Search Documents

By JOHN R. SUMAN

IT SEEMS particularly appropriate that the Institute's Regional Meeting should be held in Minnesota this year. Whether we like it or not, we cannot help looking at things now in the light of the World War and the all-out effort we, as a nation, are making to defend our resources, our institutions, and our way of life. The ability to do this lies in large measure in the ability to forge weapons of defense-the machines of war. The basic ingredients of any defense system, or war machine, are the raw materials of industry-iron ore, providing steel for guns, shells, tanks, and warships; coal for stoking the nation's furnaces; oil to furnish power for war planes, ships, trucks, and mechanized weapons; and all the other materials that play a vital role in the operation of modern armies and navies. The tremendous requirements of full-scale defense programs are indicated by the large number of commodities that are now under priorities because the supply is not sufficient to meet both defense needs and all normal civilian consumption. But out of all these items two are of paramount importance-steel and petroleum. In this age no nation can hope to main¬tain a position as a first-class power in the world without a highly developed industry, particularly the heavy industries based on steel, and without access to the necessary resources for those industries. In 1918, 70 per cent of the iron and steel production of the United States was required for defense purposes. In 1940, 15 per cent of our iron and steel production was consumed for defense purposes, and with the acceleration of the defense program, it appears that the proportion of steel output required for defense purposes will reach 40

Jan 1, 1941

By Earle C. Waite

THE Industrial Minerals Division this year held no individual sessions of its own except the business meeting Tuesday afternoon. One session was held jointly with the Society of Economic Geologists, one with the Milling Methods Committee, and two with the Society of Economic Geologists and the Mining Geology Committee. At all of these meetings the attendance was better than usual and the Tuesday afternoon session, with nearly 400 present, probably set a new record for the Division. Joint sessions seem extremely popular when papers of mutual interest are presented. On Monday afternoon, mica was the predominating subject. The North Carolina mines provided most of the information presented, although the discussion brought out similarities with the New England mines. B. C. Burgess particularly stressed the fact that with the existing curtailment of mica from India it is necessary to get the most mica in the shortest time from the mines in this country. He said that the Colonial Mica Corp. hopes to have 1000 mines operating in the near future. This seems a great number, but when one considers that these mines employ from 3 to 28 men, mostly nearer the low figure, the output of each mine is relatively small. Although the price of mica is from six to ten times the prewar price, the yield of 8 to 150 lb. of mica per ton of raw ore does not provide high returns to the producer.

Jan 1, 1943

By AUGUSTUS J. MONKS, Norman L. Weiss

THE Santa Barbara Unit of the Compania Minera Asarco, of which the San Diego mill is a part, is in the Parral District of southern Chihuahua. Although the concentration of sulfide ores has been practised in Santa Barbara since 1900, the San Diego mill, completed in 1921, was the first plant in northern Mexico to attempt the treatment of oxidized lead ores. From the milling point of view the many ores that have been treated at San Diego are very similar, the differences among them being rather of degree than type. Since 1921 the number of ores from different sources treated simultaneously has varied from four to eleven; in no case have any distinctive characteristics warranted the separate treatment of any of these. The zone of oxidation, source of the ores milled at San Diego, extends to a depth of 300 to 400 ft. below the surface. These ores carry more gold and less silver, lead, copper, and zinc than the underlying sulfide ores; the gangue minerals appear comparatively unchanged by oxidation and leaching. Lead occurs in diverse minerals, chiefly in cerussite, galena, and angle-site, the proportion of the lead in galena varying considerably in the different mines. An average of the feed to the mill would show the following approximate distribution of the lead content:

