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By E. F. Klein, R. L. Eacret

Introduction In contrast to the general type of crushing mechanism in which the crushing surfaces alternately approach and withdraw from each other, described earlier in this section, and continuous-pressure break¬ers such as rolls and roller mills that will be described in a later chapter, impact crushers load by striking pieces of rock while in free fall and hurling them at high speed against stationary surfaces. Because the impact crusher depends for its effectiveness upon high velocity, wear is greater than in the slower-moving jaw and cone¬type wear parts, and for this reason its use is strictly limited to rela¬tively soft, friable, and sticky rocks that are characteristic of many nonmetallic mineral deposits. A few of these are phosphates, lime¬stone, barite, clay, asbestos rock, and coal. However, several examples of their use on soft lead-zinc and precious metal ores have been known. Although the use of impact crushers is expanding today into the range of ores containing as much as 15-18% silica, Taggart16 set the practical limit at 5%, and in the 1940s and 1950s several installa¬tions in the US and western Europe exceeded the limits of economical maintenance and were quickly superseded by the slower-moving, con¬ventional crushers. A rock that tends to be plastic or bouncy in a jaw or gyratory crusher when the force is applied slowly to reach ultimate strength, may become brittle with rapid loading and thus increase the effective¬ness of the applied forces. For this reason it is to be expected that as the quality of hammers, grates, plates, and cages improves with advances in steel technology, the use of high-speed crushers of this kind will increase. Terminology Modern usage differentiates between the impactor and the hammer mill, the former relying primarily on the impact of hammers (fixed or free-swinging) and secondarily upon pieces striking one another or steel surfaces; the hammer mill relies on both the centrifugal impact force of free-swinging hammers and the attrition and shear action between these hammers and well-placed grates suspended at the bot¬tom just below the hammer circle. The hammer mill, because of its grate discharge, restricts discharge of oversize rock to the grate open¬ing, while at the same time providing a trap for removal of tramp iron or other uncrushables. The impactor discharges free, so generally works with a screen to control product sizes. The question of terminology, impactor vs, hammer mill, creates difficulties because the similarities appear to outweigh the differences by far; if one were to list the similarities in order of importance and then the differences, he would be forced to conclude that they would best be dealt with as a single kind of crusher. Taggart16 gave it four names and added "as it is variously known," but it must be remembered that in 1945 the machine was nearly exclusively of the flailing-hammer type, while today the fixed-hammer rotor is also com¬mon. In this chapter the terms impactor and hammer mill will be used where they seem to apply. It is perhaps unfortunate that this terminology is being confused with rock breaking at the mine, usually with hand-held tools, e.g., the article "High-Energy Impact Rockbreaking" by Grantmyre and Hawkes, CIM Bulletin, August 1975. General Description Impact breakers, impact crushers, and hammer mills accomplish material breaking and reduction primarily through impact action of the material with fixed or free-swinging hammers revolving about a central rotor. The material to be crushed enters through an opening at the top or top side known as the "feed opening" or "hopper opening" and falls into the path of rotation (hammer circle) of the hammers. Initial breakage is accomplished in midair by collision of the dropping feed material with high-speed hammers. The second stage of breakage occurs when the pieces hit plates or breaker bars which line the crusher boxlike frame. Hammer mills rely further on a shearing and attrition action between free-swinging hammers and grid bars or grates at the crusher bottom which restrict discharge of oversize material until it is broken sufficiently to pass through the grid opening. The term hammer is used in reference to the piece which strikes the material, whether it is fixed on the rotor or free-swinging. It

