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By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*

CHARLES G. ROEBLING Charles Gustavus Roebling, president of the John A. Roebling's Sons' Co., of Trenton and Roebling, N. J., and of the New Jersey Wire Cloth Co., of Trenton, and vice-president of the John A. Roebling's Sons' Co., of New York, died at his home, No. 333 West State Street, Trenton, on Oct. 5, 1918. Mr. Roebling, who was born in Trenton, was a son of the John A. Roebling who finished the plans for the Brooklyn Bridge just before he died. The bridge was completed by his sons, Charles G. Roebling and Col. Washington A. Roebling. Upon graduation from the Rensselaer Polytechnic Institute in 1871, Charles Roebling became associated with the Roebling company as a mechanical engineer. He was engineer and builder of the suspension

Jan 12, 1918

AVING started to tell you of working potter's clay for making crucibles and shells, the wish came to me to tell you of the practice of this art also. Although it may seem at first glance to be outside the order and purpose of my writing, he who considers well will see that it is not unrelated to it but proper, since it is wholly dependent on the agency and power of fire if it is to be brought to its perfection. Moreover, the potter's glazes and colors are all substances of various metals or impure minerals and therefore belong to fire. Since it is my intention to treat of fire, minerals, and metals for you, I surely should not have omitted this, particularly because it is a necessary art which enriches and is greatly praised both for its ingenuity and its beauty. The art of the potter has two sources as its principal basis. One comes from the art of design, the other from various alchemical secrets and elemental mixtures. In regard to these, I find that, in my opinion, all this art depends in the last analysis on four things: on good judgment in general, and on the art of design so as to be able to make the vessels beautiful and of good shape, as well as to ornament them with painting; after baking them well the first and second times, the next thing is to know how to make and apply the glaze well and to paint them with varied and appropriate colors. The fourth is to see that you have good, fine clay without small stones or lumps-indeed this is to be considered as the first thing. Now this that I have called clay is what many call cretaceous earth and some call argil. It is found and dug up when the masters wish to make use of it and is put in a container to be moistened. When it is moistened, it is beaten on a bench with an iron rod and very well prepared. Mixing it carefully, every small stone, lump, or other hardness that it contains is removed and cleaned away. Then a shaft [145V] of iron is fitted as the journal in a large wheel. On the other end of the journal a small wheel is made which forms an instrument for working that is called a lathe. Having put some clay on this, it is made to rotate by pushing with one foot, and, by rotating it, vessels are worked into a pleasing shape and size. Then they are taken off and put on a board to dry. After drying artificially or naturally they are painted red,

Jan 1, 1942

By authority of the Secretary of War, and in response to frequent requests, the following suggested list of reading is issued by the War Department for the information of civilian engineers desiring to inform themselves on military subjects: These references have been selected, first, with a view to giving to engineers unfamiliar with the art of war a general survey of that sub-

Jan 1, 1916

By A. M. Crawford

INTRODUCTION Grouting is an engineering operation which has been practiced for many years and a considerable amount of experience and skill has been developed in this field. However, a review of the current literature (Houlsby, 1982) reveals that the theoretical background and experimental observations that are necessary to adequately predict or describe the performance of a particulate grout (e.g. cement based) in a jointed geologic media are somewhat inadequate. In the near future it is envisaged that the use of grout and grouting techiques will be used to tackle even more difficult problems than have been considered in the past. One problem that is currently being faced by the rock mechanics engineer is the development of geologic repositories for the disposal and containment of high level radioactive waste. In such structures there will be only one opportunity to ensure the success of the containment system. This success will depend to a large extent on the adequate and successful performance of the grout curtains to be utilized around the shafts and shaft liners. Regrouting will not be possible. There are other problems in rock mechanics in which it is frequently necessary to inject particulate media into passages of small dimensions, and where typically the size of fracture being injected is of the same order of magnitude as the particle dimension. For example, in the oil industry in hydraulic fracturing the enhancement of fracture conductivity is maintained by means of proppants introduced into the fracture.

