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By AIME AIME

THE non-ferrous 'metals industry of the Soviet Union found itself in a very low position at the beginning of the reconstruction period in 1922, due to the absence of modern smelters and the run-down condition of the existing ones. Up to. 1924 there was no great demand for newly smelted non-ferrous metals due to the considerable stocks' of copper, zinc, lead, tin and aluminum in the courtry and also to the undeveloped condition of Soviet industries. However, in 1925 it became necessary to obtain new stocks of non-ferrous metals and in that year 12,000 tons of zinc, 14,000 tons of lead and 2,000 tons of tin and aluminum were imported into the U. S. S. R.

Jan 1, 1929

By J. D. Livingston

THE hardening of alloys by the precipitation of a second phase has long been an important technological process. One approach towards improving our understanding of this phenomenon has been a correlation of mechanical properties with such parameters as particle size and inter par ticle spacing.' Several reviews of such data have appeared.2-4 A major limitation to this approach has been that for most alloys the particles are submicroscopic in size in the range of optimum hardness. Precipitation-hardening copper-cobalt alloys, therefore, are of interest, because the ferromagnetic properties of the precipitate make it possible to measure particle size, number of particles, and so forth, from magnetic measurements alone.5, 6 Livingston and Becker7 have applied these techniques to a study of precipitation hardening in an alloy of 2 pct Co in copper. It was found from magnetic measurements that nearly all the cobalt to be precipitated was out of solution within a few minutes at 600°C, whereas the peak in tensile yield stress was not attained until a much longer aging time. Thus during the first 1000 min of aging time at 600°C the Yield stress was increasing while a constant volume of precipitate was coarsening, i.e., while particle size and interparticle spacing were increasing. Peak yield stress was reached at an average particle radius of about 70A. The earlier study was confined to one alloy at one aging temperature, so that the volume fraction of precipitate was fixed and, therefore, particle size and interparticle spacing could not be independently varied. The work has now been extended to several alloys of varying percentage cobalt in copper, and to aging at various temperatures. It was hoped that such a study might clarify the relative importance to precipitation hardening of particle size, interparticle spacing, and volume fraction of precipitate. EXPERIMENT The alloys studied contained 0.7, 1.3, 2.0, and 3.2 wt pct Co in copper. They were prepared from electrolytic copper and electrolytic cobalt in a vacuum -induction furnace, worked to 3/8-in.-diam rod, and machined into tensile specimens with a gage section 1 1/2 in. long and 3/16 in. in diam. All specimens were given a solution treatment consisting of a 30-min anneal in nitrogen at 1000° C followed by a quench into iced brine. Subsequent aging was done in nitrogen and followed by a water quench. Average grain diameter was approximately 0.01 in.

Jan 1, 1960

By C. R. Breck

THERE has been a running discussion over the past several years with respect to the life and adequacy of our natural gas reserves. Some of the experts agree on one phase of the subject at least-that eventually it will be necessary to augment deliveries of natural gas in the northern markets by the development of a more or less comparable synthetic gas made from coal. The purpose of this paper is to point out: 1. It may be later than a good many people think-the demand for addi¬tional domestic and commercial pipeline gas in at least one section of the North will probably be felt rather keenly before an adequate synthetic pipe¬line-gas project, developed on economic lines, could be completed, even if initiated in the near future. 2. The evidence is considerable that such a project would be technically sound and economically self-supporting, although the margin of profit at first might be so small and the magnitude of an economic enterprise so great -that financing would be impossible without Government aid in some form or other. The part of the country referred to is the heavily populated section in the northeast of the United States. To simplify an examination of the situa¬tion, let us take the potential marketing areas within range to the north and east of the three pipelines: 1. Tennessee Gas Transmission Co. as it enters Erie County, New York state. 2. Texas Eastern Transmission Corporation just before the tap that sup¬plies the general Philadelphia area. 3. Transcontinental Gas Pipe Line Corporation as it enters the state of New Jersey. The sources of gas for these three pipelines are in Texas and Louisiana. The ultimate maximum combined capacity of the three lines at the points stated is approximately 1,200,000,000 cu ft per 24 hr at the maximum load factor probable of attainment in normal operation. The areas supplied by the three lines north and east of the points stated, or assumed as eventual markets, are: 1. Central New York state, from Buffalo to Albany (both inclusive).

