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By J. A. M. van Liempt

Since the discovery of von Laue, that a crystal forms a natural grating for X-rays, our knowledge of the structure of solids has gone forward with rapid strides. This progress is not only of purely scientific interest, but has also yielded direct technological results. One of the most valuable results is the broadening of our knowledge of the structure of pure metals and alloys. To promote these studies it is often desirable to have at our disposal pieces of metal consisting of one single crystal. As is so often the case in the natural sciences, we obtain the best results by making our earliest experiments on pure, simple materials and avoiding unnecessary complications. The Cryogen Laboratory at Leyden followed this method with much success, because the work was done at such low temperatures that the heat movement of the atoms was almost absent. Similarly we can simplify the studies of metals by leaving out of consideration the influence of the grain boundaries and the mutual influence of the crystals by using unicrystalline instead of polycrystal-line metal. Methods of making single crystals have been scientifically studied during the past few years. Some methods were already known in the arts, but these have been improved and new methods have been developed. The methods for making metallic single crystals may be divided into the following groups: A. From the liquid state B. From the gaseous state C. Electrolytically D. By recrystallization in the solid state Method A 1. Tamwmnn's Method1—Tammann succeeded in making bismuth single crystals of a maximum length of 20 cm. by undercooling the molten metal 0.1 to 0.3' G. below its melting point in glass tubes of a maximum

By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.',' Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact'on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By John F. Blandy

Every new mining district has had its own peculiar experiences in inventing and experimenting upon new methods for the various operations of mining, and more particularly in the processes of crushing and dressing ores. As a matter of course, during this period many old things have been reinvented, patented, and cast aside, there to remain until at a future day other geniuses shall bring them forth again as new. In this respect the Copper Region of Michigan has not been behind other mining centres, and probably in no other part of the country has more money been expended in devising new machines and improvements upon old ones for the crushing of the rock. The appliances for washing the sand have not been so varied, simply for the reason that, having but one mineral, or rather metal, of high specific gravity to separate from rock material which varies but little in its character in any one mine, it requires much less care than is necessary in most mining centres of the world. At the beginning of operations in that district most of the work was in the control of Cornish miners, who introduced the simplest of Cornish mills, namely, wooden stem pestles, with wooden shafts and cams. These were well suited to the small mines, and particularly to the limited means of transporting more expensive machinery. As these facilities improved, they were enabled to change to iron, and to vary their patterns of rods, shafts, cams, and mortars. The most approved pattern, finally obtained, is the square or round stem, with collar adjustable by means of keys. In its present form it is a bar of cold rolled shafting, an eye in the top, an adjustable collar with key-plate and keys, the head and a shoe of chilled iron. The stem is fitted into the head by a slight taper. The battery has heretofore been of wood, lined with chilled cast plates, and bed-plate of the same, but within the past year the California pattern has been introduced. The screens are of sheet-steel, drilled with 16 holes to the inch. During this period of trial and gradual improvement in the pestle stamps, in the years 1855-6, the Ball steam-stamps were introduced, and after years of labor and expense, have been made the most efficient and powerful machines ever yet used for the purpose. It is ostensibly the Nasmyth steam-hammer, and yet the