Jan 1, 1984

By K. Thirumalai

Rock response to heating depends on properties of rock material and varies widely between different rock types. By dissipating energy, surface melting limits rapid heating and fragmentation of rocks achieved by surface heating methods. This study advances a concept of rock fragmentation by rapid internal heating of a localized inner volume of rock. The working of the method to achieve fragmentation of rocks (Charcoal granite and Dresser basalt) having poor response to surface heating is analyzed. Experimental data on elevated temperature rock properties required for the study are presented. Based on the properties of test rocks, a high frequency (50 MHz) dielectric heating method of generating localized internal heating was selected for experimental study. The test rocks were fragmented without melting under localized heating below 600ºC. The heated volume required for fragmentation was observed to be less than 2 percent of the test block volume. A practical application of the method for in situ fragmentation of rocks is suggested.

Jan 1, 1971

By J. Henry Harden

I DESIRE to call the attention of the Institute to a new form of drawing-board trestle. With the ordinary four-legged trestle, commonly used, one has not the means of adjusting the height of the board to the draughtsman. To obviate this inconvenience, and at the same time to enable one to incline the board, I have devised an arrangement of curved and straight slots and thumb-screws, by means of which the board can be raised three or more inches, and placed at any desired angle of inclination on either side. Figures 2, 3 (Plate I) show side and end elevations of the trestle for a single board, and Figure 4 for two boards. The latter form is adapted for use in schools, or where it is desired to economize space.

Jan 1, 1874

By Baoshen. Liu, Lin Dezhang

Vertical and horizontal movements beyond the perimeter of the open pit have resulted from the development of deep and extensive open pits; the surface point always moves towards the centre of the open pit. The surface movements are not only great in relation to the stability of the open pit slope and the safety of mining operations but also are of significance to the stability of structures and ser- vices on the surface beyond the perimeter of the open pit. Recently, some studies on factors contributing to the surface movements have been carried out. Particular attention has been paid to prediction of vertical and horizontal movements, differential subsidence and horizontal strain and careful assessment of their influences on existing structures in the adjacent area. In the application of the theory of stochastic medium, it is assumed that ground subsidence process has the property of Markov Process. Based on the superposit ion principle, surface movements due to open pit mining are derived from the Kolmogorov Equation, and calculated in a digital computer. Quantitative calculation of surface movements is made according to the method employed in this paper and compared with the results of measurement in Morwell Open Pit, Victoria, Australia and Baiyin Open Pit, Gansu, China. The method of calculation gives reasonably satisfactory results.

Jan 1, 1983

By Reamy Joyce

CONDITIONS in underground mining are so variable that in approach-ing the problem of the economies effected by the use of pressure-treated mine ties and mine timbers, it is necessary to secure specific data for each mine. Facts must first be dug out to show the service life of untreated timber and the reason for its failure. Generally speaking, decay is the usual cause of failure, but in some mines mechanical destruction is an important factor. Occasionally the two causes combine to produce fail-ures, and it is difficult to determine positively which factor is responsible. In making comparisons, it is always necessary to start with the cost in place and for this reason there must be accurate information covering the labor cost of installation and the labor cost of renewals. When treated timber is used, it is necessary to know the specifications for the treating process, whether the timber was painted, dipped, treated open tank, or impregnated under pressure according to standard specifica-tions. It is also necessary to know the preservative used and the amount of the preservative that was retained by the timber after treatment. It is also well to know whether the timber was thoroughly air-seasoned before treatment or was green at the time it was treated. The kind of timber available, both untreated and treated, must be known and all of the factors listed above must be taken into consideration in the study of any problem.

Jan 1, 1939

By R. B. Haagensen, E. Martinez, V. Kudryk

The sample under investigation contained approximately 16% BaSO, and was 80% -325 mesh. Established methods for floating barite did not produce concentrates of satisfactory grade or barite recovery because of low barite content and the presence of 6% calcite in the feed. By using a new long-chain sulfosuccinamate collector in combination with relatively high concentrations of sodium silicate, a barite concentrate was produced that would be acceptable as an oil-drilling mud using a simple rougher-cleaner circuit. No desliming of the fine-ground feed was necessary. Barite recovery was over 80% and the concentrate produced had a specific gravity higher than 4.3. During the course of the investigation, a procedure was developed to obtain semiquantitative determinations of barite, calcite, quartz, and feldspar in test samples using an infrared spectrophotometer. Samples were also analyzed in a thermobalance for determination of the calcite content. The use of these instruments made it possible to obtain quick mineralogical assays and proved to be of invaluable assistance in guiding the flotation testing.

