large deviation from the vertical are conducive to sticking. Finally, preventrve and remedial methods ore evaluated, and a theory is presented on the release of stuck pipe by spotting oil. INTRODUCTION Since drilling with long strings of oversize drill collars has become standard practice in many areas, the incidence and severity of the stuck pipe problem has increased. It has been noticed that in the majority of these cases the sticking could not possibly be attributed to key seating or caving of shales. It appeared that, due to the differential pressure between the mud column and the formation fluid, the collars were pressed into the wall and so became "wall stuck". Points to note about differential pressure sticking are: (1) sticking is restricted to the drill collars, (2) the collars become stuck opposite a permeable formation, (3) the sticking occurs after an interruption of pipe movement, (4) circulation, if interrupted, can be restarted after the sticking is noticed, and (5) no large amounts of cuttings are circulated out after restarting circulation. Helmick and Longleyl investigated pipe sticking by differential pressure in the laboratory and found an empirical relationship between the differential pressure, the sticking time and the required pull-out force. In this paper an explanation of the mechanism is given based on Terzaghi's theory of clay consolidation. A qualitative description is given in the following paragraphs while the derivation of fonnulas is given in Appendices. This paper is a first attempt to explain pressure differential sticking and many points will require additional theoretical and practical investigation before the problem can be fully understood. PRESSURE DIFFERENTIAL STICKING AS A CONSOLIDATION PROBLEM In any borehole, where the mud pressure is higher than that exerted by the formation fluids, a mud cake is formed opposite the permeable sections of the hole and a continuous flow of filtrate takes place from the mud, through the cake and into the formation. This radial flow pattern requires a certain distribution of the hydraulic and the effective (grain-to-grain) stresses inside the mud cake. Any quantitative or qualitative change in the external pressure conditions will produce a change in the flow pattern and, consequently, also in the internal stress distribution inside the cake. In view of the low permeability and the high compressibility of a clay mud cake, the adjustment of the internal stress distribution is slow and is accompanied by a change in volume. Time dependent stresses are thus created which gradually diminish as the new state of equilibrium between internal and external pressures is approached. Some 30 years ago, Terzaghi developed his "Theory of Consolidation" to account for the time-dependent stresses and settling of clay formations under the influence of external loads. He derived a differential equation by which the time-dependent hydraulic stress and the consolidation can be computed for any point inside the layer during the consolidation process. His theory is based on the assumption that the change in stress is solely due to a change in water content and it may only be applied to one-dimensional consolidation phenomena. Other investiga-tors5,10 have expanded his theory to include processes of more than one dimension. The difference between the external pressures on the mud cake before and after sticking is a qualitative one (isolation of part of the cake by the static contact with the drill collars after pipe movement has been stopped)', and the time-dependent stresses thus created may be investigated by means of Terzaghi's theory. By this analysis the changes in the nature of the contact surface between the drill collars and the mud cake during the sticking can be explained; and the friction force between the two may be computed as a function of the sticking time, the borehole dimensions and the mud cake characteristics.

By Robert Stefanko

Shortwall mining represents a compromise between the room-and-pillar and longwall systems. Figure 1 shows that the shortwall layout is very similar to that for longwall panels, the primary difference being that the shortwall is generally 150 to 200 feet wide while longwalls are 350 to 600 feet wide. The development of entries is divorced from the production of the walls with both systems. However, the depth of the web is considerably different in the shortwall system. Because a standard continuous miner is employed, a depth of 10 feet is normally mined on a single pass. This greater web thickness requires the use of a specially constructed support that can support the much longer cantilever bar that must extend over the working area. This is accomplished by not only increasing the length of the bar but also strengthening it structurally; however, the key to success lies in articulating the cantilever from the base and supporting it with a short hydraulic jack leg. This arrangement provides the additional strength required in the support. It should be apparent that a shortwall support is more costly than the type used for longwall.

