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By N. L. Hancox

Previous researchers have used the cutting and rejoining model to represent a porous body when attempting to place Archie's law on a theoretical basis and calculate rock permeabilities (F = Ø-m, where F = formation factor, = - porosity and m = a constant). In using the model, a porous solid is assumed to consist of sections with parallel sides containing straight. continuous pores of total porosity 4 (pore to total volume or, for a homogeneous body, pore to total area). The joining of pores at an interface between two sections is assumed to be random which results in a common pore area Ø2. This reduced area Ø2 is then taken as that area which limits electrical conduction or fluid flow in the body. Agreement between experimental results and results calculated using a model is not always good Because of this, various modifications of the model are presented — for instance, the random nature of the joining is questioned. Formation factor measurements on specially constructed porous specimens are described in this paper. it is concluded that the common pore area limits flow completely only if sections containing straight pores are very thin, and that, in most natural materials, the common pore area at an interface must be greater than that given by random joining. However, the model is still useful in permeability calculations, provided that the fractional area limiting flow is determined from formation factor measurements. INTRODUCTION Two important properties of porous media are permeability k, which describes the ease with which a fluid can flow through a porous medium, and formation factor F, defined as the ratio of the resistivity of a saturated specimen to the resistivity of the saturating liquid which describes the electrical properties of the saturated material. k is defined by Darcy's law,l k= µqL/P Ae . . . . . . . . . . . . . . . [1] where µ = liquid viscosity, q = flow rate, L = length of specimen, p = pressure across the specimen and = - the effective area over which flow occurs, F is given experimentally by Archie's law,2 F = Ø-m ,..............(2) where 4 is porosity defined as the pore to total volume or, for a homogeneous body, the pore to total area; and m lies between 1.3 for loose sand and 2 for cemented sand. Consider a porous body of total cross-sectional area A and length L, saturated with a liquid of resistivity R and with an effective area for conduction of Ae. Then, from the definition of F given previously, F=A/Ae , ................(3) or, from Eqs. 2 and 3, Ae = A Øm ..............(4) Thus, in any attempt to calculate k or F, some assumptions must be made concerning the pore structure of the body and a value derived for A,. To determine Ae, Childs and George3 and Wyllie and Gardner4 suggested an elementary statistical representation often referred to as the cutting and rejoining model of a porous body. The body is assumed to be composed of two or more parallel-sided sections of porosity 4, containing straight, continuous pores with a common pore area of Ø2 at an interface between two sections. The value is given by a random joining of the pores in either section. Two such sections,

Jan 1, 1969

By F. C. Stanford

The work of an engineer is to direct natural forces so that the: bring about the results that he wishes to secure. Heretofore he ha concerned himself chiefly with physical forces and inanimate objects until he has secured a truly marvelous degree of control over them The great problem of the present age is to secure a like degree of know1 edge and control of the human factor. Progress has already been made along this line, but it is only a beginning. Wilhelm Ostwald says tha scientific knowledge enables a man to be a true prophet; but it must be remembered that a good many people do not seem to be able to main tain a high average in prophecy. In short, 'the average of knowledge is not equal to the average needs of the present time, but continually fails to keep pace with it. It has been aptly said that the really essentia need of the period is for more brains; if we only had sufficient knowledg and sagacity we could not only solve all difficulties, but prevent then from arising. This generalization holds good for an industrial organization. Th most vital need of the management is for more brains. The logica course for an engineer in charge of an industrial organization is, therefore to direct whatever forces may be at his command toward the development training, and guiding of all the brains in his organization. This is easie said than done, for it involves the carrying on toward two objective: the maximum of productive work, and the development of the individual who perform it. This is essentially like the rebuilding and enlarging of plant, keeping it in full operation the while. On the other hand, if th aim is merely for maximum production from an organization, withou offering opportunity for development, the final outcome will necessari be like that of a plant that is driven at full capacity without stoppin for repairs or improvements; it eventually becomes so run down th either a complete rebuilding is necessary or else it has to be abandone

Jan 1, 1918

By AIME AIME

NINETEEN states have on their statutes laws requiring engineers practicing within their borders to be licensed sixteen other states have such laws under consideration. While mining engineers are not specifically referred to in every case, they are referred to by implication. In only a few states have mining engineers taken any active interest in this subject, either in support or in opposition, yet it is a matter of very grave importance to them. By some it is thought that it is now too late to take any active steps toward preventing or repealing a type of legislation for which there appears to be a growing demand from some source. And it is further thought that the best course for those who are interested is to endeavor to guide legislation so that the remaining states may enact laws containing as few objectionable features as possible.

