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By M. R. Tek, K. H. Coats, D. L. Katz

The nature and the limits of validity of Darcy's law US applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the ,8 factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been conridered. In light of the current numerical results the significance and linlitation of the rate of flow function Y proposed by Smith" has been discussed. INTRODUCTION The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments, Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (Dvp/u), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis' reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots.' The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer." The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. Some fluid dynamicists define turbulence as a flow

By Andrew S. M’Creath

THE treatment which a steel receives, and the uses to which it may be applied, are frequently determined by the percentage of carbon which it contains; and especially is this the case in the different steel works in this country. The part which this element plays in the composition of steel is such an important one that a process for its accurate determination becomes an absolute necessity.

Jan 1, 1877

By Thomas J. O’Neil

Once again, the United States Congress is debating the minerals depletion allowance. If the past is any indication, the debate will quickly become politicized. Representatives of the densely populated but mineral-poor Northeast will no doubt claim that percentage depletion is sheer robbery of tax dollars perpetrated by corporations to line the pockets of wealthy investors. Many southern and western legislators, on the other hand, will portray the depletion allowance as our only savior from mineral deprivation, blackmail from foreign producers, and a stone-age nonmineral existence. Although this characterization of the usual minerals depletion debate may be overstated, the most unfortunate aspect is that the genuinely important role of the depletion allowance in domestic minerals production is often obscured in congressional hearings. This article will try to provide a basic understanding of the minerals depletion allowance, the underlying rationale, and the increasingly important role the allowance will play in the future. Although the discussions and conclusions can be extended to the metal mining industry in general, most of the examples are drawn from the copper industry.

Jan 10, 1974

By P. P. Gregory

NATURAL petroleum gas occurring in the oil-bearing reservoirs is found to exist either as free gas associated with the oil and/or in solution in the oil. In some virgin fields practically no free gas is encountered under the reservoir conditions of pressure and temperature, although in other fields a considerable section of the ``pay" horizon is occupied by free gas. In other words, a given oil field may or may not have a gas cap before the exploitation takes place. However, when the reservoir pressure is reduced to a point below the critical saturation pressure by withdrawals of fluids from the producing formation, the gas dissolved in the oil inevitably begins to come out of solution and becomes free gas. Under the con-trolled methods of production and drilling, a portion of this gas is pro-duced with the oil to the surface and a portion of it remains within the reservoir to accumulate at higher structural levels toward which it migrates by virtue of its low specific gravity. The rate of growth of a gas cap in a-given structure depends primarily upon the rate of decline in the reservoir pressure. If the rate of pressure decline is rapid, the gas cap likewise will grog rapidly. On the other hand, shrinkage in the gas-cap area was noted in some fields in which reservoir pressures were increasing.

Jan 1, 1938

By William Garrett

I have heard it said that the late Mr. Holley made use of this remark: " There is an inherent, cussedness about rolls which, so far, no man has been able to find out." I think this can be safely claimed in reference to steel, as there are certain peculiarities about it that are pretty hard to account for. Previous to the introduction of the Bessemer process there was, as it were, a great chasm between iron and crucible steel; and, outside of what futile attempts had been made in puddling steel, nothing had been done to fill this gap. The Bessemer steel struck a medium between the two, the softest of it not being able to take the place of good iron, while the hardest was not suitable to encroach very far upon the crucible-steel trade. The open-hearth process made quite an inroad into the latter, but only for the lower and cheaper grades; and, beyond a doubt, for the finest grades of tool-steel, the cruciblesteel business has a long life before it. On the other side of the line comes the " basic " process, which brings us a step nearer iron ; but to fill up the gap completely, comes the Clapp-Griffiths process, which makes a grade of material—call it what you will—that is as soft as iron, welds as readily, and is in a fair way to supersede iron altogether. For fifteen years, I was in the employment of the Cleveland

Jan 1, 1886

Jan 1, 1892

By W. F. Stowasser

A downdraft traveling grate process to agglomerate pelletized iron ore concentrates has been successfully demonstrated in a pilot plant at Carrollville, Wis. Work there followed several years of development in the Allis-Chalmers Mfg. Co. laboratories, and the pilot plant phase was carried out in co-operation with Arthur G. McKee & Co., consultants and engineers to the iron and steel industry. End result of the process is conversion of iron ore concentrates into a form which can easily be transported and smelted in the blast furnace.

