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By L. D. Patts, J. D. Noll, S. E. Mischler, G. H. Schnakenberg

In this study, we evaluated the ambient diesel particulate matter (DPM) concentrations (at the intakes and exhausts of the mine) as the entire vehicle fleet of a stone mine switched from using 35% biodiesel to using a water emulsified fuel (PuriNOx). Elemental carbon (EC) was reduced by 45% when a PuriNOx blend containing 10% water replaced 35% biodiesel and by 57% when a PuriNOx blend containing 20% water was used. Other factors such as engine duty cycle and production changes could potentially cause some day-to-day EC fluctuations, and no direct comparison to commonly used dieselfuels (No. 1 or No. 2) was achieved. Therefore, a second study was performed in a controlled “isolatedzone” environment to fametal mine, comparing PuriNOxto No.1 diesel fuel in a load haul dump vehicle. The EC fraction of the DPM was reduced by about 71% when the PuriNOx blend containing 10% water was used and by about 85% when the PuriNOx blend containing 20% water was employed. This study did not determine how the water emulsified fuel would affect the engine or power.

By Jurgen te Kook

State-of-the-art for subsidence calculation are stochastical models. Although these models were successfully used all over the world they have their limitations due to the fact that they are not based on mechanical laws. For example the models did not take the rock mass structure and the rock mass characteristics into account. Therefore in a research program the skills of geomechanical numerical models for subsidence calculation were investigated. A case study shows that numerical models which are in principle based on the elastic theory are suitable for subsidence prediction. Due to the principles of these models the results are not sufficient in the case of multiple seam extraction. More extended geomechanical numerical models like FLAC and UDEC were investigated in further steps of the research work. Up to now large area geomechanical models require unrealistic long calculation times if the level of detail is similar to that of small scale calculations. Due to this it was necessary to implement a simplified description of the rock mass structure and characteristics. Different case studies show that this approach is successfull for subsidence calculation by numerical geomechanical models even for multiple seam extraction.

Jan 1, 2008

The relationship between the maceral composition of coal and the strength of the coke produced from that coal has received a great deal of attention in recent years.Studies using two Bulli Seam coals, and blends of Bulli and Wongawilli Seam coals, from the IIIawarra Measures of the Southern Coalfield of New South Wales were carried out.The optimum range of vitrinite was found to lie between 45 per cent and 60 per cent (mineral matter free).Above and below this vitrinite range coke strength deteriorated. Coke strength indices increased with rank, and the optimum vitrinite content increased with an increase in rank. These changes require confirmation as trends by testing a third level of rank. It was noted that vitrinite content decreased with an increase in the specific gravity of separation of the coal.Use of petrographic analyses will increase confidence in choosing coals for coking, provided the coals are well known. Such analyses offer the possibility of greater flexibility in coal purchases and the possibility of producing a marketable blend from coals, which have limited market potential. Critical base coals for blends can be conserved.Significantly more work is required before coal reserves can be utilized to optimum advantage. This work would require extension of the studies discussed in this paper and, in particular, the testing of a wider range of rank.

