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By L. R. Blair

Many hydrated silicates have been synthesized and sold for commercial use. However, this paper discusses only hydrated calcium silicates and, to a lesser extent, hydrated magnesium silicates. Synthetic calcium silicates were first formed by man when he found that mixtures of silica or silicates and lime in water set up to form cements. The material which was responsible for the cementing properties was calcium silicate hydrate, although this fact was not recognized until early in this century. In the early 19001s, synthetic calcium silicates, reinforced with fibers and formed simply by reacting calcium hydroxide and silica in water with fiber at atmospheric or under low pressure autoclave conditions, found increased use in thermal insulations and in building products. These insulations were found to have a low thermal conductivity and would withstand temperatures up to 650°C. This, combined with their very low densities (from 8 to 50 Ib per cu ft) and fairly high strength, also made them suitable for use as building products. Following the disastrous Morro Castle fire of the 1930Js, calcium silicate board products were used as partitioning material in all shipboard construction in the U.S. As autoclaving techniques were improved and developed, it was: learned that under hydrothermal conditions new and useful calcium silicates which could be used under more extreme temperatures (up to 980' C) could be prepared. These had high surface areas and other unique properties which suited them for use as fillers, pesticide carriers, low temperature insulating materials, and adsorbents for the removal of fatty acids from various solutions. Hydrated magnesium silicates have not been studied as extensively as the calcium compounds. Their first important use was in the filtration of dry cleaning solutions for the removal of fatty acids. With the introduction of detergents, it was found that these products lost their advantage because of their high affinity for the detergent chemicals. However, in recent years these chemicals are finding increasing use as decolorizing agents for fats and anti-caking agents for resins. Some materials with very high surface are finding new use as adsorbents. CALCIUM SILICATE HYDRATE COMPOUNDS AND THElR CONDITIONS OF FORMATION Within the past ten years much has been done in the field of calcium silicate hydrate chemistry. As a result of this work it has been found that at least 25 different forms of calcium silicate hydrate can either be formed synthetically or found as naturally occurring materials. The stability and composition relationships among these 25 compounds present a very complicated picture, and many of these very closely resemble other forms and are difficult to dis-

Jan 1, 1962

By CHAS. A. R. LAMELY

In the extreme northeast corner of the State of Washington, on the Canadian border, lies the Metaline mining district. This district is old in history, but young in production. The Metaline district is a zinc-lead area of the replacement type in dolomite and limestone. The ore bodies of the Josephine horizon are in many ways similar to the ore bodies of the famous Tri-State zinc fields. The beds are faulted and folded and have varyng low dips in varying directions, and underlie large areas of the district. Production started in 1927 on a very limited basis. The property is now mining and milling 700 tons per day. The mine is opened by adit tunnels and a vertical shaft. As the ore horizons gained depth, it was necessary to sink inclines to follow the ore horizon (see Fig 1). From 1927 to date, approximately 600,000 ft of diamond drill was put down This work indicated that sufficient tonnage existed to justify a redesigning of the whole operation, surface and under- ground. After four years of general study, the following program was planned :

Jan 1, 1949

By Betty J. Laswell, Gerald W. Laswell

Rotary drilling in modern open-pit mining is usually considered the lead phase which not only establishes the production rates but frequently limits them. From this viewpoint alone, the drilling phase must be maximized. The drill phase is the step that permits all the other operational phases to function within their design limits. This means that, in most cases, the drill is literally run to destruction to ensure that the shovel will be able to smoothly and consistently load a manageably size muck, the haul trucks can carry a balanced load without having a boulder dropped through the bed, and the crusher can devour constant rock size.

Jan 8, 1978

By George Bain

SOME problems concomitant with commercial exploitation of marble are presented as examples of interesting, useful and profitable fields for application of scientific knowledge. The marble industry is only one such field and is selected because its varying new aspects are familiar to the author. However, what is true for marble is equally so in principle for many industrial minerals. The problems of any stone industry are to maintain markets, create new outlets for stone already in demand, and develop varied uses for varieties that are not so popular. Here the geologist has a different role from most of his colleagues in metal mining. The producing branch may ask about the expectable variation in thickness or size of a deposit as development proceeds. The stock department may call for the available amount of a given type of stone before accepting a large order. The sales force requires data on the use for stone from certain parts of deposits in order to divert grades to the most suitable use. The service depart-ment wants defects rectified and the cause determined to avoid recurrence. The mills want data on durability and cutting quality of abrasives. The geologist occupies no special department; he is on general call, as may be illustrated by a few types of problems that may be classified as: (1) dominantly geological in character, (2) dominantly chemical in character, (3) dominantly physical in character.

