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By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

Production of crude oil in Bahrein Island during 1938 reached the new high of 8,297,998 bbl., an increase of 535,734 bbl, over the 1937 production of 7,762,264 bbl. The monthly average during 1938 was 691,500 bbl. and the daily average 22,734 barrels. To the close of December 1938, a total of 52 producing wells have been drilled. During the year 13 producing wells were completed and 11 wells were drilling or partly completed as of Dec. 31, 1938. The total footage drilled as of Dec. 31, 1938, amounted to 165,339 ft., of which 60,739 ft. was drilled during 1938. The production from the main pay comes from a depth of approximately 2200 ft. and the gravity of the oil is 33" A.P.I.

Jan 1, 1939

Production of crude oil in Bahrein Island during 1938 reached the new high of 8,297,998 bbl., an increase of 535,734 bbl, over the 1937 production of 7,762,264 bbl. The monthly average during 1938 was 691,500 bbl. and the daily average 22,734 barrels. To the close of December 1938, a total of 52 producing wells have been drilled. During the year 13 producing wells were completed and 11 wells were drilling or partly completed as of Dec. 31, 1938. The total footage drilled as of Dec. 31, 1938, amounted to 165,339 ft., of which 60,739 ft. was drilled during 1938. The production from the main pay comes from a depth of approximately 2200 ft. and the gravity of the oil is 33" A.P.I.

Jan 1, 1939

By Charles J. Deegan

The purpose of this paper is to point out some features of the position of fuel oil and it's relationship to the economic balance and price structure of the petroleum industry. The term "fuel oil" as used in this paper includes crude used as fuel as well as refined gas oil and fuel oil. The period covered, from 1922 to date, may be characterized as the new normal era after the post-war inflation and deflation. In order to establish a proper perspective, the figures on consumption of the principal products of petroleum are shown in Table 1. This table shows that fuel oil and gasoline made up the bulk of the total demand in 1928 just as they did in 1922. There has been so much comment about the enormous increase in gasoline consumption that it may come as a surprise to some people to find that fuel oil is still at the head of the consumption list, in point of volume at least, and seems likely to hold that place for at least another year. Having established the fact that gasoline and fuel oil are by far the most important products, the remainder of this paper will deal almost entirely with these two items.

Jan 1, 1929

By David Cornell, D. L. Katz

Procedures for computing turbulent flow of gas in steady state near the well bore and a graphical method for predicting unsteady state laminar flow at distances from the well have been combined to compute pressure gradients in gas reservoirs. Methods are discussed for predicting single and multiple transients at constant flow rate in an infinite reservoir, predicting constant How rate. in a finite reservoir, reproducing and interpreting back pressure test data, and prediction of the behavior of a closed-in gas well. An example of the graphical method is given for a single transient and the results are compared to a published analytical solution. A typical calculation of the pressure gradient in a reservoir and the production of gas is made .starting with data from a hack pressure test. INTRODUCTION The calculation of pressure gradients throughouse a ga-reservoir at any point in its production history is a complex problem involving turbulent flow near the well bore and unsteady state flow of the gas from the reservoir. The problem is complicated further by the variety of boundary conditions that may be imposed upon the flow. Such boundary conditions include finite or infinite reservoirs. constant or variable rates of production, constant or varying bottom hole pressures, complex initial pressure distributions throughout the reservoir, and pressure maintenance through cycling. In addition to these problems there are the practical difficulties associated with natural gas reservoir analysis These might include: (1) variation. in the permeability and porosity throughout the formation. (2) variations in the thickness of the formation, (3) communication of the producing formation with other producing zones. (4) radial variations in permeability due to influx of drilling fluid. acidizing. or the buildup of liquid in the formation around the well, (5) partial penetration of the producing zone. (6) water flood, and many others. These problems will be considered eventually. In the mean- time, it is necessary to present methods of handling the case of radial flow through a homogeneous, regular, producing stratum to a single well uncomplicated by other factors. The idealized case of steady state, radial flow from a natural gas reservoir was studied by Elenbaas and Katz5 and by Mac-Koberts.' An analysis of the unsteady flow of gases through porous media has been made by Aronofsky and Jenkins' for the one dimensional laminar case with the boundary conditions of constant downstream pressure and uniform initial pressure. Solutions for the partial differential equation for unsteady state radial flow of liquids through porous media have been given by Van Everdingen and Hurst" for the constant bottom hole pressure and constant production rate cases for laminar flow in a reservoir initially at a constant pressure. The analogous heat transfer equation has been treated by Perry and Berggren9 for the case of quenching a cylindrical hole in an infinite medium to a constant temperature. The back pressure curve, which involves the variation of the bottom hole pressure as it is determined by the behavior of the reservoir as a whole. has been studied by Rawlins and Schellhardt,10 Binck-lev,' Baumel and Breitung,' and others. No complete. adequate treatment has been given for the unsteady state, radial flow of gases into a cylindrical hole from a porous medium with or without the presence of turbulent flow and for any set of boundary conditions. If one relies only on analytical solutions of the basic equations, a new solution must be obtained for each new boundary condition. Furthermore, the complexity of the mathematical expressions for boundary conditions other than the very simple cases limits the use of analytical solutions. Graphical methods exist, however. that are general in nature, accurate, and readily employed. The analysis of steady and unsteady, laminar and turbulent, radial flow for various boundary conditions with application to specific natural gas well problems by means of graphical procedures forms the content of this paper. STEADY STATE RADIAL FLOW EQUATION FOR LAMINAR AND TURBULENT FLOW A steady state radial flow equation for laminar and turbulent flow through unconsolidated sands has been given by Muskat as discussion of the work by Elenbaas and Katz.5 This equation is based on the properties of unconsolidated

