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By J. A. Capp

For certain classes of electric railways a steel conductor is preferable to the oldcr atld more commonly used overhead trolley-wire. The third-rail presents a rather better appearance, because of the absence of an overhead structure; it is easily installed, cheaply maintai~ied, presents s large area for conducting and collecting the current, and is therefore particularly suitable for high speed and heavy service. With costs calculated on the basis of equal coilductirity in rail aud trollej-wire, the third-rail constrrictiol~ is cl~caper than thc overhead trolley. But the average interurban road will lise a trolley-wire of considerably less conductivity than would be obtained with the smallest size steel rail (about 60 lb. per pard) that mould ordinarily be used, and here the first clost of trolley construction would generally be less thau that of the third-rail. While no third-rail installation has jet bee11 in operation long enough to give figurcs of value, it ~vould appear that the cost of maintenance of the thirdrail construction should be less than that of the overhead trolley. This consideration, together with that of sightliness and adaptability (particularly in the case of terminals, yards and very heavy or high-speed service), will frequently off'set the higher cost of the third-rail construction and make it the preferable means of' conducting the current from thc generator to the car-motor. For the first third-rail installations, old track rails were used when obtainable, and these old rails were supple~rlented with new rails of standard T-section and composition. With the coming of the very heavy, high-speed service during the past few years, the resistance of these old and new standard T-rails was found to be so high that they mould not carry the high currents necessary without too great a drop in the line-potential. The rails would, therefore, have to be suppleme~~ted with addi-

Jan 1, 1904

By John Fulton

Early in the year 1875, some difficulty was experienced in the " Old blast-furnaces " of the Cambria Iron Company, at Johnstown, Pennsylvania, arising from the increased use of native coke, prepared in Belgian ovens near the furnaces, in mixture with Connellsville coke, in the production of Bessemer pig-iron. This was the more surprising at that time, because a very caulplete coal-crushing and washing apparatus, after the Bradford plan, had just been put into successful operation, affording a pure coal for coke-making. It was confidently expected that this thorough cleansing of the coal would improve the quality of the coke and fit it for the increasing manufacture of Bessemer pig-iron. But the trouble with the native coke continued. Experiments in fuel charges-increasing and reducing them—failed to correct the irregular working of these furnaces. Increasing the charge of native coke produced abnormal heat at the top of the furnace, reducing it cooled the furnace below. At this stage of affairs, the Hon. Daniel J. Morrell, general manager of the Cambria Iron Company, requested the writer to make the requisite investigation to determine the nature of this coke-difficulty, and to ascertain why the Johnstown coke could not be used in blastfurnace work as well as Connellsville. This task at first did not appear to present any special difficulties, but subsequently it expanded into proportions that caused no little anxiety. The first effort was directed to procuring average samples of Johnstown and Connellsville coke. At this period of the investigation, it was assumed that the whole matter could be intelligently solved by comparing the chemical analyses of the two cokes: Johnstown Coke. Connellsville Coke. Moisture,.......... 0.30 Volatile matter,......... 0.46 Fixed carbon,.90.48 89.57 Ash,.8.96 9.11 Sulphur,.0.56 0.82 Phosphorus,..... 0.014 100.00 100.274 Analysts, T. T. Morrell. A. S. McCreath.

Jan 1, 1884

By Lloyd Pollish, Robert N. Breckenridge

SUCCESS in any underground mining operation is determined by accessibility of the orebody, which in turn is dependent upon maintenance of passage- ways to the mining zones and temporary support of the voids caused by extraction of ore. This is accomplished by one or a combination of the following methods: timbering, back-filling, pillaring, or, more recently, rock bolting. Timbering has usually been the principal means of maintaining these underground openings necessary for mining operations. Timber, however, does not prevent ground movement beyond the scope of localized sloughing, which is indicated by the gradual failing of the timber itself. Besides this, timbering has always been a costly process, and with the decline of available supplies of timber close to the mining areas, mining men have constantly sought other methods of controlling ground.

Jan 7, 1954

The discovery of nickel at the Wallace Mine in 1846, recorded in the Report of Progress of the Geological Survey of Canada, 1.848-49, was not the first find in the Sudbury mining district. As long ago as 1770 a company had been formed to work the rich deposits of, copper whose existence was then known. .But it was during the first mentioned year that, incited thereto by fresh finds and a favorable report by Mr. W. E. Logan, then Provincial Geologist, two [ ] groups of Canadians organized "The Montreal Mining Company and "The Upper Canada Mining Company." By the former company the Bruce Mines Location' was purchased and work was immediately commenced upon it. The Wallace Mine acquired by the Upper Canada Mining Company, was abandoned after a shaft had been sunk and a few test pits opened.