Jan 1, 1953

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Feb. 10 to Mar. 10, 1915: W. R. Van Liew, Batoum, Russia. Edward S. Jones, Scranton, Pa. Olof Wenstrom, Boston, Mass. Scott Turner, Tromso, Norway. D. G. Miller, Denver, Colo. A. H. Boyd, Denver, Colo. E. E. Olcott, New York, N. Y. M. M. Thompson, Morsemere, N. J. Francis R. Pyne, Elizabeth, N. J. F. C. Merry, Brooklyn, N. Y. Charles W. Goodale, Butte, Mont. Charles A. Filteau has been appointed General Manager for the Inca Mining & Development Co., Province of Carabaya, Department of Puno, Peru. Charles T. Kruse has been appointed Superintendent of the Jones & r, Loughlin mines in the Marquette and Menominee ranges.

Jan 4, 1915

By Edward Steidle

THAT veterans are crowding the colleges is no longer news; 78 per cent of the 1916-47 enrollment in mineral industries curricula in the United States were veterans, but the rapid comeback from an estimated 1262 total mineral industries students in 1944-45 to 11,422 in 1946-47 is almost astonishing. The figure, which includes 1008 graduate students, is a substantial increase over the previous top record of 9619 in 1938-39. A small part of the increase is caused by the larger number of women entering the field, of whom there were c 9 in 1916-47. Petroleum leads the curricula with 34.5 % of the enrollment, metallurgy is second with 28%, and mining is third with 18%. Table 1. shows all curricula offered and those accredited by ECPD. Using the Mississippi River as a dividing line, 31 colleges in the East and 27 in the West offer curricula in the mineral industries.

Jan 1, 1948

By C. A. Queener, W. L. Mitchell

In recent years bismuth telluride has received considerable attention, primarily due to its value as a thermoelectric material. Since there seems to be little dependence of thermoelectric effect upon crystal orientation1 many of those who have previously worked with this material have been unconcerned with knowing its crystallographic angles to any degree of accuracy. However, when one studies deformation modes, lattice stresses, or the aniso-tropy of mechanical properties of a material, knowledge of the interplanar angles and their relationships as depicted in a stereographic projection becomes essential. Lange2 originally published crystallographic data which described the structure of bismuth telluride as rhombohedral with the space group A more recent work by Francombe3 presented data which corroborated and refined the original findings of Lange. In addition, Francombe established that there is no coexistence of rhombohedral and hexagonal lattices in bismuth telluride as was suggested by Vasenin and Konovalov,4 and that the structure can be treated as a pseu do hexagonal structure with an axial ratio, c/a, of 6.95 for convenience of presentation and study. The interplanar angles and standard projections for several unalloyed hexagonal metals have been previously published,5-9 but the present work appears to be unique in that it presents data for a rhombohedral compound in pseudohexagonal form. As a pseudohexagonal structure, this material has an extremely large axial ratio as compared to the usual range of approximately 1.5 to 1.9 for the hexagonal metals. Since the interplanar angles are a function only of c/a, the angular relations between various planes for Bi,Te3 will be grossly different

Jan 1, 1965

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By AIME AIME

IN accordance with the provisions of Art. XII, See. 3, of the By-laws of the American Institute of Mining and Metallurgical Engineers, the Board of Directors hereby give notice of their intention to amend the By-laws as follows : Art. V, Sec. 2. Amend by substituting the word "senior" for ('first" before the words "Vice-president" in line two of the third paragraph of said section which relates to the calling of special meetings of the Board in the absence or disability of the President.

Jan 1, 1930

By C. W. Hall

Owing to its isolation and comparatively small tonnage, the Yoquivo district is not widely known; though financially important and, geologically, quite interesting. San Francisco dc Yoquivo, the center of the mining district, is in the western part of the state of Chihuahua, Mexico; about 35 miles west of. San Juanito, on the Kansas City, Mexico & Orient R. R. The town can be reached from the railroad by a good trail over a rugged country. The elevation of Yoquivo is 6500 ft., and peaks surrounding the town are 2000 ft. higher. The mining towns of Concheno and Ocampo are 25 miles northwest, and Uruachic is 20 miles southwest. The climate, temperate and healthful, is almost ideal. The rainy season begins in July and ends the latter part of September. There is usually, though not always, some precipitation in all months except April, May, and June: The mountains are covered with pine and scrub oak. Water, wood and lumber are plentiful for all ordinary purposes, and hydroelectric power is available for. about six months of the year, when wood for steam, power is utilized as an expedient. The district has been worked: recurrently for over 60 years. The Yoquivo province lies on the steep western-slope of the Tara-humara division of the Sierra Madre range of mountains. The province is traversed by many deep canyons, most of which flow west. The town is situated on the San Francisco arroyo, which makes a confluence with the Huevachic stream 212 m. southwest; the Huevachic in turn joins the Candemeña river farther down and these two drain the western flank of the Tarahumara mountains and form the headwaters of the Mayo river. The claims of the Yoquivo Development Co., which, is the only organization in the district with a record of any considerable production,: lie within an area roughly 112 m. square. The area extends from the, San Francisco arroyo north, and from the Dolores arroyo west, and is confined to the andesitc formation.