Jan 1, 1930

By John D. Sullivan, Edwin J. Rogers, Chester R. Austin

THE problem of making a building unit combining the necessary physical and mechanical properties and good thermal insulation has been foremost in the minds of architects and ceramic and construction engineers for many years. This paper presents the results of studies on thermally expanding shales or clays to produce light-weight cellular products suitable for making building units. An expanded clay block suitable for building purposes should be large enough so that substantial savings may be effected in labor costs in laying the wall. The permeability should be low and it should have sufficiently good "dry-wall" characteristics to permit exposing the exterior surface to the elements, and to permit plastering directly the inside wall surface. The thermal conductivity should be low and the mechanical properties should be adequate. Obviously, a unit possessing satisfactory qualities for constructing an outside wall would be satisfactory for interior walls and for back-up purposes. The results of studies on bloating various shales or clays† and the properties of the expanded products are reported. In another paper1 basic factors involved in bloating of clays are discussed. Manufacturers of ceramic products, particularly structural clay, may encounter bloating of the ware during burning, and precautions must be followed to avoid this phenomenon. About 1927 the C. F. Burgess Laboratories, Madison, Wis., while carrying on an investigation for the American Face Brick Research Corporation, conceived the idea of intentionally bloating clay while holding it in a restrained condition, with the hope of producing a unitary cellular mass. Work was carried on until about 1931, when studies were terminated because of business conditions. These studies were continued later by The Western Brick Co., Danville, Ill., which developed a process of "inwardly expansive bloating." The major purpose of the latter investigation was to produce back-up tile to compete with concrete blocks made from Haydite or cinder aggregate. Haydite is a light-weight aggregate formed by heating certain clays or shales rapidly in a rotary kiln. While the investigations at the C. F. Burgess Laboratories or at Western Brick Co. were not carried far enough to lead to the commercial production of material for the construction of walls, particularly outside walls, they showed that certain clays could be thermally expanded and that it was possible to produce a material of low permeability with a large percentage of the total voids or cells closed. Commencing in 1939, the Ozark Chemical Co. sponsored a research program at Battelle Memorial Institute for the purpose of determining whether it is technically feasible to make thermally expanded building units, and specifically to get answers to the following questions:

Jan 1, 1942

By Jerome Strauss

IN his review of developments in 1943, Gilbert Seil, Chairman of this Committee on Reduction of the Ferroalloy Ores, tabulated the consumption of the alloying metals in relation to the steel production of that year. In the year just closed the approximate tonnage was of the same order, differing only to a minor degree or suffering some correction with more precise figuses available, as indicated in the following estimates: Consumption Metals in Tons Steel 92,000,000* Manganese 700,000 Silicon 200,000 Chromium 200,000 Nickel 75,000 Molybdenum 20,000 Tungsten 8,000 Vanadium 1,700 Titanium 1.600 Boron 10 `Production figure. The technologic studies instituted during 1942 and carried forward with such great vigor during 1943 continued into 1944 although in some instances were brought to a close either by completion of the specific development

Jan 1, 1945

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

Organization Place Date 1919 American Society of Mechanical Engineers... New York, N. Y. Dec. 2-5 American Institute of Chemical Engineers.... Savannah, Ga. Dec. 3-6 Geological Society of America..: Boston, Mass. Dec. 29-31 American Society of Heating and Ventilating 1920 Engineers New York, N. Y. Jan. Mining and Metallurgical Society of America.. New York, N. Y. Jan. 13 American Institute of Min. and Met. Engineers New York, N. Y. Feb. 16-19 American Ceramic Society Philadelphia, Pa. Feb. 23-26 American Electrochemical Society Boston, Mass. Apr. 8-10* *On Apr. 9, a joint meeting will he held with the A. I. E. E.