Jan 1, 1921

By J. C. Irvine

Meramec Mining Co., a joint venture of Bethlehem Steel Corp. and St. Joe Minerals Corp., mines and pelletizes iron ore at the Pea Ridge mine. The Pea Ridge property is located near Sullivan, Miss., about 113 km (70 miles) southwest of St. Louis. The ore body was delineated in the mid-1950's by St. Joe during a lead exploration program. The first test holes drilled on the Pea Ridge magnetic anomaly revealed the presence of a large magnetite deposit; further drilling in 1956 and 1957 confirmed that the ore body was mineable. Meramec Mining Co. was incorporated in 1957 and shaft sinking began late in the year. Production began in April 1964. The ore body is overlain by about 400 m (1300 ft) of flat-bedded sediments. It is tabular, about 800 m (2600 ft) long and up to 180 m (1600 ft) thick. It dips about 80° and is of unknown depth. The ore is mainly high-grade magnetite with small zones of specular hematite. The wall rock is a Precambrian rhyolite porphyry.

Jan 9, 1976

By Howard C. Pyle, John E Sherborne

Core analysis is a recent development in the field of petroleum technology. The earliest work on this subject was done in connection with evaluating and planning secondary oil recovery by water-flooding. Present-day analysis of sands of flush fields requires new and independent interpretations of the data provided by cored material. Particular attention is being paid to the development of rapid, routine methods for measuring physical characteristics of sandstone, such as permeability, porosity and grain size, as well as the sand's fluid content. Permeability may be defined as the fluid-passing capacity of a rock. For a sandstone to be permeable it must be possible to pass a measurable quantity of fluid through the material in a finite period of time. The common unit of permeability is the darcy, which may be defined as the rate of viscous flow, in milliliters per second, of a fluid of one centipoise viscosity through a porous medium having a cross section of one square centimeter, under a pressure gradient of one atmosphere (76.0 cm. Hg) per centimeter.' For convenience the subunit millidarcy, or one-thousandth darcy, is often used. Porosity is defined as the fluid-containing capacity of a rock and is usually expressed as a percentage ratio of the total pore volume to the rock or bulk volume. Since measurement of only the effective or communicating pore volume is often made, porosities are distinguished as total or effective.2,3 Net effective porosity is defined as the net pore volume available for oil and gas. Oil and water content of sand is measured and expressed either as the percentage saturation of the total pores or of the bulk rock. The oil content may also be expressed as the percentage saturation of the net effective pores. In connection with water-flooding, methods of core analysis were developed to furnish data that could be used in determining the quantity of recoverable oil14-6 and the probable rates at which various sands or divisions of a sand open to the wells would take water or produce oil. In flush fields, the analytical data are used to predict the productivity of a cored interval. They indicate the presence of oil, gas and water and may

Jan 1, 1939

By Howard C. Pyle, John E. Sherborne

Core analysis is a recent development in the field of petroleum technology. The earliest work on this subject was done in connection with evaluating and planning secondary oil recovery by water-flooding. Present-day analysis of sands of flush fields requires new and independent interpretations of the data provided by cored material. Particular attention is being paid to the development of rapid, routine methods for measuring physical characteristics of sandstone, such as permeability, porosity and grain size, as well as the sand's fluid content. Permeability may be defined as the fluid-passing capacity of a rock. For a sandstone to be permeable it must be possible to pass a measurable quantity of fluid through the material in a finite period of time. The common unit of permeability is the darcy, which may be defined as the rate of viscous flow, in milliliters per second, of a fluid of one centipoise viscosity through a porous medium having a cross section of one square centimeter, under a pressure gradient of one atmosphere (76.0 cm. Hg) per centimeter.' For convenience the subunit millidarcy, or one-thousandth darcy, is often used. Porosity is defined as the fluid-containing capacity of a rock and is usually expressed as a percentage ratio of the total pore volume to the rock or bulk volume. Since measurement of only the effective or communicating pore volume is often made, porosities are distinguished as total or effective.2,3 Net effective porosity is defined as the net pore volume available for oil and gas. Oil and water content of sand is measured and expressed either as the percentage saturation of the total pores or of the bulk rock. The oil content may also be expressed as the percentage saturation of the net effective pores. In connection with water-flooding, methods of core analysis were developed to furnish data that could be used in determining the quantity of recoverable oil14-6 and the probable rates at which various sands or divisions of a sand open to the wells would take water or produce oil. In flush fields, the analytical data are used to predict the productivity of a cored interval. They indicate the presence of oil, gas and water and may

