Search Documents

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By L. C. Graton

INTRODUCTION CLEAR recognition by Lindgren1 of the important control exerted by physical conditions on the formation of ores laid the foundation for that long-sought attainment, a classification? of mineral deposits based consistently on origin. In probably no other portion of the realm of mineral deposition has the importance of physical influences been so manifest or the validity of Lindgren's genetic classification been so well proved as in that extremely important family of ore deposits which are now universally classed as hydrothermal and generally regarded as of magmatic derivation. While many varieties of deposits, some of them possessing great scientific interest and economic importance, fall outside the limits of this hydrothermal group, inclusion within it of most of the veins and a vast number of the replacement deposits of the world gives to this grand genetic class at once a dominating importance and a powerful scientific appeal. Nowhere are these vein and replacement deposits of hydro- thermal lineage more generously distributed, more extensively exploited or more thoroughly known than in the Cordilleran province of the United States. One of the respects in which these hydrothermal deposits command the interest of both geologists and mine operators is in their relation to depth: the great vertical range through which many of them have already been developed, the disappointing failure of others at relatively shallow levels, and the noteworthy downward changes in character and tenor exhibited by still others. In this hydrothermal category (if the Rand be granted place here) are included the ores of all the very deep mines of the world, ranging from 5,000 to nearly 8,000 ft., as well as of many other mines undoubtedly destined in time to attain corresponding depths.

Jan 1, 1933

By G. S. Rice, Clark H. H.

When mines in the interior coal fields of the United States began the practice of blasting the coal without undercutting, or what is known as…

Jan 1, 1915

By T. E. Davidson, A. P. Lee

It is known from the early work of Bridgman that the two lowest-pressure transitions (I-II and II-III) are accompanied by substantial and abrupt changes in resistivity and Volume. However, unlike the temperature -induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of the pressure-in&ced transitions. This current work involves an examination of the structural and transformation characteristics of the bismuth I-II and II-III transitions under hydrostatic pressures. The relationship of initial structure to the transformation pressure, rate, resistivity change, and resultant structure is discussed. It is shown that the transition pressure and transformation rate are independent of the presence of grain boundaries and associated anisotropy-induced deformation. An observed hysteresis in both the I-II and II-III transitions is shown. BISMUTH is one of the most interesting of the elements exhibiting pressure-induced polymorphs since it undergoes several allotropic transformations at pressures below 90,000 atm. It is known from the early work of bridman1,2 that the two lowest-pressure transitions (1-11 and 11-111) are accompanied by substantial and abrupt changes in resistance and volume. However, unlike the temperature-induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of these pressure-induced transitions. It is the purpose of this work to examine some of the structural and transformation characteristics of the bismuth 1-11 and 11-111 transitions under hydrostatic pressures. Another interesting characteristic of bismuth is that, in its polycrystalline form, hydrostatic pressures of sufficient magnitude will induce severe progressive plastic deformation in the region of the grain boundaries.3 This deformation, which has also been observed in several other metals, is attributed to the high degree of anisotropy in the linear compressibility of bismuth, resulting in shear stresses in the grain boundaries when it is exposed to hydrostatic pressure. Most thermally induced allotropic transformations in metals, whether of the diffusionless ather-ma1 (martensitic) or isothermal nucleation and growth types, are dependent upon structure and prior history,4 viz., grain boundaries, deformation, and so forth. One logically wonders then whether the transformation characteristics of the pressure-induced polymorphs in bismuth might also depend upon initial structure, particularly with respect to the presence of grain boundaries and associated plastic deformation. In this investigation, the role of grain boundaries and plastic deformation on the characteristics of the bismuth I-II and 11-111 transitions will be established. The rather unique residual microstruc-tural changes associated with these transitions will be presented and discussed. The occurrence of a measurable hysteresis in both the I-II and 11-111 transitions will be demonstrated. The type of transformation mechanism based on the observed transformation rate will be discussed. EXPERIMENTAL PROCEDURE A) Apparatus. The hydrostatic pressure system utilized in this investigation is similar to that previously reported by Bridgman' and Birch and Robertson,5 and has been previously described.3 For the purpose of this work, the pressure medium utilized was a 1:l mixture of pentane and isopentane. Pressure measurement was by means of a manganin coil in conjunction with a Foxboro Recorder. The manganin coil was mounted in the bottom closure and inserted inside the pressure cavity. Based on calibration against a controlled clearance piston gage at approximately 10,000 atm, the estimated error in the pressure measurement was +2 pct. Assuming the nonlinearity in the pressure coefficient of resistivity between 10,000 and 28,000 atm to be not greater than 1 pct, then the estimated error in the range of the I-II and 11-111 transitions was +3 pct. B) specimen Material and Preparation. The bismuth utilized throughout this investigation was of