Jan 1, 1976

By N. B. Pilling, R. E. Bedworth

The corrosion of metals is one problem on which time and thought have been expended for many years. In the effort to avert the destructive action of a hostile environment, attention has been directed almost entirely to the conditions under which most metallic structures are called upon to perform, and the extensive and complicated phenomena attending the corrosive action of atmospheric agencies, acting at the ordinary atmospheric temperatures, have been studied, but there is unanimity of opinion regarding many fundamental facts. One neglected phase is the corrosive action of various gases upon metals exposed to temperatures considerably higher than the atmospheric range, and more especially the attack of atmospheric oxygen upon exposed metallic surfaces. That the problem is difficult is connoted by the practical dominance of industrial electric heating by alloys of one type (nickel-chromium). Proprietary interest may account, in part, for the paucity of information available upon even the most general factors determining the behavior of metals and alloys when exposed to such exacting conditions. The present paper gives some conclusions reached as the result of experimental work, extending over several years, on the mechanism and contributory factors of the high-temperature oxidation of a number of simple unalloyed metals; it is free from experimental detail and proof. High-temperature metallic oxidation may be considered as a phase of metallic corrosion. The scheme outlined below, in which corrosive agent and environment are the principal criteria, is one way of analyzing the several groups of corrosion phenomena. Erosion.—Disintegrating or destructive action by physical causes. Corrosion.—Disintegrating or destructive action by chemical causes. Low-temperature Corrosion.—Solid participating phases essentially immobile: (a) Gaseous agent; (b) liquid agent: action electrolytic and action non-electrolytic. High-temperature Corrosion.—Solid participating phases possess diffusive mobility: (a) Liquid agent; (b) gaseous agent: reducing gases, oxidizing gases. (1) Water; (2) miscellaneous elemental and combined oxygen.

Jan 1, 1923

By R. E. Bedworth, N. B. Pilling

The corrosion of metals is one problem on which time and thought have been expended for many years. In the effort to avert the destructive action of a hostile environment, attention has been directed almost entirely to the conditions under which most metallic structures are called upon to perform, and the extensive and complicated phenomena attending the corrosive action of atmospheric agencies, acting at the ordinary atmospheric temperatures, have been studied, but there is unanimity of opinion regarding many fundamental facts. One neglected phase is the corrosive action of various gases upon metals exposed to temperatures considerably higher than the atmospheric range, and more especially the attack of atmospheric oxygen upon exposed metallic surfaces. That the problem is difficult is connoted by the practical dominance of industrial electric heating by alloys of one type (nickel-chromium). Proprietary interest may account, in part, for the paucity of information available upon even the most general factors determining the behavior of metals and alloys when exposed to such exacting conditions. The present paper gives some conclusions reached as the result of experimental work, extending over several years, on the mechanism and contributory factors of the high-temperature oxidation of a number of simple unalloyed metals; it is free from experimental detail and proof. High-temperature metallic oxidation may be considered as a phase of metallic corrosion. The scheme outlined below, in which corrosive agent and environment are the principal criteria, is one way of analyzing the several groups of corrosion phenomena. Erosion.—Disintegrating or destructive action by physical causes. Corrosion.—Disintegrating or destructive action by chemical causes. Low-temperature Corrosion.—Solid participating phases essentially immobile: (a) Gaseous agent; (b) liquid agent: action electrolytic and action non-electrolytic. High-temperature Corrosion.—Solid participating phases possess diffusive mobility: (a) Liquid agent; (b) gaseous agent: reducing gases, oxidizing gases. (1) Water; (2) miscellaneous elemental and combined oxygen.