Jan 1, 1907

By Joseph Daniels

The Fritz Engineering Laboratory was built under the direction of John Fritz, and presented by him to the University. A view of the building, looking east, is shown in Fig. 1. The building was started in 1909, and completed in 1910, although all of the equipment was not placed until later. Mr. Fritz gave his personal attention to the details of construction and equipment, and it was his custom to drive over every day to the University from his home in Bethlehem and spend some hours watching the work, offering suggestions, making changes, and planning new work. The result is a building and an equipment which embody his practical ideas. The laboratory structure is of the steel mill-building type, of light-colored brick, 91 by 114 ft., of which a section is shown in Fig. 2 and the floor-plan in Fig. 3. The steel frame carries the roof and traveling crane-way. Ample light has been provided by numerous windows in the side and end walls, in the clerestory, and by a skylight 84 ft. long and 9 ft. wide in the north roof. The main aisle of the building is 49 ft. 2 in. between centers of crane-columns, and has a clear height of 40 ft. The remainder of the width is taken up by two side aisles, 18 ft. high. The laboratory consists of four sections: (1) A general testing-section containing the testing-machinery, a small machine shop, and an office; (2) a cement-testing room; (3) a room for making and storing concrete test-specimens; (4) a hydraulic section.

Jan 1, 1912

Bill S.1431 for the creation of a Department of Natural Resources has received a propitious hearing before the Senate Committee on Government Operations. Interior Secretary Rogers C. B. Morton was one of the prominent witnesses who testified in favor. The department had been proposed, Morton said, with "the conviction that the development of all natural resources would be harmonized with the most practicable possible means to protect and preserve the environment, consistent with the social and economic needs of the Nation." Another opinion on the pro side came from Atomic Energy Commissioner Clarence E. Larson, who said that a "total picture" had become essential to the establishment of a policy for developing energy resources in the best public interest. Commissioner James T. Ramey, on the other hand, was one of the AEC dissenters. Ramey said he believed the reorganization of resource responsibilities would hinder efforts to deal with energy-environmental problems and prevent the use of AEC "expertise and facilities" to the greatest advantage. As Arnold Weber, associated director of the Office of Management and Budget, pointed out, however, retiring AEC Chairman Glenn T. Seaborg is in favor of the new department. Another supporter, and one who can cast a vote on the bill, is Sen. Frank E. Moss. Final Standards for emissions from new stationary sources will be published by the Environmental Protection Agency on October 27. The initial proposals, appearing in the Federal Register on August 17, called for limiting emissions per million Btu of heat input (maximum 2-hr average) to 0.2 lb of particulate matter, and, where solid fuel is burned, to 1.2 lb of sulfur dioxide and 0.7 lb of nitrogen dioxide. While the new rules are mainly for new plants, the EPA is also proposing them for "existing plants which are modified in such a way as to increase or alter. . . their emissions."

Jan 1, 1971

By H. C. Spaulding

The rapid increase, during the last few years, in the number and magnitude of applications of electric power-transmission to commer cial uses in this country, has been due principally to three causes: first, the ability and enterprise of those who have been identified with the progress of electrical industries, since electric illumination became an economic fact instead of a laboratory-experiment: sec ondly, the readiness of the American people to adopt new and ad vanced methods as soon as their superiority has been fairly demon strated; and thirdly, tile economy and flexibility of the apparatus employed, when properly designed and constructed, and installed under suitable conditions. Basing our judgment on the world's advance in scientific devel opments during the past century, we may reasonably conclude that in no other country would the pioneeis of electrical invention, whose names have now become household words, have received the prompt and plentiful financial support which has enabled them to inaugurate undertakings of exceptional magnitude, even in this era of tremendous monetary organizations. And, on the other hand, we have seen, in the numerous financial and engineering failures inseparable from such rapid development, the natural results of a too implicit faith in electrical omnipotence. It is not to be wondered at that conservative engineers have been slow to adopt this new and mighty agent in the solution of exten sive problems, and under circumstances where a single failure means not only a greater or less financial sacrifice, but the loss, in a greater or less degree, of professional reputation. Be mechanical engineer, while recognizing the fact that thousands of horse-power are to-day transmitted by electrical means, from sunning the lathe in a dentist's office to the operation of a fifty-ton travelling crane; from passing a cooling draught of air through a