Jan 1, 1953

By L. Messulam, A. S. Appleton

Iwo major studies of the Fe-Cr-C system are available in the literature. The earlier one of Kinzel and crafts' forms the basis for the data most commonly quoted in works of reference (e.g., Metnls HandDook) though the later work of Bungardt el a1.' is more extensive and amenable to analysis in terms of isothermal sections and so forth. However it is evident from examination of either of these studies that the delination of phase boundaries on the basis of the data obtained can only be very approximate. Indeed in several instances the data are so inconclusive that this delineation is a matter of opinion. This note is to report an analysis of experimentally determined carbon activity data in this system, which, originally intended as a means of checking the self-consistency of the data for a number of alloys, enables some conclusions to be drawn concerning the 10503C isothermal section of the iron-rich corner of the system as deducible from the data of Bungardt

Jan 1, 1967

By Eugene Jablonski

Statistical data on the Polish producing business are available only for the first half of 1939. Because of the invasion of the country during September by Germany and Russia all sources of information have stopped, and it is impossible to get even an approximate picture of the status of the industry after that date. The long declining trend of Polish production, which was finally checked during 1938, kept a further upward tendency during the first half of 1939, and there is good reason to believe that the upward trend would have been maintained. It is true, there was little hope of reviving the slowly dying Boryslaw field, although there still remained a slight possibility for an extension in its southwestern direction. Repressuring plans were still discussed, but. could not be put into effect because of extremely complicated and split-up lease ownership. The Gorlice-Lipinki ficld continued to be the main factor in the increase of the country's production. During the first half of 1939 this field received a further important extension in a southern direction. The Schodnica field continued to use repressuring with success. At the end of June, 21 exploratory wells were drilling, 14 of which were within thc Carpathians and 7 in the Miocene geosyncline of the Carpathian Foreland. All of the wildcat wells drilled within the Carpathians were on the struct,ural cxtcnsion of old established fields, but part of the wildcats of the Foreland were on new geological and geophysical prospects. The Opary gas field of the Foreland discovered last year has been further developed. The Government-owned Polmin completed its third gasser. This well penetrated two sands; the upper one, 118 ft. thick, was found at 1312 ft., with an initial pressure of 570 lb. and capable of produeiring 10 million cu. ft. per day. The second sand, 91 ft. thick, was found at 1690 ft., yielding 20 million cu. ft., with a pressure of 760 lb. The well Mieczyslaw, drilled about 3 miles further north on the flank of the structurc, found the first sand watered. The Pioneer No. 5, at Chodonice near Przemysl, which reported somc gas last year, was 5696 ft. deep at the end of June, still drilling in Miocene. Anothe well in the same vicinity drilled by the Gasolina was 1708ft. deep.