Jan 1, 1985

By W. F. Hower, W. Brown

Large-scale sand consolidation tests were conducted in an effort to determine the reasons for the successes and failures of this method of sand control. Several different consolidating materials were used in treating both clean and bentonitic sands that were packed in a chamber having a capacity of 3.3 cu ft. The results were essentially the same for all of the different consolidating materials, The data show that low-viscosity consolidating materials pumped at a relatively slow rate gave the best results. Where the formation has produced sand, the treating fluids can compress the formation, thus permitting the channeling of fluids to another horizon. Pressure-packing these zones before attempting to consolidate is recommended. Sands containing more than 4 per cent of water-swelling clays are not good candidates for consolidation. It is indicated that loose sand, particularly when it is bentonitic, can be fractured during the placement of the treating fluids. INTRODUCTION Sand production in oil and gas wells has plagued the industry for many years, and numerous cures for this problem have been suggested. Most methods have been successful to a certain degree, but the great variety of well conditions that exist in the different areas has magni- fied the problem and limited the successful use of the various systems. Four review papers1-4 present a wealth of information concerning the degrees of success that have been obtained by the different sand-control methods. The bridging of sand grains by the use of gravel packs and screens has been quite successful. However, these methods do not leave the casing clear for all types of multiple completions, and the cure does not last for the production life of the well in some instance:;. The control of loose sands by sand consolidation with resins has never been as successful as desired. It has always been hoped that such a treatment would eliminate all sand problems for the life of the well, but. initial applications, starting in the middle 1940's, were only moderately successful. Lott, et a1,3 reported a success ratio of approximately 50 per cent and made the following conclusions. The highest percentage of successes were obtained where: a. Consolidation of a zone was made at the time of initial completion or prior to the production of sand. b. The interval treated was less than 12 ft in length. c. Between 30 and 50 gill plastic/ft of producing interval was displaced through the perforations. REASONS FOR SAND CONSOLIDATION FAILURES Our own experiences in the field of sand consolidation point toward the following conditions as the major reasons for the failure of sand consolidation attempts. 1. Mud-plugged perforations and mud invasion of the formation. 2. Sand in the casing covering all or part of the perforations. This sand could be either formation sand or one of the coarser sands used as propping agents in hydraulic fracturing. 3. Holes in the casing. 4. Channels behind the casing. 5. Attempting to treat too long a perforated section. 6. Too high a percentage of water-swelling clays in the formation. 7. Formations that have produced sand. Recent attempts were made to treat perforated sections ranging from 10 to 30 ft, in wells that have produced sand, by using a straddle packer that was raised and lowered through the perforations as the consolidating material was being pumped. In most instances, the pressure required to pump fluid into the formation varied considerably as the tool was raised and lowered. This suggested the possibility that significant differences in permeability were present or that only part of the formation had produced sand. There were times when a sudden break in pressure indicated that a fracture was being formed. Research conducted several years ago concerning the problem of the control of water in air and gas drilling indicated that shale sections could be fractured quite easily. In addition, it was determined that it was easier to pump fluids into shale bodies by fracturing the shale itself, or the interface between the shale and sand, than to pump into a fluid-saturated formation. Formations that produce sand are usually adjacent to shale bodies and frequently have shale streaks of various thicknesses inter-bedded in the sand. Therefore, where shale is exposed to fluid pressure it