Jan 1, 1971

By M. R. TECK, N. Rudd, L. K. Thomas, D. L. Katz

The authors are to be congratulated for presenting the first comprehensive paper on the theory and practice of threshold pressure determination in connection with underground gas storage. It is of particular value since most previous experimental work on this subject has been proprietary to the commercial laboratories engaged in such testing and to their clients. This dlscussion is presented in amplification of the subject paper, not in criticism, and is based upon our experience with approximately 5,000 threshold pressure determinations. Our comments are directed primarily to the experimental procedures as described by Thomas et al. It should be noted that, while clay mineral-rich lithologies are the most common caprock materials, the samples used (Table 1) include low permeability sandstones and carbonates, but do not include shales or other formations in which clav minerals exert a dominant effect. While our experience on samples analogous to those investigated by the authors generally confirms their findings, we have found that even more rigorous experimental conditions must be imposed where clay minerals are the controlling factor. These additional conditions result from the well-known molecular character of the clay minerals themselves in which water is interlaminated with, and bonded to, silicate sheets, thus becoming an essential component of the molecule. In many clay minerals the character of the intersheet bonding, and thus the dimension of the lattice, is strongly affected by variations in the identity and concentration of cations present in the intersilicate water. On a supermolecular scale, adsorbed water films on particle or "flakes" of shale provide much of the cohesive force necessary to maintain mechanical strength. The thickness of these films is variable and inversely proportional to intergranular pressure within the dimensional limits involved in caprock investigation. The thickness of the intersilicate water layers may also be subject to pressure under some conditions. These considerations are reflected in several necessary modifications of the experimental procedures described by the authors. Two of these are, in our judgment and experience, of such importance that they cast real doubt on the validity of data obtained on argillaceous materials without their application. The very careful resaturation procedures proposed by the authors should give good results in connection with the relatively "inert" lithologies used in their experiments. Our experience suggests, however, that they would create more problems than they would eliminate if applied to argillaceous materials. 1. Drying of the sample at the temperature and for the duration indicated by the authors not only will dessicate the sample with consequent shrinkage cracking, parting along bedding planes, and even total disassociation in the case of fissile shales, but it may also alter the character of the clay minerals themselves — in some cases irreversibly. 2. Prolonged evacuation to 2 microns Hg further dessicates the sample and is even more effective in reducing the intersilicate water content. 3. Resaturation with water differing in pH or chemical content from that existing originally in the sample also serves to alter the nature of the sample, particularly its structure and strength. 4. Our experience has been that, even with the thorough precautions proposed by the authors, complete resaturation of very fine grained materials is rarely obtained. Yet our experience confirms the

Jan 1, 1969

By Richard R. Klimpel

Introduction Froth flotation is one of the most common unit engineering operations in use today. Its aim is to upgrade the quality of coal by removing ash/pyrite and separating selected minerals from undesired gangue materials. Flotation has been successfully practiced at the industrial scale for more than 50 years. Its use is increasing due to the ever decreasing feed grades of the coals and minerals being processed. Flotation has also shown itself to be a flexible process that lends itself well to many solid/solid separations. Thus, with surprisingly little equipment modification, separations can involve very different particle sizes and densities, and relative weight ratios of materials to be separated. In addition, the flotation process is economic, especially when compared to size reduction, its associated precursor process. Flotation also lends itself to continuous operations with a given equipment configuration. The operation must exhibit an ability to vary feed rate of solid to the process by as much as 50% without a total collapse of separating efficiency. In addition, the mechanical flotation cell is scaleable from 2.8 to 57 or 85 m3 (100 to 2000 or 3000 cu ft) with surprising ease relative to other unit engineering operations over the same relative size increase. The separating medium used is water. Most of the chemicals required - pH regulators, frothers, collectors, activators, and depressants - are all relatively inexpensive and common. They are not usually used in large quantities. Froth flotation is certainly one of the most versatile and forgiving unit operations in the chemical, mining, and agricultural industries. The problem with the industrial flotation process is that it is fairly easy to get reasonable results and relatively difficult to get excellent results. Why is it so difficult to fine tune the froth flotation process? There are some obvious reasons and a few not-so-obvious factors. The obvious category would certainly contain the tendency of natural feed materials (ores and raw coals) to have variable physical, metallurgical, and surface properties. This occurs even when special care is taken to minimize such differences with blending. There is another obvious reason for difficulty. An inherent broadness of the feed particle size range to flotation results from using any of the common industrial-scalefine grinding devices - ball-, rod-, or autogenous mills. Research has been done into the chemical reagent and equipment aspects of flotation. It has shown strong interactions (limitations) of chemical reagents and equipment on larger and smaller particles. The point is that current flotation practice works best on average- or medium-sized feed particles. The greater the amount of large or small particles, or of both large and small, the more difficult it is to achieve excellent flotation results. Other reasonably obvious factors include: • variations in mineral type and liberation sizes; • water chemistry variations such as those involving Ca", C03, or Fe", or various soluble metal cations; • the presence of stray organic materials such as returning soluble reagents or partially degraded reagents in reuse water; • the lack of reliable on-line instrumentation for monitoring and control; • frequent equipment malfunctions of all types; • excessive feed rates for installed plant capacity; • poor operator interaction with the process; and • poor reagent dosage control. There are less obvious, but real limitations to flotation. These are inherent in the design and operating characteristics of the most common cell design in use today - the mechanical flotation cell. Individual performance attributes of the chemical reagents used, along with their manner of use, also carry limitations. The bulk of this paper will deal with chemical reagents and their use. Chemical reagents In 1979, the author and his co-workers were asked to invent and implement, at the industrial scale, new flotation reagent chemistry. After reviewing some of the literature (Sutherland and Wark, 1955; Klassen and Mokrousov, 1959; M. Fuerstenau, 1962; D. Fuerstenau, 1976; and Leja, 1982), a series of carefully controlled plant scale tests were set up. These tests were designed to understand existing reagent scale-up from the laboratory to the plant. They were to quantify at the plant level the effect of some of the more important, controllable chemical reagent factors (frother and collector type, frother and collector dosage, pH effects). This is a learning experience that all researchers involved in flotation theory should experience. It quickly became apparent that: • because a factor is important

