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By David B. Morris, Paul I. Eimon

Computer-assisted data storage and retrieval in the geosciences is coming of age. A growing awareness of the need of the geological and mining community for effective access to existing data has triggered studies and development programs on many levels; governments, professional societies, industrial concerns, and the academic world are all active in this field. Developments in the past decade in computer hardware and software lend hope to the geoscientist searching for a means of expediting the flow of data. The new concern of the earth sciences coming together with the blossoming child of technology, computing, has led to serious study of the geoscience information problem. Active system development is under way in several areas. The papers presented at this Symposium effectively sample the spectrum of present day activity in machine-based geologic data storage and retrieval. These papers show the reader where the action is in this field today. Both long-range studies and plans and operational systems are discussed. Several studies and research efforts have been undertaken on a national or international scale. Robinson discusses the activity of the international geological community in these Proceedings. He speaks from a position of authority as Chairman of the International Union of Geological Sciences' Committee on Storage, Automatic Processing and Retrieval of Geological Data. A study of a "coordinated information program for geological scientists in the United States" documented by Smith, et al.1 proposes a "long-range information program ... responsive to the entire geosciences community . . . (to) draw on the best of large-scale information systems technology." The European geologic community is embarked on project Geosemantica 70, started at the Ecole Nationale Superieure des Mines de Paris. Dixon discusses some results of this work in a following paper. The Canadian study of geological data storage and retrieval on a national scale is reported in a volume edited by Brisbin and Ediger.2 The Canadian report presents detailed recommendations for recording and coding geologic data for automatic process-

Jan 1, 1969

By Pierre Filiatreault, Brian Straight, Stephanie Thibeault, Devin Castendyk, Londie Cameron

"Working on or near water at active, closed or abandoned mine sites is inherently dangerous. Between 1996 and 1999, the U.S. Mine Safety and Health Administration (MSHA) reported 17 fatalities involving drowning at U.S. metal, non metal and coal mines (MSHA, 2000). Openpit mines which fill with water following mine closure, called pit lakes, present numerous risks to environmental monitoring teams including: a) drowning, b) hypothermia, c) falls to the ground from the top of high walls, d) collapse of unstable access roads, e) rock falls and avalanches from pit walls, f) avalanchegenerated tsunamis traveling across the lake surface and g) rapid degassing events.Some pit lakes are simply not safely or easily accessible for ongoing monitoring. However, the routine collection of water samples from the entire water column on a regular basis is needed to monitor the evolution of water quality over time, verify the accuracy of numerical predictions and, ultimately, manage lake water chemistry and ecological risks. For pit lakes with surface water discharge, regular monitoring is used to appropriately design and adjust water treatment plants in order to produce acceptable site discharge water quality.As a product of these risks and the need for water samples, mining companies spend considerable expense on pit lake safety as part of monitoring programs. This includes training personnel for on water duties and hazards, purchasing or hiring specialized equipment and personnel (such as boats, boat operators, personal floatation devices and cold-water clothing called mustang suits), stabilizing pit walls and maintaining safe access roads to the lake surface and employing spotters who can directly communicate with emergency medical services to watch sampling activities because cell phones and radio signals can be blocked by pit walls. Some sites utilize redundancy to prepare for unexpected incidents and accidents. For example, one Canadian mining company requires two boats on the water during pit lake sampling events, with a third boat on the shoreline, gassed and ready to go. In addition, water samplers are required to hold Marine Emergency Duties training to ensure the entire boat crew is sufficient and competent for the safe operation of the vessel in the event of an accident."

Jan 7, 2017

In this paper, a number of novel hypotheses that provide a fresh perspective on the characterization of strata movements associated with longwall mining are developed by analyzing subsidence measurements with an influence- function-based computer program. With this influence-function technique, easily obtained surface displacements can be used to determine some of the complicated, expensive, and difficult to measure movements of the immediate roof strata in a longwall panel. The primary hypothesis developed by this analysis proposes the existence of an area of partial roof caving near the edge of a panel called the "edge effect." A second hypothesis, interrelated with the first, promotes the importance of the effect of gate-entry closure on the observed strata movements. Both the primary edge effect hypothesis and the secondary hypothesis concerning gate-entry closure are justified and quantified in an extensive analysis of surface subsidence that uses supporting information from related theories, design criteria and insitu measurements. Next, the edge effect and the gate closure hypotheses are extended further and used to provide an explanation of the complex subsidence interaction of adjacent longwall panels in what is termed a "redisturbed" effect. Finally, in the conclusions of this paper, the importance of accurately understanding these longwall strata movements for proper subsidence prediction or gate design is stressed.