Jan 1, 1981

By M. G. Benz, J. F. Elliott

The austenite solidus of the iron-carbon system has been determined using a series of diffusion couples, each of which consisted of a specimen of austenite held in contact with a melt saturated with austenite. After the equilibrium distribution of carbon had been established by diffusion at a specified temperature, i.e. the austenite specimen had become austenite of the solidus conzposition, the diffusion couple was cooled, sectioned and anazlyzed for carbon. The solidus was found to be a straight line: A revised iron-carbon temperature-composition diagram is presented, COMPOSITION has a marked effect on the temperature at which austenite begins to melt and the austenite solidus of the iron-carbon system describing this effect has been the subject of many investigations.1-10 The significant results of these investigations are presented in Fig. 1. The experimental methods and purity of the materials used in them are summarized in Table I. In plotting the data in Fig. 1 no attempt has been made to convert these results to the International Temperature Scale of 1948," except for the data of Adcock,5 as this conversion would do little to reduce the uncertainty that exists as to the position and shape of the solidus. A point of major concern in evaluating these data is that the alloys studied, except those used by Adcock, were not binary alloys of iron and carbon, Table I. Also, it would appear that several of the methods did not permit equilibrium to be established through the system being studied. All that can be said for the results of these investigations is that they indicate only approximately the location of the solidus with the uncertainty as to its location at 1 pct C being approximately 100°C. The current investigation was undertaken to provide reliable data by which the austenite solidus could be established. It was hoped that information on the liquidus also could be developed at the same time, but experimental limitations prevented this as austenite segregated from the liquid on cooling. After a careful study of possible experimental methods and extensive laboratory tests, it was decided that the use of a series of austenite-liquid diffusion couples would provide the most reliable results. This paper describes the method and its results and also includes a complete iron-carbon temperature-composition diagram based on what are considered to be the best available data. EXPERTMENTAL METHOD The diffusion couple used for this investigation consisted of a small cylindrical pellet of austenite held in contact, at a specified temperature, with a melt saturated with austenite. The composition of the cylindrical austenite pellet was chosen to be approximately 0.1 wt pct C less than the estimated

Jan 1, 1962

By Howard Scott, Henry S. Rawdon

The method of demonstrating the structure existing in a metal or alloy at high temperatures, by etching a polished sample after it has been heated to the desired temperature, is quite familiar to metallog-raphists. The usual procedure1 2 is to heat the specimen, previously polished for microscopic examination, to the desired temperature, in a neutral atmosphere (hydrogen or nitrogen), then admit the etching gas (chlorine, hydrochloric acid or similar gas) for a few seconds, and finally, after flushing out the etching gas with the neutral one, cool the specimen in the neutral atmosphere. The pattern produced by etching at a definite temperature is usually taken as a record of the microstructure prevailing at that temperature. It has frequently been pointed out that changes in composition of the surface metal occur during the preliminary heating in the neutral atmosphere, so that the appearance produced by the etching at high temperature may not exactly represent the condition of the interior of the specimen. To overcome this uncertainty, the heating has sometimes been done in vacuo,3 the etching gas being admitted when the desired temperature was reached, then pumped out and the specimen cooled in vacuo. The studies of Rosenhain, Humfrey, and other workers 4, 5, 6, 7, 8 dem-

Jan 1, 1922

By Howard Scott, Henry S. Rawdon

The method of demonstrating the structure existing in a metal or alloy at high temperatures, by etching a polished sample after it has been heated to the desired temperature, is quite familiar to metallog-raphists. The usual procedure1 2 is to heat the specimen, previously polished for microscopic examination, to the desired temperature, in a neutral atmosphere (hydrogen or nitrogen), then admit the etching gas (chlorine, hydrochloric acid or similar gas) for a few seconds, and finally, after flushing out the etching gas with the neutral one, cool the specimen in the neutral atmosphere. The pattern produced by etching at a definite temperature is usually taken as a record of the microstructure prevailing at that temperature. It has frequently been pointed out that changes in composition of the surface metal occur during the preliminary heating in the neutral atmosphere, so that the appearance produced by the etching at high temperature may not exactly represent the condition of the interior of the specimen. To overcome this uncertainty, the heating has sometimes been done in vacuo,3 the etching gas being admitted when the desired temperature was reached, then pumped out and the specimen cooled in vacuo. The studies of Rosenhain, Humfrey, and other workers 4, 5, 6, 7, 8 dem-