By R. W. Brown, J. L. Loper

The process of sand erosion has been harnessed to perform a useful function—the directed perforating of oilfield tubular goods and formation rock. In this process the sand is carried by a liquid medium and the resrrlting slurry is forced through a nozzle at an extren~ely high velocity. Upon impingement against casing or formation, the fast-moving sand particles erode a perforalion in the casing followed by cavity formation in the medium behind the casing. The many factors influencing the rate and extent of this penetration are inherently difficult to establish experimentally. Equations describing submerged jet behavior have been applied to these conditions. The following paper develops the equations for predicting the performance of the perforating jet. INTRODUCTION The cutting power of high-velocity sand has been well known in the petroleum industry for many years. Sand carried by a high-velocity gas stream causes severe erosion. This effect has been the cause of numerous production problems in certain areas. It was logical to expect that this phenomenon would one day be adapted to useful industrial applications. Development of mobile, high-pressure, high-horsepower pumping equipment in the last decade has made this possible. The sand erosion process involves pumping a fluid containing abrasive solids through a set of nozzles at a high differential pressure (2,000 to 4,000 psi). The pressure conversion into kinetic energy imparts high velocity to the sand particles which, upon impact with the formation face or casing wall, erode the material in an organized pattern. This paper attempts to establish the effects of the various parameters and to predict the performance and limitations of the process. The following factors will be considered: nozzle differential pressure, perforation size, sand concentration, nozzle stand-off distance and backpressure. In general, this discussion is presented along theoretical lines and is substantiated by field results and data where reliable field data exists. POWER EQUATIONS The penetration rate of a high-velocity hydraulic jet is proportional to the power or energy of the jet at the point in quesion. The power of the submerged jet will decrease with distance (or penetration) into the cavity created by the jet. As the cavity is extended into the formation, the power of the jet diminishes to a value equal to the threshold cutting power of the particular formation which is defiined as the lowest power level at which the formation will be abraded by the jet. Obviously, when this point is reached, no further cutting of the formation can occur. It is assumed that this power level for a particular formation is a function of the hardness of that formation. The following equation can be written for the hydraulic process of formation abrasion.

By Persifor Frazer

Comparative columns expressing the series of rocks of the lower half of the Mesozoic age in this country and in Europe are not yet definitely established. The following represents a co-ordination of the beds in England and Germany,* with a list of materials to be worked in from this country .†

TEE Institute assembled on Wednesday evening at the Western University, and was called to order by President Raymond. Mr. James Park, Jr., of Pittsburgh, made the address of welcome, which was responded to by President Raymond. The Council reported the following names, with approval, for election : Ashburner, William, . . . . . San Francisco, Cal. Asmus, George, . . . . . . New York. Baillie, Nathaniel, . . . . . Uniontown, Pa. Bowie, A. J., Jr., . . . . . San Francisco, Gal. Brown, A. J., . . . . . . Treasure City, Nev. Butler, J. G., Jr., . . . . . Youngstown, Ohio. Chamberlin, J. G., . . . . . Leetonia, Ohio. Clark, R. Neileon, . . . . . Canyon City, Colorado. Cornell, A. B., . , . . . . Youngstown, Ohio. De Crano, E. C., . . . . . San Francisco, Cal. Engelmann, H., . . . . . . Salt Lake City, Utah. Faber du Faur, A., . , . . . New York. Janin, Louie, Jr., . . . . . San Francisco, Cal. Johnson, George J., . . . . . Salt Lake City, Utah., Kent, Joseph C., . . . . . Phillipsburgh, N. J. Kent, William St. G., . . . . Phillipsburgh, N. J. Liebenau, Charles von, . . . . Silver City, Idaho. McClintock, A. H., . . . . . Wilkes-Barre, Pa. Miller, Thomas N., . . . . . Pittsburgh, Pa. Millholland, James A., , . . . Mount Savage, Md. Peters, Ed. D., Jr., . . . . . Dudley, Colorado. Reese, Jacob, . . . . . . Pittsburgh, Pa. Schirmer, J. F. L., . . . . . Denver, Colorado. Smith, W. S., . . . . . . Fairplay, Colorado. Stoelting, Hermann, . . . . . Georgetown, Colorado. Sweet, W. A., . . . . . . Syracuse, N. Y. Tripple, Alexander, . . . . . New York. Van Arsdale, W. H., . . . . . Swansea, Cal. Willard, Dwight D., . . . . . Bordentown, N. J. The following resolution was then offered and passed : Resolved, That gentlemen present, not members, be invited to take part in the discussions of the Institute at the various sessions of the present meeting.