Jan 1, 1986

By Charles L. Kimbell

In overall aggregate, the world's mineral industry in 1987 experienced a more satisfactory year than in 1986, at least insofar as its performance could be assessed from traditional statistical indicators. Production, trade and consumption seemingly advanced in the case of the majority of commodities, and prices for a number of commodities advanced. It was by no means certain, however, whether 1987 investment in mineral industry ventures would top the levels of 1986, when, in the case of petroleum industry investment expenditures there had been a sharp decline, this in contrast to evidences of a slight upturn in steel industry investment. World crude mineral output value was estimated at more than $1,084 billion, and the value added by minerals industry processing of this material probably raised the total value of the industry's production from primary materials to more than $2,600 billion constant 1983 dollars. Less easy too assess was the value of mineral commodities moving in international trade, but with a resurgence in oil prices from the 1986 levels, an increase above the 1986 $500 billion mark seemed assured. There are no comprehensive aggregate statistics on mineral consumption comparable to those on production and trade, but quantitative growth recorded for most major commodities suggested a favorable trend, particularly when coupled with a general (though by no means universal) upturn in unit prices.

Jan 1, 1989

E. W. King, Bozeman, Mont.: The form of measuring up ore in sight looks very plausible, as illustrated in the paper of Mr. Emmons, but from my experience of many years of mining in Montana and Nevada, I have found it is very hard to measure up anything nearer than a guess of what you have in sight, except in the case of a true vein, or a flat vein where the boundaries are well defined. I have been interested in several miues with Dr. A. R. Ledoux, and I know that my foreman and myself, going into the mines and using our best judgment, could seldom see more than 30 days' supply actually in sight, and yet we were running from 100 to 250 tons a day, and keeping it up year after year. Prof. John D. Irving, New Haven, Conn.: I understand from Mr. Emmons that this is a method which has been found applicable in the copper-mines in Tennessee, where the record could be made with a good deal of accuracy, and where the work in the mines allowed the necessary development to be done, so that the record could be kept up. I do not think there was any intention in his mind to imply that this was applicable to all cases, especially such as Mr. King has mentioned. President Charles Kirchhoff, New York, N. Y. : I think the point is that the paper impresses the necessity for doing it where the possibilities exist. There has been too little attention given to this very matter, particularly in the United States; but I think our English friends are following it very much more zealously, and the demand for it there is possibly greater than it is here, because English boards of directors handle mines that are often very much further away than our own are, and the English public and the English engineers generally are very much more insistent upon seeing how much longer current dividends are going to last, or current assessments are going to continue.

Jan 1, 1913

By R. C. Allen, Ralph Arnold

The writers have no new system and no new principle of taxation to propose. The general subject of taxation is as old as governments are and as familiar to taxpaying Americans as the general thesis on the inalienable rights of man. We believe, therefore, following the committee of the National Tax Association, that improvement in the general conditions of taxation, including mine taxation, maybe brought about mainly through a better adjustment of known and tried principles and methods of taxing to modern complex forms of property and income, and that not much is to be expected from abandonment of experience for new ways and means, methods and principles, should anything new be discovered, which in our opinion is very doubtful. The committee referred to has constructed the general framework of its Model System of State and Local Taxation1 on familiar forms of taxing, by eliminating some that ' have proved bad, suggesting improvements in others, and adopting the best, leaving plenty of room for the accommodation of the general plan to the varying conditions of taxation in the several states. Unfortunately, the taxation of mines is dismissed by the committee with the statement that the subject has been reassigned for further investigation and report by a special sub-committee, frankly recognizing that the peculiar difficulties of this phase of the subject require special study and investigation. Much may be hoped for from the labor of this sub-committee if the problem is approached from the viewpoint of recommendations already published. In this paper, the writers state their opinion on some of the broader aspects of mine taxation with too little attention to the grounds on which they rest. Contrary to inclination space requirements compel them to resort to summary statements without adequate discussion for a satisfactory presentation of the whole subject. All they can do is to qualify the witnesses and record the testimony. The senior writer was introduced to the practical aspects of the subject of this paper in 1913, when, as State Geologist of Michigan, he was