Jan 12, 1988

By Howard W. Wainwright

The Bureau of Mines is engaged in a research program on the characterization of tars produced by low-temperature carbonization of coal and their economical upgrading to more valuable materials, Throughout the years, hydrogenation has played an important role in the treatment of these tars, mainly as a means of converting the whole crude tar or selected fractions to motor fuels; diesel oil, lubricating oil, or various solvents. In some instances, production of specialty chemicals has been the objective. The purpose of this report is to summarize, without critical review, the information of the past 25 years on the hydrogenation of low-temperature tars and related substances as presented in the literature or its English translation. Published articles and patents not abstracted in the main body of this report are included in a bibliography at the end. HYDROGENATION REACTIONS The hydrogenation of tar follows three general types of reactions; 1. The removal of oxygen, sulfur, and nitrogen in the tar to form water, hydrogen sulfide, and ammonia, respectively: [ ]

Jan 1, 1961

By Roy Peratrovich

An innovative cost-saving design for a 1,100 ft bulkhead on the Tanana River at Nenana in central Alaska won Alaska Construction & Oil magazine's Construction Achievement Award. The designers utilized materials available nearby at low cost. They planned sheet pile enclosures, self-anchored back into shore without cell closures. They made it practical for inexperienced local workers to do the building. And they completed the project on time and below a reduced budget.

Jan 1, 1985

By W. D. Bensema

Two different techniques were used to make measurements of the absolute value of electromagnetic noise in an operating coal mine, Itmann No. 3 Mine, located near Mullens, West Virginia. The electromagnetic environment created by 250-volt-dc and 550-and 950-volt-ac machinery in two longwall panels was measured and is reported. One technique measures noise over the entire electromagnetic spectrum of interest for brief time periods. It is recorded using broadband analog magnetic tape, and the noise data is later transformed to give spectral plots. The other technique records noise amplitudes at several discrete frequencies for a sufficient amount of time to provide amplitude probability distributions. The specific, measured results are given in a number of spectral plots and amplitude probability distribution plots.

Jan 1, 1974

By Scales PJ, Ralston J

Fine coal particles have been examined with respect to dustiness and its connection with various physical and chemical properties. It appears that a given coal will tend to be dusty ifthe moisture content is low and if the inert maceral content and overall rank are high. The hydrophobicity ofa coking coal (Young-Wallsend) and a steaming coal (Blair Athol) was examined in detail by a dynamic contact angle technique. The YoungWallsend coal had a higher contact angle, on average, than the Blair Athol sample. This result has important implications for dust suppression and associated processes.