Jan 1, 1891

By Earl S. Greiner, Eric R. Jette

The literalure on the binary alloys of iron and silicon has been reviewed by Stoughton and Greiner.1 Another even more extensive and detailed survey of the present knowledge has been prepared under the auspices of the Alloys of Iron Research Committee by Greiner, Marsh and Stoughton. Since the latter surrey has already been issued in its preliminary form, it will be unnecessary to review the literature in the present article. However, in this connection there should be noted the important work on the crystal structures of the iron-silicon alloys by Phragmén,2 who investigated the entire system, identified the various phases and determined the homogeneity ranges of these phases. It was evident in the surveys cited above that in the range from 0 to 15 per cent silicon, which includes the commercially most important, alloys, the results obtained by thermal analysis, microscopic examination and the determination of electrical, magnetic and mechanical properties were extremely confusing. From time to time various compounds between iron and silicon have been postulated to account for the results yielded by the classical methods, and much argument has ensued. It was presumed that if compounds occurred which are sufficiently diverse in their properties to account for the characteristics of the alloys, they should be recognizable as separate phases but satisfactory proof of this sort has not been found by thermal or microscopic methods. Contributing to the confusion is the fact that the electrical, the magnetic and some of the mechanical properties are "structure sensit'ive"; i. e., they are influenced to a marked degree by the presence of minute amounts of impurities, the specific characters of these impurities, the grain size, the character of the grain boundaries, small general or local strains, etc. Thus interpretations of the discontinuities in the various property versus composition curves that identified these discontinuities with phase changes or compound formation have always been open to question.

Jan 1, 1933

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By C. H. Brehaut, W. N. Taylor, R. S. Douglas, H. A. Shannon

THE name for this new method of mining is derived from a composition of Horizontal, Radial, Diamond, and the drilling is from raises. This method, worked out at Copper Mountain, B.C., is believed to be distinct in many features from other known methods. GEOLOGY The ore deposits of Copper Mountain are related to the Copper Mountain stock, which is an ideal example of the magmatic differentiation in that it grades from a basic gabbro at the border to an almost pure orthoclase-pegmatite core. The "contact" ore bodies lie along the contact of the gabbro and an older complex of volcanics and sediment termed the "Wolfe Creek" formation. These older rocks, collectively referred to as greenstone, had been fractured prior to the intrusion of the stock and were highly metamorphosed during the intrusion. The "outlying" ore bodies are somewhat different in character, though a similar structural pattern prevails. It is believed that a deep-seated magma of which the Copper Mountain stock is a part has given off solutions that caused a partial granitization of some of the volcanics. Mining problems are caused further by the presence of a series of soft barren dikes intersecting a great many of the ore bodies, which are about 30 ft. wide, strike north-south, and dip at a high angle to the east; and are further increased by the presence of four major faults, with a great many minor faults running at acute angles from them. Fault zones average 8 ft. in width, and consist of gouge and breccia. They strike northeast and dip steeply to the northwest. The faults cut through the ore zones and the dikes, and continue on into the gabbro. The general mine structure with two types of ore bodies, bounded by weak walls and intersected by several series of soft barren dikes and major faults, indicated that a method of mining should be devised that would remove the ore at low cost with the least disturbance of the waste walls and dikes. THEORETICAL ESTIMATE OF STOPING WITH THE DIAMOND DRILL After consideration of various methods, the most suitable one appeared to be horizontal drilling to break the ore in a manner similar to shrinkage stoping. Drilling vertical holes or rings from a bench and breaking to an open slot was eliminated because the weak walls of ore, dike or waste would not permit this type of opening. It was then decided to drill either horizontal radial holes from a raise or parallel holes from a slot cut across the ore body. After discussion, the latter method was believed unsuitable, for the following reasons:

Jan 1, 1945

Photographs of Officers

Jan 1, 1923

By C. F. Nagel

THIS paper is written primarily for those who are familiar with the processes mentioned but who desire a further insight into some of the fundamental principles. It does not give a complete description of the various practices employed in the working of aluminum and its alloys, but presents a few illustrations of the essential respects in which aluminum differs from other common metals, and emphasizes the controlling factors of the processes under consideration. HEAT TREATING Certain aluminum alloys are capable of having their mechanical properties greatly altered by a heat-treatment process. The degree of this improvement may be illustrated by some typical properties of duralumin (Table 1). It is essential that the material be in the wrought condition in order to obtain maximum heat-treatment effects. [ ] In the case of duralumin, the process consists of heating the metal to a prescribed temperature and then quenching it. Immediately after quenching, the material is relatively soft though not as soft as in the annealed state. If allowed to stand at room temperature, the material changes, increasing in hardness and strength without loss of elongation, but at the expense of the plasticity. This action is very rapid at first, gradually diminishing in intensity and to all practical purposes being completed in about four days. This process of hardening is termed