Jan 1, 1920

By P. Lauzon, C. Oprea, S. Zhou, G. Oprea, J. Rigby, T. Troczynski

Hydration of basic refractories could occur during storage, drying after installation or in use. In order to assess the hydration resistance of various commercially available magnesia-chrome bricks, hydration tests were performed in steam at 110, 120, 130 and 150°C. The changes of the modulus of elasticity by the impulse excitation method, apparent porosity, air permeability, average pore size and pore size distribution were correlated with the hydration data. Mineralogical and microstructural changes were also studied on selected specimens by XRD and SEM/EDS. The hydration mechanisms were discussed in correlation with the chemical and mineralogical compositions of the experimental bricks, in particular with the nature of the mineralogical phases at the grain boundaries.

Jan 1, 2004

By M. E. Hawkins

This Bureau of Mines report provides information on all of the 329 proved salt domes in the Gulf Coastal States and offshore area of the United States. It includes specific data related to location, depth to the cap rock and to the salt, storage facilities for LPG, and production of salt, sulfur, petroleum, and rock related to or associated with the dome structure in the subject area. Also included is a brief history of the salt, sulfur, and petroleum industries as related to the salt domes. Gulf Coast salt domes were the scene of the first discovery of a large deposit of rock salt in North America, the birthplace of the Frasch sulfur industry, and the location of the first large oil gushers that ushered in the modern liquid fuel age.

Jan 1, 1966

By Bruce W. Gonser, Robert J. Nekervis

EACH metal has a unique combination of properties that distinguishes it from other metal;. Su& a combination may account for applications that cannot be met very well by anything else. This is particularly true of tin, one of the earliest metals used by man. Table i shows the consumption of tin in the United States by usage for the years 1949 and 1950, which may be considered to be generally typical of current usage. The major applications-tinplate, solders, bronze, and babbitt-were well established a century ago. Applications for the metal and (probably later) of tin alloys started more than 5000 years ago. Fortunately for the ancients, tin is one of the metals whose oxide is easily reduced by carbon. Nature further simplified the refining problem by providing only one ore of commercial importance, cassiterite (SnO2). Tin is easily reduced from cassiterite. All that is necessary is high heat in the presence of carbon. It is quite possible that back in the dawn of history, tin was discovered when black alluvial sand was thrown on a fire, either to bank it or to put it out. SOURCES OF TIN All the important tin-producing centers are in the southern hemisphere, far away from the' industrial consuming centers. Fig 1 shows their location and 1950 production. Reserves are adequate, and the industry is able to produce considerably more tin than is

Jan 1, 1953

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the length of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel per day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel per day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from the commonly understood barrel per day value, in that the conditions surrounding the sale of one lease or property at a fair market value may

Jan 1, 1922

By Claude Cunningham

The primary reason for blasting is to fragment rock. In production blasting, the fragment sizes produced are known to exercise an overwhelming influence over working costs: handling costs and tonnage throughput are directly affected by secondary breaking, loading and crushing, all functions of fragmentation. In addition, particular size fractions are frequently of intense interest in terms of market or process requirements.

Jan 1, 1995

By R. J. Sweigard

Three case studies were undertaken to investigate the role of land use potential evaluation in reclamation planning and to determine the impact of regional differences on the evaluation process. The three surface mines studied were representative of operations in the Appalachian, Interior, and Northern Great Plains provinces. The scope of the investigations included a survey of regional characteristics, a detailed investigation of the mining operations and site conditions, and an assessment of local land use planning activities in the area of the mine. Special attention was given to key factors that presently determine the use of reclaimed land. Also, for each case study, the postmining land use potential was evaluated using site planning principles. Specifically, the environmental, economic, and social impacts of several potential postmining land use plans were considered.

Jan 1, 1983

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the lengt of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel-per-day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel-per-day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable-yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from she commonly understood barrel-per-day value, in that the conditions turrounding the sale of one lease or property at a fair market value may

Jan 1, 1923

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the lengt of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel-per-day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel-per-day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable-yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from she commonly understood barrel-per-day value, in that the conditions turrounding the sale of one lease or property at a fair market value may

