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By F. M. Drake

IN this paper I propose to describe a plant which I lately erected for the Mount Stewart Lead and Silver Mining Company of Leadville, New South Wales, Australia. I am indebted to Mr. W. F. Burrow, of the Roads and Bridges Department of New South Wales, for the drawings which I present herewith, he having reduced and assembled them from my working drawings. The works are situated on a sloping hillside, but sufficient fall mas not available to have the furnace as high as desired, and at the same time have a good slag-tip and sufficient depth on the ore-floor to store a supply of ore and flux. The ore is delivered on the ore-floor (which is of the full width of the furnace-building, and extends back into the hill a distance of seventy feet) by two overhead tramways (not shown in the drawings), one on each side. From these the ore-mixture is made up on one side, while it is being taken to the furnace from the other. The fuel also is delivered by these tramways. The fluxes are stored on a floor directly at the back of the boiler and engine room. The boiler is a Cornish one, 6 feet 6 inches in diameter by 25 feet long. Its flue is 3 feet in diameter and does not contain Galloway tubes. The working-pressure is 40 pounds per square inch. The engine is an old-fashioned one, with a cylinder 16 inches in diameter by 30 inches stroke. Both the engine and boiler had been part of the plant of a defunct gold-mining company. They were very extravagant in their consumption of fuel. The blast is supplied by a rotary pressure-blower, of the Baker pattern, made in England. It has a capacity of 60 cubic feet per revolution. The furnace, which has several novel points, is shown in detail in Figs. 1, 2 and 3. The jackets are of cast-iron, and are higher than those generally used. They are different, too, in that the feedwater inlet is through a hand-hole plate near the bottom. This plate is fastened to the jacket by stud-bolts, and is provided with a baffleplate, which prevents the cooling water from impinging against the inner plate. The outlet is by a goose-neck at the top, which dis-

Jan 1, 1893

By R. H. Marshall, J. Welchner, E. S. Rowland

THIS paper presents results on an exten¬sion into the realm of high-carbon steels of some work recently published' on the effects -of time at temperature, quenching temperature and prior structure on the hardenability of one 0.20 and four 0.40 per cent carbon alloy steels. It was shown at that time that unless the conditions of time, temperature and prior structure are substantially the same in performing the hardenability test as in conducting harden¬ing of parts in production, the correlation of hardenability information with the [ ] hardness and properties of production parts is often not of satisfactory accuracy. The general effects of these variables on the austenitic grain size, distribution of excess carbides and critical cooling rate have been known for many years and one or more have been investigated by Shepherd ,2 3 Davenport and Bain,4 Digges,5,6 Digges and Jordan,7 Post and associates' and Roberts and Mehl,9 to mention only a few. There has been no systematic investigation, however,' into the quantitative variations produced on the hardenability of commercial high¬carbon steels by changes in these factors of time, temperature and prior structure. PROCEDURE A plain carbon hypereutectoid steel, S.A.E. 52100 and Graph-Mo, a molyb¬denum-bearing high-carbon steel contain¬ing some graphite, were chosen for this investigation. The chemical analyses of these electric-furnace steels are given in Table I. [ ] The procedure used was exactly that reported previously,' hence the details will not be repeated here. Normalized (1650°F.) and spheroidized prior structures were utilized on all steels with hot-rolled and quenched (1600°F. oil) prior conditions added for the plain carbon steel. The end-quench test developed by Jominy10 was selected for use in this investigation and, with the noted exceptions, the American Society for Testing Materials standard. procedure was followed. The effect of time at temperature was examined at intervals of 0, 10 and 40 min. and 4 hr., and a few i6-hr. tests were run. Salt-bath heating of the specimens was employed to control and minimize the