Jan 2, 1926

A list of publications of the United States Bureau of Mines, complete from its establishment to the end of June, 1931, may be had upon request. In addition a monthly leaflet of new publications is issued and is sent to those on the mailing list of the Bureau. Publications are separated into three main divisions: 1. Sales Publications.-Those for which a charge is made. Any orders or remittances in payment for sales publications should be sent directly to the Superintendent of Documents, Government Printing Office, Washington, D. C., and not to the Bureau of Mines. Sales publications are classified into (1) Bulletins, (2) Technical Papers, (3) Economic Papers, (4) statistical reports of the mineral resources of the United States, (5) Monographs, (6) Handbooks, and (7) Schedules. Bulletins and Technical Papers present the results of scientific and technical investigations. Economic Papers are analytical studies of production statistics, sources, resources, .distribution, and industrial flow of mineral commodities. The Annual Report, entitled "Mineral Resources of the United States," includes chapters, published separately, on the production and consumption of metals and of nonmetallic minerals. Monographs give detailed results of extensive cooperative investigations of special

Jan 1, 1933

By d&apos, John C. Entremont

Pure iron was inductively melted in small refractory crucibles and optical pyrometer and immersion thermocouple readings were simultmzeously taken. The resulting emissivities of the liquid iron surface obtained were found to be greatly affected by both the gaseous atmosphere and geometrical changes in the physical setup. Quantitative values for these effects are indicated. FOR many applications in both the laboratory and plant, optical pyrometry is still the best means of measuring temperatures in the incandescent range. A prerequisite in evaluating the correct temperature is a good value of the emissivity of the surface. To obtain the emissivity from the tabulated values of the literature can be very confusing and often far from correct. There are many reasons for these difficulties, and it is not within the scope of this paper either to enumerate or to discuss them all. Its purpose is to show quantitatively how several factors affect the apparent emissivities obtained from experimental measurements on liquid iron surfaces. The black body is the reference state for the quantitative values of emissivities and is defined1 as a body which absorbs all radiation incident on it, reflecting none; such a surface emits more radiation per unit area per unit time than any surface which reflects any radiation, and is given a value of unit emissivity. All bodies having reflective power thus have emissivities less than unity and are considered nonblack or grey bodies. The ratio of the radiant energy emitted by the flat, nonblack surface to that of a perfectly black surface of equal area and temperature is the emissivity of the surface. The above definitions are applied to flat, polished, opaque surfaces, very seldom encountered in actual measurements, and for this reason many authors have suggested that the word "emittance" be used for real bodies rather than emissivity. The emittance has reference to the material and its configuration rather than to its properties in the idealized state. Recent observations of molten iron in a small refractory crucible indicate that not only the configuration of its surface but the geometrical arrangement of its surrounding and the nature of the surrounding atmosphere have a pronounced effect on the emittance. Neglect of changes in such conditions may lead to errors as large as 40°C at 1600°C. Thus it is suggested that the term "apparent emissivity" be used and that it be recognized that its value pertains to a particular experimental arrangement only. As a result of not recognizing these differences in emissivities, which are obtainable from changes in the physical setup of an observation, many investigators have incorrectly quoted their values as those of the emissivities of particular materials rather than as an apparent emissivity for their particular arrangements. As a consequence, values of the emissivity of liquid iron ranging from 0.3 up to 0.55 are found in the literature. In an effort to establish an accurate optical temperature scale for liquid iron solutions in which de-oxidation studies were to be carried out, it was observed that the temperature relationship, obtained by simultaneously taking immersion thermocouple