Jan 1, 1986

By Bruce W. Woolpert

During the SME Board of Directors’ midyear meeting in Monterey, CA Aug. 25, I discussed trends in the construction aggregates industry. Many construction-material suppliers may not have yet fully internalized the changes that are taking place. But the changes are significant. And they have shifted the focus in the aggregates industry from “assets” to “people and innovation.” Construction-material suppliers serve many customers. A typical quarrying operation at Graniterock would have more than 1,000 customers, mostly civil engineering contractors. Along with the push toward people and innovation, there is increased emphasis on vertical integration from aggregates to ready-mix concrete and hot mix asphalt, to final construction. If a company is not vertically integrated, it will at least have strong partnerships with other firms, to deliver a high-quality finished project on time.

Jan 1, 2002

By Mark Ferra

Flotation is used in mining to produce concentrates of copper, gold and several other valuable ores. In 2017, a copper mine near Globe, Arizona improved their rougher cells productivity using technically advanced electro-hydraulic actuators in the flotation process by enabling excellent tank pulp level process stability. The new actuators controlled the dart valve position to allow pulp to leave the cell. Tank cell pulp level can change due to feed and discharge fluctuations from neighboring tanks. When traditional pneumatic actuators are used, they have sluggish response times and overshoot due to the inherent physical property of air being compressible. Electro-hydraulic actuators have the benefit of hydraulic stiffness to deliver accurate and repeatable (0.1%) dart valve positioning. The froth layer has more opportunity time to maximize mass transfer into the launderer. The results are an increase in copper recovery by 2-4%. INTRODUCTION In 2013 there was an international flotation technical conference well attended by respected flotation specialists for both mining companies and academia. During the technical session a leading metallurgist was discussing pulp level measurement and said that when he was on the cell deck he stated, pneumatic actuators air cylinders stroking up and down. The presenter then claimed with confidence that "I listened to actuator move so the pulp level in the tank was being controlled!" No one questioned his assumption and I can assert that the audience was quite technical and not shy in their critiques of speakers. The flotation community simply believed that the existing pneumatic technology was enough with no alternative. Having a stable flotation cell pulp level is critical to effective copper recovery. Controlling pulp levels in flotation cells is a complex task that includes modulating dart valves in each cell. The use of REXA Electraulic actuators will decrease the process dead time and maintain froth height in a controlled manner, especially from pulp slurry volume fluctuations from neighboring cells. By reducing flotation cell pulp level tank height variation, a copper mine in Arizona has realized a 2-4% recovery improvement by increasing the froth transfer to the launderers in the rougher cell circuits compared to pneumatic actuators. This paper examines the benefits of using an electro-hydraulic actuator to ensure proper pulp level control and reduce the process operational cost. It will focus on actuator positioning the dart valves to maintain pulp level setpoint at a copper mine in Arizona.

Jan 1, 2019

A unique sluicing process for recovering tailing impounded in a valley was developed by Electrolytic Zinc Company of Australasia Ltd., West Coast Mines, Rosebery, Tasmania.Earthmoving equipment could not be used as most of the material to be recovered was semi-fluid. A conventional sluking method was also impracticable as there was no suitable working face from which the process could be commenced.Operations started from a flat surface, using special techniques for sinking through the tailing and establishing producing working faces as the sinking process continued.After about 2 years the bottom of the dam was reached and conventional sluicing methods could be used.

Jan 1, 1973

By R. H. Richards, A. E. Woodward

In Rittinger's Aufbereitungskunde of 1867 occurs (p. 195) the following table, which shows the rate of falling in water of fragments of minerals, of irregular shapes and of five different specific gravities: Diameter of particles in millimeters. 10 8 6 4 3 2 1 .5 Sp. Or. Velocity in meters per second. Auriferous silver, 16..9 .8 .7 .57 .5 .4 .29 .20 Galena,. ..7.5 .62 .55 .48 .39 54 .28 .20 .14 Pyrites,. ..5.0 .49 .43 .38 .30 .26 .22 .15 .10 Quartz,. ..2.6 -30 .27 24 .19 .17 .14 .10 .07 Coal,. ..1.3 .13 .12 .10 .08 .07 .06 .04 .03 With the purpose of extending this valuable table, to cover a larger number of minerals and sizes of each mineral, and of making it more easy of application in deciding upon a sieve-scale for any group of minerals, we have prepared the curves of velocity of fall of bodies in water shown in Plates I., XI., 111. and IV., using Rittinger's formula V= 2.44d(8 —1) where V= velocity in millimeters per second. " D = diameter of particles in meters. " 8 = specific gravity of the mineral. These curves embrace a large number of specific gravities, and for each specific gravity the relation of the diameter of the mineral particle to the velocity of its fall in water is given for all diameters and velocities used in practice. The second diagram is an enlargement of the lower left-hand corner of the first, the third bears the same relation to the second, and in like manner the fourth to the third. Plate I, therefore, covers the work of the coarsest jigging 2 inches in diameter; and under