Jan 1, 1944

By T. V. Philip, R. E. Lenhart

C. G. Dunn(General Electric Research Laboratory)— It is well recognized that understanding of the formation of the cube-on-edge texture in annealed commercial cold-rolled Si-Fe strip is important industrially as well as scientifically. I would like to make a few remarks on this subject, discuss some points in the present paper, and list two remaining problems that appear to be particularly outstanding. Attention should be drawn to the paper by P. K. Koh,23 which also considers the kinetics of secondary recrystallization in 3 pet Si-Fe, produced commercially by the Allegheny Ludlum Steel Corp. Koh covered a much larger temperature range than do either the present authors or P. N. Richards, whose work is mentioned in a footnote. Koh found an induction period (of short duration) even for isothermal anneals at 1260oC (2300°F). Koh and Dunn24 also found a change in texture during the 1260oC anneal for the same material. On the other hand, the material in coil D, according to Philip and Lenhart, underwent no sec-condary recrystallization, only continuous grain growth. The grade classifications of the four coils studied would suggest, however, that all four materials had developed the cube-on-edge or (110) [001] texture, but to varying degrees. Since no data on this are given and since watt loss depends

Jan 1, 1962

By Stephen Krickovic

THERE is today no proven continuous mining machine that can be used under all the varying conditions found in most bituminous coal mines. During the last five years, however, both the machines and methods of using them have been improved. Coal operators can now exercise a fair degree of selectivity, except those who must struggle with thick and hard partings and operate in seams less than 40 in. thick. It must be realized, then, that more than one type of continuous miner may be used advantageously in the same coal mine. Although this appears to violate the standardization generally sought after, the gain can more than offset added maintenance and, to a lesser degree, operating problems. It is equally important to realize that most coal mines will require one or more conventional loader setups in the plan of total mechanization. Seam variations, adverse physical conditions, and special designs of main headings for haulage and ventilation, to name only three reasons, may render 100 pct use of continuous miners uneconomical. Of course, this situation may change. In one mine, prior to 1954, machines that ripped coal from the face achieved only average results, as compared to the impressive performance of boring-type units in another coal mine. A boring-type unit was therefore selected for the first mine in the belief that the chance of success would be greater if it were used in a combined cutting and wedging operation, cutting a full face in its forward movement. The miner was located in a part of the mine where a special projection could be readily developed, a solid area scheduled for mining according to the overall progress plan. All openings surrounding the particular area were carefully investigated for the presence of sulfur balls. Fig. 1 (opposite) shows the representative seam section, containing the several pyritic bands 1/4 to 1/2 in. thick; a characteristic Pittsburgh seam parting averaging 5 to 6 in. of slate, coal, and slate; and the occasional py-rite lenses 2 to 3 in. thick. Under normal conventional mining methods, the top 10 or 12 in. and the bottom 4 in. are left in place to offer roof protection

Jan 1, 1958

By AIME AIME

STRIP coal mining in the United States has-become noted for its massive equipment, especially its power shovels. Notable among the latest examples of this trend is the Bobolink mine of the Binkley Mining Co., at Seeleyville, Ind.,. eight miles from Terre Haute. This is only one of the Binkley company's operating properties; in all, the company owns or controls 26 mines, in fourteen seams. The Bobolink, however, is the largest strip mine in America and probably also in the world. It has an estimated life of fifteen years. The shovel used to strip the over¬burden is electrically operated, of Bucyrus-Erie make, and was. shipped to the property for assembling, a job

Jan 1, 1936

By Claude Ferquson

MORE men are killed and injured in the metal mines of the United States from falls of rock and ore than from any other cause. Dan Harrington, of the U. S. Bureau of Mines, recently stated that "falls of men and material continue to take about 50 per cent of the lives annually lost in our mines (coal or metal) and this kind of accident is now and has been one of the most difficult to prevent." The fact that comparatively little has recently been written on this important subject for the benefit of the metal miner is the incentive for the present paper. Little will be said that will be new, but I hope to place fresh emphasis on certain well-known' principles' and to reiterate and stress previously stated rules so that the average experienced miner, as well as his buddy who may not be so experienced,' will sit up and take notice. It is not within the scope of this paper to discuss mining methods from the standpoint of safety and the prevention of accidents from falls of rock. It is up to the mine management to select the system of mining best suited to the character of the ore deposit and its wall conditions. This is something that the miner can do little about; although in many mines the management encourages the workmen to make suggestions that will improve existing