Jan 1, 1923

By Richard H. Sibson

Changes in seismic style along the San Andreas fault system appear to correlate with strike-parallel variations in regional heat flow. Large earthquake ruptures are associated with colder segments of the fault zone, while comparatively high levels of microearthquake activity and small to moderate shocks occur along the hotter segments, often in association with aseismic creep. Such behavior is consistent with geotherm and strain rate dependent profiles of shear resistance versus depth, constructed for quartz-bearing rocks. These profiles suggest that the transition from frictional to quasi-plastic behavior with depth should increase by a few kilometers passing from the hotter to the colder portions of the fault zone, giving rise to long-wavelength concentrations of distortional strain energy near the base of the seismogenic zone in the cold segments. Some support for this hypothesis comes from the observed deepening of microseismic activity passing northwest and southeast from the central Californian active region to the currently locked, ~400 Ian segments of the San Andreas fault that ruptured in 1906 and 1857.

Jan 1, 1982

By P. Somasundaran

An experimental and theoretical treatment of the depressing effect of inorganic electrolytes on the amine flotation of quartz is presented. Experimental data obtained for the amine flotation of quartz as a function of pH with potassium nitrate as depressant was used to test the models for the effectiveness of inorganic ions as depressants. The validity of commonly used assumptions are examined. The surface tension data obtained for dodecylammonium acetate solutions as a function of KNO3, concentration indicated that the collector adsorption on bubble cannot be neglected in the treatments, since this adsorption changes significantly with the addition of the inorganic electrolyte. It also indicated the possibility of significant changes in the specific adsorption potential of the collector occurring with the addition of inorganic electrolytes.

Jan 1, 1975

TO THE BOARD OF DIRECTORS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-The following report covers briefly some of the more important activities of the Institute during the year 1923. In my report for the year 1922, I drew attention to the falling off in membership of the Institute due to the depressed condition of the mining industry in several lines and the inability of many of our members to find profitable employment in mining or its associated branches. A number who were unemployed during 1922 established connections during 1923, but a still greater number have been forced to resign or drop their membership during 1923. Fortunately, the number dropped is not so great as in the previous year. The Employment Service conducted by the four Founder Societies bears witness to the trend in business. For the young men just out of college, there are plenty of opportunities at small salaries, there are plenty of opportunities for them as laborers; but for the mature members, those of experience, there are few calls. During the last eighteen months, our Employment Service has been able to place only six of our members out of every hundred engineers for whom it has found work. Another loss which this Society has suffered, but which is not felt so keenly by our sister societies, is in its foreign members. The A. I. M. E. has always had a large foreign membership, but of recent years exchange has been so heavily against many European and South American countries that a large number of members residing abroad have been compelled to relinquish their membership. Almost invariably these members express keen regret because of the necessity that confronts them, and almost invariably the writers express hope that present conditions will not last long and that they will soon be able to ask-for reinstatement. Having stated the darkest side of the picture first, it may now be drawn to your attention that in spite of these losses the number of persons applying for membership was decidedly encouraging.

Jan 2, 1924

By S. N. Sharma, William Davis

Because of diminishing energy resources and rising energy costs, every industry is forced to carefully examine its pattern of energy consumption. The copper industry is no exception; current smelting practice begs for technological innovations that would improve the efficiency of its energy utilization. The thermochemical simplicity of copper metal production, as shown in Fig. 1, is deceptive. Designed from the same basic principles, there are four major commercial processes either in use or under construction; and others, such as the Mitsubishi process, are being developed.

Jan 5, 1977

By V. V. Clark

WHEN a district is more or less primitive, and a trained mining engineer attempts single- handed to prospect it according to old standards, he generally fails. He has not the ability to live out in the open alone for months at a time and carry on with enthusiasm and determination like the old-time prospector. But the same engineer, placed in an organized group where modern prospecting methods are employed, is immediately put on his mettle and his chances of winning are greatly increased. Marsman Investments, Ltd., with headquarters in Manila, has at the present time, Sept. 4, 1937, six prospecting parties in the Netherland East Indies. Three of these groups are combing their assignments for lode mines, studying structures, developing and reaching out into veins and zones with diamond drills. The other three are searching for placer mines with pans, pits, and Empire drills. I am in charge of one group seeking commercial gold placers on the Island of

