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NOT all the lead in the country comes from the big operations. A member sends in this photograph of the wash-up from the "Old Timers Lead Mine," at Galena, Ill. He omitted to inclose a flow-sheet of the concentration process, which detracts somewhat from its value to the technical man, and cost figures are lacking. Perhaps he was run off the lease when his questions on milling recoveries became too searching. Still and all, according to the picture the plant ap-pears to be operating efficiently. It is reasonable to believe that the cost of electric power per ton milled is held to a low figure. We commend the proper pro-fessional stance of the gentleman on the business end of the hand jig, though we look in vain for the time honored spring board to aid him in giving the most efficient stroke.

Jan 12, 1927

By Arthur L. Hall

The purpose of this symposium is to challenge industry to better air classification, and as a first step toward fulfillment, to spotlight three fairly recent, aerodynamically designed, highly efficient air classifiers. This discussion does not intend to imply that present practice is bad. Actually, when present air separators are used for the jobs for which they were originally designed, they give high production and uniform operation, with a minimum of maintenance. The customers of nonmetallic mineral pigment producers, however, are making increasing demands for finer products, such as 99.9 pct -20µ, which appears to be beyond the economic capabilities of standard air separators industrially used over the last 10 to 30 years. Here is an actual example. A 10-ft diam pebble mill is in closed circuit with a conventional 12-ft diam centrifugal air separator, grinding 20-mesh wollastonite to a series of fine grades up to 99.97 pct - U.S. No. 325 mesh (44µ). Fig. 1 shows variations in fineness of mill discharge (or air separator feed), recycle for regrinding (or air separator tails), and product as measured by a wet rotating sieve test. For example, when the mill is turning out a product 80 pct -325, the mill discharge or separator feed is 30 pct -325, and the coarse tailings or recycle is only 5 pct -325. Hence 25 pct of the 30 pct available is accepted as product. This is efficient separation, and the ratio of recycle to feed is only about 2: 1. How- ever, to make a product testing 99.97 pct -325 the separator feed is 62 pct -325 and the coarse tailing 60 pct -325. In this case the recycle ratio is about 13: 1 and the economic limit to produce fineness has been substantially reached with this given equipment and process arrangement.

Jan 10, 1957

By John V. Beall

BROMO Seltzer blue has gone to war. The blue of the Bromo Seltzer bottle is a product of cobalt, the Nation's No. 1 strategic metal. When the National Production Authority, on Nov. 21, 1950, ordered a 70 pct cutback in domestic use of cobalt, a stab of pain was felt in the hearts of the glass, porcelain enamel, steel, paint, pottery, and electrical and electronic equipment industries. The reason: A full-scale wartime economy with astronomical requirements for jet engines, high velocity projectiles, armor plate, electronic equipment, and the many products needed to win a war. There is little potential comfort for cobalt users in nonessential manufacturing, and the military will be pinched for optimum supplies of the metal. However, if proper measures are taken immediately and current plans are completed, in two years there will be far more cobalt available than ever before. When normal times return, cobalt supplies should be sufficient to meet peacetime military requirements, and greatly expanded domestic requirements that will result from new technological development for wartime but adaptable to peacetime products. The pres-

Jan 1, 1951

By J. Hoover Mackin

The iron ore bodies of the Iron Springs district are replacement deposits of magnetite and hematite in Jurassic limestone around the borders of three intrusions of quartz-monzonite porphyry. Production in the period 1923-1965 was about 72,000,000 tons, nearly all of which was direct-shipping ore from open pits. The intrusions are laccolithic in form; all three were emplaced at the same stratigraphic horizon, which had been a zone of decollement gliding during the Laramide orogeny. The intrusions and associated volcanic rocks are post-orogenic. There was no change in the thickness of the limestone during the metallization. Comparison of the composition of the limestone and stratigraphically equivalent replacement ore indicates that, with every million tons of iron, there were additions of 40,000 tons of silicon, 20,000 tons of magnesium, and 10,000 tons of aluminum. The ore-forming fluid was derived from the exposed porphyry. The iron was first incorporated in hydroxyl-bearing mafics, which crystallized in depth and were carried upward in the magma that formed the hypabyssal intrusions. The mafic phenocrysts decayed deuterically in the new environment, releasing iron into the interstitial fluid of a consolidating crystal mush in the interior of the intrusions. Primary tension joints, which opened in areas of late intrusive distention, served as roots through which the ore-forming fluid was drawn from the crystal mush.