Jan 1, 1964

By John Wulff, David A. Stevenson

The rates of solution of copper, nickel, and three copper-nickel alloys in liquid lead were studied at 527° and 727°C under dynamic conditions. The relative velocity at the solid-liquid interface was varied from 8.65 to 125 cm per sec. Analysis of the data for the pure metals indicates that the solution rate is transport corztrolled at lower velocities, but a transition to mixed control occurs at higher velocities, higher temperatures, and higher percent saturation. 1 HE present work concerns the effect of relative velocity at a solid-liquid interface on the dissolution kinetics of pure solid materials in liquid metals. This general problem is of interest in electrode kinetics, in electrolytic processes, and more recently in the field of liquid metal corrosion. Considerable work has been done on dissolution kinetics in aqueous environments because of the obvious importance to electrolytic processes.1,2 In purely metallic systems investigation has been more limited. There are, of course, extensive data from loop tests which are used in an engineering evaluation of liq- uid metal corrosion. Here, however, the dissolution process is complicated by several interdependent processes. In general, one of two factors is considered to be rate limiting in the dissolution process: the transport of material from the solid-liquid interface into the bulk liquid, or an activation process directly at the interface. A number of studies of the dissolution rates of solid metals in liquid metals under static conditions have been published.3- Since the attendant hydrodynamic conditions imposed by thermal gradient convection and concentration gradient convection are difficult to analyze, it is doubtful if a clear interpretation of the experimental findings of these papers in terms of the mechanism involved in the dissolution process can be made. A clearer picture of the dissolution process is provided by

Jan 1, 1962

By Henry M. Howe

MY attention has been drawn within a few days to a series of articles in Volume XVIII of the Engineering and Mining Journal, 1874, by Mr. J. A. Church, in which it is stated, among other

Jan 1, 1875

By AIME AIME

SINCE the preparation of the Fall Meeting announcement the Montana Section has extended an invitation to the members traveling to Spokane to make at least a short stop at Butte, en route. Accordingly, the train schedule below has been worked out as an alternative to that announced in the general circular. This will permit a half day in which to visit either mines at Butte or the smelter at Anaconda and an opportunity for an evening meal with our Montana members. An interesting time is assured either way and the chance to renew acquaintance with Butte friends will be well worth will

Jan 1, 1929

By John Birkinbine

" Whether an iron-ore should be roasted is a question which very seldom arises ; at least, this question seldom ought to arise. With the exception of the red impalpable oxide, the whole series of ironores require roasting—even the specular iron-ore, if it is very compact—but the best oxide, if too compact, works badly in the furnace. All other ores should be subjected to calcination. Some ironmasters are in the habit of using the hydrates raw, but this should riot be done where clay-ores are smelted or where the hydrates contain either chlorides or phosphates. But in the latter case, the pig metal will be cold-short if there is too much phosphorus. Under all circumstances, however, it is best to roast the ores if we expect good metal and well-regulated furnace operations. " The object of roasting ores is to produce higher oxidation and to expel injurious admixtures. In both cases liberal access of atmospheric air is required ; we should, therefore, so arrange our roasting operations as to fulfil these conditions, from which it will appear that different ores require different treatment."* The above may be considered an extreme, and perhaps erroneous view; but there is no question as to the absence of a general appreciation concerning the value of preparing ores of iron for smelting in the blast-furnace.