Jan 1, 1923

By Robert Hoy

If the reader finds that the basic information in a commodity chapter is insufficient, he can consult the appropriate sources in this chapter to find more detailed or more up-to-date information. In these days, technology develops so rapidly that this 4th edition will be somewhat out of date even by the time it is distributed. A comparison of this edition with the 3rd edition (1960) of Industrial Minerals and Rocks will clearly demonstrate how rapidly the scene changes. One of the best sources of new information, of course, is attendance at technical meetings. For example, the papers presented at the national and sectional meetings of AIME usually discuss new developments in the respective divisions of the society. Frequently this information is available in Preprints. In addition some are printed in Mining Engineering and/or the Transactions of the Society of Mining Engineers of AIME. Furthermore, other professional and trade journals contain articles pertinent to the field. A journal introduced in 1967, Industrial Minerals, published by the Metal Bulletin, Ltd., London, is an excellent source of information. The Mining Journal, Ltd., also in London, publishes a weekly journal, a Mining Magazine (monthly), and a Mining Annual Re- view. The latter covers the field from three aspects: (1) by commodities, (2) through technical developments, and (3) geographically. Other useful magazines and periodicals include Engineering and Mining Journal, Pit and Quarry, Rock Products, and World Mining, all published in the United States. In addition many new books related to industrial minerals have been published since the 3rd edition of Industrial Minerals and Rocks. Most of these, of course, are included in the bibliography of each chapter in this volume. Another excellent information source is the proceedings of the Forum on Geology of Industrial Minerals. This group, which held its 11th annual meeting in 1975, is sponsored by a state geological survey or another mineral agency on a rotational basis. The proceedings have been published by the various sponsors and are available as indicated in Table 1. Two major sources of basic industrial mineral and rock data in the United States, and also a good source for many foreign countries, are the U.S. Geological Survey and the U.S. Bureau of Mines. The two agencies publish many reports and maps on a variety of geo- logical and mining subjects. In addition, each agency has an indexed list of all their publications with a free service announcing new publications. (New Publications of the Geological Survey, U.S. Geological Survey, Washington, D.C. 20242) and New Publications-Bureau of Mines, Publications Distribution Branch, U.S. Bureau of Mines, 4800 Forbes Ave., Pittsburgh, Pa. 15213). The U.S. Bureau of Mines (USBM) publishes annually Minerals Yearbooks which provide statistical data on mineral products including production, consumption, imports and exports, as well as information on new developments. Another very useful USBM series is called Mineral Facts and Problems. Editions were published in 1960, 1965, and 1970. Three other major series of publications by the Bureau are Information Circulars, Reports of Investigations, and Mineral Trade Notes. The latter is particularly good for news of foreign developments. A new Professional Paper No. 820 of the U.S. Geological Survey, 1973, summarizes data on the mineral resources of the entire country. The USGS, in cooperation with USBM, other Federal and various state agencies, has also prepared summary reports on mineral and water resources of given areas which include

Jan 1, 1975

By E. A. Gulbransen, W. S. Wysong

The behavior of molybdenum and its surface oxides in oxidizing and reducing gas atmospheres and in high vacua at elevated temperatures is a question of scientific and technical importance. The use of molybdenum as a metal or as an important component in alloys in oxidizing atmospheres at elevated temperatures has been limited because of the unprotec-tive nature of its oxide film and the volatility of this oxide at moderate temperatures. This communication will present results of a vacuum microbalance studyl, 2 of the following problems: (I) the oxidation kinetics in the temperature range of 250°to 450°C; (2) the reduction with pure hydrogen of thin oxide films formed on molybdenum; (3) the volatility of the thin oxide films; and (4) the vacuum oxidation of molybdenum at high temperatures. Molybdenum is an interesting metal to study for the following reasons: (I) although the oxide-to-metal-volume ratio is greater than one, the metal is not considered protective; (2) the metal oxidizes readily at temperatures of 2 50°C and higher; (3) the oxides of the metal are reduced at temperatures as low as 500°C by pure hydrogen; (4) the oxide Moo3 melts at 795°C; and (5) the oxides of molybdenum are volatile at moderate temperatures. The following variables are studied in the oxidation kinetics: time, temperature, pressure, surface preparation, surface area, concentration of inert gas in the lattice, cycling procedures in temperature, vacuum effect and high temperature vacuum oxidation. The general interpretation of many of these factors has been previously discussed. Literature The oxidation of molybdenum has not been studied critically. Although many studies have probably been made on the kinetics of the oxidation process, none has been reported in the literature available to us. The crystal structures found in the oxidation of molybdenum have been studied by Hickman and Gulbransen." Their results showed that Moo2 is the oxide which is stable in contact with the metallic substrate throughout the temperature range 300 to 700°C. As the film thickens in the low temperature range, MoO3 becomes predominant on the surface. Above 400°C, Moos is no longer observed, MoO2 being the only oxide found. Hagg and Magneli6 have shown from an X ray study that the a-phase, orthor-hombic Moo3 is stable up to 1050°C. Two other phases, ß and ß with compositions close to MoO2.90 are also obtained. The formula for the 0 phase is not given but that of the ß phase is defined as Mo9O26 The 0' phase is found to be built upon a monoclinic unit cell. A ?-phase is isolated from a preparation MoO2.75 heated for 17 hrs at 670°C. This phase is