Jan 1, 1922

By J. H. Swisher, E. O. Fuchs

Rate equations were derived to describe the kinetics of internal oxidation of cylinders and spheres. The derived equations for cylinders were checked experimentally by means of sub scale thickness and electrical conductivity measurements on Cu-Cr alloy wires. The properties of the internally oxidized samples were examined with conductivity applications in mind. It was possible to produce uniform dispersions of Cr2O3 in copper with an initial chromium content as high as 3 wt pct. While electrical conductivities only a few pct less than that of OFHC copper were obtained, the Cr2Os particle size and spacing were too large for effective dispersion hardening. T.HE process of internal oxidation has been used widely in basic studies of the permeability of gases in metals. In a review article, Rapp1 has discussed the principles of internal oxidation in considerable detail. From a technological standpoint, internal oxidation is often considered undesirable, since it is a means by which inclusions can be introduced into an otherwise clean material. Another important aspect of internal oxidation is its use as a means of dispersion hardening a material. Broutman and Krock2 discuss this and other methods for making dispersion hardened alloys. The only internally oxidized material known to the authors which is commercially available is a Cu-BeO alloy.3'4 This alloy is made from Cu-Be alloy powder, using a so-called Rhines pack. It has a tensile strength of 80,000 psi and retains its strength at relatively high temperatures. The objectives of the present study were to derive rate equations for the internal oxidation of cylinders and spheres, to check the derived equations for cylinders experimentally, and to examine the structure and properties of internally oxidized Cu-Cr alloys. The Cu-Cr system was chosen for this study because uniform dispersions are obtainable at high alloy contents, which is a desirable characteristic in dispersion hardened materials. RATE EQUATIONS FOR VARIOUS GEOMETRIES A number of authors5--9 have derived equations to describe internal oxidation kinetics. These derivations differ somewhat in mathematical assumptions and approximations, and all except one of the derivations deal exclusively with the internal oxidation of plates. The exception is a brief treatment of cylindrical and spherical geometries given by Meijering and Druy-vesteyn9 as a part of a comprehensive paper on the general subject of internal oxidation. These authors did not obtain rate data to check their derivations, although they did show that the hardness profile across an internally oxidized sample is directly related to the rate of interface movement. For cylindrical and spherical geometries, a quasi-steady-state approximation is needed to circumvent mathematical complications in obtaining a solution to the basic differential equations. In using this approximation, we consider the concentration gradient of dissolved oxygen in the internally oxidized zone or sub-scale to be the same as the gradient which would be present if there were no movement of the subscale interface. The steady-state approximation introduces an error of about 1 pct in computing the rate of internal oxidation of an Fe-1.0 pct Mn alloy plate, if the present method is compared to the more exact method of Wagner.7'10 The details of the derivations of the rate equations for cylinders and spheres are given in the Appendix, and only the results of these derivations are given below. The final equations obtained by Meijering and Druyvesteyn9 can be shown to be equivalent to our Eqs. [1] and [2], although the two approaches are somewhat different. Cylindrical Geometry. [2] where r1 is the outer radius of the cylinder or sphere, cm, r2 is the radius of the unreacted core, cm, see Fig. l(a), D is the diffusion coefficient of oxygen in copper, cm2 per sec, %O is the concentration of dissolved oxygen at the surface of the specimen, wt pct, %Cr is the initial chromium concentration in the alloy, wt pct, and t is the reaction time, sec. Plate Geometry. The analogous rate equation for a plate has been derived previously for internal oxidation of Fe-Al alloys.8'11 For Cu-Cr alloys, we may write the same equation as follows: [3] where r1 is the half-thickness of the plate, cm, and r2 is the distance from the mid-plane to the subscale intherate is An analysis of Eqs. [1], [2], and [3] shows that for a plate the rate is completely parabolic. The initial

Jan 1, 1970

By Herman F. Kaiser, Charles S. Barrett, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By Charles S. Barrett, Herman F. Kaiser, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By Frederick C. Hull