Jan 1, 1884

By R. M. Goldhoff, J. W. Spretnak

IN connection with establishing the mechanism by which boron enhances the hardenability of heat treatable steels, this research work has been undertaken. Spretnak and Speiser1,2 indicated the need for studying high temperature effects in boron steels and, chief among these, the possible nonhomogeneous distribution of boron in iron grains. The occurrence of this effect may be of significance in explaining the mechanism of enhancement of hardenability by boron as well as in explaining some of the observed characteristics of boron steel behavior. Primarily, then, this work was undertaken a) to establish whether or not boron is adsorbed in ? solid solutions, b) to determine the nature of any such adsorption effects, i.e., whether it is positive or negative as well as its temperature coefficient, and c) to establish the magnitude of any such effect. While past literature on this specific subject is rather sparse, a number of authors have postulated that the observed temporary loss of hardenability as well as the occurrence of the characteristic boron constituent in these steels is due to the nonuniform distribution of boron in austenite.3-0 Experimental Techniques Attempts to obtain direct evidence of grain boundary effects in boron steels have been unsuccessful, both by using the technique of Chalmers' in which small concentrations of solute made radioactive by irradiation are detected by autoradiographic means, and by means of studying cleavage fractures with the electron microscope.8 The present study attempts the design of experiments to measure the effect of boron on properties which might be subject to variation because of grain boundary effects. A study of the theoretical aspects of grain growth indicates that such studies may be pertinent. Another valid type of experiment involves the measurement in polycrystalline materials of properties whose values depend on the bulk of the grain, being negligibly influenced by grain boundaries. One such property is the lattice parameter measured by X-ray diffraction. The value of the lattice parameter reflects the average conditions which obtain over a relatively large number of atoms in a fixed crystalline lattice, and is therefore mainly dependent on bulk grain material. Measurement of lattice parameter variation over the austenite range of temperature in iron with and without boron should give evidence of concentration variations in the bulk grain material if adsorption effects are significant. Finally, use is made of the Grange and Garvey3 metallographic test for boron in which a characteristic boron constituent can be developed in austenite grain boundaries. The very occurrence of this phenomenon suggests grain boundary enrichment of boron and a study of the occurrence of this constituent and its varation with austenitizing temperature should help to detect grain boundary effects. Materials One lb ingots of pure iron, an Fe-B alloy, an Fe-C alloy, and an Fe-C-B alloy were prepared. The melting technique included an initial melting of electrolytic iron under vacuum followed by remelting under hydrogen and, finally, by melting under argon with the addition of alloying elements. Each ingot was surface machined between meltings. A quantitative spectrographic analysis was obtained on the pure ingot and, in addition, oxygen, nitrogen, and carbon were determined by the vacuum fusion method. The results of these analyses are given in Table I. Semiquantitative spectrographic analyses were performed on the alloy ingots, while quantitative determinations of the alloy additions were obtained. These analyses are shown in Table 11. The cast ingots were subjected to the following sequence of fabrication treatments: forging to 5/8 in. bars, swaging to 0.300 in. rounds, drawing to 0.025 and 0.010 in. wire. Portions of each ingot were retained in the swaged condition for experimental use. For certain portions of the work typical commercial steels were used. These materials were supplied by the Republic Steel Corp., Canton, Ohio, and correspond to AISI 8640 and AISI 86B40 compositions.