By G. S. Tint, M. Herman, V. V. Damiano

Dislocation arrays and substructures were studied in cadmium doped zinc crystals using a newly devised etching technique. Cadmium precipitates delineating the dislocations were revealed by etching a surface closely parallel to the (0001) slip plane. Cinephotomicrography of the continuous etching process revealed the three-dimensional aspects of dislocations in the bulk crystal. Dislocation etch patterns were studied in both deformed and annealed crystals after suitable aging at room temperature. The effect of annealing was evidenced by a rearrangement of the dislocations into low-angle boundaries and hexagonal networks. ETCH pit techniques have been used extensively to study dislocations in both deformed and annealed bulk metal crystals. Ideally one hopes to obtain a one-to-one correspondence between the etch pits and the points of emergence of the dislocations at the surface. One then attempts to deduce the way in which dislocations are arranged in the bulk crystal from the arrangement of etch pits on the surface. It is clear that one can obtain only limited information of the dislocation configurations inside the crystal from etch pit studies of single surfaces. Considerably more information is obtained if one is able to follow the course of the dislocations through the crystal using progressive etching technique. Techniques of this sort were used by Gilmanl to study dislocations on the slip planes of NaCl crystals and by Damiano and Tint2 to study dislocation arrangement in zinc crystals grown from the melt. The present paper makes use of a technique first described by Tint and Damiano3 to observe and continuously record the dislocation structures which appear while a crystal surface was being progressively etched. Studies were made on cleaved (0001) surfaces to reveal the dislocations along their length on the surface closely parallel to the slip plane. The technique for revealing segments of dislocations along their length by etching is well known. Wilsdorf and Kuhlmann-wilsdorf4 revealed disloca- tions along their length in aluminum containing a few percent copper, when precipitates segregated along the dislocations. The technique was used by Low and Guard5 to study dislocation configurations on the slip plane in Fe-Si alloys containing carbon. In the present work the technique was applied to zinc containing cadmium since it was shown by Gil-man6 that a cadmium-rich phase could be made to precipitate from supersaturated solutions along dislocations in zinc. Segments of dislocations delineated by the precipitates were revealed by etching a surface prepared by cleaving the crystal. The three-dimensional nature of dislocations and substructures was thus studied from the cinephotomicro-graphic record of the continuous etching process. EXPERIMENTAL Single crystals of zinc containing the order of 0.1 pct Cd were prepared by slowly lowering a graphite crucible containing the melt through a temperature gradient of 15°C per cm at a rate of 1.5 X 10-3 cm per sec. "As grown" crystals were aged for periods of 1 month at room temperature, then cleaved in liquid nitrogen, and etched according to the procedure used by Gilman.' The etchant containing 32 g of CrO3, 6 g of hydrated Na2SO3 in 100 ml of water behaved as a chemical polish for zinc and etch pits were produced at the site of precipitates or inclusions. After the precipitates or inclusions were removed from the surface, the etch pits left behind were eventually polished smooth. This behavior enabled one to continuously observe the surface while the specimen was immersed in the etchant. Best results were obtained when the specimen surface was vertical and the reaction products of polishing were continuously removed by gravitational convection. Some crystals were heavily deformed in excess of 25 pct strain, others were lightly deformed the order of a few pct by compression such that the deformation occurred essentially by basal glide. Some crystals were etched immediately after deformation, others were allowed to age at room temperature for several weeks prior to etching. Heavily deformed crystals were annealed at various temperatures and etched on the cleavage plane immediately after annealing, others were allowed to age at room temperature for several weeks prior to etching. The etched structures of deformed and annealed structures were studied. Similar experiments were conducted on 99.9999 pct pure zone refined Tadanac zinc crystals which

Jan 1, 1963

By H. Leslie Bullock

From aluminum to zirconium, the quantitative preponderance of quartz as a gangue material is well recognized. lf this material is to be efficiently removed, its variations must be understood. Variations with temperature are especially important. Too little attention has been given to the thermal polarization of quartz. Under closely controlled conditions, electrostatic upgrading is very reliable. For efficient separation, contact charges must be fostered and charges due to radiation, surface coatings, or thermal polarization avoided. This paper lists thermal transition points of quartz and shows their effect on actual separations. Simple separation tests with all factors except temperature held constant are recommended for determining transition points. With silica making up more than 27% of the earth's crust, its oxides comprising more than 59% of all igneous rocks, and quartz accounting for most of the main free oxides, the mining engineer is in constant contact with quartz, which may occur as a valuable mineral to be purified or, far more frequently, as a gangue material to be removed as completely and economically as possible. As a means of effecting such purification or removal, dry beneficiation is becoming more and more desirable owing to local water scarcities, wet waste disposal problems, or freezing conditions. One method that has been gaining particularly rapid acceptance is electrostatic beneficiation, or the separation of dry free-flowing materials by means of opposite surface charges, differences in potential, or differences in conductivity. Electrostatic beneficiation dates back to the 1870's, but only in recent years have newly developed methods and apparatus and a growing knowledge of solid-state physics widened the field for its economical application. Because the term "electrostatic beneficiation" has been rather loosely used in the literature, it has come to include both electrostatic and electrodynamic procedures. Attracting type separators, however, in which oper- ation is based on differences of surface charge or potential, are truly electrostatic, because the separation occurs in a substantially static field set up between oppositely charged surfaces. Separations with this type of equipment may occur at potentials as low as 1000 v and seldom require potentials as high as 30,000 v. In the new contact charge dielectric separators1 the variation in charge is produced by continuous contact and separation of the particles in the moving feed stream and these charges are fostered by the use of non-conducting support and feed surfaces and by handling the feed in the form of streams of appreciable depth. This favors uniformity of feed and allows higher production rates. The distinctive surface charge differences are set up on the separation of the particles according to Coehn's Law,2 which states that equal and opposite charges are generated on the separation of any two materials in contact and that the substance having the highest dielectric constant will be positively charged. The basic contact charge concept is reliable, but all electrical charges are transient and modified by the electrical conditions of the surroundings. Pyro-electric, photoelectric and radiant effects may modify or totally destroy the contact charges necessary for efficient separation, or contact with conducting surfaces may neutralize them. Such hostile conditions must be carefully guarded against, since they have led to many costly failures in the past. The most consistent difference in surface charges to insure good separation is produced by repeated uniform contact and separation of particles in the moving stream. The thickness of the feed stream possible with this method reduces the effect of contact with the supporting surfaces, but as some contact is inevitable, the best results may be assured by having the dielectric constants of the supporting surfaces between the dielectric constants of the substances to be separated. In general, the hard smooth surface of quartz makes it an ideal substance for electrostatic separation from most minerals. For instance, with calcite, starting with a feed containing 1.9% acid insolubles, one can produce a concentrate containing 0.30% acid insolubles with a tailings containing 21.7% acid insolubles and a yield of 92.8%. The color can be held at 92 or above and the tint at 1.7 or lower. Working with specularite iron ore, laboratory work has given a concentrate of 68.8% Fe., with an iron unit recovery of 96.7%. Excellent results are also in pros-