Jan 1, 1890

By H. J. de Haan, L. Schenk

Scope for Thermal Recovery in Shell's Heavy Oil Fields in Venezuela The main heavy oil reservoirs on the East coast of Lake Maracaibo (Fig. I), known as "Bolivar Coast", initially contained some 20 billion bbl of oil in place with gravities in the range of 10 to 15° API. The current total production rate is about 400,000 B/D. Since the recovery to date is on an average only 12.5 percent of the initial oil in place, these fields offer a vast potential for secondary recovery methods. The reservoirs are characterized by moderate depth (generally 1,000 to 3,000 ft; maximum 5,000 ft), good formation properties such as net oil sand thickness (50 to 300 ft), high porosity (30 to 40 percent) permeability (1 to 3 darcies) and oil saturation (initially about 80 percent) and high oil viscosity (100 to 10,000 cp in situ), all of which are favorable for the application of thermal recovery processes. Since 1957, steam drive, steam "soak" and underground combustion have been tested or are being tested in this area.1-3 This paper deals with a major steam drive test in the Tia Juana field. The test was commenced in Sept., 1961, on the basis of encouraging results of laboratory experiments and pilot field tests, which will be discussed briefly. Early Laboratory Investigation of the Steam Drive Process In 1956 a series of model experiments was carried out in the Koninklijke/Shell Laboratorium, Amster- dam, to investigate the displacement of heavy oil by steam.' The prototype studied was a horizontal, un-consolidated heavy oil reservoir, subjected to a linear steam drive. The model, representing a slab from this reservoir along the main flow direction, consisted of a steel tube filled with oil-saturated sand, provided with layers of rock at the top and bottom to simulate conductive heat losses to cap and base rock. Lateral heat losses, perpendicular to the main flow direction, were minimized by insulating the sides of the model. Heat flow and viscosity and gravity forces were scaled by taking the steam injection rate and sand permeability inversely proportional to the geometric reduction factor of the model, and using materials (oil, steam, cap rock, etc.) identical with those of the prototype. The main feature of the process was a frontal displacement mechanism that was observed within wide ranges of injection pressure and rate, oil viscosity, initial oil saturation and sand permeability. The high stability of this front can be attributed to the high volumetric steam flow rates, combined with the reduction in oil viscosity. High recoveries were obtained due to the low residual oil saturation of about 15 percent in the zone swept by steam. The latter value pertains to the specific test conditions (heavy oil, uncon-solidated sand) and may be lower for light oil, due to the effects of steam distillation. The applicability of this experimental approach is limited, as it does not take into account the fact that

Jan 1, 1970

By L Tolmay, L Nair

Investor confidence can be compromised when one observes large discrepancies between the SAMREC reserves and the mining plan. It is therefore up to the responsible persons to ensure that all contributing factors get taken into account when determining a reserve declaration. Confounding factors could be further aggravated by large oscillations in the commodity price thus resulting in major changes to the mining plan, if the accepted price was either too optimistic or pessimistic. Additional factors that must receive our attention are, uncertainty in geological facies type, mining practices, geology and grade estimation. The paper outlines (in the authors? opinion) some of the important factors that need to be taken into account, in order to ensure proper alignment between the estimates of the life of mine (LOM) reserve grades, and the corresponding actualisation of the mining plan. These parameters provide an historical insight into what actually happens when attempts are made to implement the mining envisaged in the LOM plan. In turn these allow judicious application of discount factors that enable a realistic estimate of SAMREC reserve classification and declaration. Some of the factors that will be covered are: - 1) Flexibility of developed reserves and the ability to maintain this. 2) Mining control mechanisms and their overall efficacy. 3) The ability to extrapolate facies types and its effect on grade control. 4) The ability to control the mining mix and value variation. 5) Finding a happy medium between optimism and pragmatism.