Jan 1, 1968

By Ling Yang, John Henderson

Self-diffusion coefficients of copper in molten copper have been measured by the capillary reservoir method in the temperature range 1140o to 1260°C. The results can be represented by the equation D = [(1.46 * 0.01) x 10-3) exp [(-9710 * 710)/RT] cm2/sec. The energy of activation agrees within the limit of experimental uncertainty with that for viscous flow. The relationship between the diffusivity and coefficient of viscosity is best described by the equation D = kT/4pnr cm2/sec. MEASUREMENT was made of the self-diffusion coefficient of copper in molten copper in the temperature range 1413º to 1533ºK, using the capillary reservoir technique and CU64 as the radioactive tracer.The procedures for filling the capillaries, making the diffusion run and evaluating Dcu from the counting results were the same as described previously.1,2 All experimental operations involving the melt were carried out in a purified argon atmosphere. A graphite crucible, enclosed in a McDanel tube, was used as a container for the melt because of its satisfactory nature as a refractory material and the low solubility of carbon in copper. Graphite was also used for the capillary material. A McDanel thermocouple sheath, to which graphite radiation shields were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube, the capillaries could be lowered into or raised out of the melt. A Globar furnace with a constant temperature zone (± 2°C) of 2 in. was used to heat the assembly. The temperature of the furnace was the equilibrium value corresponding to a given setting of the transformer. Temperature was measured with a Pt-10 pct Rh/Pt thermocouple and varied during a run

Jan 1, 1962

By C. F. Weinaug, R. W. Farley, J. F. Wolfe

A rapid, accurate method for predicting the dew points of gas condensate systems and their subsequent normal and retrograde phase behavior with pressure decline has been developed. The method predicts dewpoint pressure, volume percent liquid, condensate content of produced gas, and the liquid and gas compositions at pressures below the dewpoint pressure. Use of a modified form of the BWR equation of state, which was established by regression calculations on experimental data from several gas condensates, provides depletion behavior predictions that are significantly improved over predictions using K-values based on convergence pressures and Standing's correlation for density. INTRODUCTION Prediction of complex hydrocarbon-mixture thermodynamics is fundamental to reservoir and gas process engineering. In particular, accurate descriptions of phase behavior are needed to plan production operations for gas-condensate reservoirs. Although analysis of reservoir behavior during producing and cycling operations can be made for simple reservoir models, extensions of these studies to more complex reservoir systems are still difficult, both with regard to numerical techniques and the phase behavior of the fluids. This report presents a mathematical method for handling the complex phase relationships encountered in retrograde condensates; it represents an advance in reservoir behavior technology in that it will aid the development of closed-form mathematical representations of total production systems. A typical phase diagram for a complex hydrocarbon mixture is shown in Fig. 1. When the reservoir temperature T, is higher than the critical temperature Tc, and lower than the critical-condensation temperature Tct' the mixture is a gas condensate. Decreasing the pressure on a condensate while maintaining nearly constant temperature will result in two phases forming at the dew point. Further decrease in pressure will cause additional liquids to be formed. This phenomenon is called retrograde condensation. As pressure continues to decrease, normal phase behavior regions are encountered (liquid vaporizes as the pressure decreases) until the low-pressure dew point is encountered. When a gas-condensate reservoir is produced, gas is withdrawn and the volume of fluids in the reservoir remains nearly constant as the pressure declines. Heavier components tend to accumulate in the liquid phase as a result of retrograde condensation, while lighter components tend to concentrate in the vapor phase. Thus, as the gas is produced the composition of the gas and the condensate

Jan 1, 1970

By A. N. Rogers

Jan 1, 1883

By Hugh S. Spence

IN MAY, 1930, G. LaBine and E. C. St. Paul, prospect¬ing round the southeastern shore of Great Bear Lake, in the North West Territories of Canada, discovered pitchblende at what is now LaBine Point. At the same time, they also found native silver in a small sheared break on an island lying off the point. Late in 1930, samples of the pitchblende were sent to the Mines Branch, at Ottawa. The material consisted of several fair-sized slabs of botryoidal pitchblende banded with a brownish quartz. A small amount of chalcopyrite was visible as small particles and fine veinlets, and the pieces were rather heavily stained a yellowish-green by secondary copper-uranium salts. Analyses were run in the Mines Branch Ore Dressing Laboratories on two samples, and small-scale concentration tests were made on one of them. The results of this work were published in a Memorandum Series report (No. 48) of the Mines Branch, in March, 1931.