By P. A. Witherspoon, S. P. Neuman

Evaluating the permeability of a caprock overlying a potential gas storage reservoir is a very critical problem. Pumping water from the reservoir can be used as an evaluation tool in analyzing this problem. Fluid level changes that occur in the aquifer us well as in the caprock can be measured with appropriately placed wells. If the leakage of water from the caprock into the aquifer is considerable, the effects will be apparent in the aquifer. If the leakage is slight, however, it will not be possible to detect it with certainty from observations in the aquifer alone. Fluid level measurements in the caprock must be relied upon. and improved methods of analyzing such effects have been developed which are based on a theoretical analysis of fluid flow through a caprock of infinite thickness. An example applying these methods to field data is discussed. INTRODUCTION One of the most critical problems in evaluating an aquifer gas storage project is determining the tightness of the caprock overlying the formation to be used as the storage reservoir. A formation that has previously held oil or gas obviously has a suitable caprock, but an aquifer that contains only water gives no such assurance. A number of aquifer projects in the United States have been troubled by gas leaking out of the intended storage zone, and the ensuing difficulties have led to the development of new evaluation methods. One of these new methods is pump testing wherein water is removed from the aquifer at some controlled rate prior to injection of gas. This fluid withdrawal causes a pressure drop to move out through the aquifer for considerable distances in a matter of days or weeks. Depending on the properties of the caprock, a pressure transient can also pass upward (as well as downward) through the caprock layers adjacent to the aquifer. Thus, if the operator has placed observation wells at appropriate distances from the pumping well, the rapidity with which the pressure transients reach different points in the system can be used to investigate the fluid transport properties of both the aquifer and its caprock. The usefulness of pump testing has been recognized by groundwater hydrologists for many years as a means of determining the potential yield and properties of aquifers used in water supply They have introduced the term "leaky aquifer" for a system in which an aquifer is overlain (or underlain) by semipermeable caprock layers. The ease with which water leaks into the aquifer during pumping can, of course, be very beneficial in bringing additional water to the pumped well. Hydrologists have therefore devoted considerable attention to this prob-lem. From the gas storage standpoint, however, the tighter the caprock layers that overlie the intended storage reservoir, the better are the conditions for minimizing or eliminating any vertical migration of gas. Thus, after a suitable geologic structure has been found, the emphasis in aquifer storage projects is in determining that the caprock is tight. Attention has recently been focused on the use of pump testing as one approach to solving this problem.23,24 This paper presents a further development on evaluating the permeability of a slightly leaky caprock when the caprock is of infinite thickness. From the practical standpoint, this means that the caprock layers are thick enough that pressure transients do not reach the outer boundaries of the system during the pumping test. In a subsequent paper, an analysis of the case where the caprock is of finite thickness will be presented. PREVIOUS WORK ON LEAKY AQUIFERS Jacob" developed a partial differential equation describing the flow of water in an aquifer of permeability k that is overlain by a leaky caprock of permeability k'. Fig. 1 shows a schematic cross-section of the system under consideration. One of his principle assumptions was that if k > > k', the direction of flow is essentially vertical in the caprock and horizontal in the aquifer. Neuman19 confirmed the validity of Jacob's assumption using a mathematical model. Another assumption was that a permeable source layer overlies the caprock (Fig. 1) and is able to maintain a constant hydraulic head at the upper boundary of the caprock. By neglecting the effects of compressibility within the caprock, Jacob1* developed a solution for a bounded circular aquifer. Later, Hantush and Jacobx5 used the same assumptions to solve the case of an infinite radial aquifer that is pumped at a constant rate. Their solution may be expressed in di-mensionless parameters by