Jan 1, 1958

By R. L. Rickett, S. H. Kalin, J. T. Mackenzie

Aluminum killed low carbon steel, § which is now used extensively for severe deep drawing or other difficult forming operations, is unusual in that its grain structure, after cold reduction and box annealing in accordance with conventional continuous sheet or strip mill practice, often is elongated, although at times it is equiaxed. Since this unusual structure has been found superior for many, but not all, severe forming operations, recrystallization of the steel, both at constant temperature and on continuous heating, was investigated and compared with that of rimmed steel in the hope that something might be learned about the mechanism of, and the factors controlling, the formation of such elongated grains. In this structure, the grains are elongated both in the lengthwise direction of the strip and transverse to this direction, even though nearly all of the extension in both hot and cold rolling is in the lengthwise direction. The grains are thus roughly pancake-shaped, being longer and wider than they are thick, as observed also by Burns and McCabe,1 and as illustrated by the typical structures shown in Fig 1. Fig la, representing a conventional longitudinal section, shows the length and thickness of the grains, whereas Fig Ib shows their length and width as seen by examining a section parallel to the sheet surface. Both illustrate the very irregular grain boundaries usually associated with the elongated grain shape. A finer equiaxed grain structure in this same grade is shown in Fig Ic. Either the elongated or the equiaxed structure may be present in the annealed product, and in rare instances the two types may coexist in a single specimen, as shown in Fig 1 d. Isothermal Recrystalliza-tion of Rimmed and Alamimum Killed Steel An aluminum killed steel known to have an elongated grain structure after conventional processing (Steel B, Table l), was selected for the initial recrystallization studies; for comparison, a rimmed steel, A in Table 1, was used. Samples of each in the form of hot rolled strip 0.075 and 0.095 in. thick, respectively, were cold rolled on a small laboratory mill in steps of about 0.010 in. per pass to obtain total reductions of 40 and 60 pct. Small pieces of the cold reduced strip were heated in lead at selected constant temperatures for one of several periods of time, then cooled in air. Rate of heating in the lead was, of course, very fast. Hardness of the cooled specimen was measured and a longitudinal section examined metallographically. Isothermal recrystallization curves for these two steels at 1050°F, based on hardness of the air cooled specimens, are shown in Fig 2 in which the amount of recrystallization corresponding to each plotted point is indicated. The marked difference in the behavior of these two types of steel is evident. After a corresponding amount of cold reduction, the rimmed steel recrys-tallizes in a much shorter time than the killed steel and the shape of its recrystallization curve, (plotted on a logarithmic time scale), is very different. The curve for rimmed steel indicates that recrystallization is analogous to isothermal transformation of aus-i.enite in that it proceeds at a progressively faster rate up to some 50 pct recrystallization, then at an increasingly slower rate. For the aluminum killed steel, however, the start of

Jan 1, 1950

By C. Schlumberger

IN the course of the past few years the authors and their associates have had different opportunities to study the electrical phenomena which accompany the oxidation of pipe lines. The causes of such phenomena are very similar to those which have been described under the name "spontaneous polarization" with reference to metallic orebodies,1 and can be investigated in the same manner. These investigations, however, until recently were of a scientific and theoretical character, and had not found any important practical application. During the year 1931, however, the authors treated several industrial corrosion problems for public utility companies. These problems usually had to be studied in towns or in densely populated areas, where it was well-nigh impossible, or very expensive, to dig pits and trenches in order to make electrical measurements on the pipe itself. The authors were thus led to evolve a method and apparatus permitting the study, from the surface, of the direction of the currents flowing from pipe lines. The purpose of the present paper is to discuss the results obtained in the course of these investigations. However, in consideration of the importance and interest of the work carried out by other scientists along the same lines, a separate chapter will be devoted to a summary of the results achieved up to the present time in the study of pipe line corrosion.