Jan 1, 1940

By Eugene Jablonski

Statistical data on the Polish producing business are available only for the first half of 1939. Because of the invasion of the country during September by Germany and Russia all sources of information have stopped, and it is impossible to get even an approximate picture of the status of the industry after that date. The long declining trend of Polish production, which was finally checked during 1938, kept a further upward tendency during the first half of 1939, and there is good reason to believe that the upward trend would have been maintained. It is true, there was little hope of reviving the slowly dying Boryslaw field, although there still remained a slight possibility for an extension in its southwestern direction. Repressuring plans were still discussed, but. could not be put into effect because of extremely complicated and split-up lease ownership. The Gorlice-Lipinki ficld continued to be the main factor in the increase of the country's production. During the first half of 1939 this field received a further important extension in a southern direction. The Schodnica field continued to use repressuring with success. At the end of June, 21 exploratory wells were drilling, 14 of which were within thc Carpathians and 7 in the Miocene geosyncline of the Carpathian Foreland. All of the wildcat wells drilled within the Carpathians were on the struct,ural cxtcnsion of old established fields, but part of the wildcats of the Foreland were on new geological and geophysical prospects. The Opary gas field of the Foreland discovered last year has been further developed. The Government-owned Polmin completed its third gasser. This well penetrated two sands; the upper one, 118 ft. thick, was found at 1312 ft., with an initial pressure of 570 lb. and capable of produeiring 10 million cu. ft. per day. The second sand, 91 ft. thick, was found at 1690 ft., yielding 20 million cu. ft., with a pressure of 760 lb. The well Mieczyslaw, drilled about 3 miles further north on the flank of the structurc, found the first sand watered. The Pioneer No. 5, at Chodonice near Przemysl, which reported somc gas last year, was 5696 ft. deep at the end of June, still drilling in Miocene. Anothe well in the same vicinity drilled by the Gasolina was 1708ft. deep.

Jan 1, 1940

By H. L. Overton, J. B. Lipson

The concept of sodium single-ion equivalent activity as developed by Gondouin, Tixier and Simard,' was used to determine the filtrate resistivity-activity relationships for 150 laboratory and 49 field drilling muds. With the exception of the native and phosphate high-resistivity muds and the calcium-treated muds, the filtrate resistivity-activity relationships were found to be within 20 per cent of that for pure sodium-chloride solutions. Gondouin, et al,* previously suggested a method of treating the high-resistivity muds in quantitative electrical log analysis. A new treatment is presented which uses the P-alkalinity of the filtrate as a correlating parameter in handling the calcium-treated muds in quantitative electrical log analysis. INTRODUCTION Gondouin, Tixier, and Simard in 1957 introduced new interpretive procedures for analyzing the self-potential curve of electric logging. They re-emphasized the previous work of the Schlumberger brothers, Wyllie and others, and re-defined the activity concept in terms of a number which they termed the effective resistivity. Their procedures are particuarly effective when the connate-water resistivities are less than 0.08 ohm-m or greater than 0.3 ohm-m. For gyp muds where the calcium content is known, a procedure was presented which allows calculation of the connate-water resistivity with improved accuracy. These procedures assume that one of the fluids in the system is a pure sodium-chloride solution, but they are not limited by the assumptions. For the fresh and saline connate waters, for instance, it is assumed that the drilling mud filtrate is a pure sodium-chloride solution. For the gyp mud interpretive procedure, it is assumed that the connate water is a pure sodium-chloride solution. Brown,' on the other hand, has suggested that it would be extremely fortuitous if drilling mud filtrates could all be treated electrochemically as sodium-chloride solutions, and he cites some examples where discrepancies exist. A study has been made of the deviations of sodium single-ion equivalent activities, an of drilling mud filtrates from that of pure sodium-chloride solutions. Drilling fluids in common use on the Texas and Louisiana Gulf Coast and laboratory-controlled muds were investigated. Using a cell patterned after Gondouin, et al, (Fig. I), the equivalent activities were measured. It should be remembered here that the activity measured is merely an index which uses numbers that represent the sodium single-ion equivalent activity a,., of the mud filtrate. The membrane potential developed across the cell was determined with a null-type potentiometer. The resistivities of the solutions were measured by the four-electrode method. The resistivity system was calibrated by using saturated KC1 solution as a standard. Chemical properties of the drilling fluids studied were measured with standard API-approved equipment for the particular property in question. For the activity measurements, two shale discs were chosen to serve as cationic membranes. These two discs were both 1 1/4 in. in diameter and, respectively, 1/4 and 1/8 in. in thickness. The membrane potential, Em, was determined using the shale discs as cationic selective membranes separating two standard sodium-chloride solutions of known mean activity. Then by comparing the constant Km in the following equation, with the theoretical value of — 59 mv at 75OF, the perfection of the membrane was determined. The variation of Km for the two membranes used in this experimental work, as well as one of the many unsuitable membranes, is shown in Fig. 2. The measurement of the activity of mud filtrate involves the balancing of its combined individual activities against a standard solution of known mean activity. At the point where there exists zero potential across the membrane cell, the activity effects may be assumed equal for all practical purposes. The mechanics of making a null reading of this sort requires having a large number of different mean activity solutions. A more practical method involves