Jan 1, 1969

By H. Rush Spedden, A. M. Gaudin

IN the belief that a critical study of its operating problems might be a sound investment, the Cuban American Manganese Corporation initiated an ore-treatment research in cooperation with the Massachusetts Institute of Technology One of the early objectives of this research naturally became the relationship of the microscopy of the Cuban ores of the Corporation to their flotation treatment The operations in Cuba have already been described by F S Norcross, Jr 7 and the laboratory study of manganese oxide flotation goes back a number of years 4 Broadly speaking, the difficulties encountered in the flotation of manganese ores are that the consumption of reagents is extremely high, the concentrate contains more silica than is desirable and the tailing losses are relatively high An appreciable betterment on any of these scores would achieve a definite betterment in costs, quantity of minable ores, and quality of product The microscope study discussed in this paper was made on samples from the Quinto mine, from the Ponupo mine, and from mill products at various stages of passage of the ore through the mill The writers have had access to Company records and in particular to the petrographic studies made on thin sections of ore by the late Professors R J Colony and Philip Krieger, of Columbia University They acknowledge their debt to both of these men for the help derived from the reports Manganese oxides are black, friable, smudging It is therefore, very difficult to judge operations by inspection The mineralogy of manganese compounds seems to be confused, and the authors believe that many more minerals have been described than actually exist Much of this difficulty is due to the prevalence of the structural conditions that will be discussed further in this paper, namely, the porosity and the friability of the ores, and the extremely intimate association of minute manganifeous mineral crystals with impurities of various sorts By all odds the most important manganese mineral in Cuba is the one that in this paper is called "psilomelane " The name "psilomelane" has been used in so many different ways that the choice of it for this ore may not be approved by all However, it seems to be the best under the circumstances This mineral accounts for about 97 per cent of the manganese in the ores of the Quinto and Ponupo mines and in the mill feed The remaining odd 3 per cent consists mostly of pyrolusite together with minor amounts of other manganese oxide minerals DESCRIPTION OF PSILOMELANE Aggregate Structure In grains or lumps, psilomelane has a characteristic fibrous appearance and seems