THE grain size of a metal or alloy is one of the most important factors determining its properties. In steels, for example, grain size affects hardenability, toughness and machinability; in brasses, grain size is related to hardness and deep-drawing quality. In the field of heat-resistant alloys, grain size has a marked effect on ductility, creep and endurance strength. In order to determine these effects, as well as to control the properties of materials, many accurate and rapid measurements of grain size must be made. This paper presents a new and improved method for the estimation of grain size. USUAL METHODS of EVALUATING GRAIN SIZE A frequently used method of estimating grain size is that of comparing the image of a polished and etched specimen on the ground-glass screen of a metallographic microscope with standard grain-size charts. Several types of standards are available for use with different classes of microstructures. Geometric Grids.-The Metals Handbook1 has a series of hexagonal grids ranging in size from ASTM No. I to 8. Idealized Grain Networks.-Idealized grain-boundary networks for ASTM grain sizes I to 8 are included in the American Society for Testing Materials Tentative Standard E19-39T. Standard Micrographs.- The Metals Handbook and ASTM Tentative Standard EI9-39T contain micrographs of hypoeutectoid and hypereutectoid steels ranging in grain size from No. I to 8. The grain size of annealed brass (diam¬eter of the average grain in millimeters) is obtained by comparison with 10 micrographs of varying grain size in ASTM Tentative Standard Es-39T. A handicap to accurate evaluation of grain size by this method is the fact that it is difficult to compare photographs in a dimly lighted room with the image on the ground-glass screen, or, if the general illumination is increased so that the printed standards may be clearly seen, the contrast of the image of the unknown is decreased. It is easier to estimate grain size by comparing a micrograph of the unknown with the grain-size standards. However, photographing every specimen on which the grain size is desired is too costly in time and materials to be practicable. For hardened steels, the Shepherd or Jernkontoret fracture grain-size standards are very accurate and useful, but this method obviously cannot be applied to ductile alloys such as brass, stainless steels and austenitic heat-resistant alloys. Jeffries' method for grain-size measurements consists of counting the number

Jan 1, 1947

By H. S. Bell

It seems unnecessary to dwell upon the advantages of the modern pipe still as compared with the older type of distillation equipment used by oil refiners. The relatively low installation cost, coupled with remark-able operating efficiencies of pipe stills, precludes the consideration of other types except in rare instances where some peculiarity of product or plant may have an influence. The question of the actual heat required to distil petroleum is quite involved. We have extensive data on the latent heats of the various hydrocarbons under different conditions of pressure. We also have information regarding the specific heats of various oils and the effect of temperature thereon. Because of the complexity of petroleum and of each fraction, it seems impossible to analyze theoretically the partisl-pressure effect of the great number of hydrocarbons upon one another during distillation. If a distillation curve and percentage analysis of any crude or product are available, it is possible to construct a curve with ordinates representing per cent. distilled and B. t. u. per pound or per gallon, or other desired unit. To do so the crude is split into fractions, of 5 or 10 per cent. The boiling point and gravity of each fraction being determined, it is possible to evaluate the heat required. As each fraction is removed, the residue must be raised to a higher temperature and latent heat supplied for the successive fraction. As the calculations progress, the latent heats decrease while the specific heats increase. Such a curve is illustrated by Fig. 1 for a typical 39.9° Be. North Texas crude. The chart is illustrative of batch distillation. Theoretically, if the oil were heated by a single flash in a pipe still, the partial-pressure effect of the light products would result in the removal of the same amount of vapors at a lower temperature. Practically, we find that because of the necessarily extensive fractionating equipment required when separating many products all in vapor phase, the oil has to enter the separator at temperatures corresponding to or even above those required in the batch still. Furthermore, in single-flash distillation the vapors evolved in the heater must be superheated to the outlet temperature. Very little is