By Wilbur H. Somerton

In order to evaluate the quantitative determination of porosity by various neutron logging systems, four test wells were constructed to simulate some of the possible variab1e.r found in field logging conditions. All of the test holes contain sections of limestone with one section of sandstone included in one well. Each well has a representative section of high, medium, and low porosity. Three borehole sizes are represented by three of the test wells, all containing fresh water. One test well contains saturated brine. Statistical and tune constant checks are made for each system evaluated. Runs and repeat runs are made with the sonde centered and eccentric. Factors evaluated are the effect of borehole size, sonde position, salinity, chemical composition of rock, and statistical variation. A semi-quantitative method of evaluation of these effects is used giving the average maximum per cent error possible for each. Drift and calibration procedures are also discussed. The effect of the various factors appears to be largely a function of the phenomena detected as well as the means of detection. Graphic illustrations of some of these effects are presented. It is concluded, that for accurate log interpretation, the hole size and sonde position should be known. INTRODUCTION The use of neutron logs for the derivation of porosity has become an accepted practice in many areas. In recent years, many different neutron logging systems have been offered to the industry. The neutron sources presently available are of the radium-beryllium or polonium -beryllium type. Detector types used are ionization chambers, Geiger-Mueller-type counters, proportional counters, or scintillation detectors used to detect or measure gamma rays, thermal neutrons, epithermal neutrons, fast neutrons or combinations of these. It is well-known that all systems do not respond alike in all environments. As a result, testing facilities and an evaluation method were developed for use in evaluating the porosity discriminating ability of neutron logging systems using conditions simulating those normally encountered in the field. With such an evaluation, the suitability of a logging system can be determined lor selected field conditions. TEST FACILITIES The testing facilities consist of wells containing rocks of various porosities, constructed to include as many parameters as practicable. Three pits were drilled to a depth of 20 ft and the fourth to a depth of 9 ft, all having 48-in. diameters. Rat holes were dug to a depth of 6 ft in the center of each pit and fitted with sections of pipe having appropriate diameters. The top of this pipe was located approximately 8 in. above the pit bottom. A 6-in, layer of cement was then poured on the bottom and while still wet, 42-in. OD corrugated, galvanized culvert pipe was set on bottom and centered in place. This pipe extends approximately 1 ft above the surface of the ground. The annulus around the culvert pipe was then filled with cement to the top. A 1- or 2-in. layer of sand was placed on the cement bottom to provide an adjustable bed on which to place the series of rocks set in each hole. A cross section of a typical test well containing the porous rocks is shown in Fig. 1.

By J. J. Bodmer

The substances or materials employed in this manufacture, are the same as those used in the preparation of mortar and concrete, viz., the different kinds of lime and sand. Instead of, or in conjunction with, sand there may be used calcined clay, blast-furnace slag, clinkers or ashes from furnaces, natural puzzolana, powdered chippings from stone quarries, etc. Of the different kinds of sand, pitsand—siliceous sand, as it commonly occurs mixed with gravel—and the sand found on the seashore, where the salt has been washed out by long exposure, whilst out of reach of the tide, may be used. The purer the above-named materials are from admixtures of clay, earth, or organic substances, the more complete will be their combination with the lime, the quicker will the manufactured brick or block set, and the more satisfactory will be the quality which it ultimately attains. For this reason, subdivided blast-furnace slag is preferable in most cases to sand, and the only sand which, in reference to setting capacity, is analogous to blast-furnace slag, is the volcanic sand occurring in different localities in North and South Wales, as an almost pure calcined silica. The lime used for the manufacture may be either slaked or unslaked. In the first case, (slaked), in order. to obtain satisfactory results, the lime must be strongly hydraulic. The use of unslaked lime, however, is by far preferable. A process for using fresh or unslaked lime has been patented in England by Major-General Scott. Lime thus prepared is called " selenitic lime," and consists of a mixture of fresh (unslaked) lime with sulphate of lime, or plaster of Paris. The graystone lime, for instance, found by the Medway, is mixed with from 5 to 7 per cent. of plaster, which has the effect of keeping the lime from slaking when water is added. This mixture also partakes of the nature of cement, and when used for mortar, or concrete, attains in a shorter time a greater degree of hardness than the same lime would ever have obtained after being slaked. Bodmer's process for the manufacture of artificial stone bricks consists chiefly in the use of automatic measuring, forwarding, and mixing apparatus, by means of which the materials are supplied and unite in a continuous stream, and are accurately measured. They

By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*

By Henry Wurtz

Observing in the Engineering and Mining Journal, of January 16th, 1875, page 35, a report of a brief discussion upon the nature and origin .of this unique and interesting coal, I take the liberty— on thus finding it a subject of interest to members of the Institute, and especially as my name came into this discussion—to cornmunicate some results which may serve at least to overthrow certain erroneous ideas that have prevailed. While I would not claim to -have made much approach to an understanding of this mineral—the whole of what I call Apozoic Mineralogy being as yet dark and almost unknown ground—yet I believe I have shown that few minerals of such importance and abundance, and so long before the world, have been so singularly misunderstood. On first examination of a sample of the substance to which the name of carbonite has been given, my surprise was not small, at failing to recognize in it one individual characteristic of true coke; neither the hardness, lustre, color, streak, porosity, sonorosity, structure, fracture, nor any of the so-called "pyrognostic" characters. Indeed, comparison with any coke, or variety or modification thereof, seemed altogether fantastic. Therefore the controversy regarding supposed trap dykes, whose existence at the locality is denied by some, seems useless, as we have no question of a natural coking, there having been no coking at all.