Jan 5, 1955

By E. C. Harder

HERBERT K. SCOTT, London, England (communication to the Secretary*).-I am acquainted with the manganese-ore deposits of Russia, India and Brazil, and agree generally with the statements contained in the paper regarding those deposits. The information given by Mr. Harder regarding the Chilean deposits is very welcome. When examining the Caucasian deposits, I endeavored to determine the quantity of ore originally contained in the deposit, and by deduction, the amount remaining for extraction. These calculations were rendered possible by the great extent of the outcrop and the extensive work that had been carried on in the deposit. In making the first estimate, the quantity of manganese ore and associated sterile material in the bed was measured in a large number of

Jan 12, 1916

By W. R. Ingalls

SOME months ago, I had occasion to make an investigation that introduced the subject of blue powder that is produced as a byproduct in zinc dis-tillation. Although every zinc smelter is aware that more or less blue powder production is inevitable and there is a common practice as regards the treatment of it, the specific and quantitative data respecting the subject were more imperfect than would have been expected. I had reports from eight important works. Some of the data were especially determined for my investigation. Speaking generally, there is a good deal of uniformity in the figures, all of which show that the blue powder product, bears a large proportion to the ore originally charged into the retorts; that a large proportion of the retort capacity is devoted to the redistillation of blue powder; and that of the spelter product of a furnace about 30 per cent. is derived from blue powder, i.e., it is zinc that has been distilled twice. The figures from the works are given in the following table:

Jan 4, 1922

By H. A. Doerner

METALLURGICAL problems relating to manganese and chromium ores have striking similarities. Ferroalloys, essential to the steel industry, are produced from both ores. Most of these alloys are obtained from imported ores, as domestic deposits have not yielded enough ore of metallurgical grade to meet more than a small fraction of vital needs. A survey of domestic manganese and chrome de- posits reveals numerous small, dispersed bodies of fairly good ore, none of which appears to be capable of yielding significant amounts of marketable products. To stimulate development of such deposits and to increase Government stockpiles, General Services Administration is offering $115 per long ton for limited amounts of chrome ores and $110 per long ton for 48 pct manganese ores that meet metallurgical specifications, with bonuses or penalties for grades above and below specifications.

Jan 4, 1953

By D. Ott

Results of a research project on investment or lost wax casting will be presented. The project was concerned with various aspects of the process as they are typical for the production of jewellery from gold alloys. During these investigations testing methods for investment quality as well as for casting quality and the various process parameters were developed and charateristic defects as they occur in practice were traced back to their origin in the process. Investigated were various static casting and centrifugal casting methods in different atmospheres as well as vacuum casting in devices of different design. It was shown that independent of the method a close control of the many process parameters interfering with each other is essential for a quality casting.

Jan 1, 1984

By D. Hugh Trollope, L. A. Fekete

L.A. Fekete (Project Engineer, Johnson B & Assoc. Engineers, Houston.) - The author tries to classify rock slopes in: a) homogeneous monolith, b) random, c) block-jointed systems. This may be practical at a specific mine, but it does not describe the mechanical behavior of the slopes in general. The difficulty with the problems of earth mechanics is the same, as with other structural problems: To

Jan 1, 1963

Jan 1, 1941

By W. A. Bruce

THIS paper presents the essentials of a mathematical method of studying the pressure behavior of an oil reservoir as the fluids are withdrawn. Methods are shown whereby the behavior of a reservoir can be used to predict the future relationship between withdrawals and pressure. The oil reservoir is considered as a small part of a large porous continuum, which contains for the most part water. The expansion of this water resulting from a decrease of pressure in the oil zone causes a movement of water that is an important factor in the relationship between fluid withdrawals and reservoir pressure. Examples are given to illustrate the methods of pressure prediction for a circular reservoir containing undersaturated crude, the pressure distribution over a field that has a uniform production rate, the effect of a fault line near a field, the mutual interference of near-by fields, and the perturbing influence of a gas cap. Applications of the analysis to sell-spacing problems are shown.