Jan 1, 1938

Frank 11. Probert, Neudorf, Anhalt, Germany (communication to the Secretary): I have read with much pleasure Mr. Collier's valuable paper. But the system of timbering which he describes as used in the levels, stopes, etc., though it must be admitted to be very strong and safe, seems to me somewhat extravagant. The amount of timber required every month for such a system must be enormous; and only where suitable material could be cheaply obtained would such a plan be economically practicable. The first point which strikes me is the unusually great diameter of the timber employed. In the mines of Pfaffenberg and Meiseberg, which are under my supervision, the country-rock consists of argillaceous slates, traversed by innumerable small fissures or joints, dipping at all angles and striking to all points of the compass. Undoubtedly, this net-work has been caused by the upheaval of granite masses in the vicinity. Each fissure is accompanied by a more or less well-c1efinc.d gouge or fluccan, caused by the rubbing together of the slates at or after the original disturbance. In such

Jan 1, 1900

By George F. Becker

A Nere record of Emmons's professional career would very inadequately represent the man. That he was eminent mc know, and our successors will realize in due time; but they must depend upon us for knowledge of a singularly ~vholesome, modest, unselfish personality, and of a character that did honor to a profession in which trustworthiness is indispensable. Those members of the Institute who met Emmons are his friends, and I never knew .one of these who was not the better for that friendship. Emmons was born in Boston, Mar. 29, 1841, the son of Xathaniel H. and Elizabeth (Wales) Emmons, and was named Samuel Frankliri after an ancestor who was of the sarne family as Benjamin Franklin. He took the degrcc of Bachelor of Arts at Harvard in 1861, and soon afterwards went abroad to complete his education. From 1862 to 1864 he attended the courses at the fieole Impkriale des Mines at Paris, Elie de Beaumont arid Daubrke being among his professors. The year 1864-1865 he spent at Freiberg under Cotta and other famous teachers; after which he spent another year in traveling through Europe. Like many other renowned geologists, he approached his ultimate profession from its economic side, and was thus from the first imbued with a sense of high responsibility in the promulgation of scientific opinions or conclusions. With hypotheses which were interesting merely because they were ingenious or even plausible, he would have nothing to do. In 1867 he joined the Geological Exploration of the Fortieth Parallel at its organization under Clarence King, serving at first as a volunteer, but soon receiving a regular appointment. This expedition was the first one of purely geological character sent out by the United States government. As Emmons has shown in his admirable presidential address on " The Geology of Government Explorations," its work was founded on a com-

Jan 1, 1912

By Herbert Clark Hoover, Lou Henry Hoover

As stated in the preface, the nomenclature to be adopted for weights and measures has presented great difficulty. Agricola uses, throughout, the Roman and the Romanized Greek scales, but in many cases he uses these terms merely as lingual equivalents for the .German quantities of his day. Moreover the classic language sometimes failed him, whereupon he coined new Latin terms adapted from the Roman scale, and thus added further confusion. We can, perhaps, make the matter dearer by an illustration of a case in weights. The Roman centumpondium, composed of zoo librae, the old German ceniner of 100 pfundt, and the English hundredweight of 1112 pounds can be called lingual equivalents. The first weighs about 494,600 Troy grains, the second 721,900, and the third 784,000. While the divisions of the centumpondium and the centner are the same, the Libra is divided into 12 unciae and the pfundt into 16 unizen, and in most places a summation of the units given proves that the author had in mind the Roman ratios. However, on p. 509 he makes the direct statement that the centumpondium weighs 146 librae, which would be about the correct weight if the centumpondium referred to was a ceniner. If we take an example such as " each centumpondium of lead contains one uncia of silver", and reduce it according to purely lingual equivalents, we should find that it runs 24.3 Troy ounces per short ton, on the basis of Roman values, and 18.25 ounces per short ton, on the basis of old German. If we were to translate these into English lingual equivalents of one ounce per hundredweight, then the value would be 17.9 ounces per short ton. [ ]