By J. H. Anderson, G. A. Parks, B. K. Jindal

Both temperature and humidity are important variables in electrical separations. By independent control of temperature and water vapor pressure, it is shown that charge depends primarily upon relative humidity, not on temperature or water pressure alone. All the effects of temperature changes other than modification of humidity are apparently small. However, humidity control can be achieved through manipulation of the more tractable variable, temperature. Both temperature and humidity are important variables in electrical separations. Some of their effects have been described in general by Fraas1,2 and by Ralston.3 The influence of temperature and humidity may be considered a problem in industrial separations because humidity, especially, is not normally controlled, hence leads to unpredicted quality control problems. The problem is significant whether the separation is based on conductivity differences or on contact electrification. There is no doubt that water adsorbs from humid atmospheres onto mineral surfaces resulting in conductivity changes.'-8 An empirical relationship between conductivity and humidity is1.4-6,8 where a and b are constants peculiar to the substrate, and s and h are the conductivity and relative humidity respectively. Some authors have taken advantage of differences in a and b among minerals to make or propose electrodynamic separations in which h is the key control variable. Fraasl,2 reported that the charge developed on quartz and feldspar through contact with aluminum is sensitive to humidity, as illustrated schematically in Fig. 1. Lawver9 found that the charge developed by quartz on contact with several materials was tem-

Jan 1, 1967

By Emmanuel Detournay, Charles Fairhurst

A method is proposed for computing (a possible solution of) the ground reaction curve, for use in tunnel support analysis, in cases where the initial stress field is not hydrostatic. Rock around a circular tunnel is assumed to behave as an elasto-plastic material with a Mohr-Coulomb yield envelope.

Jan 1, 1982

By A. E. Nehrenberg

IN an earlier publication' it was shown that the.. shape assumed by a volume of growing austenite is inherited from the prior structure. The matrix grains of pearlitic microstructures are equiaxed, and austenite grows in an equiaxed manner in these prior structures. Martensite and bainite, on the other hand, have an acicular grain structure, and the austenite produced in such structures grows in an acicular manner. In the discussion of this paper' it was pointed out that in cold-rolled tempered martensite, austenite grows in an equiaxed, rather than an acicular manner. The results of an experiment carried out to arrive at an understanding of this behavior are illustrated by the micrographs. Fig. 1 shows the acicular microstructure produced by heating tempered martensite to a temperature within the Ac1-Ac3 range, 1350°F. When tempered martensite is cold rolled, then heated to the same temperature, the equiaxed structure shown in Fig. 2 is produced. A sample of cold-rolled tempered martensite heated at 1350°F just long enough for the formation of a small amount of austenite is shown by Fig. 3 to have an equiaxed (recrystallized) ferrite grain structure. The small particles of. austenite which formed at 1350°F in the equiaxed ferrite matrix are likewise equiaxed. Thus, the equiaxed growth of austenite in cold-worked tempered martensite is not a contradiction of the principles described in the previous paper, for the growth pattern reflects the matrix grain structure existing at the time of austenite formation. References A. E. Nehrenberg: The Growth of Austenite as Related to Prior structure. Trans. AIME (1950) 188, pp. 162-174; Journal of Metals (January 1950). 2 J. R. Vilella and R. A. Grange: Discussion of ref. 1. Trans. AIME (1950) 188, pp. 1378-1381; Journal of Metals (November 1950).