Jan 1, 1932

By N. A. Rose, E. L. Spain

THIS study was undertaken primarily to determine the reasons for certain variations in the soundness of gravel aggregate taken from a number of widely separated points on the Tennessee River. Under laboratory tests, concrete made with these various aggregates in some cases exhibited marked differences in specific gravity crushing strength and durability. Gravel was studied in detail from Chattanooga to the mouth of the river and to a lesser extent from Chattanooga to Knoxville. The causes of variation were determined, and variational curves were constructed, which accurately predict the composition of aggregate at any point on the river and therefore its relative suitability for use in concrete. The aggregate at any point is suited for making sound concrete; the variance of suitability is due to varying percentages of sandstone and weathered material, which are less sound than other constituents. INTRODUCTION When it is stated that the aggregate from one point is inferior to that from another, it must not be construed to mean that the gravel is unfit for use. The classification upon which such aggregate ratings are based is largely arbitrary, thus inferiority or superiority is merely relative. Samples of gravel were selected from stockpiles at the dams of the Tennessee Valley Authority under construction, from the stockpiles of private companies along the river, and from samples taken by the gravel- exploration barge of the T. V. A. One hundred or more gravels of each size studied were selected at random by taking small handfulls while walking around the piles. These were separated according to the different mineral or rock constituents present, and the percentage of each constituent was obtained by counting. At least three such samples were taken from each size, and all checked with one another within a few per cent. The results were then averaged. In order to check on the accuracy of such sampling, a whole sample was taken from one point after the gravel was thoroughly mixed. The two methods gave approximately identical results. SOURCES AND TYPES OF MATERIALS The sources of gravel found in the Tennessee River are numerous and varied. The river itself traverses several geologic provinces, each

Jan 1, 1937

By Herbert Clark Hoover, Lou Henry Hoover

We give the following brief notes on early works containing some reference to mineralogy, mining, or metallurgy, to indicate the literature available to Agricola and for historical notes bearing upon the subject. References to these works in the footnotes may be most easily consulted through the personal index. GREEK AUTHORS.-Only a very limited Greek literature upon subjects allied to mining or natural science survives. The whole of the material of technical interest could be , reproduced on less than twenty of these pages. Those of most importance are : Aristotle (384-322 B.c.), Theophrastus (371-288 B.c.), Diodorus Siculus (1st Century B.c.), Strabo (64 B.c.-25 A.D.), and Dioscorides (1st Century A.D.). Aristotle, apart from occasional mineralogical or metallurgical references in De Mirabilibus, is mostly of interest as the author of the Peripatetic theory of the elements and the relation of these to the origin of stones and metals. Agricola was, to a considerable measure, a follower of this school, and their views colour much of his writings. We, however, discuss elsewhere1 at what point he departed from them. Especially in De Ortu ct Causis does he quote largely from Aristotle's Meteorologica. Physica, and De Coelo on these subjects. There is a spurious work on stones attributed to Aristotle of some interest to mineralogists. It was probably the work of some Arab early in the Middle Ages.[ ]

Jan 1, 1950

Held at San Francisco, Cal., Thursday to Sunday, Sept. 16 to 19, 1915 COMMITTEES Arrangements CHARLES W. MERRILL, Chairman EDWARD H. BENJAMIIN H. C. HOOVER FRED `V. BRADLEY W. C. RALSTON ABBOT A. HANKS G. H. CLEVENGER Excursion and Accommodations ABBOT A. HANKS, Chairman E. T. BLAKE R. H. BEDFORD C. G. DENNIS FREDERICK BRADSHAW C. E. GRUNSKY, JR. EDMUND JUESSEN ARTHUR B. FOOTE F. A. KEITH GEORGE 0. BRADLEY CHARLES JANIN E. N. ENGELHARDT R. S. HASELTINE N. CLEAVELAND

Jan 12, 1915

By R. J. Sweigard, R. V. Ramani

Demands on available lands will continue to increase due to the projected population increase and industrial expansion. Though there is an upper limit on available lands, the multi-use nature of the lands will make it possible to meet these demands. However, this will not happen without adequate planning. Land uses can be broadly categorized as nonrenewable and renewable. Lands with minable resources can be dedicated at some Point to the extraction of resources. Such a dedication, however longterm, is only temporary because of the nonrenewable nature of the minable resources. The land will be available before and after mining for other uses. Planning for such lands must have the objective that, as far as practicable, no nonrenewable uses are preempted and no renewable uses are permanently destroyed. This paper addresses primary aspects of this planning process. These aspects include a discussion of planning responsibility, data needs and availability, the integration of mine planning and post-mining land use planning, and a long-term plan for resource conservation and utilization. Minerals, with agriculture and forest products, are the primary sources of wealth. Therefore, to amid land development that may preempt future mineral resource utilization, local planning groups must be aware of the mineralization and mining potential. Much work needs to be done to identify and characterize the mineral resources. Even more land use planning is needed for lands with mineral deposits.