Jan 1, 1939

By Howard Pyle

CORE analysis is a recent development in the field of petroleum technology. The earliest work on this subject was done in connection with evaluating and planning secondary oil recovery by water-flooding. Present-day analysis of sands of flush fields requires new and independent interpretations of the data provided by cored material. Particular attention is being paid to the development of rapid, routine methods for measuring physical characteristics of sandstone, such as permeability, porosity and grain size, as well as the sand's fluid content. Permeability may be defined as the fluid-passing capacity of a rock. For a sandstone to be permeable it must be possible to pass a measurable quantity of fluid through the material in a finite period of time. The common unit of permeability is the darcy, which may be defined as the rate of viscous flow, in milliliters per second, of a fluid of one centipoise viscosity through a porous medium having a cross section of one square centimeter, under a pressure gradient of one atmosphere (76.0 cm. Hg) per centimeter.1 For convenience the subunit millidarcy, or one-thou-sandth darcy, is often used. Porosity is defined as the fluid-containing capacity of a rock and is usually expressed as a percentage ratio of the total pore volume to the rock or bulk volume. Since measurement of only the effective or communicating pore volume is often made, porosities are distinguished as total or effective.2,3 Net effective porosity is defined as the net pore volume available for oil and gas. Oil and water content of sand is measured and expressed either as the percentage saturation of the total pores or of the bulk rock. The oil content may also be expressed as the percentage saturation of the net effective pores. In connection with water-flooding, methods of core analysis were developed to furnish data that could be used in determining the quantity of recoverable oil,4-6 and the probable rates at which various sands or divisions of a sand open to the wells would take water or produce oil. In flush fields, the analytical data are used to predict the productivity of a cored interval. They indicate the presence of oil, gas and water and may

Jan 1, 1939

By J. J. Jakosky

All electrical geophysical methods depend for their operation upon the effects produced by the flow of an electric current. By studying these effects it is possible to predict the general axis of current flow. The greater flow of current is in the path of greatest effective conductivity; and since the effective conductivity of a mineralized zone is different from that of its surrounding envelope (usually much greater), it is possible to locate such a mineralized zone by the distribution of current. Due consideration must be given, of course, to geological structure, to type of mineralization, and to other factors. A number of methods are used to cause this flow of current, and various methods arc available for detecting the presence of such current flow and for studying its effects. In a rather detailed way, this paper will discuss the theoretical and practical phases of the inductive methods of geophysical prospecting. Electromagnetic Generation of an Electeomotive Force The inductive method is so named because the current flowing in the conductor is obtained by electromagnetic induction, instead of by the use of ground electrodes through which a current is passed as in the applied potential systems, or by direct contact with the orebody. An alternating current flowing in a coil will create an electromagnetic field around the coil. This field will have the same frequency as the current and will radiate or travel outward from the coil in closed magnetic or flux circuits. These flux circuits (in air or a homogeneous medium) will be perpendicular to the plane of the coil and will extend or travel outward with uniform velocity in every direction. Maximum feld exists in the plane of the coil. Such a coil used for transmitting or as the "energizer" will exhibit similar figure-eight characteristics to those exhibited by the direction-finding coil which will be described in detail later.