Jan 1, 1928

By John C. Martin

The discovery of a new gas reservoir demands that the planning of a sottnd well-spacing program be initiated early in the development stage. It is the purpose of this discussion to illustrate by actual field examples the application of basic well-spacing principles, previously developed for oil reservoirs, to the problem of well spacing in natural gas fields. These studies are presented for the field use of geologists and engineers who are concerned with the initial planning of the proper development of the newly discovered gas reservoir. INTRODUCTION The phenomenal growth of a vigorous natural gas industry emphasizes the increasing importance of natural gas as a source of energy, fuel, and raw materials to our nation's economy. Since 1945 marketed production of natural gas for the U. S. has increased 21/2 times to a record high of 10.6 trillion cu ft during 1957. As major participants in the gas industry, we share an added interest to develop and produce our natural gas reserves with constantly improved efficiency. The subject of well spacing is vitally important to the gas industry, for the well itself plays a significant role in the development of the natural gas reservoir and in control of the recovery process. Maximum utilization of wells is an integral part of sound conservation practices. The discovery of a new gas reservoir demands that careful choice of well location and well spacing be made and that the planning of a sound well spacing program be initiated early an the development stage. With the drilling of the first development well, efforts of the geologist and engineer must be directed toward acquisition of adequate technical evidence upon which a firm recommendation for a spacing program may be based. With this technical appraisal as a foundation, operators and state regulatory agencies jointly can go far in providing a framework for sound development of gas fields to achieve a program of conservation that avoids the unnecessary well. WELL-SPACING CONCEPTS Through laboratory and field investigations of the mechanism of the recovery of oil and gas, of fluid behavior, and of effective control of reservoir and well, a crystallization of ideas regarding reservoir behavior has emerged as a well-developed technology. Associated with a better understanding of the fundamental principles underlying reservoir and well behavior has been the growth of concepts concerning the role of wells and their spacing in the development and operation of an oil or gas reservoir. In addition to serving as outlets for the withdrawal of fluids from the reservoir, wells are recognized as having two other important functions: (1) providing access to the reservoir to obtain information concerning the characteristics of the reservoir and its fluids, and (2) serving as a means by which the natural or induced recovery mechanism may be effectively controlled. Beyond a minimum number of wells required to fulfill these two functions, additional wells will not increase recovery. With particular emphasis upon well spacing in oil reservoirs, many studies of the well spacing-recovery relationship have evolved the concept that the ultimate oil recovery is essentially independent of the well spacing.' These fundamental concepts are no different when regarding the role of wells and their spacing in the natural gas reservoir. They are equally applicable to the consideration of well spacing in gas reservoirs. For the gas reservoir, the problem of well spacing then revolves around the question of drainage and the degree or extent to which a well may drain gas from its surrounding reservoir environment. Theoretical and Experimental Work During the past 30 years, theoretical and experimental work carried on to study the physical principles involved in the flow of fluids through porous media has shed light upon the matter of drainage. Fundamental mathematical equations have been derived to describe the mechanism of flow of oil and gas through porous rocks. With the recent advent of high-speed digital computers, attempts have been made with mounting success to develop solutions, employing numerical techniques, to mathematical expressions that describe more rigorously the physical behavior and mechanism involved in the unsteady-state flow of compressible fluids, such as a gas, through porous rock. In 1953, Bruce, Peace-man, Rachford and Ricez published a stable numerical procedure for solving the equation for production of gas at constant rate. The results of these calculations are significant with respect to this matter of drainage, for they indicated (1) that depletion of the gas reservoir resulted in a drop in pressure at the extremity of the