Jan 1, 1985

By Verne E. Hooker, Robert M. Becker

The evaluation of in-situ rock stresses from measurements of the change in diameter of a borehole that is stress-relieved by overcoring has become a common practice. Generally the stress evaluation has been based on isotropic relations whereas rock in varying degrees is aniso tropic. A plane elasticity solution fora circular hole along one axis of an orthotropic medium has been adapted to evaluation of in situ stress. The necessary elastic parameters for this evaluation may conveniently be obtained from static tests on the overcore in conjunction with a consistent orthotropic thick-wall cylinder solution. The method and equations for the laboratory and field evaluations are summarized and illustrated. The determination of in-situ rock stresses from boreholc deformation measurements has gained widespread acceptance. Hastl measured the change in diameter of a borehole that was stress-relieved by drilling a larger concentric core; this overcoring method has produced a major portion of the field data for recent stress evaluations in rock. These evaluations are based on the elastic properties of the rock, which are conveniently determined by testing the overcore.6-8 The stress evaluation and the overcore testing procedures generally assume isotropic relations whereas rock is anisotropic in varying degrees. Recently, an anisotropic plane stress solution was adapted for evaluation of in-situ stress9 and a related plane strain solution was developed for the testing of stress-relief core. 10 The present paper unifies the stress evaluation and overcore testing procedures for a general class of anisotropic rock. Equations are presented for calculating the state of stress in a plane normal to the borehole, and a consistent thick-wall cylinder solution is given for determining the necessary elastic properties. In addition, a complete example of stress evaluation from laboratory and field data is presented, and the order of error in computing the state of stress from isotropic relations is illustrated. Several limitations of the results should be emphasized. All results assume small linearly elastic deformations of a homogeneous medium. Rock characterized by orthotropic, transversely isotropic, and isotropic elasticity is considered; however, the anisotropic results assume a special relation among certain elastic constants in addition to geometric orientation with respect to a plane of elastic symmetry. For some stress determinations in rock, these may be severe limitations. On the other hand, the anisotropic evaluation procedure involves little additional effort and is much more flexible than the corresponding isotropic evaluation procedure. The collection of field data is identical. The laboratory determination of elastic parameters is no more difficult and time-consuming for the anisotropic than for the isotropic model. Only the calculations require some additional effort for the anisotropic evaluation, and this additional effort is eliminated by use of a small computer. The flexibility of the anisotropic procedure is greater because more than two independent elastic constants are available in fitting rock data. For the special relationship assumed among orthotropic constants, five independent elastic constants are available for the determination of in-situ secondary principal stresses as compared with two independent elastic constants for the isotropic model. Much of the material presented is either directly from the literature or adapted from the literature through superposition or the usual transformations. Consequently, only enough detail for clarity of presentation is included. RELATIONS FROM ANISOTROPIC ELASTICITY Materials that have three mutually orthogonal planes of elastic symmetry are called orthotropic. By directing the axes of the coordinates perpendicular to these planes, Hooke's law for an orthotropic solid 11 is