Jan 1, 1950

By F. M. Lewis, J. F. Meyers

This second progress report of grinding presents comments regarding ball consumption and data pertaining to the hydroscillator, which is closed circuited with the tricone mill. A study and postulate of how balls function is presented. The paper summarizes cost reduction obtained by the method of "grinding for the tail race" rather than for "mesh tons." AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of —200-mesh produced a very creditable figure. Hydroscillator Operation The machine as now developed has proved dependable and easy to operate. It starts easily under full load and responds quickly to operating adjustments. The hydraulic holes in the oscillating plate do not plug when shut down under full load. Absolutely clean hydraulic water is essential. An Elliott water screen or similar device should be an essential part of the machine to keep all scale and trash of all kinds from the hydraulic compartment. The shift operators have expressed approval of the machine. In table I we show a typical screen analysis of the hydroscillator rake sand as compared to conventional classifier rake sand on our ore. We have previously reported that of the 28.7 pct reduction in power, the hydroscillator contributed 6 pct, on a —200-mesh basis. This is a conservative figure. Some of our test runs indicated that the saving was as high as 10 pct. Laboratory studies by the Dorr Co. engineers indicate that still greater efficiency is possible. Nevertheless, the 10-ft plate is overflowing 2100 tons per day at 3 to 4 pct + 65-mesh, which is a very creditable performance by

Jan 1, 1951

By William E. Ford, Edward Salisbury Dana

Normal phosphoric acid is H3P04, and consequently normal phosphates have the formulas R3PO4, R3(P04)2 and RPO4, and similarly for the arsenates, etc. Only a comparatively small number of species conform to this simple formula. Most species contain more than one metallic element, and in the prominent Apatite Group the radical (CaF), (CaCI) or (PbCI) enters; in in the Wagnerite Group we have similarly (RF) or (ROH).

Jan 1, 1922

By P. G. Shewmon, W. M. Robertson

The derivative of the surface tension with orientation, ??/??, for copper has been measured over the entire unit triangle. This derivative or torque term was determined from the variation of the dihedral angles at the intersection of twin boundaries and free surfaces. High-temperature anneals in graphite with a hydrogen atmosphere gave torque terms of 0.097 at (111), 0.066 at (100), and 0.0257 at (110). A variation from -36oto +23oC in the dew Point of the H2 had no effect on these values, nor did a change from 99.98 to 99.999 pct Pure copper. The removal of graphite from the system decreased ??/?? slightly. Considering the surface near a low-index plane to be smooth except for occasional steps, the free-energy increment per cm of step is calculated, and it is shown that the observed variation of ??/?? is consistent with a random distribution of steps and an interaction energy between steps. Integration of ??/?? gave the relative values of y at (100), (110), and (111) as comPared to ymax: (Y111/Ymax) =0.974, (Y110/Ymax) =0.996, (y100/Ymax) = 0.983. The ratio of the surface tension of coherent twin boundaries to the surface tension of the free surface was found to be (yT/ys) = 0.027 * 0.011. In a crystalline solid the surface tension y (surface free energy per unit area) depends on the orientation of the surface relative to the crystallographic axes of the crystal. Measurements of this variation of y with surface orientation have been reported for metals only within the last few years. Consider the grain boundary groove shown in Fig. 1. Here the three surfaces are all normal to the plane of the paper, and each has a different surface tension, y1, y2, and y3. If the system is at equilibrium, the total surface free energy must remain unchanged for a slight vertical displacement of the intersection (points A, B, and C are kept fixed). As shown by Herring,' the following equation is obtained:

Jan 1, 1962

By William S. Springer

A NEW preparation plant has been put in - operation to treat coal from the recently opened Concord mine, located about 15 miles west of Birmingham, Ala., by the Tennessee Coal, Iron & Railroad Co., a U. S. Steel subsidiary. The mine produces metallurgical grade coking coal from the American seam for use as coke in the company's blast furnaces at the Fairfield and Enseley works. The capacity of the operation is 1000 tons of run-of-mine per hr, approximately half of which is delivered to the by-product coke plant at Fairfield after beneficiation to metallurgical grade. The remaining portion of the mine run is rock and refuse removed during preparation. No boiler coal or other fuels are produced by this mine. Preparation of the coal is done both under- ground and on the surface. The underground primary crushing station removes some tramp iron, and screens and crushes the oversize, most of which is rock, to protect the main slope conveyor. The surface plant consists of a crushing and screening plant, large blending bins, a two- process washing plant, a water clarification and

Jan 1, 1950

By Ross E. BROWNE, Ross B. HOFFMANN

IT seems strange that a theory so devoid of value in its application to our practical problems should attract such widespread acclaim. This appears still more remarkable when one considers the foundation on which it is built. The criticism naturally suggested is as follows: First; the special theory of relativity is based on an assumption which is counter to the fundamental conception of relative motion. Second; the theory claims only a slight modification of Newtonian mechanics-a modification so minute that, even if true, it would have no practical value in its application to any visible occurrence here on earth.