Jan 1, 1932

By Julian Avery

IN its dual role of pig-iron smelter and gas producer, the blast furnace is a remarkably satisfactory and efficient apparatus. Many metallurgists and engineers have pointed out, however, that since the primary function of the blast furnace is to produce pig iron at the lowest possible cost, its function as a gas producer should be subordinated to this primary pur-pose. During the past 10 years or more, improvements in blast-furnace technique and economy have, in fact, been directed primarily to increasing efficiency in the use of the reducing power of the gases produced by com-bustion of coke at the tuyeres, to reduce iron ore within the furnace. The net over-all result is a decrease in the fuel value of the top gas per unit of volume, and per ton of pig iron, which is evidently more than offset in value by the corollary saving in coke and the possibility of increased furnace capacity, for otherwise there would be no point in making such improvements. The purpose of the present paper is to suggest that, while progress has been made in this direction, there is another approach to the problem of increasing the chemical and thermal efficiency of the blast furnace in its primary role as a pig-iron smelter, which appears to offer possibilities of improvement in over-all economy of a different order of magnitude than results thus far obtained by the use of other expedients. The present argument is based in large part upon the hypothesis that the effi-ciency and economics of pig-iron smelting are seriously and adversely affected by the phenomenon known as "solution loss," and that the problem of solution loss can be successfully attacked by increasing the over-all pressure; i.e., the "top pressure" under which the furnace is operated. It is indicated that pressure operation may also be expected to result in concomitant benefits, which may be summed up as generally improved operating conditions, together with a substantial saving in fuel and/or a substantial increase in furnace capacity.

Jan 1, 1938

By M. J. Mullikin, J. B. Conway

Equations capable of representing combined first -and second-stage creep behavior include the Andrade, Cottrell-Aytekin, Garofalo, and de Lacombe equations along with a third-degree polynomial in t1/3. Employing some recent high- temperature creep data for arc-cast tungsten the effectiveness of these expressions was evaluated. It was found that, in this instance, the most accurate representations were afforded by the third-degree polynomial in t1/3 and the de Lacombe equation. Also noted was the fact that the Andrade equation gave results just slightly inferior to those obtained with the third-degree polynomial, definitely better than those due to the Cottrell-Aytekin equation, and slightly superior to those furnished by the Garofalo equation. EXPRESSIONS designed to describe combined first -and second-stage creep behavior must possess certain specific characteristics. At time zero the equation must reduce to a strain value corresponding to the instantaneous deformation on loading. Then in the early moments following load application transient-creep behavior must be described to reflect a creep rate which constantly decreases with time. And finally at larger time values linear (or at least nearly linear) strain-time behavior must be accounted for to yield the steady state or minimum creep rate. Some equations, such as the one based on the parabolic creep law, yield fairly satisfactory results in transient analyses but are not effective at all when combined first- and second-stage data are to be analyzed. Other equations give equally accurate results in both instances although in general the complexity of the equation is slightly increased. For example the Andrade1 equation: has found fairly general application in expressing first-stage creep behavior. Furthermore the contribution of the exponential term becomes more and more prominent as the time increases and causes this equation to exhibit a point of inflection at large values of time. With a proper selection of equation constants the curve can be made fairly flat in the region of the inflection point indicating a desirable equation form for combined first- and second-stage creep analysis. Another equation form with the proper characteristic is that of Cottrell and Aytekin:2 e =a +bt1/3 +ct [2] Obviously as time increases the first derivative of this expression approaches a constant value to suggest application to combined first- and second-stage creep analysis. Similarly a third-degree polynomial in t1/3: e -a + bt1/3 + ct2/3 +dt [3] has the same characteristics. Expressions of this type have been shown3 to be very effective in the analysis of transient-creep behavior and the fact that the first derivative has the same characteristic as Eq. [2] suggests use in the combined analysis.