Jan 1, 1940

By Clyde E. Williams

THROUGHOUT its history the American iron and steel industry has constantly striven to improve the quality and reduce the cost of its products. No one needs to be told how well it has succeeded. Its success in making steel products at such a low cost has been achieved mainly through large-scale production. While costs have gone down as the rate of production and the degree of mechanization increased, quality of product has been actually improved. Thus high-tonnage records are important only in the light of high quality of the steel. Quality is the watchword! Continual improvement in quality has come as a result of research, not only in the laboratory but in the large commercial units in the plant. In fact, so many operations of the industry are on such a huge scale that experimental work must be done under commercial operating conditions so every progressive steel plant is a research laboratory.

Jan 1, 1938

By H. W. Camp

Although the situation in the oil industry during the past year has not been conducive to large expenditures for development and research, there is little indication that such expenditures have been curtailed. While few outstanding achievements have been reported, considerable progress has been made in the development of new product,s and the adaptation of petroleum derivatives to new uses. The most important question facing the refiner today is the antiknock quality of his gasoline. This year has seen the widespread adoption of the term "octane number" as a measure for anti-knock values, and in the latter months of the year the public has been made acutely aware of this condition through competitive advertising. Gasoline is no longer priced on volatility and gravity alone, but on octane number as well; and premiums are being paid for material of relatively high octane rating. The situation has grown more and more competitive and has forced refiners continually to raise the octane rating of their regular and competitive grades, and at this writing the same situation exists for premium grades which have possessed relatively high anti-knock properties for some time. Straight-run gasoline produced from paraffin-base or semiparaffin-base crudes has an inherently low anti-knock value, and in order to convert this material to a higher quality it has been found necessary to crack an increasing percentage of the crude oil charge. By completely cracking the heavier portions of the crude and blending back with the straight-run gasoline, it has been possible to produce an average of 63 to 65 octane number gasoline on average Mid-Continent crude. This operation carried to the fullest extent does not suffice, however, and the recent and rapid development of the so-called '(reforming unit," has resulted. The straight-run gasoline fraction is cut into two parts: a light, low boiling point gasoline; and a heavy gasoline or naphtha. The latter containing the low anti-knock portions of the gasoline, is sent through a re-forming unit and subjected either to high temperature or pressure, or both, which materially increases its octane number. On average Mid-Continent the blend of low boiling point straight-run,

Jan 1, 1932

By Edwards Wichers

The purpose of this paper is to set forth the matters of principal interest in connection with work done in the past few years on the purification of the metals of the platinum group, including the study and modification of methods already in the literature and the development of new procedures. For the most part, the results will be given in summary form, reserving the publication of detailed data and directions for a forthcorning paper to be issued by the Bureau of Standards. In recent years increasing interest has been shown in the preparation of the pure platinum metals, both by those concerned with the manufacture of the metals and their alloys for scientific and industrial purposes and those who are engaged in the study of the chemical or physical properties of the elements. The purification of the metals usually has been regarded as a matter so involved and difficult as to require the attention of specialists. It is hoped that this paper will show that any of the metals can be prepared in any desired degree of purity by relatively simple straightforward chemical methods. For the most part, it is thought that the methods given are suitable for small-scale refineries as well as for the laboratory; also, that they will bring the time required for the purification of any of the metals within reasonable limits. The new procedure suggested for purifying platinum should prove to be much shorter than any methods described in the literature. Treatment of Platinum Ore As is well known, the principal source of the platinum metals is a mixture of several native alloys of the metals, found chiefly in naturally concentrated deposits in stream beds or alluvial material. Without attempting to enumerate all of the minerals present, it may be said that the concentrated ore from such sources contains all of the six platinum