Jan 12, 1919

Jan 1, 1970

By M. G. F. Sohnlein

IN a Bolivian tin concentrator an appliance was needed to furnish a suitable product for fine jigging from a pulp of the following composition: Mesh Per Cent. +20 8.0 +40 36.5 +60 9.0 +80 10.5 +100 5.5 +150 4.51 -150 25.0 99.0 Loss 1.0 IN the jigging process, particles of cassiterite as small as 0.1 mm. can be recovered, provided they are not present in excess, that is if the material treated on the jigs contains sufficient coarser sands to keep the interstices between the grains open. Removing the fine material from the pulp by screening, to prepare the jig feed, is impractical, because that means the use of an 80-mesh screen or finer, and is not as effective as hydraulic classification. A screen would eliminate mineral grains from the feed which can be recovered by jigging, and in addition would throw more gangue and low-grade middling on to the jig. Formerly a one-spigot Richards vortex classifier had been used to accomplish this separation, but the tangential openings through which the hydraulic water enters became clogged by fine vegetal matter with which the water was contaminated, and which it was impossible to remove from the water. Consequently the work of the classifier was imperfect and a good deal of slime was sent to the jig. When designing the plant referred to in this paper it was decided to use a hydraulic classifier as shown in Fig. 1. The essential features had been copied from the Anaconda classifier.1 This remodeled classifier consists of a truncated pyramidal wooden hooper A with an attachment of cast iron

Jan 4, 1916

By G. A. Bole, F. W. Davis

The purpose of this paper is not to report, to the Institute, the results so far obtained in the survey, by the Bureau of Mines, of the metallurgical requirements for open-hearth refractories, but to present an outline that we hope will serve as a basis for discussion. The systematic survey that the Bureau proposes to make has not been outlined, although considerable preliminary work has been done in the way of interviewing open-hearth superintendents in several of the larger steel plants from the Chicago district eastward. At the several conferences so many of the opinions were diametrically oppoeite, when considering the same point, that it was thought that such an opportunity as the Institute offers in the way of a clearing house for moot metallurgical topics should not be overlooked. For this reason, the paper has been prepared as a basis for a discussion which, it is believed, will be of value in outlining the program of the Bureau. D. A. LYoN, Assistant Director. The importance of securing suitable refractories for metallurgical operations is daily becoming more universally recognized; particularly in the manufacture of open-hearth steel, where the life and earning power of the furnace depends largely on the judgment and care exercised in the selection of the correct quality of refractory for each of the parts. Any innovation that would make available to the steel manufacturers refractories with longer life or better suited to their needs than those now employed, and at a cost that would permit of their use, would be of enormous value to the industry at large. It is quite probable that revolutionary changes would not be necessary. Material now used in some parts of the furnace might, by more suitable preparation, be made of much greater service; in other parts, possibly entirely different material would be necessary in order to effect much improvement. Inasmuch as different parts of the furnace structure perform different functions and are subjected to different service conditions, a refractory suitable for one part will be entirely unsuited for another. For this reason, to make a comprehensive study of the refractory requirements of the processes, we should consider the furnace as built up of a number

Jan 1, 1924

By Jean Bonnemaison

Societe Miniere & Metallurgique de Penarroya Noyelles-Godault works are located in the northern part of France. The complex includes a lead smelter, a zinc smelter, shops for production of manufactured products and all necessary general services. The zinc smelting complex described in this paper was designed in 1959 to replace an old horizontal retort distillation furnace and was first operated in May 1962. It includes: - a sinter plant producing the zinc sinter for the Imperial Smelting furnace : zinc, lead and bulk zinc-lead concentrates are sintered on a Dwight-Lloyd machine with a working area of 80 sq.m. Cadmium sludges are treated by the wet method in a separate plant for recovery of cadmium. Sulphur dioxide contained in gases goes to a gas washing tower and is subsequently made into sulphuric acid in a plant with a capacity of 550 m.t. per day. - a smelting plant where the process developed by Imperial Smelting Processes Ltd. is applied : the blast furnace which was modified in 1967 has an area of 17.5 sq.m. at the tuyeres level and a section of 24 sq.m. at the top of the shaft. It has a theoretical zinc capacity of 100,000 m.t. per annum. Air blast is heated by means of covers up to the theoretical temperature of 950ºC. Zinc produced is either directly cast into slabs for sale as standard 'good ordinary brand' zinc, or sent to a refining plant where the New Jersey process designed to produce 'special high grade' zinc is in application. Mixes of zinc containing various amounts of lead, cadmium or aluminum are prepared to customer specification in a mixing plant.