Jan 1, 1963

By EDWARHD HALSE

Discussion of the Paper of Dr. H. M. Chance, presented at the Lake Superior Meeting, September, 1904. EDWARD HALSE, Puerto Berrio, Colombia, So. Amer. (communication to the Secretary*) : The Taviche mining-district is generally known as a Taviches," being named from the two villages called respectively San Pedro Taviche and San Jeronimo Taviche. It is so called by José G. Aguilera, in his paper on the Geographical and Geological Distribution of the Mineral Deposits of Mexico;' and in published reports by the late N. W. Rudston Read ;2 and by Juan de Dios Villarello.3 The region is a large one, measuring about 24 miles long and 7 miles wide. Dr. Chance, in his interesting paper, tells us very little about the nature of the ores, and, with regard to the geology of the district, contents himself with observing that ? the country, as a rule, consists of eruptive rocks; and no evidences of sedimentary strata appear near the mines.? The latter part of the above statement is hardly correct. The formation is mainly eruptive, being hornblende-audesite of Tertiary age, which is limited on the east by the calcareous (Cretaceous) formation, and on the west by the Huronian rocks of Ocotlan. Limestone is seen close to the Santa Càtarina mine, at the northern end of the region. In the surface-working known as La Cueva, a little northeast of San Pedro, limestone forms the eastern wall of the deposit which consists of spots (moscas) of pyrargyrite in white opaque or transparent quartz. Ill one place the ore is associated with stibnite, and the quartz frequently exhibts a

Sep 1, 1905

By A. C. Fieldner

DURING 1939, 286 by-product coke ovens were completed and put into operation. These included 140 Witputte ovens for the Carnegie-Illinois Steel Corp., at Gary, Ind.; 61 Koppers-Becker ovens for the Ford Motor Co., at River Rouge, Mich.; 65 Semet-Sotvay ovens for the Great Lakes Steel Corp., Zug Island, River Rouge, Mich.; and 20 Curran-Knowtes ovens for the Midwest-Radiant Corp. plant at Mitlstadt, Ill. The Millstadt plant is unique in carbonizing a washed coat containing 3.50 per cent sulphur. The gas contains approximately 2500 grains sulphur per 100 cu. ft.; this is successfully removed with sodium carbonate solution by the Seaboard liquid purification process. The coke is intended primarily for use as a smokeless domestic fuel in the city of St. Louis.

Jan 1, 1941

By William Hume-Rothery

MR. CHAIRMAN, LADIES AND GENTLEMEN: I need not say how much I appreciate the honor of being asked to lecture to you, and how much I would thank you for your kind invitation. It is encouraging to feel that the abnormal restrictions of the war have been relaxed sufficiently to allow a free exchange of scientists between our two countries, and I hope that some of you will be persuaded to go to England, and to visit us at Oxford, so that I may repay a little of the kindness I have received from you. As this is one of the first lectures since the end of the war, I have thought it well to describe some of the advances in the theory of alloys which were made in the years between the two World Wars. From the point of view of theoretical science, these years have been of outstanding interest in the history of metallurgy. They have been years in which the development of new and more accurate experimental methods has led to the revelation of many new facts. At the same time, the theoretical developments have enabled some of these facts to be viewed as parts of a general scheme, and we may say that some of the foundations of metallurgical science have been laid. This work was naturally stopped by the Second World War, and it can therefore be reviewed as one definite stage in the development of our Science. To illustrate the new advances, I shall deal mainly with the alloys of copper and silver, since these have revealed many of the general principles. SOLID SOLUTION At the beginning of our period, the first steps in X-ray crystal analysis had been taken, and copper had been found to crystallize in the face-centered cubic structure (Fig I). The determination of this structure naturally was of immense importance in the understanding of our subject, because it meant that we were at last in a position to appreciate the underlying structure out of which the crystal of copper was built. The earlier science of metallography had shown that in many alloys of copper the addition of a second metal in not too large proportions resulted in the formation of a homogeneous alloy which was regarded as a solid solution of the one metal in copper. Fig 2, for example, shows the so-called equilibrium diagram of the copper-zinc alloys, and here you will see that there is a solid solution of zinc in copper extending to something of the order 35 to 40 at. pct zinc.