Jan 1, 1928

SLAG composition, slag constitution, reactions in slag, and reactions between slag and metal-in other words, the physical chemistry of slags-are matters of great importance to the open-hearth operator, whether or not he makes use of any detailed knowledge of them. Although this is a relatively young branch of the science of steel- making, much progress has been made; however, much remains to be learned, and many of the statements that can be made at present are probably--or even certainly-subject to future change. Nevertheless, the physical chemistry of slags is sufficiently developed to provide a reasonably secure basis for real understanding of steelmaking reactions. FUNDAMENTALS OF SLAG CONTROL By way of introduction, some time is spent in this chapter on effecting an easy transition from some of the more "practical" manifestations of slag to discussions couched in the more formal language of physical chemistry. This necessitates a certain amount of repetition, but it is felt that the purpose of the chapter is best served in this way. Reactions in the metal phase have products that find their way into the slag and are important components thereof; they are discussed in detail in the preceding chapter. Some substances distribute themselves Between slag and metal in definite fashion, and others are found only in the slag. Their reactions are a large reason for this chapter. Limitations of Slag Control. The open-hearth process is essentially oxidizing and cannot be otherwise operated. (Oxygen gradients in the furnace, the mechanism of oxygen inflow, and similar subjects are discussed in Chapter XIX.) As shown in the calculations of material and heat balances for the charge (see Chapter XV), from 25 to 50 lb. of oxygen will flow from air or combustion gases into the charge or molten bath during the heat for each ton of liquid steel

Jan 1, 1944

By J. J. Rutledge

On Sept. 4, 1914, Mine No. 1 of the Union Coal Co., Adamson, Oklahoma, suddenly caved, entombing thirteen miners whose bodies were never recovered. The seam of coal mined, the Lower Hartshorne, averaged 5 ft. in thickness and dipped at an angle varying from 22" to 30n. The strata overlying the coal seam were sandstones and shales. The mine was worked by the pillar-and-room method, the rooms being driven directly up the dip of the seam. All coal was blasted off the solid. Rooms were turned on short centers and room pillars were thin and irregular, as shown in Fig. 1. Fig. 2 is a cross-section of the form; showing the mine workings. Some cracks had been observed on the surface, it is said, at least a month before the squeeze occurred, but the collapse of the mine workings came very suddenly. As is usual when squeezes occur on such steep dips and the pillars fail, the crush progressed rapidly down the dip until it reached solid coal; there was a line of break, or draw, over in the solid coal. Several well-defined cracks appeared on the surface, after the mine had squeezed, but there was no appreciable subsidence of the surface, the weight seemed to be thrown entirely to the dip. About one year after the squeeze, and after the workings of the adjoining mine, NO. 4, had been retimbered and made safe, the writer inspected the tenth north (right) entry, or lift, off of No. 4 slope, which was below and fairly near the lowest caved portion of mine No. 1. The roof shale was composed of thin layers, which had been bent in somewhat the same manner as the leaves of a book having flexible covers are bent when the book is folded or rolled up in the hands. Though the mine workings are immediately beneath the streets and buildings of the mining town of Adamson, business was not disturbed by the squeeze, so far as any subsidence of the surface was concerned. No surface monuments were available and no elevations were taken, but the mine workings had been accurately surveyed and traversed, and the streets of the town overlying the mine workings had been carefully platted on the mine map, so that it was possible to locate accurately the cracks on the surface.