Jan 1, 1929

I SHALL proceed in this chapter to tell you about lead. Because this metal is overabundant in wateriness, and also because it has its other substances in poor elemental mixture, it is highly impure. It is called an imperfect, leprous, and little-fixed metal, which it clearly shows itself to be because of the ease of liquefying it and because it is easily converted largely into a dross that is almost earthy and also because of the stain that it leaves when it rubs against anything. Nevertheless, when we consider its effects, we judge it to be a metal that we are greatly indebted to. Even though Nature in creating us has put into our souls such a thirst and desire

Jan 1, 1942

By R. V. Ramani, Y. J. Wang, R. Mishra

Abstract-The validity of the concept of mine resistance in ventilation systems is examined. Mine resistance is the proportionality constant relating the head generated by a fan and the quantity flowing through it when the fan is connected to a mine circuit. It is the total effect of all branches in the mine ventilation circuit. Its importance lies in the fact that for new mine projections, and in the extensions of existing mines, ventilation calculations are usually based upon adjustments of the mine

Jan 11, 1978

By John E. Hockett

The need for basic information about the relationship between resistance to dejormatim (flow stress), temperature, strain, and strain rate, for the solution of metal-fovming problems, is pointed out. Some early attempts to satisfy the need are mentioned. A brief description of a machine called a Cam Plastome-ter is given, including the processing of results of testing in the machine. Next, a program of testing aluminum in compression over a wide range of constant true-strain rates (0.1 to > 200 sec-1) and a modevately broad range of temperatures (223° to 673°K) is described. The results of this program are presented in the form of true-stress us true-strain cuvves. The data in these curves are presented in the form of relationships between true stress and true-strain rate in sermilogarithmic and log-log form, as functions of temperatures—for several true strains. Finally, true stress, for a given true strain, is displayed as a function of log true-strain rate and absolute temperature, i.e., a surface. SINCE the publication of Hill's book1 on plasticity theory, increasingly rapid advances have been made in analytical solutions to forming problems. Methods in common use are the slab method, the uniform deformation energy method, the limit analysis method, the slipline field method, and the semiexperimental method called "visioplasticity". These approaches, and examples of their use, are covered in detail by Johnson and Melloor2 and by Thornsen, Yang, and Kobayashi.3 unfortunately, practically all of the above work has had to rely upon a number of basic assumptions, e.g., homogeneous deformation and Coulomb (sliding) friction; and virtually no dependence of the mechanical behavior of the deforming metal, upon temperature, strain, and strain rate, has been included. It is with this dependency that this paper is concerned. Loizou and sims4 looked at the above relationship for lead using both a constant compression-speed Cam Plastometer and a constant true-strain-rate Cam Plastometer designed by Orowan.5 Alder and Phillips8 investigated the relationships for aluminum, copper, and steel in the same constant true-strain-rate Plastometer. cook7 tested twelve steels at temperatures ranging from 1170° to 1473°K in the same Plastometer over a range of true-strain rates of 1.5 to 100 sec-'. The writer tested commercially pure aluminum at room temperature and depleted uranium at temperatures from 573" to 873°K at strain rates from 10-3 to 1.0 sec-1 in a Cam Plastometer designed and built at Los Alamos Scientific Laboratory.8 During the past few years the Cam Plastometer at Los Alamos has been used for a number of relatively minor experiments on brass, mild steel, duralumin, Armco iron, and depleted uranium. In this time the machine has been continually modified and improved. It was decided to utilize fully the wide range of strain rates now available with the machine by testing a material about which some information was already in the literature. Prior work on commercially pure aluminum6 appeared to deserve confirmation and expansion. So it was decided to explore the resistance to compression of this material over the currently available range of constant true-strain rates and a convenient range of temperatures. This paper is a report of that exploration. I) EQUIPMENT AND PROCEDURE The principal item of equipment is, of course, the Cam Plastometer, the working part of which is shown in Fig. 1. In this figure, an aluminum specimen may be seen between two tungsten carbide platens, in position for a room-temperature test. Above the upper carbide platen is a load cell. Output from the load cell is amplified and applied to a galvanometer in a recording oscillograph. Auxiliary equipment includes the oscillograph, the control console, a counter, and a time-mark generator. The counter is first used in adjusting the time base. Then it registers the count, of sixty pips per revolution generated by the rotating cam, in each second. These pips and the time base are also applied to galvanometers in the oscillograph. Thus, load, time, and cam position are recorded simultaneously. Heating of a specimen prior to compression is done