Jan 1, 1967

By A. Raja, C. C. Harris

Apparatus for maintaining constant — but adjustable — pulp level and rate of froth removal are described. The results of preliminary experiments into the effect of scraping speed on the rate of solid and liquid recovery with a semi-batch system are presented. Glass spheres restricted to a narrow size range is the solid under investigation. Graphical methods for estimating the mass of recoverable material and the zero error are given. The semi-batch procedure1 is extensively used in laboratory flotation testing, though the method is subject to variability of moderate severity. Raffinot2 concluded from a statistical study of the difference between replicate tests, that the ptincipal source of errot was the test itself and not sampling or chemical analysis. These differences can be ascribed principally to changes in pulp volume and reagent concentration, and uncontrolled rate and depth of scraping. Semi-batch testing has been criticized1 on these grounds as a means of investigating flotation kinetics. This paper discusses and describes modifications to laboratory flotation equipment which reduce the number of manual operations and lead to improved control. Kinetic studies were the primary reason for developing the apparatus described. It should, however be a useful aid in normal flotation testing. Some preliminary results of experiments are presented.

Jan 1, 1967

By P. J. Closmann

Steam zone growth as a function of time has been calculated for the case of constant rate steam injection into a preheated reservoir. To simplify the calculation a linear temperature profile has been assumed in the cap and base rock at the start of steam injection. The results indicate that at early times augmentation of steam zone growth due to preheating should be greatest. At longer times the steam zone development becomes close to that calculated with no preheating. INTRODUCTION With the increasing application of thermal recovery processes to recover viscous oil, cyclic steam injection has become important in many large-scale projects. In this process, the cycle of steam injection followed by oil production is repeated a number of times. At the beginning of the second and later cycles, steam is injected into a reservoir that has already been heated but that has lost part of its heat both in produced fluids and by conductive heat loss away from the injection zone. In such a case, the temperature level of the injection zone and the temperature distribution of the surrounding rock will affect the growth of the steam zone developed during the subsequent steam injection. Knowledge of the size of steam zone developed is important in determining the amount of oil displaced and the extent of heating in the reservoir. It is also useful to be able to compute the size of the steam zone for cases where thief zones take most of the injected steam. This paper presents a fairly straightforward method of estimating the steam zone developed in a preheated formation, based on certain simplifying assumptions. Some cases of steam injection into a reservoir at its original temperature have already been considered elsewhere.1-3 Because it is difficult or impossible to obtain an accurate representation of the temperature distribution in the reservoir some time after initial heating has taken place, in this work, a linear temperature profile in the cap and base rock is assumed (Figs. 1A and 1B). The linear profile has the advantage of yielding heat flow equations that

Jan 1, 1969

By James P. Sloss

WHAT is the likelihood if any-that a real gold mining industry will be developed in the southern Appalachian region? Has the increase in the dollar value of gold from $20.67 to $35 per ounce potency to turn the trick? Suppose it be assumed that the price of gold will, at worst, not recede, and that the cost of digging ore and treating it of which the average level of commodity prices and wages is a fair index-will, at most, not exceed that prevailing in 1926. One may or may not accept these as reasonable assumptions; but one must arbitrarily remove some of the potential variables if one is to get anywhere on a problem like this. As a matter of fact, this article is not going to venture a conclusive answer to the question that has been posed; but it will endeavor to present some of the factors that have a bearing on the problem. The writer spent ten days visiting a dozen properties in Virginia and the Carolinas early in April, 1935, and in doing so got a first-hand slant on mining conditions in the domain of King Cotton.