Jan 1, 1928

By P. H. Dudley

A quarter of a century of service of steel rails on our oldest railroads, many of which have changed their standard sections three or four times, has furnished, and is furnishing, excellent opportunities to study their wear and behavior in the track. Such experience is valuable for the design of new sections, now required to meet the constantly increasing severity of railroad service. Before presenting the new sections for consideration, I will briefly call attention to some features of past experience. For convenience of study, rails may be separated according to their weight and height into four groups, viz.: 1. Hails weighing per yard from 52 to 60 pounds, and 34 to 4 inches high. 2. " " " " " 60 " 72 " " 46 to 44 " " 3. " " " " " 72 " 90 ' 41/8 to 5 4. " " " " " 85 or more " " over 5 " I Experience in this country is confined mainly to sections in groups Nos. 1, 2 and 3. • During the past few years I have had the opportunity to run my car over many thousands of miles of railway laid with the principal sections in use, and to obtain diagrams showing their deflections, permanent set, and, in a great measure, their manner of wear. The First Group.—The first steel rails imported, and those manufactured here, were light sections—included in the first group—and many of them, being rolled in rolls used for rolling iron sections, have pear-shaped heads, 2 3/8 to 2 1/2 inches wide, the base being heavy and from 1/4 to 1/2 inch narrower than the height. These rails were laid upon ties of solid timber, at least 8 inches face, spaced 2 feet from center to center. The moments of inertia of these rails were low, only ranging from 8 for the lightest sections to 12 for the heaviest. The deflections were, of course, great; but the quality of the metal was excellent. It was physically hard and

Jan 1, 1890

By John R. Don

In the South Island of New Zealand an unusually favorable opportunity is offered for the analysis of the older crystalline rocks, underlying the sedimentary rocks which form the "country" of the gold-deposits. The Manipori formation of this island, comprising the greater part of the mountainous district west of lakes Manipori and Te Anau, in Otago, consists of an enormous thickness (estimated by Professor Hutton1 at 160,000 ft.) of crystalline schists, gneiss, syenite, and syenitic gneiss, with associated masses of granite; the whole forming the most picturesque fart of New Zealand. The famous West Coast sounds occur in this formation. No paying auriferous lodes have been discovered in it; and for this reason an examination of the rocks is specially interesting here. Stelzner, Posepny, and others, who have criticised the conclusions of Sandberger, have laid great stress on the fact that all the silicates analyzed by him were taken from the vicinity of orebodies containing those heavy metals which he notes as occurring in the silicates of the country-rock; their contention being that these metals, supposed to occur as silicates in gneiss and other crystalline rocks, were really contained as sulphides, and were therefore impregnations from the neighboring orebodies. The same objection, whatever be its weight, might be urged with equal justice against Mr. Becker's derivation of the mercury and gold of the lodes of the Pacific Coast from' the granite underlying their country-rock. In the case of the

Jan 1, 1913

By Henry M. Howe

In discussing the classification of iron to-day, we are to leave out of consideration the general division into non-malleable or cast iron and malleable iron, as to the adequacy of which no question has been raised; and to confine ourselves to the subdivisions of malleable iron. This has been classified, according to the extent to which the properties imparted by carbon are present (viz., resilience, hardness,strength, and, above all, the capacity for being hardened by sudden cooling from a high temperature), into (1) wrought iron which cannot be hardened, and (2) steel which can be hardened; and this classification I shall, for briefness, term the carbon classification. Until within a few years all authorities, both metallurgical and general, have concurred in explicitly recognizing the carbon-given qualities, and preeminently the capacity for being hardened, as the essential qualities of steel; this is laid down with clearness by every writer on the subject. For several years this old classification has not been sufficient to meet all our needs, since the genius of Bessemer, Siemens, and, I may add, Holley, has produced wrought iron which has been perfectly melted, and thus freed from certain mechanical adhering impurities. This causes what we call homogeneousness for want of a better word, and gives rise to many important qualities which the old wrought iron had not; qualities universally recognized, though not readily described. I shall, for briefness, style them the fusion qualities, and a classification based on them, a fusion classification. These qualities render the new product so vastly superior, for most purposes, to the wrought iron formerly known, that it is neces-