Jan 1, 1942

By Margaret Armstrong, Normand Champigny

"In order to define the ore/waste boundaries as finely as possible, mine planners often insist on kriging very small blocks (relative to the spacing of the available sample grades). These kriged estimates for very small blocks are over-smoothed. For several simple sampling patterns the relation between the block size and the variogram range, and the kriging results were studied. Meaningful estimates of individual blocks are obtained when the variogram range is large compared to the block size and the sample spacing. For a variogram range less than half the sample spacing, the kriged block estimates were found to be uncorrelated with the actual grades. The over-smoothed estimates should not be used for calculating recoverable reserves IntroductionNowadays most mining companies know that the geostatistical estimation method, kriging, gives the best estimates of individual block grades. As most mining engineers and geologists are now familiar with the basics of geostatistics, the definitions of the variogram and of kriging will not be repeated here. An appendix containing definitions and mathematical formulae is given at the end of the article for the sake of completeness.Even though it is well known that the kriged estimates for very small blocks are over-smoothed, mine planners who want to define the ore/waste limits as finely as possible (especially for selective underground mines), are often tempted to krige very small blocks. So we ask how small is ""too small""? Clearly ""smallness"" cannot be expressed in yards or metres. It depends on the nature of the orebody under study and this is reflected in the variogram model chosen to describe it.To answer this question, the changes in four key parameters are studied:• the kriging variance,• the variance of the estimated grade,• the slope of the linear regression of the true but unknown grade on its estimated value, and• the coefficient of correlation between the actual grade and the estimate;as a function of the block size and the variogram range. (Definitions of these four parameters are given in the appendix). Ideally the kriging variance should be low while the variance of the estimated grade should be equal to the dispersion variance of the blocks. The slope should be l.0, and so should the correlation coefficient.These four parameters have been calculated for several simple 2-D examples. The effect of using kriged block estimates that are too heavily smoothed are shown, and the dangers of trying to use these estimates for predicting recoverable reserves for small blocks (i.e. selective mining units) are pointed out."

Jan 1, 1989

By Richard Thomas Newcomb

Chapters 5a, 5b, and 6 discuss the long- run supply of minerals and the characteristics of reserve search and production peculiar to extractive industries. It is now necessary to complete the picture by examining supply and demand in commodity markets to show how mineral prices are determined and how both price and production trends might be predicted over long periods of time. These practical interests can be served best by reviewing first some of the characteristics of the short-run static market models familiar to all readers of elementary economic texts, and then extending the theory to models of a more dynamic nature. It is important at the outset to note that economic theory provides a wide variety of economic models based on varying assumptions concerning the behavior of economic agents, the properties of the goods, the time period considered, and so on. Each variety of model offers certain analytical advantages and suffers certain shortcomings. The art of the applied economist or practioner lies in knowing enough both about the technology and practice of his problem and about theory to select the appropriate models for his analysis. In our approach it will be useful first to consider the role of markets for minerals and mineral products in relation to the efficient determination of what and how goods are produced in the whole economy, i.e., a general system of markets, before getting down to the task of analyzing supply and demand conditions in specific markets. The former study is called general equilibrium analysis, while the latter is called partial. By equilibrium is meant a state of the sys- tem under study in which supply equals demand in each market, and the prices which equilibrate the quantities offered and asked are called equilibrium prices. The tendency of prices to return toward equilibrium values if temporarily displaced, or to converge to new equilibrium values if important new conditions for supply or for demand are placed, defines "stable" equilibrium systems. The short-run describes a period in which adjustments to fixed capital are not made, although variable factors such as labor or materials can be adjusted. The long-run envisions a period in which fixed capital and other such constraints can be adjusted. Thus, it may take a sharp increase in price to bring out additional supply of a factor in the short-run with existing plant, while new capacity might permit additional quantities in the long-run without an increase in supply price.