Jan 1, 1953

By J. Jolly, R. V. Wheeler

This short note on the probable character of the organic sulfur compounds in coal can do no more than indicate lines of research. We have no new experimental work to describe, nothing comparable in value with the careful studies of American coals by Powell and Parrl and Yancey and Frazer. A study of the manner in which sulfur compounds exist in British coals (and their behavior on heat treatment) is rendered increasingly necessary by the fact that the British reserves of good coking coals of reasonably low sulfur content are fast being depleted. We believe that it is essentially by a study of the modes of formation, occurrence, and decomposition of the various types of inorganic and organic sulfur compounds in coal that it will be possible, with hope of success, to attack the problem of purifying coals, otherwise eminently suitable for coking, from these objectionable ingredients. Sulfur, so far as is at present known, does not normally occur in the free state in the coal conglomerate, but is chiefly distributed, irregularly, in three forms : 1. As primary constituents of the coal conglomerate, organic in nature and probably associated with those molecular complexes that have resulted from the degradation of the proteins of the plant tissues responsible for the formation of the coal mass. These constituents can be classed as "organic sulfur." 2. As metallic sulfides, e.g., iron pyrites. 3. As metallic sulfates, e.g., calcium sulfate and ferrous sulfate. (The occurrence of these compounds varies with the occurrence and degree of degradation of class 2.) It is usually found that sulfur compounds of class 3, the metallic sulfates, are present in coal in small proportions only, amounting to about 1 or 1.5 per cent. of the total sulfur. The compounds in classes 1 and 2 are therefore of more importance. Class 1 alone will receive considera-

Jan 1, 1925

By Robert S. Moehlman

Is recent years, exploration and development by diamond drilling has become a popular attack on the problem of finding new ore shoots and developing extensions of known shoots. Diamond drilling has been used in recent years in extensive sampling of disseminated copper deposits, in preference to churn drilling. At the Harvard gold mine, near Jamestown, California, Philip R. Bradley, Jr., general superintendent, reports that: "The Harvard work was a singular example of the reliance that can be placed on diamond drilling in evaluating an ore body." Drilling at the Harvard mine will be discussed in a subsequent section of the paper. So popular has diamond drilling become, indeed, that many who have had slight experience with drilling are inclined to regard it as a cheap cure-all. This paper proposes to show some of the limitations on the application of drilling and some of the steps that should be followed in drilling programs to obtain reliable results. Cost oF Drilling Drilling has the advantage, over shaft sinking and drifting, of lower cost and greater speed. As compared with churn drilling, the advantage of bringing up a coherent sample instead of fine cuttings for a sample is obvious. Diamond drilling is generally more expensive, however, and more engineering effort is required in combining the average of core and sludge samples. Exploration of drift walls by hammer drills to a depth of less than 30 ft. is generally cheaper than diamond drilling, but beyond this depth the diamond drill is cheaper and more efficient. The principal factor in determining cost of drilling is the character of the ground drilled. Broken ground with many fissures is most expensive to drill. Hard ground is less of a problem with diamond drills than with ordinary machine drills. Hardness or softness affects only the speed of drilling. Caving, easily washed, sandy or clayey ground requires continual cementing and casing, which is the greatest cost problem. Thus, soft, incompetent ground is more costly to drill than hard, massive ground. Cost of drilling per foot in good to fair ground varies from less than $I per foot, achieved in some districts in Ontario, the Mother Lode, and Missouri, to $5 per foot in many western states. In bad drilling ground, costs may range from $5 to $15 or more per foot, thus approaching the cost of drifting. Other factors that increase the cost per foot are: I. Short total length of hole drilled, so that the cost of moving in crews and equipment must be spread over a relatively few feet. 2. Cost of drilling per foot increases with depth beyond about 500 ft.. as more time is consumed in pulling rods' 3. Cost of preparing drilling stations, getting air underground to stations? etc' 4. Inaccessibility and lack of water on the job make for higher costs.