By E. C. Tveter, L. A. Roe

The authors present a general outline of the theory and development of heavy-liquid application to mineral processing. Patent literature and processes are reviewed with special emphasis on liquid recovery systems which have been employed or proposed. Advantages and disadvantages of the process are discussed together with the recent developments which have revived interest in this old concentration method. The most important single factor in this resurgence of interest is concluded to be the narrowing gulf between chemical engineering and mineral dressing which has opened the field for new concepts of mineral plant design. A partial summary of patents on heavy liquid separations is included. In spite of the fact that heavy-liquid separation with organic liquids has been used in the laboratory for over 50 years, this process has never graduated to large scale commercial use for any extended period. However, a variation of this process, the sink-float or heavy-media separation process has found wide acceptance and is used to separate minerals from diamonds to gravel. Materials used to increase the specific gravity of the pulps used as heavy media include sand, clay, barite, magnetite, galena, hematite, atomized lead and ferrosilicon. Because of the greater ease of recovery, the magnetic materials, magnetite and ferrosilicon, are the preferred media today. In the U. S. alone, heavy-media iron ore plants with a capacity of over 10 million tons of concentrate per year are in existence. Heavy-media separation involving use of solid, inorganic particles suspended in water rapidly found a wide range of commercial use with the introduction of magnetic media. The minerals engineer is experienced in working with suspensions and quickly learned to develop and control such media at a cost compatible to the type of separation desired. The natural superiority of a heavy liquid with uniform chemical and physical properties has never been questioned since its first use in laboratory mineral separatory procedures. It offers the only method for gravity separation of fine particles of relatively close specific gravity. The most important early attempt to make heavy liquid separations commercial were made by the DuPont Co. which began experimental work on Virginia limonite in 1904. The appended "Partial Summary of Patents" compiled by W.L. O'Connell of The Dow Chemical Co. demonstrates the quantity and sequence of this work. Both inorganic and organic parting liquids were investigated and numerous patents were issued on the use and recovery of these liquids. The work culminated in the heavy liquid plant of the Weston Coal Co. at Shenandoah, Pa. Chemical engineering design of this plant was the responsibility of Francis I. and Hubert I. DuPont. Heavy-liquid separation of coal almost achieved commercial status at this plant which actually processed over 20,000 tons of coal. The liquids used were tetrabromethane, pentachloroethane and trichlo-roethylene, with liquid losses ranging from 8.9 to 12.4 oz per ton of cleaned coal. The reasons for failure of this plant are not clear but probably involved toxicity problems as well as other problems in chemical engineering. Excellent economics were reported. A more recent pilot plant was built in 1954-55 by Norris Goodwin for the Inerto Co. to treat hectorite clay. This plant employed carbon tetrachloride in jigs with liquid recovery by evaporation. Although good separation was achieved, incomplete removal of the CCl, from the clay prevented commercial operation. The only present operations known to the authors employing heavy liquids for gravity separations are limited to the use of calcium chloride in certain coal washers and bromochloromethane in a small batch operation (one ton solids per day) for the separation of beryllium metal particles from slag materials. This is not strictly a minerals beneficiation problem but it has demonstrated the feasibility of such separations. PROBLEMS Critics of early attempts to commercialize heavy-liquid separation of minerals summarize the draw-

Jan 1, 1963

By Eugene F. Poncelet

GLASS squares compressed on edge by steel jaws in poor contact with them developed jagged "partial-contact" cracks caused by the formation of local tensile stresses. Compressed by steel jaws in perfect contact, they developed smooth "release cracks" during release of the pressure, caused by the formation of local tensile stresses during the release of the pressure. All these cracks were parallel to the pressure. A Microflash photograph of a disintegrating specimen under sufficient pressure reveals a network of fractures roughly normal to each other, also "release cracks" and a disintegration cloud. The Griffith theory is amended to account for the formation of a first crack. A new theory, based on the theory of thermal agitation and wave propagation, is proposed to account for the progress, velocity and forking of cracks. The network of fractures is shown to have been caused by reflection at a free boundary of pressure pulses emanating from a first crack. Postulating equal distribution of energy in the pulses emitted on either side by a crack in particles, the smaller fragments are shown to continue fracturing preferentially while some of the coarser fragments remain as residual pieces. As comminution of the smaller fragments proceeds, the solid is reduced to a collection of residual particles of smaller and smaller sizes, accounting for the disintegration cloud. EXPERIMENTAL PROCEDURE Apparatus A crushing device was built, consisting of a steel frame and two polished, hardened steel jaws to crush plate-glass samples. This device was placed between the plates of a hydraulic press (Fig. 1). For centering the pressure, the upper jaw was guided vertically and provided with a rounded top. Later it was replaced by a steel jaw ground out of a 2 1/2-in. steel ball, the lower surface being ground to an optical flat (Fig. 2). Four rollers were used to eliminate side thrust. Screws and centering blocks served to center the specimen in the crushing device. Hard steel shims placed under the shoulder of the upper jaw limited the "follow through" of the jaw after failure of the specimen. Stress distribution was first examined with a polariscope mounted on an optical bench, using monochromatic light. It was found convenient to mount polaroid, quarter wave and monochromatic plates directly on the device itself. A Microflash unit* was used as light source for the photographs. A gold-paint pattern was fused on the plate-glass specimens and connected into the spark-