Jan 1, 1947

By Edgar C. Bain, William E. Griffiths

The results of an inquiry into the structural nature of some 70 iron alloys containing both nickel and chromium over a considerable range of concentration are briefly described in this paper. This study is a part of a comprehensive program of investigation into alloys involving chromium in progress at the Union Carbide and Carbon Research 1aboratories. All the compositions studied contained carbon in amount comparable to commercial alloys. The B Constituent In addition to locating the limits of composition for the three principal types of structure (polyhedral ferrite, martensite and austenite) and their combinations, certain other features of the system were observed. A hitherto undescribed brittle constituent (designated here as the "B constituent") was discovered. It is very hard, non-magnetic and forms in two modes from chrome-ferrite by recrystallization. It is the stable low-temperature condition for the equal-proportion chromium-iron materials containing less than 10 per cent. nickel. Although it partakes of the nature of an inter-metallic compound, yet it may exist over a considerable range of composition. It is non-existent above a temperalure zone, varying with composition, from 800° C. to 950° C., and heating above this critical temperature develops chrome ferrite persistent after average cooling rate; a few hours just below this temperature will develop the complicated brittle crystalline type. The B constituent, when found in the grain boundaries of alloys of lower chromium content, contributes a serious brittleness removable, however, by heating and cooling rapid enough to prevent its re-format'ion. By suitable means of precipitution, the hard B constituent can be made to strengthen the already stiff alloy matrix in the manner of submicro-scopic particles, as exemplified in duralumin or the Sykes iron-tungsten and iron-molybdenum alloys. A possible explanation is offered for the familiar brittleness developed in chrome iron at temperatures above about 475" C. and removable by

Jan 1, 1927

By F. C. Schora, H. P. Meissner

Both a graphical and an analytical technique are presented for calculating stream compositions and temperatures in adiabatic staged systems in which solids travel countercurrently to a gas stream. Such a system might be a tower containing several plates, on each of which the descending solid is fluidized by the rising gas stream. Examples are presented in which chemical reactions occur, including the oxidation of SO, by a solid catalyst and the gaseous reduction of iron oxides. COUNTERCURRENT staged processes involving reactions between solid and gas streams are becoming more common. These operations are generally carried out in a series of beds of fluidized solids, with each bed or "plate" acting as a stage. Fig. 1 is a schematic diagram of such a series of stages located in a column, down through which a solids stream moves from stage to stage counter to a rising gas stream. Typical reactions carried out in such systems are the dehydration of aluminum trihydrate, the calcining of limestone, and the gaseous reduction of iron oxides. Calculation of the performance of these counter-current systems rapidly becomes more complex with increases in the number of stages and in the number of chemical reactions occurring. Calcula-tional procedures for isothermal operations of such systems have been described.4 Actual tower operations, however, are generally adiabatic, and in consequence far from isothermal. The object here is to present both graphical and analytical techniques applicable to such adiabatic towers operating continuously and in steady state. In this introductory discussion, the graphical techniques presented are of the McCabe-Thiele type, rather than of the Pon-chon type. In all the examples presented, it will be assumed that both thermal and chemical equilibrium are attained in each bed. The assumption that the gas and solid streams leaving each bed are at the same temperature as the bed is in accordance with the familiar behavior of actual fluidized solid systems. Chemical equilibrium, on the other hand, is not necessarily attained in any given stage between these two streams, even with deep beds, since reaction rates may be slow. In the last section of this paper, discussion is presented of methods suitable for use when chemical equilibrium is not attained. The adiabatic tower in Fig. 1 has "n" stages numbered from 1 to n, starting with the bottom stage as number 1. In analyzing this tower's performance, it is important to express gas flow rates in terms of a key component or element which remains completely within the gas stream throughout the tower. Similarly, solid flow is best expressed in terms of a key compound or element which remains within the solid phase throughout the tower. Thus, in burning limestone with a hot flue gas, the gas flow might be expressed as G, the pound mols of nitrogen flowing through the tower per unit time, while solid flow might be expressed as S, the pound atoms of calcium in all forms in the solid stream per unit of time. Defined in this way, both G and S are constant throughout the tower. The enthalpy of the gas and solid streams are now best expressed in terms of these key components. That is, the gas stream enthalpy H is expressed as Btu in the total gas per mol of the key component in the gas. Similarly, the solids stream enthalpy h is expressed as Btu in the total solid stream per pound mol (or pound atom) of the key component in this stream.