Jan 1, 1946

By H. O. Jahns, R. A. Greenkorn, R. E. Haring, L. K. Shallenbarger

This paper is a study of the effects of heterogeneity on flow in an analog of porous media, the Hele-Shaw model. l-3 A set of experiments in heterogeneous Hele-Shaw models showed streamlines through and around heterogeneities of various sizes, shapes and levels. (A level, we define as the ratio between the transmissibility of the heterogeneity and that of the rest of the model.) The heterogeneities were restrictions or expansions of the flow stream analogous to variations in the transmissibility of porous media. The experimental data agreed well with numerical results and with an analytical solution, which we derived for a circular heterogeneity in an infinite field. This study considers the flow-stream distortion due to the shape, size and level of heterogeneities. Size and level are much more important than shape provided the heterogeneity is not long and narrow. Our analytical solution shows that a circular heterogeneity in a large field can be replaced by an equivalent circle of either zero or infinite permeability. The radius of the. equivalent circle is a simple function of size and level of the actual circle. INTRODUCTION With the availability of high-speed computers and numerical procedures to predict reservoir behavior, we are faced with an important question. How much information about the reservoir do we need to justify the cost of the computer in any given case? To answer this question, we have to know how various reservoir parameters affect flow behavior. Reservoir heterogeneity is one of these parameters. In this study, we used a simple, two-dimensional model of porous media, the hele-shaw model, to investigate the effect of heterogeneity on flow behavior. We restricted ourselves to linear, single-phase, steady-state flow in a rectangular field with a single heterogeneity at its center. The analogy between flow in Hele-Shaw models and in porous media is easily verified. Let us first consider a homogeneous Hele-Shaw model with constant plate separation h. (The Hele-Shaw model is constructed by placing two plates, usually glass, very close together and allowing liquid to flow between them. Streamlines are made visible by introducing colored fluid into the space between the plates at a number of points across the model.) We assume a cartesian coordinate system with its origin in the middle between the plates and the z axis directed perpendicular to the glass plates (Fig. 1). The fluid flow is always in a direction parallel to the glass plates and varies from a maximum value to zero in the very small distance from the middle (z = 0) to either plate (z = h/2). For slow motion of an incompressible fluid, neglecting inertia and body forces, we have the viscous flow equation: where p is the fluid pressure, p the viscosity, and v the velocity vector with components u, v and w in the x, y and z directions, respectively. In our rase. and the derivatives of 3 with respect to x and y are small as compared with the derivative in the z direction. Therefore, approximately, with Vp and v being two-dimensional vectors in the x-y plane. Two integrations with respect to z give

Jan 1, 1965

Discussion of the paper of J. C. Febles, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 79, July, 191.3, pp. 1267 to 1283. J. W. RICHARDS,. South Bethlehem, Pa. :-In looking at these precipitating launders the idea has come to me that the iron could probably be kept much cleaner if there were laid on the bottom of the . launders some sheet copper, with which the iron would be in contact, and as the solution passed over the tendency would he to precipitate the copper on the sheet copper and thus keep the iron cleaner than it is under present conditions. As soon as a piece of iron becomes coated with copper, its surface becomes inactive, and the presence of a sheet of copper in electrical contact with the iron would tend to precipitate the copper on the sheet copper and to keep the iron clean.

Jan 11, 1913

By H. G. HYMER

B ECAUSE of its remote geographical position and inaccessibility, little is generally known of the mining and prospecting in Northern Rhodesia. In this rather new and promising region, the development of mines presents many difficulties. Although many mineral discoveries have been made, progress in .prospecting the huge mining concessions has been handicapped by the lack of roads, communication, transportation, native population and incomplete knowledge of geology.