Jan 1, 1970

By J. H. Moran, E. E. Finklea

The pressure build-up technique is a recognized method of determining permeability from conventional drillstem tests. In this paper an effort is made to extend such techniques to the interpretation of data obtained from the wireline formation tester. Such a study is necessary because of the differences, for this case, in the magnitude of the flow parameters (rate of flow, amount of recovered fluids) and in the flow geometry (flow through a perforation vs flow across the face of the wellbore, etc.) involved in the solution of the equations of flow for compressible fluids. The perforation is replaced by a spherical hole, and the effect of the borehole is neglected, so that the flow can be considered to be radial in a spherical co-ordinate system. Arguments are presented to justify this idealization. Assuming single-phase flow, general relations between pressure and flow rate are developed for a homogeneous medium. The study is then extended to permeable beds of finite thickness. It is shown that the early stages of pressure build-up tend towards spherical flow, while the later stages tend towards cylindrical flow. The thinner the bed, the more quickly flow approaches the cylindrical model. The prevalence of thin beds in practical work makes this analysis quite important. Cases involving permeability anisotropy are treated. INTRODUCTION From wireline formation tester operation, two types of data are obtained: (1) the nature and amount of recovered fluids, and (2) the pressure history recorded during the test. A number of papers have been written dealing with the interpretation of formation production on the basis of the recovered fluids.'.' In general, the methods described have been quite accurate for both high- and low-permeability formations. The present paper will deal with an analysis of the pressures observed. An analysis of the pressure build-up curves obtained in hard-rock country has already been attempted on the basis of the formula proposed by Hor-ner. Although this approach has met with success in many instances, some questions have been raised as to its validity. It is the aim of the present study to place the analysis of pressure build-up in the formation tester on a firmer basis, from which more detailed methods of interpretation can evolve. Because of the great differences between the operation of the wireline formation tester and the conventional drillstem test, modifications are necessary in the interpretation. The major difference relates to the flow geometry. Once the flow geometry has been established other features such as multiphase flow, skin effect, afterflow, etc., well described in the literature, can be introduced. It will be assumed that the mechanical operation of the formation tester is already known to the reader.6 t will suffice here merely to state that the tester provides the means for taking a relatively small sample of the fluid immediately adjacent to the borehole, and for recording the subsequent pressure response. In comparison with conventional drillstem tests, the time required for a satisfactory pressure build-up response is much shorter, because of the relatively small quantity of fluid withdrawn by the wireline tester. This feature is highly desirable in the case of low-permeability formations. For an analysis of the pressure response within the formation, three simple flow geometries are considered— linear, cylindrical and spherical. The spherical and cylindrical flow geometries are most pertinent to the formation tester; therefore, they will receive the major emphasis. Since the configuration of the borehole and the perforation made by the tester complicate the flow geometry, it is necessary to allow for them in the drawdown response. However, because of the volume of formations contributing to the pressure-response, the details of the perforation shape are unimportant in the build-up period. Since relatively small amounts of fluid are withdrawn from the formation, in contrast to a conventional drill-stem test, a study of the "depth of investigation" and the significance of drawdown as well as build-up data will be included. Because the "depth of investigation" will be shown to be rather large, the effect on the build-up curves of the finite thickness of the permeable bed is considered. It is this consideration that leads to the importance of cylindrical flow geometry. Also included is a discussion of permeability anisotropy and its effect on the interpretation of the tester results. The pressure curves recorded by the formation tester will follow two general patterns, depending upon whether the formation is of high or low permeability. Fig. I (a and b) schematically illustrates these two responses. In Fig. 1(a), the high pressure recorded during fill-up of the tool is essentially the pressure differential across the choke in the system. In Fig. l(b), the flow rate is

By Walter B. M. Davidson

Phosphorus is one of the elements having the widest distribu tion, and phosphoric acid plays an important part in the composition of the crust of the earth. It is allied in various chemical combina- tions with many bases, of which lime, alumina and iron are the most common. It is difficult to state in what chemical combination phosphoric acid predominates in the crust of the earth, for while phosphate of lime, as the mineral which is sought for and found in deposits of economic value is the most familiar, it is probable that the phosphates of alumina and iron are the most usual forms in which phosphoric acid exists in all soils not essentially calcareous. It has been shown by thousands of analyses that all fertile soils contain from a trace to 0.5 per cent. of phosphoric acid. All limestones, dolomites and chalks contain it in proportions which, though usually small, are large enough to make careful analysis necessary in the selection of limestone as flux for iron-smelting. It is generally Trenton limestones that are found best for this purpose, the more recent strata being more phosphatic. In some places phosphoric acid replaces carbonic acid, and the limestone or chalk becomes phos phatic to a large degree, or sometimes pure phosphate of lime. The waters of the ocean, from very early periods, have contained phosphoric acid. Different analyses show varying contents; it is asserted that some portions of the Gulf Stream are more phos phatic than the surrounding waters of the Atlantic. Many springs, usually from limestone regions, contain soluble phosphates in vary ing quantities. I think it safe to assert that phosphorus is nearly the most widely and evenly distributed element on the surface of the earth, and probably the most subdivided. This can be readily understood when the important part which phosphoric acid plays and has played in the vital cosmos is taken into consideration. Phosphorus was on the earth in gaseous, liquid or solid form before the dawn of life, and since then all animal and vegetable creation have combined with the