Jan 1, 1944

By G. Derge, Ling Yang, John Henderson

Self-diffusion coefficients of aluminum have been measured by the capillary reservoir technique in liquids of the CaO-SiO2-Al2O3 system containirg equimolar portions of CaO and SiO2, in the temperature range 1400o to 1520oC. For the melt containing 6.0 mole pct Al2O3 the results can be expressed by the equation D = [(4.3 * 0.3) x 104] exp [(-85,000 * 17,500)/RT]cm~sec-'; for the melt containing 12.5 mole pct Al2O3, by the equation D = (5.4 i 0.2) exp [(-60,000 * 10,00O)/RT] cm2sec-: A concept of the constitution of these melts has been developed which proposes that the ratios O/(Si +Al) and Al2 O3/CaO determine the dominant species present. In recent years considerable work has been done on the system CaO-SiO2-A12O3 with a view to elucidating the structure of liquids of this system. Conductivity,' electromotive force, 3 density,4 and activity5 measurements have all contributed to an understanding of the problem, but as yet there is no entirely satisfactory theory that can account for all the observed experimental results. In principle, measurements of self-diffusion coefficients should give further information which is not obtainable in other ways. Self-diffusion coefficients for calcium, silicon,6 and oxygen7 have been measured. The present investigation extends the series of self-diffusion coefficient measurements to include aluminum and develops a concept of constitution for liquids of this system which is compatible with all the observed experimental results. EXPERIMENTAL The technique used in the measurement of the self-diffusion coefficient of aluminum was the capillary-reservoir method,8 A126 being incorporated in the melt contained in the capillary and inactive aluminum in the reservoir melt. This method was chosen because it minimizes convection currents' in the diffusion zone. It has the further advantage that the boundary conditions are such that a slight modifica- tion of Anderson and saddington's8 solution of Fick's Law yields an equation which requires measurements only of the length and the initial and final average specific activities of the solidified melt within the capillary. where t is the diffusion time, Co is the average specific activity of the melt contained in the capillary at t = O, C is the average specific activity of the melt contained in the capillary at t = t, 1is the length of the capillary, and D is the self-diffusion coefficient. The equation is of somewhat different form than those previously applied to high temperature diffusion studies because the specific activity of the melt in the reservoir was negligible both before and after diffusion. The diffusion apparatus is shown schematically in Fig. 1. It consisted of a silicon carbide resistance furnace containing the inactive melt in a graphite crucible, internal dimensions 7/8 by 4 in., enclosed in a 1 1/4- by 1 1/2- by 30-in. McDanel tube. A 3/8-in. McDanel thermocouple sheath to which graphite radiation shields and a graphite protection tube were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube the capillaries could be lowered into or raised out of the melt. Temperature was measured with a Pt-Pt 13 pct Rh thermocouple which was calibrated periodically against a standard couple. The furnace temperature was controlled to ± 5°C through the thermocouple immersed in the melt. Temperature variation over the depth of the melt was less than ± 3°C. The inactive melts were prepared from pure native quartz, assaying better than 99.9 pct SiO2, A.R. grade A12O3 and A.R. grade CaCO,. The same quartz and CaCO3 were used in preparing the active melts, the