Jan 1, 1929

By M. E. de Morton

Low frequency-internal friction measurements on annealed chromium have shown a marked increase in damping below - 40°C which is strongly strain amplitude dependent. An interpretation of these results is given in terms of the motion of antiferromagnetic domains assumed to exist below - 40°C. A time effect on internal friction was measured after slight overstraining. After heavy deformation a pemzanent, five-fold increase in internal friction was observed at -45°C and the character of the internal friction us temperature curve markedly changed. Full recovery of damping was not attained until after heating to 800°C. A qualitative interpretation of some of these effects is given. THE aim of this preliminary investigation was to study the internal-friction characteristics of chromium containing comparatively small quantities of interstitial solutes in the fully annealed and heavily worked condition. Marked anomalies in a number of physical properties of chromium at temperatures near 40°C have been observed1 and an investigation by neutron diffraction' has shown that chromium at room teyperature is weakly antiferromagnetic with a Nee1 temperature at approximately 200oC. No irregularities in the degree of antiferromagnetic ordering have been observed at -40°C, the transition temperature, and a complete explanation of this transition in chromium is still awaited. Recently weiss3 has suggested that an ordering effect of nitrogen in the face-centered interstices of the bcc lattice of chromium could be responsible for the superlattice detected below 200 °C in the neutron diffraction experiments. EXPERIMENTAL MATERIAL AND METHOD Specimens 10 by 0.030 in. diam were prepared from ingots of arc-melted electro-deposited chro-

Jan 1, 1961

By T. S. Lovering

An economic geologist is concerned primarily with finding deposits of economic value, estimating their tenor and quantity, their shape and position. Thus the primary problems can largely be lumped under three headings: position, character and quantity; and all three are phases of the broader problem of genesis. Distribution, tenor and quantity are of immediate practical importance and are studied constantly by all who exploit mineral deposits. Although the emphasis changes from year to year, the problems of genesis seem more remote and rarely get the serious consideration from the field man that the other three do. Our understanding of the problems of the genesis of mineral deposits has come largely as a by-product of more evidently utilitarian work in the past, and probably will continue to grow in the same manner lor many years to come. However, it might be economically fruitful for the producers to have many competent investigators spending their time chiefly on the problems of genesis of mineral deposits. Many years ago, when first engaged in work for the United States Geological Survey in Colorado, I expressed a conviction which was just then dawning on me by saying that economic geology was turning out to be 80 per cent structural geology, to which Mr. B. S. Butler replied, "Yes, and more than 80 per cent of structural geology is lithology." At the present time there seems to be a widespread feeling among economic geologists that the problems of position or distribution are largely problems of structure and rock types. Types of Research Ptesearch in any branch of geology can be conveniently divided into two types: field research and laboratory research. Ideas are usually dug up in the field, pruned or developed in the laboratory, and taken back to the field for proving. For either the first or last step the field data should he as complete as possible, and the structural geology of nearly all our mineral deposits still needs more detailed delineation. In general, this means mapping on larger seales. Ideally the structural map should give a factual picture of a11 visible effects of stress; there is still room for vast improvement in the technique of presentation. Information that is much

Jan 1, 1940

By T. S. Lovering

An economic geologist is concerned primarily with finding deposits of economic value, estimating their tenor and quantity, their shape and position. Thus the primary problems can largely be lumped under three headings: position, character and quantity; and all three are phases of the broader problem of genesis. Distribution, tenor and quantity are of immediate practical importance and are studied constantly by all who exploit mineral deposits. Although the emphasis changes from year to year, the problems of genesis seem more remote and rarely get the serious consideration from the field man that the other three do. Our understanding of the problems of the genesis of mineral deposits has come largely as a by-product of more evidently utilitarian work in the past, and probably will continue to grow in the same manner lor many years to come. However, it might be economically fruitful for the producers to have many competent investigators spending their time chiefly on the problems of genesis of mineral deposits. Many years ago, when first engaged in work for the United States Geological Survey in Colorado, I expressed a conviction which was just then dawning on me by saying that economic geology was turning out to be 80 per cent structural geology, to which Mr. B. S. Butler replied, "Yes, and more than 80 per cent of structural geology is lithology." At the present time there seems to be a widespread feeling among economic geologists that the problems of position or distribution are largely problems of structure and rock types. Types of Research Ptesearch in any branch of geology can be conveniently divided into two types: field research and laboratory research. Ideas are usually dug up in the field, pruned or developed in the laboratory, and taken back to the field for proving. For either the first or last step the field data should he as complete as possible, and the structural geology of nearly all our mineral deposits still needs more detailed delineation. In general, this means mapping on larger seales. Ideally the structural map should give a factual picture of a11 visible effects of stress; there is still room for vast improvement in the technique of presentation. Information that is much

Jan 1, 1940