By P. H. Dudley

I have taken the liberty of calling the researches herein mentioned industrial, to distinguish them from those strictly scientific, where every known appliance is used to insure accuracy in determining principles. The industrial researches are made to ascertain wherein we have failed to embody, in practice, the principles which have been fully demonstrated by the more purely scientific investigations. So far the researches have been mostly confined to the conditions of combustion as used in locomotive furnaces, although we have examined, to some extent, furnaces under marine and stationary boilers. The products of complete combustion are gases, and, knowing what we should have, it is at once shown by analyzing the products whether the desired reactions are taking place. In spite of imperfect furnaces, lack of system in the arrangement of grate-bars and exhaust nozzles, the results are not altogether vitiated, because the analyses are not closer than one-tenth of one per cent., as under the present conditions it is hardly possible to collect gas exactly under the same conditions at different times. All of 'our industrial operations have developed in the past few years so rapidly, nearly all of them paying, that,, until within the past three years, comparatively little attention has been given to their economy outside of the profession. Great corporations have not asked and considered the question in earnest, can we utilize our heat so as to produce the same effect at less cost? The applications of heat are so extensive, entering into every branch of industry, the principal power used to carry on metallurgical processes, to conduct transportation, that its econonlical generation becomes of universal importance; in fact, its economical generation and application is the leading industrial question of the day. It is stated by those who have given the subject much attention, that in our best steam-engines not over 10 per cent of the theoretical value of the fuel is utilized, and upon locomotives it is far less, probably not exceeding under the most favorable circumstances 5 or 6 per cent. In recent experiments made with the dynagraph, in drawing trains upon the Lake Shore and Michigan Southern Railway from Cleveland to Erie, 941/2 miles, we found the force required to draw a stock train of 709 tons to be 2,498,396,320 footpounds, exclusive of the force to move the locomotive itself. We

By H. K. van Poollen, H. C. Bixel

A treatment is given of the transient pressure behavior of a well located at the center of a circular region surrounded by a radial discontinuity. On either side of the discontinuity, the values of permeability, viscosity, compressibility and porosity are uniform but may be different from those on the other side of the discontinuity. The results are obtained by solving a pair of finite difference equations. The numerical solution to these equations is obtained using a digital computer. The results are compared with previously published, approximated analytical solutions to the same problem. Solutions, presented graphically, show pressure decline for constant rate fluid production. The range of variables studied include dimensionless time from '0.001 to 100 and storage capacity ratio from 0.001 to 1,000. The well behaves as if it were in an infinite reservoir for dimensionless times less than 0.25. Reservoir properties near the well can be estimated in the usual manner. An overlay technique is used to match an experimental curve with one of the theoretical curves. It is possible to estimate the distance to a discontinuity by substituting the actual time t and the corresponding dimensionless time tD at which a match occurs into the equation a = (0.000264 tk1/tD , µ1 cI)I/2 where kI/ I µI cI is the diffusivity near the well, and may be estimated from data taken at early time. Several buildup curves are computed. These curves show that for early shut-in times, correct values for transmissibility are obtained from conventional analysis. However, erroneous values of static reservoir Pressure are obtained unless data at large shut-in times are taken. INTRODUCTION A mathematical treatment of the transient pressure response of a well located at the center of a region bounded by a circular discontinuity is given. Within a region (Fig. 20) the properties of both the rock and the fluid are considered to be constant on either side of the discontinuity. While these properties are considered constant, they may be different on opposite sides of the discontinuity. A discontinuity of this type could be a fluid-fluid contact or a sudden change in rock characteristics such as thickness, porosity or permeability. Analytical solutions to this problem are available. 1-3 However, they are so involved that they are of little practical use. An approximate solutionl is available but the range of times over which it is valid has not been specified. A numerical solution to a pair of finite difference equations is used to obtain the solution given in this paper. PREVIOUS WORK One of the first solutions to the problem was published by William Hurst.1 Hurst considered unsteady-state flow of fluids through two sands in series with different mobilities in each sand. He used Laplace transforms to obtain a solution for a single well located at the center of the circle enclosing the first of the two sands. In this case, the solution for the pressure change in Region I (Fig. 20) is2