Jan 1, 1937

By William B. Heroy

During 1932 no important changes occurred in the position of Africa as a producer of petroleum. The progress of development and production in each of the areas of interest is described below. Egypt The producing fields of Egypt are Hurghada and Gemsa, located on the west short of the Red Sea, and Abu Durba in the Sinai Peninsula. Most of the production is obtained from the Hurghada field, chiefly from beds of Cretaceous age. To the end of 1930 the Hurghada field had produced 2,831,751 tons of petroleum. The Gemsa field, discovered in 1909, reached its peak of production in 1914, when 88,000 tons were produced. Of late years the production has greatly declined. Total production of the field to the end of 1930 is 182,870 tons. The total production of Abu Durba to the end of 1930 is 7069 tons. The production of Egypt for recent years is as follows: 1928, 269,324 tons; 1929, 271,520; 1930, 281,997 (1,996,000 bbl.); 1931, 288,260 (2,038,000 bbl.); 1932, 253,182 (approximately 1,790,000 bbl.). Mozambique The operations of Inyaminga Petroleum Ltd., which was engaged in drilling in the colony, have been suspended. Angola Drilling operations in this colony, conducted by Companhia de Petroleo de Angola under a concession from the Portuguese Government, were continued. A test well drilled at Cacoba, about 60 miles southeast of Luanda, to a depth of 5651 ft. was not a commercial producer. A second well was being drilled in the vicinity at the end of 1932. Morocco Until last year the search for petroleum in Morocco was in the hands of several private companies but during 1932 the National Office of Liquid Fuels of the French Government took an active interest in the develop-

Jan 1, 1933

By R. W. Leonard

A method of accurately determining the value of gold-bearing ores and gravels with a compact field-outfit is much desired by prospectors, especially when the work lies in a district far removed from railways or good wagon-roads. We are all familiar with the fire-assay of gold-ores, and fully recognize its accuracy and value; but only those who have tried to determine the value of a gold-bearing vein as a commercial venture, from fire-assays of selected samples, know how misleading is the information thus obtained, however carefully and honestly the samples may be selected. The reasons are that, for the fire-assay a very small portion of ore is treated (rarely more than six assay-tons, or a little over one-third of a pound), and a minute particle of the precious

Jan 1, 1896

By C. F. Austin

lined-cavity shaped charge is an explosive mass with a cavity at one end and the detonator at the opposite end. The cavity is lined with a dense material, such as metal, glass, or a ceramic. Such an explosive device can be a useful drilling tool. Lined-cavity shaped charges are constructed to do just one thing — create a high-velocity jet of liner particles that can bore a hole in a target. The liner must be smooth and symmetrical, and high-velocity, high-brisance explosive must be used rather than ordinary commercial dynamites. Since the depth of target penetration is related to jet length, a standoff distance should be provided to hold the charge a short distance from the target. This allows the jet to lengthen prior to target impact. The best results are obtained when the jet is perpendicular to the target surface. Charges can be positioned for firing by taping them to a stake or simply laying them on a flat surface at the proper distance and angle with respect to the target. EFFECTS ON THE TARGET When a jet strikes a rock target, the jet and target particles at the jet-target interface move outward radially with respect to the jet axis to create a tremendous compressive load on the target material immediately below the target surface. The result is a shallow crater formed by spalling at the point of target entry. After cratering ceases, the steadily deepening hole continues to form as a result of the jet's imparting radial motion to the target particles at the jet-target interface. These radially moving particles collide with one another and with the hole walls, the net motion of the spent jet particles and target particles being back out of the hole in an axial direction (the backblast). The backblast keeps the penetration free of debris during penetration, al- though loose surface rock often falls into the hole after penetration ceases. The sudden stress relief after penetration ceases sometimes results in minor hole-wall rebound, which can partially fill the hole. The hole bottom will taper as the jet velocity decreases, until the jet velocity is too low to maintain the backblast. At this point the remaining jet and the following slug material are simply packed into the hole bottom. HAZARDS INHERENT IN USE Air blast from the highly brisant explosives used in shaped charges can damage nearby structures

Jan 1, 1961