Jan 1, 1970

INTRODUCTION IT is 10. years this summer since the first of the contributions which it has been my privilege to make to the working tools of the hydrometallurgist was set at work, but a full description of what has come to be known as "Dorr Machinery" has never been published in the Transactions of the Institute, and it has been suggested to me that an account of the same would prove of interest to members, although most of those engaged in cyaniding and concentration are probably familiar with it. The account which I shall give of the development of the machines must be recognized as being written from the viewpoint mainly of my own local experience and not from that of one who was familiar with the general metallurgical practice throughout the world. Most advances in any art are conceived before the time is ripe for their development and any .invention which comes into general use will usually be found to have been tried out in a crude way and abandoned more than once. If the early experimenter went as far as the Patent Office, his work may serve no other purpose than to prevent the issuance of the broadest patent to those who later may develop a commercial process. The cyanide process in the United States early in 1904 was mainly confined to the leaching of dry crushed ores, both coarse and fine, and sand treatment of tailings from concentration and amalgamation. In the Black' hills some plants were crushing in cyanide solution, leaching sands and handling the slime by the well-known decantation process. Filter pressing, in use for some years in Australia,had been tried in several places in this country and the Moors process had been abandoned at Mercur after' a short run, but was doing good work at the mill of Lindbergh, Dorr & Wilson, at Terry, and being installed at Bodie and the Liberty Bell. A general feeling, however, still existed that, slimes were to be avoided when possible, on account of the losses in treatment and the difficulty of making a good leaching product when they were present in large amounts, especially when the crushing was done in cyanide solution.

Jan 8, 1914

By Scott Turner

IT has been considered that the training of an engineer is too often vocational training; that it is a pity all engineers cannot have had a period of liberal training before taking up' pure engineering. Offhand, the so-called liberal courses should bring more ready adaptability to deal with the unexpected, to face with assurance situations which have had no parallel in one's experience, and to move without hesitation under conditions which were heretofore unknown to one, than the specialized course in mining engineering. We hear increasing talk as to the necessity of making the engineer articulate and bringing him into public life. The social implications, and responsibilities of engineering are pointed out, as of equal importance with the prodigious marvels of engineering ingenuity. You often read of this as the logical result of the in¬creasing consciousness of the engineer as to his rela¬tive position in our modern industrial civilization. , Some wag has noted that man is the noblest work of God, but that man is the only one who has said so. Perhaps engineers are the only claimants as to the necessity of their going in for public life and service; at any rate, some liberal educators' still maintain that a well-rounded general education is the better training.

Jan 1, 1930

By Gordon B. Brox, Joseph F. Mcaleer, Charles C. Goddard, Edward P. Shea, Robert G. Ingersoll, Lester G. Zeihen, George J. Burns, John M. Guilbert, Richard N. Miller, Charles Meyer

The Boulder batholith is a composite intrusive in which the Butte quartz monzonite is the dominant rock type. Quartz porphyry dikes intruded the quartz monzonite in directions which were subsequently followed by the eastwest- striking Anaconda system of veins, the earliest major veins in the district. Anaconda veins are faulted by northwest-striking veins of the Blue system, which are most prominent in the central third of the district. Anaconda veins are the major producers in the western third of the district and also in the eastern third, where the "horsetail" zones break off from them. Individual oreshoots are thousands of feet long as well as deep on both systems of veins, but they are generally more persistent and thicker on the Anaconda veins. Viewed broadly, the mineralization in the big veins is arranged in crudely concentric zones of zinc and manganese around a central zone of copper. Only slightly offset from these zones, but earlier structurally, is a zone in which quartz-molybdenite veinlets are prominent. This zone tops at about the 2800 level and widens downward. The pattern of distribution of Cu-Fe-S series minerals in the large veins of the copper zone is not symmetrical with respect to the metal zones. There is a fringe of chalcopyrite-bornite all around the copper front. However, within the copper zone, pyrite-chalcocite-enargitecovellite- digenite assemblages are prevalent near its eastern edge from the 3800 level to the surface, whereas deep on the large Anaconda veins in the western part of the copper zone, chalcopyrite is dominant. Here the chalcopyrite grades upward into bornite-chalcocite ores and eastward into the high-sulfur assemblages of the Leonard mine. Sericite-biotite-K-feldspar alteration envelopes, containing up to about 2 per cent copper as chalcopyrite, are present on some of the quartz-molybdenite veinlets at deep mine levels in the molybdenite zone. These envelopes contrast sharply mineralogically and chemically with the later sericitic and argillic alteration envelopes around Main Stage veins. K'0-Ar'0 ratios indicate that they may be older by about 4 m.y. Secondarily enriched copper ores are mined in the Berkeley pit in the southeastern part of the district. At the present time they account for about half of Butte's production of copper.