Jan 1, 2007

By Jeff Jackson, Paul Axtell, David Graham

The Montana Department of Transportation recently awarded a contract to construct a replacement bridge across the Clark Fork River in Heron, MT. Both abutments and both intermediate bridge bents were to be founded on 6-ft and 8-ft diameter, permanently cased drilled shafts with rock sockets, respectively. Two drilled shafts per substructure location were designed for a total of eight drilled shafts. The original design included 6-ft diameter drilled shafts at the abutments but the Contractor elected to submit a Value Engineering proposal that increased them to 8-ft diameter. On the basis of the subsurface exploration program, extremely challenging subsurface conditions were known to exist, including the potential presence of large boulders within the predominantly sand and gravel soil matrix. The successful bidder elected to use an oscillator to install the permanent casing to the top of bedrock, while simultaneously removing the spoils from inside the casing with a clam-grab. On seven of the eight shafts, this approach worked well. Unfortunately, on one of the shafts, the casing met refusal on one or more boulders encountered in the predominantly sand and gravel soil overburden. Following several attempts, and despite several variations of approaches, it was determined that the casing could not be advanced beyond the obstruction without unacceptable risks to the pile-supported temporary work trestle (i.e., loss of soil and reduction in pile capacity for the foundations supporting the work trestle). To mitigate the problematic drilled shaft, a unique solution was designed and successfully constructed. The solution involved the construction of seven 16-in diameter micropiles constructed within the confines of the obstructed casing. The micropiles were drilled to bedrock through the sand, gravel, and boulders and include rock sockets to satisfy axial design requirements. The micropile casing thickness, grade and grout strength were designed to provide adequate flexural strength as well as to satisfy other design requirements. Upon completion of the micropile installation, the upper portion of the drilled shaft above the boulders and within the permanent casing was constructed as usual. This paper discusses the difficult subsurface conditions at the site, the drilled shaft construction difficulties, and the design and construction of the micropile solution.

Jan 1, 2018

By Warren M. Mahan

A rotary kiln process was developed by the Federal Bureau of Mines to produce consistently an iron product containing 3 to 7 percent nickel. Cuban laterite and serpentine ores were smelted in a gas-fired batch-rotary kiln) 5 feet in diameter and 9 feet long. The metal contained 2 to 4 percent carbon, with little or no silicon, and could be produced on a large scale with modest capital investment. A total of 121 tests was run using this procedure. The tests were conducted with a maximum temperature of 2,625° F., using linings of firebrick containing 40 to 70 percent alumina. Slags in the kiln were acid to neutral. The material in each batch passed through three stages: (1) Sponge metal, (2) carburization, and (3) balling and meltdown. Half the tests were made while firing the kiln with atmospheric-temperature air; the remainder were fired with preheated air. Tests showed that preheated air decreased fuel requirements, dust losses, and reducing agent, and increased the capacity of the kiln.

Jan 1, 1960

By L. Tonc

In 2004, the engineers at the Deer Creek Mine located near Huntington, Utah initiated the ventilation planning to exploit a remote area of the mine?s reserves. This area was located under a mountain which would not allow for the incorporation of an additional shaft or portal access near the proposed longwall panels. With this constraint along with the desire to maintain a two entry gate road system and the expected condition of frequent coal wash outs a ventilation plan was established. Different options were examined that included; increasing the current exhaust fan power, adding another exhaust fan installation, converting the ventilation fans in the active portion of the mine to a forcing system, and modifying the ventilation system in the active area of the mine to a push-pull system. The push-pull ventilation system was ultimately selected. This paper details the design process of the ventilation system upgrade, the procurement process for the new fans, and the new fan startup testing.

Jan 1, 2009

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

Jan 1, 1967