Jan 1, 1968

This report presents the comments of members of the Institute's Sub-committee on Physics of Mine Ventilation on the proposals of a special committee of the Institute of Mining Engineers (London). This report is as follows: THEORY OF MINE VENTILATION Abstract of a report submitted June 16, 1925, to the Council of The Institution of Mining Engineers by a Special Committee Laws of Flow of Aib The law of flow of air in mine galleries is, at present, expressed by two formulas differing slightly in shape but both derived from the original hydraulic formulas of Chezy and others. These formulas are: The Atlcinson Formula.—Pa = KsV2, which in transformation becomes a3 where P = pressure producing flow; K = coefficient of friction; s = surface of the mine galleries; V = velocity of flow; Q = rate of flow; a = area of mine galleries. This formula is especially applicable to mine galleries, but is unwieldy in application, as in many problems we are dealing with changes produced in the same set of airways when K, s, and a are assumed not to change, and the only variables are P and Q. Great uncertainty prevails as to the exact values to be assigned to the coefficient K in different types of airway, as different workers have given widely differing values. This formula assumes: (I) That resistance to flow is independent of the pressure within the gallery. (2) That changes in volume within the limits of pressure ordinarily met with may be neglected. (3) That changes in density and viscosity and mode of flow of the air may be neglected. (4) That the coefficient K is a constant. (5) That P is proportional to the square of the velocity. We cannot find any reliable experimental work leading us to conclude how far these assumptions are justifiable in mining practice. Equivalent Orifice Formula.—The fundamental form of this formula is Q = ~nA.\/2~11

Jan 1, 1927

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

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

Jan 1, 1969

By Bobby P. Faulkner

The Tennessee Copper Co.'s flotation plant, refer- T red to as London Mill, processes approximately 4800 tons of a massive complex sulfide ore per day. The ore is predominantly pyrrhotite and pyrite, the other sulfides being chalcopyrite, sphalerite, and a small amount of galena. Magnetite of economic value is also present. There are four concentrates produced. In decreasing tonnage, these are iron, copper, zinc and lead. The ore feeding the mill is a composite of ores from five mines which vary in grade. Therefore, in order to provide a fairly constant feed to the mill, the ore is blended several times before reaching the flotation machines. The flotation plant is divided into three main sections: bulk, copper and zinc. Fig. 1 shows a simplified flowsheet. The first two sections, the bulk and copper, were the two sections studied most closely in utilizing the computer.

Jan 11, 1966

By C. R. Criss, R. J. McCormick

ThiS paper .summarizes the development and perform. ance of the Coldwater Oil field, Isabella County, Mich. Production is obtained at a depth of 3750 ft from a dolomite reservoir, which is probably both Rogers City and Dundee. There appears to be no persistent barrier to vertical fluid movement between the Rogers City and Dundee, and both formations are believed to have a common original oil-water contact. No we1ls are open to production at the level of the Dundee. The discovery of the field in 1944 was followed by the drilling of 81 producing wells and nine dry holes. By the end of 1952, the field had produced 12,763,000 bbl of oil, at which time 69 active wells were producing 3600 B/D oil and 21,000 B/D water. The reservoir has an effective natural water drive, and bottom-hole pressure has declined 75 psi from an original pressure of 1453 psi. Oil is undersaturated at reservoir conditions with a solution GOR of 512 cu ft/bbl and a saturation pressure of 1190 psi. INTRODUCTION Although the Coldwater Field is now in its ninth year of production, it ranks seventh in cumulative recovery, and second in current daily oil production in the State. Following complete development of the field in 1946, it has consistently contributed approximately 11 per cent of Michigan's daily production. Coldwater appears to have a greater pay thickness than most fields producing from the Rogers City forma- tion in the west central part of the Michigan basin. Except as influenced by the extent of closure and the thickness of the oil column, reservoir performance is believed to be representative of Rogers City fields in this part of the basin. For this reason, it is felt that the following presentation of factual data for the field will be of general interest. HISTORY AND DEVELOPMENT Discovery of the Coldwater field during Aug., 1944, followed favorable subsurface geological correlations and core tests drilled to a shallow stratigraphic marker horizon. The field is located in the west central part of the Michigan Basin in Coldwater Township (T16N-R6W), Isabella County. It is 60 miles west-northwest of Bay City, and near the geographic center of the southern peninsula of Michigan. The discovery well flowed 200 bbl of oil the first 24 hours from the Rogers City dolomite at a depth of approximately 3750 ft. Field production is principally from the Rogers City with a minor amount assumed to come from the underlying Dundee dolomite, although none of the wells are open to production at the level of the Dundee. Both the Rogers City and Dundee formations belong to the Devonian system (See Geologic Column-Fig. I.) In addition to Rogers City-Dundee oil production, sweet gas is produced from the Michigan Stray sand of the Mississippian system at a depth of 1400 ft. The gas reservoir has approximately the same areal extent as the underlying oil reservoir. Although gas production is an important feature of the Coldwater field, this report is concerned only with the oil reservoir. The productive area is approximately 3200 acres. The pool is developed on a 40 acre spacing pattern with wells drilled in the center of the north half of 40 acre tracts, except for a few off-pattern wells drilled along