Jan 1, 1893

By F. H. Bunge, W. H. Jr. Dailey

This paper covers an investigation of the magnetic roasting characteristics of several iron ores when treated in the form of small pebbles (1/8" to 1/2" in size), and in the form of balled fines. The roasting treatment was carried out with apparatus capable of very close control of time, temperature, face velocity, and per cent combustible in the reaction gas. The effect of rapid initial heating was not studied although it is believed that this has a major effect on the results when processing solid pebbles. The test equipment is a fixed bed type, with such a wide range of gas velocities, temperature, combustible content and etc., that the results obtained can be made to approximate those from various commercial roasting processes. The data presented in this report covers reaction rates, effect of processing variables on silica in the concentrate, flow resistance of beds, and to a limited extent, the effect of particle size. The work is far from complete and raises many more problems than it gives answers for. We believe, however, that much of the information will be useful to those engaged in investigation of magnetic roasting processes. We measured the time required for various degrees of completion of the reaction of hematite to magnetite, for finely pound material in balled form and for carefully sized crushed ore. Measurements were made for a variety of Minnesota and Labrador ores. This report covers an ore requiring fine ginding (-325 M) for liberation (Lower Kevin) and an ore requiring coarser grinding (-100 M) for liberation (Upper Olson). These ores represent approximately the range of characteristics for a group in the west end of the Mesabi Range. Our data shows that the reaction rate is very fast for the finely ground material and that tests are readily reproducible. The reaction rate of the larger size material, in the range of 1/8" to 1/2", is much slower and the results more erratic. We found that for the ores tested, the percentage of silica in the Davis tube magnetic concentrate was a function of iron recovery. Normally the concentrate had a low and relatively uniform percentage of silica up to a critical value of recovery. Above this critical recovery value the percentage of silica increased very rapidly. For example, for one particular ore roasted in the form of 3/8" diameter balls made from -28 mesh fines, the silica remained at about 7% to 8% until the recovery exceeded about 93%. Increasing the recovery beyond 93% resulted in over 25% silica with the additional recovery. The degree of conversion of hematite to magnetite (% completion of roast) required to obtain 93% recovery for balled material, varied inversely with the gas flow rate. Percentage silica in the concentrate resulting from roasting 3/16" and 1/2" solid material was relatively erratic. However, for varying degrees of iron recovery the lowest silica percentages corresponded to those obtainable when roasting fines. It is thought the probable reason for the erratic values was the variation in shattering or cracking of the pebbles during initial heating and roasting. There is some indication that very fast initial heating will greatly increase the permeability of the individual particles of ore to gas flow so that the reaction rate for coarse sizes will approach that obtainable with balled fine material.

Jan 1, 1961

By W. B. Lewis, M. E. True, M. C. Leverett

Tars paper states the theory underlying the design of two kinds of dimensionally scaled models of parts of idealized oil fields. One of these simulates an oil well and its surrounding sand for a distance of 16 ft. radially from the well. The other model simulates linear flow through layered sands. Construction and operation of the models are described and typical data are given. The unique features in the design of the models are: (I) the treatment of the permeability-viscosity quotient as a single variable and (2) the use of previously reported experimentally developed relations between relative permeability and saturation and capillary pressure, saturation, porosity, perm ability and interfacial tension. The models at present simulate flow of oil and water only, through unconsolidated sands. They are superior to unscaled models, which may give rise to erroneous conclusions. The models are designed to study the desirability of various methods of sell completion and the effects of various factors on recovery of oil from layered sands.

Jan 1, 1942