Jan 1, 1942

By AIME AIME

AT the annual .meeting of the Minnesota Section in December, Dr. Leith characterized as a question still open the exact method of origin of Lake Superior iron ores and emphasized it as an important practical problem for the future. He welcomed the step taken last year by Dr. Gruner in presenting a new hypothesis, and asked Lake Superior geologists to meet the challenge of such multiple hypotheses by unbiased, study.

Jan 1, 1932

Jan 1, 1941

[RALPH ADAIR Ore Dressing Consultant Bull Mtn. Rd., Asheville, N. C. Phone 4-1693 JAMES A. BARR Consulting Engineer Mt. Pleasant, Tennessee Washington, D.C. BEHRE DOLBEAR & COMPANY Consulting Mining Engineers and Geologists 11 Broadway New York 4. N. Y. I. R. BERENT Engineering Consultants and Contractors Mineral Exploration, Mine Evaluation, Mine Designs and Mine Management 156, Ataturk Bulvarl-Ankara, Turkey BLANDFORD C. BURGESS Registered Professional Engineer Mining Consultant Monticello, Georgia GLENVILLE A. COLLINS Mining Engineer Uranium examinations Cable "Coins" 210 La Arcade Bids. Santa Barbara, Calif.]

Jan 1, 1952

By William J. Millard

The Island of Trinidad has much the same geological history as the continent of South America. There are present in this area Cretaceous, Tertiary and Quaternary rocks, which were deposited in a basin covering eastern Venezuela and Trinidad, very much as rocks of the same age were deposited in the Maracaibo Basin in western Venezuela. Along the north coast there are metamorphosed and semimetamorphosed Cretaceous rocks which are found as semicrystalline limestone, schists and quartzites, etc. Both the Cretaceous and Tertiary rocks are petroliferous and are responsible for the production of oil in Trinidad and eastern Venezuela. The geological column in the oil-bearing region of Trinidad is shown below.

Jan 1, 1931

By Sir Robert Hadfield

I am asked to contribute a few words to "The Book of British and American Friendship." This book of the two countries ought never to have been closed. It was a colossal mistake on the part of certain of our statesmen in the past which led to the severing of the interests of the two countries which, by the greatest of all bonds-Nature-were meant to be one. However, that is past, and a new book is opened, one full of promise for the world's future. I should imagine that outside the Kaiser-Junker classes, even the Hun himself would prefer to be under Anglo-Saxon laws and customs rather than his own. At any rate, judging from the number of Huns who have

Jan 8, 1918

On April 17, the John Fritz Medal, the award of which the presiding officer, Col. John J. Carty, characterized as "the highest honor which can be conferred on an engineer in America," was presented to. J. Waldo Smith "for his most distinguished services in civil engineering, and particularly in connection with the work on the great aqueduct, which has just been completed." Col. Carty spoke very briefly of the origin of the Medal and the method of awarding it, mentioning the names of the twelve men to whom it has been awarded in former years, and then introduced Mr. Nelson P. Lewis, Vice-president of the American Society of Civil Engineers, and for many years Chief Engineer of the Board of Estimate of the City of New York, who is an old colleague and fellow-engineer of Mr. Smith. Mr. Lewis said, in part: Mr. Smith is so well known that an extended review of his professional activities will be unnecessary, but a brief outline of the development of a conspicuously successful hydraulic engineer may not be out of place. It would be difficult to find a better instance of the success which is quite sure to result from persistent devotion to all phases of a particular line of engineering work. It began in his boyhood, when, as a lad of 15, he eagerly availed himself of such opportunities as were afforded to help in the construction of a waterworks system for his home town in New England. It was a very modest plant, consisting of a small reservoir and pumping station, and about 4 miles of pipe. Probably it was the most important improvement the town

Jan 7, 1918