By Clyde E. Williams

THIS review of the progress made in iron and steel metallurgy during the past year is confined to developments in this country. It attempts to give examples to illustrate progress made rather than to appraise results. As a result of the gradually diminishing supply of rich iron ores and of predictions made as to the probable life of the iron-ore reserves of the Lake Superior District, attention of iron and steel executives was directed to the question of beneficiation of iron ores. Laboratory and plant-scale experimental work was conducted on the wash ores .of Minnesota and an investigation, was, begun on the Old Range low-grade ores.

Jan 1, 1931

By Eugene McAuliffe

THE heavy shrinkage in the production of bituminous coal has reflected adversely in the matter of tonnage produced by stripping arid mechanical loading machinery. The purchase of stripping and underground loading equipment has likewise been circumscribed. How- .ever a growing percentage of bituminous coal is being loaded by stripping and mechanical loading machinery. This situation is due to the fact that numerous strip pits were able to operate in Illinois and Indiana when under- cover mines were subjected to labor interference, a further advantage gained by their ability to produce and market coal at a price below that of the undercover mines. The mines equipped with mechanical loading. apparatus have enjoyed more continued operation for the double reason that the companies using coal-loading machinery are, generally speaking, more substantial and in better financial condition than many of the smaller properties who maintain hand-loading methods, and the market advantage due to lower production costs also reflects to the advantage of the undercover mines using mechanical loading equipment. Where a number of mines are con- trolled by one company, those not equipped with loading machinery and suffering from higher producing costs have often been closed, with the available tonnage concentrated in the more modernly equipped mines.

Jan 1, 1933

By Edward H. Robie

PONCA CITY proved an ideal selection as a place of meeting for the Petroleum Division this fall. The accommodations at the Conoco Club were just what was required for such a gathering; the committee having the arrangements in charge functioned with the efficiency of veterans and the enthusiasm of neophytes; and the members and guests followed the speakers with close attention, entered the subsequent discussions with gusto, and divulged the "low-down" at private conferences. No one minded the drizzling rain on the first day, which only served to keep up the attendance in the auditorium; the weather then cleared up in time for a group picture before the gathering went their separate ways.

Jan 1, 1932

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

By Richard W. Brummett, Robert L. Dubms

Located some 180 miles east of Los Angeles in Riverside County, California, the Eagle Mountain mine supplies iron ore concentrates for the Kaiser Steel Corporation steel plant in Fontana, California, and for export to Japan. Although the deposits were first discovered in the early 1890's, no production was realized from the area until 1948 when Kaiser Steel Corporation commenced operations. A part of the large Basin and Range province, the Eagle Mountain area's geologic column comprises a thick series of metasediments resting on Precambrian gneisses and schists that have been intruded by sill-like masses of porphyritic quartz monzonite. The metasediments are composed of three quartzite units that are separated by a schistose meta-arkose and by two ore zones. They have been folded into a large east-west trending anticlinal structure that extends completely across the Eagle Mountains. The iron ore deposits occur in two well-defined horizons in the metasedimentary series, and they are found only along the north limb of the major anticline. Host rocks for the ore zones were a series of limestones and dolomites with associated quartzites. Magnetite plus pyrite comprised the primary mineralization that formed many replacement lenses and stringers of ore within the ore zones. The primary ore has been oxidized to hematite and goethite in a broad zone at higher elevations in the deposits. Hydrothermal alteration formed actinolite- tremolite granofels, local phlogopite, and minor tourmaline in the ore zones. This alteration and the ore deposition seem related to the same magmatic event that formed the porphyritic quartz monzonite intrusion