Jan 1, 1955

By David H. Browne, John F. Thompson

The literature dealing with the physical constants of nickel is so fragmentary and unrelated that a synopsis presents unusual difficulties. It is only within the last few years that investigators have understood the importance of placing on record not only the determinations they have made but also the composition, physical treatment, and past history of the material investigated. For this reason much of the earlier literature is valueless. Determinations have been made of the same physical constants on samples differing widely in origin, composition, and treatment, and the results differ widely among themselves. In the first place nickel is almost as flexible a term as steel. Its physical properties are widely influenced by its composition and treatment. It absorbs large quantities of gases and is exceedingly difficult to prepare in a state of chemical purity comparable to gold, silver, or copper. It is vitally affected by thermal and mechanical treatment. Hence in the following pages the recorded literature, where quoted, must be accepted with a certain reserve and used, as far as possible, as a check on later observations, in which these important factors are noted. In every case where new determinations are given, an attempt has been made to record all available information concerning the composition and treatment of the material used so that the data may serve as stepping-stones toward a wider knowledge of the properties of the metal. As this synopsis is an attempt by men of metallurgical training to do what should long before have been done by physicists, it is to be expected that certain errors may have crept in. Any corrections or suggestions

Jan 1, 1921

By Blamey Stevens

(Butte Meeting, August, 1913.) THE following paper aims to make a full explanation of the phenomena of rock jointing: It may be unnecessary to give any general description of what are termed joints in rocks, but Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given. for introducing the following and other quotations into this paper "Almost all rocks are traversed by vertical or highly inclined divisional planes termed joints. These have been regarded as due in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure and movement within the crust." 1 General Explanation.-In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of the porous material may be considered to be separately compressed by the water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from moving freely by other material around its boundaries. The mass of rock thus becomes broken up. This phenomenon is known as '" shrinkage " jointing. The term " shrinkage " is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.-The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting. .

Jan 7, 1913

By Blamey Stevens

(Butte Meeting, August, 1913.) THE following paper aims to make a full explanation of the phenomena of rock jointing. It may be unnecessary to give any general description of what are termed joints in rocks, but. Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given for introducing the following and other quotations into this paper: "Almost all rocks are traversed-by vertical or highly inclined divisional planes termed joints. These have been regarded as clue in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure-and-movement within the crust."1 General Explanation.-In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of. the porous material may be considered to be separately compressed by the 'water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from. moving freely by other material around its boundaries. The mass of rock thus becomes broken up. This phenomenon is known as " shrinkage " jointing. The terra "shrinkage" is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.-The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both. before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting.