Jan 1, 1968

By Odmund Ljone

FAR north of the Arctic Circle is a totally industrial community which until 1945 could not boast a single specimen of the rat family, and where today you will be awarded a bottle of fine cognac for every rat-dead or alive. Amazing but true, the spot is Longyear City, the Norwegian mining town on the arctic island of Spitzbergen. Perhaps you have also heard of the town built on soil that never thaws, where huge blocks of ice must be melted to fill the city's fresh water reservoirs, and where the Far North dictates a way of life all its own. Here, coal is king and men must work hard for their "black gold." Spitzbergen is a rough, tough piece of Norway, made up of a half dozen isolated islands between 74 and 81 degrees north latitude. Covering twice the area of Belgium, they are home to

Jan 1, 1948

By Sherwin F. Kelly

GEOPHYSICS may be considered a vice (albeit, I submit, a comparatively harmless one) whose career is aptly described by Pope's lines: Vice is a monster of so frightful mien, As to be hated needs but to be seen; Yet too oft, familiar with her face, We first endure, then pity, then embrace. Although there may be some that have not yet succeeded in emancipating themselves from the first stage of horrified contemplation, geophysicists may be duly thankful that there are mining men and geologists that have arrived at a state of apparently irretrievable damnation.

Jan 1, 1936

By Fred C. Bond and

This paper is a continuation of two earlier papers,12 and presents new data on the grindability of various ores and other materials—the results of several years of intermittent research work on the nature of grinding and interpretation of test results. It is divided into five parts: 1. The tabulated results of several hundred grindability tests on a wide variety of ores. 2. A method of correcting screen analyses and calculating from them the surface and other properties. 3. A description of a new method of measuring the "surface energy" of an ore by pendulum impact tests. 4. Test results. 5. A general discussion of the test results and their application to grinding problems. 1. GRindability of Various Ores This part is a continuation of the paper listed as reference No. 1. The method of testing is described in detail in that paper. The sample to be tested is crushed to all through 6 mesh in rolls set at 1/16-in. opening in closed circuit with a screen. Of this sample 700 C.C. is ground dry in a laboratory ball mill under constant conditions of mill speed and ball charge in closed circuit with a screen of the desired size at 250 per cent circulating load. The mill is cylindrical, 12 by 12 in., and rotates at 70 r.p.m. It contains a charge of 285 iron balls weighing 20,125 grams and ranging from 1½ to ¾ in. in diameter. Each test is continued for a sufficient number of periods to establish equilibrium at 250 per cent circulating load, or until the composition of the circulating load is constant for successive periods. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the results are expressed as the net production in grams of screen undersize per revolution of the mill. This is designated as the

Jan 1, 1939

By Fred C. Bond and

This paper is a continuation of two earlier papers,12 and presents new data on the grindability of various ores and other materials—the results of several years of intermittent research work on the nature of grinding and interpretation of test results. It is divided into five parts: 1. The tabulated results of several hundred grindability tests on a wide variety of ores. 2. A method of correcting screen analyses and calculating from them the surface and other properties. 3. A description of a new method of measuring the "surface energy" of an ore by pendulum impact tests. 4. Test results. 5. A general discussion of the test results and their application to grinding problems. 1. GRindability of Various Ores This part is a continuation of the paper listed as reference No. 1. The method of testing is described in detail in that paper. The sample to be tested is crushed to all through 6 mesh in rolls set at 1/16-in. opening in closed circuit with a screen. Of this sample 700 C.C. is ground dry in a laboratory ball mill under constant conditions of mill speed and ball charge in closed circuit with a screen of the desired size at 250 per cent circulating load. The mill is cylindrical, 12 by 12 in., and rotates at 70 r.p.m. It contains a charge of 285 iron balls weighing 20,125 grams and ranging from 1½ to ¾ in. in diameter. Each test is continued for a sufficient number of periods to establish equilibrium at 250 per cent circulating load, or until the composition of the circulating load is constant for successive periods. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the results are expressed as the net production in grams of screen undersize per revolution of the mill. This is designated as the