Jan 1, 1931

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By M. Garfinkle, W. D. Klopp, W. R. Witzke

The tensile properties of binary W-Re alloys containing up to 33 at. pct Re were determined at temperatures from 78" to 3630°F. Elongations as high as 260 pct were observed in electron-beam-melted tungsten containing 23 at. pct Re when tensile-tested at 3630°F after a 1-hr anneal at 3090°F. All alloys tested under these conditions with rhenium contents between 20 and 28 at. pct exhibited elongations of at least 200 pct. These alloys also showed enhanced grain growth rates. The values of strain-rate sensitivity ranged between 0.2 and 0.3 for the alloys exhibiting high elongations. Houlezler, for swaged alloys tested just above the re-crystallization temperature, strain-rate sensitivities as high as 0.8 were observed. The high-temperature strengths of the high-rhenium-content alloys were also less than those of alloys with intermediate rhenium contents. ALLOYING with rhenium has two distinct effects on the mechanical properties of tungsten. One effect occurs in dilute solid solutions and is most clearly seen in the lowering of the hardness and of the ductile-brittle transition temperature at about 5 at. pct Re.1-3 The second effect occurs in the concentrated solid solution at about 25 at. pct Re, and is characterized by twinning and a larger decrease in the ductile-brittle transition temperature. An aspect of the high-rhenium-content alloy which has received little attention is the higher-than-usual tensile ductility at 3500°F.3 Anomalous high ductility has been observed in several other alloy systems. usually associated with a phase transformation or a solid-solubility limit.4'5 The phenomenon is now commonly termed superplasticity. High-strain-rate sensitivities6 and grain boundary sliding7 have been reported for materials that undergo superplastic deformation. Also, it has been found that superplastic materials usually have a very fine grain structure (less than 10 pm).8 and it has been proposedg that such a structure alone is sufficient for superplasticity. The purpose of the present study was to further characterize the high-temperature tensile properties of W-Re alloys to determine the conditions under which they might be superplastic. Tensile and selected strain-rate sensitivity tests were conducted on alloys containing 0 to 33.3 at. pct Re at temperatures from 78" to 3630°F. Grain-growth rates were also determined on most alloys at 3630°F. Fig. 1 indicates the compositions evaluated and their locations relative to the solvus line in the tungsten-rich end of the W-Re phase diagram. Twelve binary W-Re alloys containing up to 33.3 at pct Re were double electron-beam-melted and subsequently fabricated to 0.3-in. rod by extrusion and swaging. The starting materials were commercial powders of tungsten and rhenium with impurity levels as listed in Table I. The various blended W-Re compositions were hydrostatically pressed at 70 ksi. The pressed bars were drip-melted into 1.5-in.-diam ingots and then remelted into 2-in.-diam ingots at a chamber pressure of 10~5 torr. The ingots were canned in molybdenum and extruded to round bar at a reduction ratio of 6:l. The alloy extrusions were swaged to about an 80 pct reduction at 2100" to 2900°F. Buttonhead tensile specimens with a reduced section diameter of 0.16 in. and a gage length of 1.0 in. were centerless-ground from the swaged bars

Jan 1, 1970

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

The Board of Directors, at its meeting on March 22, 1918, extended an invitation to the American .Institute of Metals to become the Institute of Metals Division of-the American Institute of Mining Engineers in accordance with the terms of By-Law VII. This invitation was presented to the membership of the American Institute of Metals for letter ballot, and, at the meeting of the Board of Directors of the American Institute of Mining Engineers on April 26 191 ,it-was reported that the replies had been in favor of accepting the invitation. The American Institute of Metals therefore becomes a division of this Institute and the members thereof are entitled-to all privileges of regular