Jan 1, 1962

By K. R. Evans

The yield and fracture characteristics of a Ti-8 pct A1 alloy have been examined at room temperature as a function of exposure temperatures to 1700°F. Em-brittlenzent of the alloy is observed to occur following exposures below 1280°F, the critical temperature for formation of ordered Ti3Al particles. Presence of Ti3Al particles results in an increase in the yield and flout stresses which, for a given exposure time, are a maximum at the critical temperature. Embrittlement is attributed to the occurrence of plastically induced fracture controlled by the increase inflow stress. This interpretation is compatible with the decreasing ductility and increasing crack popagation rates observed with increasing exposure time below the critical temperature. Slip line observations and measurements of the gain size dependence of the yield stress indicate that the slip character of the alloy is not influenced by exposure treatments below the critical temperature. ThE potential usefulness of Ti-A1 alloys in structural applications has prompted considerable interest in studies of their microstructure and mechanical characteristics. The relatively recent surge of interest in the system and at the same time its complexities are indicated by the fact that despite numerous recent efforts14 there has not even been general agreement upon a phase diagram for the system. However, most of the Ti-A1 alloys of commercial interest range in aluminum content from 5.0 to 8.5 wt pct where most investigators achowledge the existence of the ordered Ti41 phase. Goldak and parrs confirmed the existence of Ti41 from X-ray diffraction analysis of the stoichiometric composition while Blackburn6 has determined its presence in commercial Ti-8 pct A1 alloys by electron diffraction analysis and dark field transmission microscopy. The embrittlement of Ti-8 pct A1 alloys was initially reported by Crossley and carew7 who showed that aging in the temperature range of 750" to 1110°F resulted in extreme brittleness. This behavior was later confirmed and correlated by Soltiss to the presence of long-range order in the commercial Ti-8 pct Al-1 pct Mo-1 pct V alloy (Ti-8-1-1) which exhibited anomalous creep and yield strength behavior at 950°F. This investigation was designed to study the mechanical characteristics of a binary Ti-8 pct A1 alloy in order to further examine the nature of the embrittlement behavior reported for the alloy system. EXPERIMENTAL PROCEDURE A Ti-8 pct A1 binary alloy was obtained from the Wah Chang Co. in the form of 0.050 in. sheet. The chemical composition of the alloy is given in Table I. Heat-treatment of the alloy was conducted in evacuated vycor capsules for the tensile sDecimens (1.25 bv 0.25 in. gage section) and in evacuated stainless steel jackets for the crack growth-rate panels. All specimens were annealed at 1700°F for 24 hr and water quenched before an exposure at elevated temperatures. Tensile testing was conducted at room temperature in an Instron testing machine equipped with a pushbutton control for instantaneous control of the cross-head motion. In this manner the change in stress, Aa, accompanying an increase in strain-rate by a factor of 10 was measured immediately after yielding. The crack growth-rate panels used were 3 by 18 in. with a precrack 0.33 in. long cut into the center of the panel. The panels were cycled at a maximum gross stress of 40,000 psi at a maximum to minimum tension stress ratio of 20. Cycling of the specimens was continued until the crack propagated the width of the panels. The crack length was intermittently measured during slow crack growth. EXPERIMENTAL RESULTS Correlation of Embrittlement to the Critical Temperature for Ordering. Blackburn6 has found that the critical temperature, T,, for the formation of Ti41 in a Ti-8 pct A1 alloy with an interstitial content on the order of that given in Table I is approximately 1245°F. The relationship between the ductility of the binary alloy used in this investigation and T, was estimated from tensile tests on specimens which were exposed for 24 hr at various temperatures followed

Jan 1, 1970

By G. E. McElroy

Much attention has been directed to mine-air flow in recent years, more especially in Great Britian where there is frequent reference to a theory of fluid flow developed by English engineers. Briefly stated, this theory is that for similar passages of the same relative roughness, in which fluid flow occurs, the conditions of flow are exactly the same for W D V equal values of the product where W = density of the fluid, D = diameter of the passage through which flow occurs, V = mean velocity of flow, and p = absolute viscosity of the fluid flowing. This, the "Reynolds Criterion" of fluid flow, had its origin in the work of Reynolds1 more than 40 years ago. Later, Rayleigh2 amplified the theory which has been conclusively proved for small pipes by the experiments of Stanton and Panne13 over a large flow range, and by Lacey4 over a somewhat more limited range. Concordant results on small pipes have also been obtained by numerous other investigators with single fluids over more or less limited ranges of flow. According to this theory, results in one medium, such as water, are immediately applicable to another, such as air; and experimental results on models are (theoretically, at least) applicable to full-scale designs. This is of great importance in aeronautics and can be of considerable value in mine ventilation research. Hodgson, in a recent paper,6 has outlined the application of this theory to mine-air flow and recent English experiments6 on the resistance of a timbered mine airway have been expressed in this form.

Jan 1, 1927