Jan 1, 1935

By Frank G. Snyder

The Precambrian of Midcontinent United States includes a metamorphic belt of probable Middle Precambrian age, a belt of Keweenawan volcanics and sediments, and widespread igneous activity that extended from Iowa to Texas. Most of the present structural configuration of the Midcontinent was developed by epeirogenic movements during the Paleozoic. The dominant elements are basins and arches. Three major metallogenic provinces occur in the Midcontinent. They include the Missouri Precambrian iron ores, the Lake Superior copper ores, and the Mississippi Valley lead-zincbarite- fluorite deposits. Several large iron deposits, occurring in rhyolite and andesite host rocks, are known. Both discordant massive bodies and replacement- type bodies occur. The iron deposits are believed to have been formed during the period of igneous activity. They are essentially the same age as the volcanics and older than the granites that intrude the volcanics. The Lake Superior copper ores include two established districts, the Keweenawan district and White Pine, and the copper-nickel deposits in the Duluth gabbro. The lead-zinc-barite-fluorite deposits include four major districts, Southeast Missouri, Upper Mississippi Valley, Tri-State, and Illinois-Kentucky, and at least eight minor districts. Ore may occur in stratiform deposits and in veins. The major districts all contain stratiform deposits, but several have produced appreciable quantities of vein ore. Only vein deposits are known in some of the smaller districts. The major features of all districts can be catalogued in terms of host rocks, structural patterns of districts, types of ore-bearing structures, and mineralogical characteristics. From these features, a Mississippi Valley type ore body, in its type area, can be defined.

Jan 1, 1968

By Paul R. Dingess, Edward H. Hare, Douglas C. Brockie

Mining in the Tri-State district of Missouri, Kansas, and Oklahoma has been nearly continuous from about 1848 until the present day, although the major activity was from about 1880 to 1955. The district, which has produced over $2 billion in zinc and lead concentrates, ranks as one of the greatest mining districts in the world. Unlike other Mississippi Valleytype deposits in the United States, which occur in Cambrian and Ordovician limestones and dolomites, the Tri-State district ores occur in Mississippian limestones containing abundant chert. Zinc is 5 to 6 times more abundant than lead. In the Picher Field, the principal sub-district which has accounted for 61 percent of the total district production, most of the ore has been mined from the single horizon, M bed. Most ore bodies, other than those of the "Sheet Ground" or blanket-type, are in large, essentially flat-lying breccia zones and have a definite mineral zonal pattern. An irregular, generally elongated central dolomitic core is surrounded progressively outward by the main ore run, the jasperoid zone, the muddy or shaly and bouldery zone, the sparry calcite limestone zone, and the fossiliferous, dominantly crinoidal, limestone zone. Some of the zones may be absent or nearly so and may overlap to some extent with an adjacent zone. Although the district has been studied by many authors, much controversy still exists about such items as genesis, paragenesis, and time of emplacement. These subjects are discussed in the paper.

Jan 1, 1968

By D. M. Davidson, P. F. Kerr

The Permian Cutler Formation in Kane Creek, Utah bears uranium ore in fissure-type vertical veins. This fissure vein formation and its associated host rock bleaching, weak argillic alteration, and base-metal sulfide mineralization along with the development of hydrothermal minerals, a 60 m.y. isotopic Pb/U age, and well-crystallized uraninite's structural control, give evidence of ore deposition in a hydrothermal environment consistent with Laramide mineralization. Mica polymorph studies indicate first, that temperature during the hydrothermal alteration or subsequent ore deposition did not exceed 200°; hence Cutler deposits are classified telethermal; and secondly, that rock alteration and ore deposition are closely related both in time and space, as is seen in argillic alteration sequence. Ore deposition in an alkaline to slightly acid reducing environment is postulated. Ore textures and mineral associations and distributions also indicate that carbonate complexes may have been transported with the deposing ores. Bleached rock formations are not primary strati-graphic phenomena. Bleaching, or changes in ferric iron content, results from a chemical process involving reduction and conversion of hematite to a soluble aqueous ion. Nearby Chinle bedded deposits (Moss Rack sandstone), containing shale lenses, fossil wood, organic debris and minor fractures, overly the Cutler formation. Chinle ores have a single reported isotopic age of approximately 200 m.y. Their chemical environment is assumed similar to that of the Cutler ores, though slightly more acidic. Two genetic, paradoxically divergent interpretations of the bedded deposits are derived from available spectrographic, petrographic, X-ray and chemical analyses. Kane Springs canyon is located southwest of Moab, Utah, south of the Colorado River and northwest of the Lisbon Valley mining district (Fig. 1). Uranium deposits occur along the northeast flank of a Kane Creek salt anticline where two geologic formations bear ore, the Permian Cutler and the Triassic Chinle. The Cutler deposits' fissure vein formation is an unusual occurrence in the Colorado Plateau. The Chinle deposits appear to be of the normal sedimentary type. Associated with the vein deposits are a number of features, including argillic alteration of sedimentary strata. The minerals of these deposits and their associated features have been studied in detail in a two year program entailing both field and laboratory techniques. STRATIGRAPHY A stratigraphic section of the lithologic units in the Kane Creek area is given in Table I.