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

The formation density logging tool provides a radioactivity measurement that yields formation densities in situ. The relationship between bulk density and porosity is well understood. With knowledge of grain and fluid densities, porosity may be computed from the indicated formation bulk densities in shale-free formations. The porosities thus determined may be used with a resistivity log for water-saturation determinations. One technique utilizes a density vs resistivity plut. A plot of density vs Sonic-log transit time is used for porosity determinations in shaly sands. This method is particularly suited to wells drilled with oil-base or salt muds. In shale-free formations, comparisons of density values nnd neutron-log readings are used to identify lithologr and, thus, to select appropriate values of grain density for porosity computations. Through the use of Formation Density, Sonic and neutron logs, the interpretation problems caused by complex matrix lithologies are simplified. Other applications of the Formation Density log are found in the identification of minerals in evaporite deposits and in yield determinations of "oil shales". INTRODUCTION Widespread field application has demonstrated that the measurement of formation density is a useful and revealing technique for well logging. Responding to the bulk density variations of the formation, the Formation Density log affords valuable data on the porosity, lithology and fluid content of the formations. Although not without its own limitations, the Formation Density tool may provide effective interpretation under conditions that hamper or preclude the use of other porosity devices. When used in conjunction with other devices, such as the Sonic or neutron, complex matrix conditions may be better understood, defined and evaluated. A previous paper' described the valuable contribution of the Formation Density tool in the logging of empty, or gas-filled, holes. The purpose of the present paper is to describe applications of the device in liquid-filled holes. THE FORMATION DENSITY TOOL The Formation Density tool was devised to measure the bulk densities of formations in situ. Actually, the device responds to electron density, but in the overwhelming majority of cases of interest, the electron density is very closely proportional to the bulk density. In other cases appropriate corrections can be made if necessary. Comparisons of log-derived densities with true densities for the more common matrix minerals are shown in Table 1. The tool consists of a gamma-ray source and detector mounted in a skid which, during the logging operation, is in contact with the borehole wall (see Ref. 1 for schematic). Gamma rays are emitted by the source and diffused through the formation. The number of diffused gamma rays reaching the detector at a fixed spacing from the source are counted. An increase in counting rate by the detector indicates a decrease in bulk density in front of the skid. Conversely, a decreased counting rate signifies an increase in bulk density. A measurement of hole diameter, between the face of the skid and that of the eccentering arm, is recorded simultaneously with the measurement of diffused gamma rays. Since the tool is a wall-contact device, the size of the borehole has little influence, provided good contact is maintained with the wall of the hole. Only in extremely large or small boreholes does the actual diameter become significant. However, for most accurate measurements the borehole size should be taken into account. Fig. 1 presents the departure curves for the conversion of counting rate to bulk density for liquid-filled holes of various sizes. It is of utmost importance that the skid maintain good contact with the wall of the hole. If, due to roughness or caving, there is mud between the skid and the formation, the tool will include in its response the relatively low-density mud, and the apparent density reading will be too low. Normally, permeable beds do not cave appreciably, so that reliable readings are usually available for zones of interest. Nevertheless, the caliper reading over the zone of interest should be examined for any wall roughness. When mud cake exists between the skid and the formation, the Formation Density log sees it as part of the formation. When thick mud cakes exist, a correction is required. For best results in wells having thick mud cakes,