Jan 1, 1949

By P. T. Kane, O&apos

Capital and energy are the dominant cost factors in nickel production from laterites. Since the 1973 energy crisis, pyrometallurgical developments have been oriented towards lower cost sources of energy and higher grade ores and hydrometallurgy towards higher recoveries and greater flexibility in types of ores treated. Energy recuperation offers some potential, but at a price. 'The lower energy acid leaching process is indicated to have the greatest potential, particularly with its inherently high cobalt recovery.

Jan 1, 1979

By Jean-Paul Drolet

"The ultimate aim of the Law of the Sea Conference, held under the auspices of the United Nations, is to ensure that all aspects of the use of the sea are covered by international law. The question facing the nations of the world can be stated as: "" Who will control and benefit from the use and the wealth of the sea?""The United Nations Conference on Law of the Sea - known as UNCLOS - which reconvened in New York during the latter part of August 1978 was the third such Conference in the UN's history. The concepts of sovereignty over the territorial sea and freedom on the high seas have remained fundamental to the international law o f the sea until our time. The legal regime based on these two concepts developed initially from state practice meant that the unilateral actions taken by one or more countries were eventually accepted and followed by others.It was not until 1958, during the first Geneva Conference on the Law of the Sea (pursued in a second Conference in 1960) that the Law of the Sea was codified and modified to a certain extent by the then independent nations of the world in the four multilateral conventions on territorial sea and contiguous zone, continental shelf, high seas, and fishing and conservation of living resources.A third Conference got under way many years later when the members of the UN met in New York at the end of 1973 for preliminary discussions . This meeting stemmed largely from the need to fill gaps in existing international legislation which did not cover the new uses of the sea. The Conference was subsequently reconvened a number of times - in Caracas (1974), in Geneva (1975) and twice in New York (1976) for what was called "" substantive negotiating sessions."" A sixth session was held in New York in 1977; a seventh, held in Geneva at the beginning of 1978, recessed and reconvened in New York at the end of August 1978. This is what is referred to, in international jargon, as the seventh session of the Third United Nations Conference on the Law o f the Sea. The following dates are the principal markers of a saga which began some twenty years ago with the purpose of regulating the use of the oceans."

Jan 1, 1981

By Philip M. McKenna

WHEN a new material becomes available to industry, it is useful to describe its properties as a guide to its most effective application; and when the new material may be produced in compositions having a series of graded properties, tests to select the combination of properties best adapted for various uses are helpful. The class of materials to be considered in this paper are hard tool materials produced by processes of powder metallurgy from hard carbide constituents and various matrices of iron, nickel or cobalt, or alloys of them with tungsten, or tungsten and carbon. The customary use of carbide hard alloys is for metal-cutting tools; although wire-drawing dies, lathe centers, follow rests, grinding rests, burnishers, rolls, extrusion dies, measuring gauges and micrometers, and a number of other tools are also made with these hard alloys as the essential wear-resisting parts. The properties and tests to be considered are those affecting these uses. In the development of tool materials since the industrial revolution we have had carbon tool steels, Mushet steel, high-speed steels, stellites, and now cemented carbide compositions. For an understanding of the latter category of materials their properties and uses relative to the older and more familiar tool materials will be considered. Hardness has been the property of greatest practical interest in tool materials. The word "hardness" is a generalized term lacking definite¬ness unless the specific test used is described. However, efforts to explain physical properties as a consequence of chemical bond, and distance between atoms in chemical compounds have been illuminating. This seems the most generalized attack on the problem, and is based upon the idea that atoms in a lattice are held together as the square of the valence and inversely as the square of the distance between the atoms. The compounds compared must all be of the same crystalline arrangement. It is interesting to note the values of the figure [V ] a number of

Jan 1, 1938

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953