Jan 1, 1968

By P. Lees, N. Parkinson, K. Hartley, D. M. Donaldson

The reprocessing of advanced fuels such as carbides, oxides, and cermets, containing up to 30pct pu has been studied. Dissolution of uranium carbides in nitric acid produces appreciable quantities of mellitic acid which has undesirable effects in subsequent stages of the process. Mixed oxides containing up to about 40 pct Pu in solid solution with UO, are soluble in nitric acid and a leaching type process in nitric acid for a stainless steel/UO,. PuO, fuel containing 30 pct Pu appears to be feasible. It offers considerable economic advantages THE reprocessing of the U-Cr alloy core of the Dounreay Fast Reactor was described by Buck and others at the Second Geneva conference.' This paper described the flowsheet and plant for processing a relatively simple fuel of good dissolution charac- over total dissolution routes. A new oxidation-sub -limation process is described for metallic fuels containing up to 12 pct Mo. New data is presented on the solvent extraction of uranium and plutonium nitrates into tributyl phosphate -odorless kerosene and of the influence of radiolytically produced acid phosphates on this part of the process. It is concluded that there are no insuperable difficulties which will prevent the satisfactory reprocessing of high burn-up plutonium fuels by a solvent extraction route. teristics and of low-plutonium content after irradiation. However, it has been clear for some time that more satisfactory operation of the reactor can be obtained by the use of a core with better irradiation performance than U-Cr alloy and a U-Mo alloy will be used for the next charge. Recent modifications to the core mean that it is now possible to carry out irradiations of fuel element subassemblies similar to those which might be used in a fast power reactor and trials with plutonium-bearing fuel elements will be made in the relatively near future. These changes have meant that a considerable amount of reprocessing development work has had to be carried out for

Jan 1, 1963

By Edgar C. Bain

Of the important phenomenon of the hardening of steel, Professor Sauveurl says: It would seem as if the methods used to date for the elucidation of this complex problem have yielded all they are capable of yielding and that further straining of these methods will only serve to confuse the issue, the point having been reached when this juggling, no matter how skilfully done, with allotropy, solid solutions, and strains is causing weariness without advancing the solution of the problem. The tendency of late has been to abandon the safer road of experimental facts and to enter the maze of excessive speculations, in which there is great danger of some becoming hopelessly lost. The conclusion seems warranted that new avenues of approach must be found if we are to obtain a correct answer to this apparent enigma. With some degree of fitness we may say this of other problems. It seems likely that one of the new avenues of approach to many metallo-graphic problems is the study of crystal structure, or more accurately, the atomic arrangement, by means of the x-ray spectrometer. The crystal structure of some materials has been carefully worked out by the mineralogist, but his methods are, in general, unsuited to commercial metals and a method that yields even better information is at hand as the result of work on the diffraction of x-rays by Laue and the Braggs2 and later by HullI3 St. John, and others. It should be understood that the contour of free crystals, which is the subject of measurements by the crystallographer, is the result of the atomic structure and, in general, bears a simple and obvious relation to it. The use of the x-ray spectrometer4 has been described frequently, so the procedure will not be given here.

Jan 1, 1923

By Edgar C. Bain

Of the important phenomenon of the hardening of steel, Professor Sauveurl says: It would seem as if the methods used to date for the elucidation of this complex problem have yielded all they are capable of yielding and that further straining of these methods will only serve to confuse the issue, the point having been reached when this juggling, no matter how skilfully done, with allotropy, solid solutions, and strains is causing weariness without advancing the solution of the problem. The tendency of late has been to abandon the safer road of experimental facts and to enter the maze of excessive speculations, in which there is great danger of some becoming hopelessly lost. The conclusion seems warranted that new avenues of approach must be found if we are to obtain a correct answer to this apparent enigma. With some degree of fitness we may say this of other problems. It seems likely that one of the new avenues of approach to many metallo-graphic problems is the study of crystal structure, or more accurately, the atomic arrangement, by means of the x-ray spectrometer. The crystal structure of some materials has been carefully worked out by the mineralogist, but his methods are, in general, unsuited to commercial metals and a method that yields even better information is at hand as the result of work on the diffraction of x-rays by Laue and the Braggs2 and later by HullI3 St. John, and others. It should be understood that the contour of free crystals, which is the subject of measurements by the crystallographer, is the result of the atomic structure and, in general, bears a simple and obvious relation to it. The use of the x-ray spectrometer4 has been described frequently, so the procedure will not be given here.

Jan 1, 1923

By David Cornell, D. L. Katz

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

Jan 1, 1953