Jan 1, 1962

(Members, are urged -to send in for this column any notes of interest concerning themselves or their fellow-members,). Members and guests R: ho called at Institute headquarters during the period Dec: 10, 1916 to Jan. 10, 1917: F. L. Antisell, Perth Amboy, N. J. William Kelly, Vulcan, Mich. F. J Brulé, Toronto, Ont., Canada. W. H. Lanagan, San Francisco, Cal. Zar T. Crittenden, The. Pas, Mau, Canada. S. Lefevre, Forest Glen, N Y Thomas F. Donnelly, Tucson, Ariz. ' D. A. Lyle, St..David's, Pa. - John Davenport, Brighton, 14 lass. -Domingo Nugués, Buenos Aires, Argon-. E. E. Ellis, Birmingham, Ala. tine. N. H. Emmons, 3d, Copperhill, Tenn. - H. L. Scaife, Clinton, S. C. W.. E. Erdofy, New York, N. Y. Mortimer A. Sears, Washington, D. C. C. L. French, New York, N. Y. E. Spurny, New York, N. Y.' , M. H. Gannon, Butte,. Mont. R. K. Stockwell, Santiago, Chile. R. E. Hoffman, Hannibal, Mo. Benjamin F. Tibby, Salt Lake City, Utah. C. Vey Holman, Rockland, Me. Arthur P. Watt, St. Francois, Mo. Arthur P. Allen has left the employ of the Calumet &- Hecla Mine and is now with the Highland Min. Co., Ashcroft, B. C., Canada. H: C. Bellinger has been appointed. general manager of the Chuqui- - c mata mine-of the Chile Exploration Co. -

Jan 2, 1917

By D. T. MacRoberts

A simple disturbance in a gas reservoir travels with a finite velocity which is nearly independent of the amplitude of the disturbance. As a result very complex transients may be set up which seriously affect observation at a well. The time of transient is much longer than commonly supposed. INTRODUCTION A change in pressure at a gas well is not propagated through the reservoir instantaneously but with a definite fin- ite velocity. Knowledge of the period ! of this transient is of value because: 1. Observations of pressure and flow-rate during the transient may affect interpretation of back-pressure tests. 2. Interference effects between wells may be used to determine continuity of formation. 3. Additional information concerning the physical characteris- tics may possibly be deduced from the behavior of a well during the transient. MATHEMATICAL DEVELOPMENT It will be assumed that the well is initially closed in and that the pressure is constant throlughout the reservoir. As the initial disturbance passes outward from the well it is further assumed that a logarithmic pressure distribution is established between the most distant point reached and the well, so that: <l> = ((/)r-<t>w) I ------------ + (/) . (1) Manuscript received at office of the Branch September 15. 1948. Paper presented at Branch Fall Meeting, Dallas. Texas. Oct. 4-6, 1948. r. = distance to any point between r and rw r = radius of drainge iw= radius of well (/) = potential (P for incompressible fluids, P2 for perfect gases) Up to the time the effect reaches the point r the production from the well will be: W= (Pr-P,,,) . (2) i b W = volume produced t = sand thickness F = fractional porosity Pr = reservoir pressure Pm = average pressure between r and rw Pb = atmospheric Pressure All pressures will subsequently be stated in atmospheres and the constant Pb will be omitted. This will be produced at a rate: dw t k (Pr³-PW2) do d 0 - . (3) log — Pw = pressure at the well k = permeability 0 = time = viscosity

Jan 1, 1949

By D. T. MacRoberts

A simple disturbance in a gas reservoir travels with a finite velocity which is nearly independent of the amplitude of the disturbance. As a result very complex transients may be set up which seriously affect observation at a well. The time of transient is much longer than commonly supposed. INTRODUCTION A change in pressure at a gas well is not propagated through the reservoir instantaneously but with a definite fin- ite velocity. Knowledge of the period ! of this transient is of value because: 1. Observations of pressure and flow-rate during the transient may affect interpretation of back-pressure tests. 2. Interference effects between wells may be used to determine continuity of formation. 3. Additional information concerning the physical characteris- tics may possibly be deduced from the behavior of a well during the transient. MATHEMATICAL DEVELOPMENT It will be assumed that the well is initially closed in and that the pressure is constant throlughout the reservoir. As the initial disturbance passes outward from the well it is further assumed that a logarithmic pressure distribution is established between the most distant point reached and the well, so that: <l> = ((/)r-<t>w) I ------------ + (/) . (1) Manuscript received at office of the Branch September 15. 1948. Paper presented at Branch Fall Meeting, Dallas. Texas. Oct. 4-6, 1948. r. = distance to any point between r and rw r = radius of drainge iw= radius of well (/) = potential (P for incompressible fluids, P2 for perfect gases) Up to the time the effect reaches the point r the production from the well will be: W= (Pr-P,,,) . (2) i b W = volume produced t = sand thickness F = fractional porosity Pr = reservoir pressure Pm = average pressure between r and rw Pb = atmospheric Pressure All pressures will subsequently be stated in atmospheres and the constant Pb will be omitted. This will be produced at a rate: dw t k (Pr³-PW2) do d 0 - . (3) log — Pw = pressure at the well k = permeability 0 = time = viscosity

Jan 1, 1949