By H. S. Price, D. A. T. Donohue

The system of equations describing displacement of a hydrocarbon liquid by a hydrocarbon vapor in a porous medium where mass transfer takes place between the phases is solved numerically for a variety of gas injection processes. Even though the method of solution is quite general, only systems with three hydrocarbon components are considered. Computer simulations of displacement processes wherein mass transfer between phases is both considered and neglected are compared, and it is shown that neglecting mass transfer can give pessimistic displacement efficiencies. INTRODUCTION The role of the gas displacement process in the recovery of petroleum has been subjected to a series of detailed analyses; as a result, a number of predictive models have been published in the literature. However, because of major simplifying assumptions, most of these models do not completely represent the physical system. As a result, the effect of making the simplifying assumptions is unknown. Therefore, a complete representation of this process — one without major simplifying assumptions —should lead to a fuller understanding of the process, and perhaps to methods of improving it. The general method of developing a model for two-phase fluid flow in a porous medium is to solve simultaneously the continuity equation, the energy equations and the equation-of-state for each phase under the prescribed initial and boundary conditions. For an isothermal system, the energy equations reduce to the momentum equation. Darcy's law. However, since natural gas is the vapor state of the reservoir liquid, interphase mass transfer may take place with concomitant changes in both the intensive and extensive thermodynamic properties of each phase. It is this phenomenon that has often been omitted in previous mathematical models. An additional relation, then, which accounts for mass transfer between the phases, must be included with the other equations to specify a complete model. Completely formulating the equations to be solved is not a difficult task1 but obtaining their solution has been intractable up to now. Availability of large-memory, high-speed digital computers now makes an attack on this formidable problem possible. This paper presents a preliminary study of the problem. Since this investigation is intended to be exploratory, it is restricted to the linear, horizontal, isothermal, two-phase viscous flow of oil and gas in an oil reservoir. In the early development of predictive models of this process, the reservoir system was considered as a unit and various forms of the material balance equation were proposed.2-4 Pressure and saturation gradients were then added in the Buckley-Leverett model.5 The Buckley-Leverett formulation considered the fluids to be incompressible; thus, the mathematical model reduces to a steady-state system. In the 1950's, studies incorporating numerical techniques were being published.6-9 These mathematical models differed in the efficiency of finite difference techniques, the inclusion or exclusion of capillarity or the number of space dimensions considered. To solve these nonlinear, partial differential equations, each phase was considered to be homogeneous with time; therefore, mass transfer between phases was neglected. The effect of mass transfer on the gas displacement process was first reported by Attra. 10 He simulated the one-dimension flow system by a series of cells in each of which the fluids were equilibrated during a time step. In addition, the pressure throughout the system during each time step was predetermined and constant-phase velocities were calculated according to the Buckley-Leverett incompressible fluid flow model. Welge et al.11 developed a model for the displacement of oil by an enriched gas where composition is considered to be a dependent variable. Fluid

By Henry M. Howe

I wish to present to you a few thoughts on some of the phenomena and laws of iron smelting. Owing to the great complexity of the subject, to the great variety of points to be taken into consideration, many of which are very poorly understood, and to the meagreness and even conflictoriness of our information with regard to some of the most important laws which govern the subject, the fruits of such thoughts as I venture to offer you must be received as speculations, not as facts. Nevertheless, in discussing old phenomena from new standpoints, thus furnishing a metallurgical parallax, if I may say so, these theoretical speculations may have their value in helping to a clearer comprehension of the phenomena and laws we now know, and in suggesting new lines of inquiry. While an increase of height in blast furnaces is not always followed by increase in their power of production, experience proves that it tends to increase it; for while we have many cases of short furnaces producing more iron than longer ones, yet enormous productions, such as those of the Lucy and Isabella furnaces of Pittsburgh, and of the furnaces of Esch sur l'Alzette, in Luxembourg, have never been reached in short furnaces. We may safely infer that height is an element essential to great production, though of course not the only essential element, and that, in the case of high furnaces which are not capable of great production, some other essential element is wanting. Moreover, experience teaches that within limits increase of height tends to increase the producing power in a still higher ratio. Thus, in the Esch furnace, which is 19.8 meters (65 feet) high, 393 tonnes (or 387 gross tons) of 31 1/2 per cent. Ore