Jan 1, 1939

By C. P. Gazzara and

The modulus of elasticity and yield strength of commercially pure, annealed titanium sheet was investigated at room temperature as a function of strain rate and direction of loading. The value of E varied with direction of measuremeni in the sheet but was unaffected by strain rate in the range 0.04 x 10-to 10-2min-1. The yield strength increased with increase it2 strain rate and varied with specimen orientation. VALUES of the modulus of elasticity, E, in tension for commercially pure titanium have been reported at from 14 to 20Xl06 psi.' Reasons suggested for this variation have been a) composition, b) strain rate, c) texturing, and d) creep. For example, alloys of titanium with aluminum, manganese, and nitrogen have yielded modulus values of from 12.5 to 16.8 x lo6 psi at room temperature.' It was shown by Klier that the modulus in titanium plate was sensi-tive to strain rate. while Dotson and kattus meas- ured variations in E as the strain rate was increased from 3X to 60 min-l. For RC-7OA, 0.040-in. titanium sheet at room temperature Dotson and Kattus found that the average values of E, for specimens in the rolling direction, increased from 14.7 to 16.0 X lo6 psi as the strain rate increased. Simultaneously, the 0.2 pct yield strength increased from 74,700 to 95,700 psi for the same specimens. Differences in yield strength and E have been reported as a function of directionality in titanium sheet.= Dotson and Kattus report such an effect, and Feola6 found in annealed titanium sheet marked anisotropy in tensile strength, yield strength, reduction in area and elongation at room temperature, with

Jan 1, 1961

By K. E. Gray, M. S. Seth

In Part I of this work,1 equations of elasticity were formulated for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure. Equations of elasticity and the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant rate of pressure or a constant rate of flow is maintained at the wellbore. In this paper, the approach presented earlier is extended to finite reservoirs for the cases of (1) steady-state flow, (2) constant pressures at the well bore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Results of this work show that radial and tangential stress gradients are high near the wellbore but diminish rapidt; away from the well; the vertical stress gradient behaves in the same way but is less severe. Radial stresses are compressive or neutral, whereas tangential and vertical stresses may be tensile, neutral or com-pressive, depending upon the boundary conditions, the physical Properties of the system and the radial distance involved (vertical stresses are always compressive in an unbounded system1. For constant boundary pressures, both radial and tangential stresses increase with time whereas they both decrease for a closed outer boundary and constant pressure at the wellbore. The vertical stress decreases with time for both systems. For steady-state systems, radial displacement may be positive or negative, depending upon the dimensions of the system, the pressure differential and the porosity. Radial displacement may be positive or negative for a closed outer boundary but is positive for constant pressures at both boundaries. INTRODUCTION The importance, utility and complexity of a realistic appraisal of the stress state at and local to a wellbore were indicated in Part I. In this paper the analytical approach presented earlier is extended to finite, cylindrical reservoir geometry for the cases of (1) steady-state flow, (2) constant pressures at wellbore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Other than the outer boundary of the reservoir being finite, the physical system and assumptions pertinent thereto are the same as before. The reader may wish to review the mathematical development through Eq. 49 of Part I before proceeding here. SOLUTION FOR GENERAL BOUNDARY CONDITIONS THERMAL STRESSES AND DISPLACEMENTS Since normal stresses do not exist at the free boundaries of a system subjected to thermal stresses, the boundary conditions are

Jan 1, 1969