Jan 6, 1918

By Philip B. Bucky

[CONTENTS t. How Does One Determine WhetherPAGE an ore Body Will Block-cave?R. W. Hughes13 Sherman R. Burdick 13 PAGER. T. Gallagher 14 Mark A. Smith 2 C. F. B. Price, Jr.14 Harry A. Leidich2Benjamin F. Tillson 14 McHenry Mosier2C. F. Jackson14,17 R. W. Hughes2R. Taborelli15 Sherman R. Burdick3Frank A. Ayer16 R. T. Gallagher 3Philip B. Bucky16 Benjamin F. Tillson 3Rollin Farminr6 Lucien Eaton 3J. L. G. Weysser15, 0,17 C. F. Jackson 3George S. Rice17 Philip B. Bucky32. How Does One Determine the Block4. What Determines the Procedure in Dimensions and the DevelopmentRemoving Caved Ore? Work Necessary to Make an OreHarry A. Leidich17 Body Cave?McHenry Mosier17,21 Mark A. Smith 5,7,() R. W. Hughes17 Harry A. Leidich6Sherman R. Burdick 18 McHenry Mosier6,7,12 R. T. Gallagher 18 R. W. Hughes6Mark A. Smith I8 Sherman R. Burdick 7Philip B. Bucky20, 21, 23 R. T. Gallagher 7C. F. B. Price, Jr20 Benjamin F. Tillson 7,11R. H. Bennett21 L. E. Young7C. F. Jackson 21, 23 Robert D. Hoffman8, 1 2Gerald Sherman 3 . 21 Gerald Sherman8Tell Ertl21 Philip B. Bucky10, 11, 12G. K. Foster 23 R. S. McClellan 12C. H. Shoemaker23 Tell Ertl 12 3. How Do the Forces Act and What Are5. What Are the Criteria for Determining the Stresses Developed in a Blockthe Efficiency of a Block-caving That Cause It to Block-cave?Operation? Mark A. Smith 12, ISHarry A. Leidich23 Harry A. Leidich13McHenry Mosier24 McHenry Mosier13R. W. Hughes24 Sherman R. Burdick 24 R. T. Gallagher 24]

Jan 1, 1942

1. How Does One Determine Whether an Ore Body Will Block-cave? Page Mark A. Smith......... 122 Harry A. Leidich........ 122 McHenry Mosier ...,.. 22 R. W. Hughes ........ 122 Sherman R. Burdick ....... 123 R. T. Gallagher........I 23 Benjamin F. Tillson...... 123 Lucien Eaton...........123 C. F. Jackson..... . .. 123 Philip B. Bucky........... 126 2. How Does One Determine the Block Dimensions and the Development Work Necessary to Make an Ore Body Cave? Mark A. Smith... 125, 127, 129 Harry A. Leidich..........126 McHenry Mosier......126, 127, 132 R. W. Hughes...........126 Sherman R. Burdick.........127 R. T. Gallagher...........127 Benjamin F. Tillson......127,131 L. E. Young............127 Robert D. Hoffman.......128, 132 Gerald Sherman..........128 Philip B. Bucky......130, 131, 132 K. S. McClellan..........132 Tell Ertl.............132 3. How Do the Forces Act and What Are the Stresses Developed in a Block That Cause It to Block-cave? Mark A. Smith.........132, 135 Harry A. Leidich........133 McHenry Mosier . .. 133 R. W. Hughes ....... 133 Sherman R. Burdick..... . 133 R. T. Gallagher..........134 C. F. . Price, Jr. ........134 Benjamin F. Tillson.........134 C. F. Jackson......134, 135,137 R. Taborelli...........135 Frank A. Ayer ... .....136 Philip B. Bucky . .........136 Rollin Farmin . . .......136 . . . Weysser.....135, 136, 137 George S. Rice...........137 4. What Determines the Procedure in Removing Caved Ore? Harry A Leidich...........137 McHenry Mosier........137,141 R. W. Hughes...........137 Sherman R. Burdick........138 R. T. Gallagher...........138 Mark . Smith...........138 Philip B. Bucky......140,141,143 C. F. B. Price, Jr..........140 R. H. Bennett...........141 C. F. Jackson..........141, 143 Gerald Sherman..........141 Tell Ertl.............141 .. .. ..................143 C. H. Shoemaker..........143 5. What Are the Criteria for Determining the Efficiency of a Block-caving Operation? Harry A. Leidich.......... 143 McHenry Mosier......... 144 R. W. Hughes........... 144 Sherman R. Burdick.......144 R. T. Gallagher . ......... 144

Jan 1, 1946