Jan 7, 1913

By J. S. Levine, M. Prats

A homogeneous and uniform cylindrical reservoir containing oil and gas is fractured vertically on completion and is produced at a constant bottom-hole pressure. The fracture has an infinite flow capacity, is of limited lateral extent and is bounded above and below by the impermeable strata defining the vertical extent of the reservoir. Results show that such a fractured reservoir can be represented by a reservoir of circular symmetry having very nearly the same production history. The well radius of this circular reservoir is about 1/4 the fracture length and is essentially the same as that obtained previously for a single fluid of constant compressibility. At the same value of cumulative oil production, gas-oil ratios of fractured reservoirs producing at constant terzinal pressure are larger than those of reservoirs having no fractures. This leads to more inefficient use of the reservoir energy in fractured wells and results in lower reservoir pressures for the same cumulative oil production. The reduction in operating life due to fracturing a reservoir is not as great as that for a slightly compressible fluid. This diflerence can be accounted for by the lower reservoir pressure in the fractured reservoir and its adverse effect on the average mobility and compressibility of the oil. As anticipated, the reduction in operating life increases czs the reservoir permeability decreases. The type of results presented in this report can be used to determine the economic attractiveness of fracture treatments per se, to setect the initial spacing to be used in developing a field, and to compare the relative merits of fracturing available wells and infill drilling. INTRODUCTION The effect of vertical fractures on a reservoir producing either an incompressible or a compressible liquid has already been discussed in the 1iterature.l,2 Those results indicate that the production history of such a reservoir is essentially the same as that of a circular reservoir having an effective well radius of approximately one-fourth the fracture length. The present work reports on the effect of a vertical fracture on a reservoir producing two compressible fluids —oil and gas—by solution gas drive. Because of the empirical nature of the PVT and relative permeability data used to obtain the performance of such reservoirs, results can only be obtained numerically and with the aid of high-speed computers. Since reservoirs lose their radial symmetry when fractured vertically, pressure and saturation can no longer be given only in terms of distance from the well. Two coordinates (such as x and y) must now be used to describe the pressure and saturation within the reservoir, and, since we are dealing with compressible fluids, time is also a variable. Thus the solution of a vertically fractured reservoir requires finding two unknowns (pressure and saturation) in two space variables (say x and y) and in time (t). Since no means are readily and generally available for solving such problems at the present time, we have used the results of previous work1,2 to approximate the effect of a vertical fracture on a reservoir producing both oil and gas by depletion. The purpose of the present wmk, then, is to investigate the possibility of using available numerical techniques (limited at the moment to one space variable) to study the two-space-variable flow behavior resulting from a vertical fracture. Results obtained in the course of this investigation are also reported and discussed. Input and output data of the numerical methods used are given in practical units: BOPD, feet, psi, cp, and md. Results are discussed fist in terms of specific reservoir and crude properties and geometries. Later, dimensionless parameters are introduced in order to extend results to different values of some of the reservoir and fracture properties. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable, circular, cylindrical outer boundary of radius r,. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below' the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. 1 indicates the general three-dimensional geometry of the fractured reservoir. Gravity effects and the effects of differential depletion resulting from variations in hydrostatic head (pressure) will be neglected. Thus, the flow behavior in the fractured reservoir is described by the

By L. L. Swift

AT the present time there are four base metals being used for automotive bearing alloys. Of course there are numerous variations in the amounts of alloying elements added to each base metal and nearly all of these alloys have the conventional, if not classical, duplex structure; that is, they are composed of a hard constituent embedded in a soft matrix. The well-known theory is that the former will wear well, while the latter will be plastic enough to allow the bearing to be broken in and conform to the contours of the shaft. The requirements of the modern bearing have been most aptly described by W. M. Corse: In order to meet the engineering demands of today a good bearing metal must be able to carry the weight of the shaft and stand up under steady or suddenly applied loads, or even blows in some types of service. A certain amount of plasticity is desired to compensate for minute irregularities in the shaft or bearing surface, and to permit yielding, thereby avoiding dangerous stresses in bearing and shaft and preventing overheating and rapid wear of parts. Less plasticity is required in a bearing metal if the surfaces of bearings and journals are machined accurately, aligned, and kept in alignment. It is desirable, of course, that a bearing metal have a low coefficient of friction. Under most operating conditions the friction depends on the unit pressure of the bearing, the speed, the temperature, and the properties of the lubricant. A good bearing metal must have a low rate of wear to reduce the necessity for frequent replacements, and adjustment of the bearings. It must wear more rapidly, however, than the journal or shaft running on it, because replacement of the journal or shaft is more difficult and costly than replacement of the hearing., The hardness of, the bearing alloy is a property closely related to several of the foregoing. With a duplex microstructure, the measurement of hardness with any of the usual commercial devices means little. The Bierbaum method of measuring the hardness of the individual constituents was developed to, fill this need. MICROCHARACTER The Bierbaum microcharacter2.3 measures the scratch-hardness of a solid by pulling a weighted diamond point over the surface. The diamond point is ground. so that it is the corner of a cube, and mounted

Jan 1, 1938