Jan 1, 1923

By J. J. Rutledge

On Sept. 4, 1914, Mine No. 1 of the Union Coal Co., Adamson, Oklahoma, suddenly caved, entombing thirteen miners whose bodies were never recovered. The seam of coal mined, the Lower Hartshorne, averaged 5 ft. in thickness and dipped at an angle varying from 22" to 30n. The strata overlying the coal seam were sandstones and shales. The mine was worked by the pillar-and-room method, the rooms being driven directly up the dip of the seam. All coal was blasted off the solid. Rooms were turned on short centers and room pillars were thin and irregular, as shown in Fig. 1. Fig. 2 is a cross-section of the form; showing the mine workings. Some cracks had been observed on the surface, it is said, at least a month before the squeeze occurred, but the collapse of the mine workings came very suddenly. As is usual when squeezes occur on such steep dips and the pillars fail, the crush progressed rapidly down the dip until it reached solid coal; there was a line of break, or draw, over in the solid coal. Several well-defined cracks appeared on the surface, after the mine had squeezed, but there was no appreciable subsidence of the surface, the weight seemed to be thrown entirely to the dip. About one year after the squeeze, and after the workings of the adjoining mine, NO. 4, had been retimbered and made safe, the writer inspected the tenth north (right) entry, or lift, off of No. 4 slope, which was below and fairly near the lowest caved portion of mine No. 1. The roof shale was composed of thin layers, which had been bent in somewhat the same manner as the leaves of a book having flexible covers are bent when the book is folded or rolled up in the hands. Though the mine workings are immediately beneath the streets and buildings of the mining town of Adamson, business was not disturbed by the squeeze, so far as any subsidence of the surface was concerned. No surface monuments were available and no elevations were taken, but the mine workings had been accurately surveyed and traversed, and the streets of the town overlying the mine workings had been carefully platted on the mine map, so that it was possible to locate accurately the cracks on the surface.

Jan 1, 1923

By M. B. Mirza, F. D. Wright

Models of photoelastic material were made to simulate a mine roof that had cracked over the edge of the pillars and at the center of the span. Models were restrained from moving laterally outward so they acted as flat arches. Uniform loading was approximated by loading the models along the bottom at eight points spaced equally along the span. It was found that for models with depth to span ratios of 1:3 to 1:6, the maximum stress at the top of the center crack could be calculated directly by the following formula: Elastic stresses in mine roofs composed of sedimentary beds are usually computed by assuming that the immediate roof bed acts as a fully restrained beam uniformly loaded by its own weight and by overlying strata. Very little work has been done to analyze stresses in roof beds or beams which contain vertical (normal to the span) or nearly vertical cracks. Yet every mining engineer has walked safely under roofs that show such cracks. As far back as 1933, Bucky' made model studies of the effect of vertical cracks on the behavior of horizontal strata. He did not make any analysis of the stresses but did show that a cracked beam will stand safely under certain conditions, and also showed that a beam restrained at the ends can crack over the supports and in the middle without collapsing as long as the ends of the beam are not free to move laterally outward. The beam, or rather, part of the beam, acts like a flat arch and supports itself by pushing outward at its supports. In 1941 Evans2 treated analytically the problem of a beam cracked along so many planes perpendicular to the axis of the beam that no tensile stress can operate. He named this type of beam a "voussoir-beam" by analogy to the voussoir-arch. In 1962 ~a~cocks~ modified Evans's solution by including the effect of the shear stress component of the resultant force at the abutment. This paper gives the results of a photoelastic study of the stresses in a beam containing vertical cracks in the center of the span and over the supports. A

Jan 1, 1963

By Keijiro Nishio

At a time of great antiquity when our Yomato tribe had not yet found its way throughout the country, there lived in Japan barbarous tribes of the stone age, whose dwellings were vertical caves covered with roof's of twigs and weeds. In a cave lately discovered at the village of Morita, 10 miles west from the port of Aomori, there were found pieces of micaceous iron-ore and psilomelane, with oval holes pierced from both sides. Apparently these objects were regarded as ornaments or curios, without being applied to any practical use. Among the traditions given in the Nihonshoki, an ancient history of Japan, there is one relating to the mining industry. According to this tradition, in the mythological age Izanami-no-Mikoto gave birth to Kanayamahiko-no-Mikoto, god of mines, and Amaterasu-Okami (the sun-goddess) was armed with swords. It came to pass at one time that she concealed herself in Ama-no-Iwato ("Heavenly Cave"), and several gods made contrivances to entice her out. Among them, Ishikori-dome, a smith, made a mirror with copper obtained from the Ama-no-Kagoyama, by means of a pair of bellows known as the Ama-no-habuki, which was made of a deer-skin. It is recorded also that Susanb-no-Mikoto, her younger brother, observed the abundance of gold and silver in Korea, where his descendants were to reign, and urged them to provide themselves with boats to convey them across the Sea of Japan. In the course of time he accomplished his object, proceeding to Korea with his son, Isotakeru-no-Mikoto. These accounts

Jan 1, 1913

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