Jan 1, 1967

By Leo J. Vogel, E. D. Hummer, David J. Akers

INTRODUCTION An efficient refuse-disposal system is a necessary part of the modem cleaning plant. The large-scale refuse system and disposal area, engineered for the lifetime of the plant, has become more important due to the greater tonnages of refuse produced from increased quantities of mechanically mined and prepared coal. Laws and increased government regulations have affected the design and operation of disposal systems. THE EFFECT OF MINE AND PLANT OPERATION Refuse disposal starts at the mining face. The mining system, the type of roof support, the machinery used, and the degree of discipline at the face contribute to the amount and type of refuse that must be removed through the disposal system. Economies gained through modification of the mining system or mining machinery may be partially offset by increased dilution of the mined coal with impurities from associated rock formations. In some cases the change in the mining system and equipment has reduced the dilution. In all cases the ratio of impurities that must be removed from the raw-coal feed to the plant not only affects the maintenance and

Jan 1, 1979

By F. V. Lenel

Resistance sintering under pressure is a method of hot pressing in which a powder compact is subjected to pressure and simultaneously heated by passing a low voltage high amperage current through it. Equipment for this process is described. Its basic characteristics such as resistance requirements for powders and compacts, temperature distribution in compacts, and gas reactions during resistance sintering are discussed. Examples of the sintering process in compacts made of a single metal or an alloy powder and in compacts made of mixtures of powders are presented. Potential commercial applications of the process are evaluated. THE usual sequence of operations in commercial powder metallurgy is to compact metal powders in a die at room temperature and sinter the compact subsequently without applying pressure while the compact is in the sintering furnaces. In hot pressing, on the other hand, the compacting and the sintering are combined. The loose powder, or in many cases a cold formed compact, is inserted into the die which is held at the hot pressing temperature, the compact is left in the die until it attains its temperature, and then pressure is applied and maintained for a given length of time. The die may be heated by surrounding it with a suitable furnace, by high frequency induction heating, or by passing current through the die. In hot pressing, compacts of high density and good mechanical properties can be produced in a relatively short time. One of the principal difficulties in hot pressing is the lack of suitable die materials which will have adequate strength at the hot pressing temperature. This difficulty can be overcome at least partially by heating only the material to be hot pressed without heating the die directly. This can be done by passing a low voltage high amperage current through the material and simultaneously subjecting it to pressure. Either loose powders or compacts can be hot pressed by this method in which the desired temperature is produced by the power dissipated in the metal powder. This method of hot pressing has been termed "electrical resistance sintering under pressure." The most significant differences between this operation and conventional hot pressing are: 1—The sintering times are very short, usually a fraction of a second and at most a few seconds. 2—The powder and die are initially cold. 3—Heat is generated within the powder itself and not conducted in from the die. 4— The pressure used is high. 5—Cooling following sintering is rapid, amounting to a quench. Resistance sintering of metal powders under pressure has been suggested repeatedly. In 1933, G. F. Taylor' proposed an apparatus which consisted of an insulating tube made of glass, or a ceramic filled with the powder to be pressed, and plungers above and below the powder. The powder was to be heated by passing an electric current through it and pressure was then applied. The apparatus was intended principally for hot pressing cemented carbides. Although the principle of resistance sintering under pressure is clearly shown in this patent, few details are given. A sintering period of a second or a fraction of a second, which is terminated by the operation of an inertia switch, is mentioned but no values for current density are mentioned. Low pressures, such as atmospheric pressure or a somewhat higher pressure exerted through a lever, are suggested. W. D. Jones' discussed electrical resistance sintering under pressure and proposed using resistance welding apparatus for this purpose. In a patent issued in 1944, G. D. Cremera described a method of electrical resistance sintering under pressure using resistance welding apparatus which was to be applied mostly to nonferrous metals such as copper, brass, bronze, and aluminum. Current densities of 400,000 amp per sq in., sintering times of 1 and 2 cycles of 60 cycle current, and pressures of 5 to 10 tsi are proposed. Cremer suggested using an

Jan 1, 1956

Jan 1, 1929

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