By John Fulton

THE increase in the production of iron has been accompanied by a growing demand for an improved quality, and more especially at the present time, in the manufacture of Bessemer steel, which is rapidly becoming an important branch of industry. This has led the makers of pig iron to a careful investigation of the composition of the materials from which their metal is produced, the inquiry being greatly assisted by a cordial alliance of science and practice. Formerly, chemical science was held in abeyance, or admitted in a hesitating experimental way ; but now it is received as a valuable auxiliary, and its decisions are accepted as final and conclusive. It is called on to assist the iron-maker in determining the quality of his stock, and to detect the presence of injurious elements in his fuel, ores, flux, or iron. The object of this paper is to submit the method now in use at the furnaces of the Kemble Coal and Iron Company in the Broad Top coal and iron region, for removing, by a process of crushing and washing, slate and other impurities from coal, designed, when coked, for furnace fuel. It is not contemplated to claim very advanced progress in this work, believing that it is susceptible of improvement, but to show that some progress has been made in a comparatively new field, and it is hoped in the right direction, since coke is probably destined to become the principal fuel in the metallurgy of iron. The Broad Top coal region occupies an isolated geographical position, standing 25 miles east from the Alleghany field. It is associated with the latter by the structure of its coal, and more closely with the Cumberland field by a similarity in the quality of coal.

By D. E. Menzie, D. L. Dauben

This paper discusses the physical parameters involved in the slow flow of high molecular weight polymer solutions in porous media. The interacting effects of polymer properties and porous media properties on flow performance are considered. Experiments were conducted with the polyethylene oxides, with molecular weights ranging from 200,000 to over 5,000,000. Frontal advance velocities ranged from I to 30 ft/day. The porous matrix consisted of a flow cell packed with glass beads. Polymer solutions were characterized by viscosity and normal stress measurements. Under certain conditions, unexpectedly high flow resistance was observed. This behavior was observed to be a function of flow rate, pore size, polymer molecular weight and concentration. The polymer solutions exhibit "dilatant" flow behavior in porour media in contrast with the pseudo-plastic behavior in simple flow systems. A theoretical ex-planation of such behavior is presented. INTRODUCTION The use of polymers in the injected water of a waterflood increases oil displacement efficiency by reducing the mobility (k,/pu) of the driving phase. A reduced driving phase mobility results in improvements in the areal sweep efficiency and in the vertical coverage in stratified reservoirs. This mobility reduction may be achieved by a permeability reduction, a viscosity increase or by a combination of the two. Early attempts at increasing the injected water viscosity were not successful because of the poor economics involved. The use of such materials as glycerin, sugar or glycols to increase water viscosity was not economically feasible. Attempts in using certain naturally occurring polymers were not too successful because of the high polymer losses to the rock. A high molecular weight, partially hydrolyzed polyacry-lamide was introduced 3 years ago as a waterflood additive.',' Initial work by Pye' indicated that the presence of these polymers in dilute concentrations decreases the water mobility 5 to 20 times more than would be expected from measurements of the solution viscosity. Such an effect would be of obvious economic value since only a small polymer concentration would be required to accomplish a large reduction in water mobility. This research was designed to study the basic flow mech anisms of polymer solutions in porous media. The interacting effects of polymer properties and porous media properties on flow performance are considered. This study indicates some of the conditions under which these interactions can lead to significant mobility effects. is valid only for Newtonian fluids. For polymer solutions and other non-Newtonian fluids the equation must be modified to consider that viscosity is a variable quantity. Modification of the Darcy equation to include non-Newtonian effects has been the subject of several recent investigations."" The modifications generally adopt a rheological model. such as an Ellis or Dower law model. to Dorous media by defining some characteristic channel radius. Most of these studies showed the porous media flow behavior to be predictable from viscometric data. Investigations involving the flow of high molecular weight polyacrylamide solutions through cores have generally encountered the high flow resistances reported previously by Pye. This high flow resistance has generally been attributed to an in-depth permeability reduction, as evidenced by a reduced permeability to water which has displaced polymer solution from the porous media. Marshall and Metzner" report high flow resistances, which they attribute to viscoelastic effects. In this paper, the effects of polymer molecular weight, pore size, flow rate and concentration are considered. The polymers used are the polyethylene oxides known as Poly-ox. This class of polymers was used because of its availability in a wide range of molecular weights and because of its known ability to propagate well through porous media. THEORY PHYSICAL PROPERTIES OF POLYMER SOLUTIONS The polymer molecule dissolves in water by means of hydrogen bonding, but retains some of its own structural identity while in solution. Nonionic polymers, such as polyethylene oxide, are generally considered to have a random coiling configration. This type of molecule has the ability to "sequester" or hold a large volume of solvent within its coils in a manner similar to that of a sponge. The random coil is easily deformed and under an applied stress