Jan 1, 1976

Jan 1, 1924

By P. G. Nahin, A. Grenall, R. S. Crog, W. C. Merrill

A progress report of an experimental investigation into the role of clay in reservoir performance is presented. The Paper gives some of the reasons for considering clay as a significant component and outlines the objectives of a broad field of stud) which it is intended to pursue. Descriptions of the analytical methods used are given; these include X-ray diffraction. elec tron miscroscopy, thin section petrography, infrared spec-troscopy, and cation exchange analysis. A suite of the more important clay minerals has been assembled and characterized l~y these methods for use as standards in core analysis. From the data obtained it appears that although no one method of analysis is diagnostic for all of the clay minerals the infrared technique shows considerable promise in this direction. For the present, one or more supplementary methods should be used to confirm the clay mineral identifications. The methods of analysis are applied to field cores taken from repesentative and widely differing strata especially as regards their susceptibility to damage by fresh water. well.; completed in the stevens and Gatchell zones in San Joaquin valley are I,articularly clear-cut examples of this behavior with stevens zone wells being more adversely affected by fresh water. cores from these zones have been studied and are discussed. It appears that differences in this behavior can be ascribed to differences in the nature of the contained clays. The value of the infrarecl spectra of the clay fractions in establishing the identity of the predominant clay minerals is given particular emphasis. INTRODUCTION It is a challenge to the technical resources of the petroleum industry that when the economic limit of production is reached, from 40 to 70 per cent of the oil in California reservoirs remains unproduced even by use of the best presently known methods of recovery. The magnitude of this abandoned volume of oil can be appreciated when it is considered that to 1950 in excess of 8 billion bbll has been produced from California reservoirs with estimated economically recoverable reserves in known fields and pools totaling nearly 4 billion bbl.24 If for every barrel of oil produced there is at least another barrel still in place, it is evident that the revenue obtained from the recovery of only a .few per cent of this volume would repay the cost of the required research manyfold. From well completion experience. production behavior, and a growing body of laboratory data it now appears certain that the mineral composition of a producing stratum has an important bearing on the productivity and ultimate yield. In addition to the organic component and water, the cores con,ist of gravel, sand. silt, and clay" in diverse variety of (a, composition and (b) texture. It is the composite effect of these two factors which is probably responsible in large measure for the way in which the oil flows to the well. The role of the clay and fine-size accessory minerals is not clear but there is a growing opinion, based on their physical and chemical properties, that it is a significant one. of particular importance are the prime facts: 1. The silt and clay fractions of the reservoir matrix possess the highest surface area per gram, and 2. The silt and especially the clay fractions are the most chemically reactive of the inorganic constituents present. Only within the last few years has the knowledge of clay mineralogy and the techniques of identifying the clay minerals reached such a stage as to enable reliable inquiry into the composition of argillaceous sediments.2,8,10,11,12,16,26 It is the purpox of this and succeeding papers to add to the fund of information on the role which these materials play in the production of petroleum from California formations by correlating their presence and associated properties with observed reservoir behavior. In the present paper attention is directed to their possible influence on damage by fresh water. OBJECTIVES The attack on this problem divides naturally into two broad phases: 1. Determination of the nature of the clays and their relationships to the other mineral components, and 2. Determination of the physico-chemical relationships between the clays and the interstitial fluids. In the work described in this paper the emphasis has been on phase 1, which stems logically from the necessity of identifying and understanding the materials to be dealt with in Phase 2. Based on the authors' present opinion that not all of the minerals which occur in oil-bearing formation are of equal importance in their effects on the flow and recovery of oil, it was decided to focus attention first upon the clay minerals content and then. later perhaps. work into the field of the normally larger size non-clay minerals and fractions. The

Jan 1, 1951

By H. A. Bourne, E. L. Haden, D. R. Reichmuth

A circumferential-toothed bit with novel tooth form gave improved penetration performance. In this design the exterior flank of all teeth were vertical when in rolling contact with the hole bottom. Rock chips were generated by the interior flank of the tooth displacing the rock inwardly and downslope toward the center of the hole. A unique two-cone laboratory bit assembly enabled evaluation of numerous cone and tooth configurations. Some of the variables investigated, in addition to weight on bit, rotary speed and rock type, were tooth interference, percent tooth, hole bottom angle, attack angle and relief angle. Most tests were conducted dry on a brittle synthetic sandsone or a ductile quarried limestone. Tooth configurations were found to be more significant in the ductile material. This was attributed to the deeper tooth penetration before rock failure. These studies showed that the attack angle (angle beween interior flank of the tooth and rock surface) was the controlling variable; changing the tooth configuration from the assymetric or semi-wedge to the more conventional symmetric or wedge form reduced penetration performance; and penetration performance of circumferential-type cutters was directly proportional to rotary speeds up to 200 rpm. INTRODUCTION Much of the published literature on rock-chisel interactions describe experiments wherein symmetrical wedges are vertically loaded or impacted against a smooth rock surface.1-6 are is usually taken to insure that the indentation is not made near the edge of the rock specimen less erroneous data be obtained. The literature describes relatively few studies in which the investigator deliberately attempted to take advantage of an edge or free surface. In contrast, anyone who chips ice or breaks up a concrete sidewalk almost always works near an edge. Chisel "indexing," which has been considered by some investigator1,2,6,7 makes limited application of an edge or free surface. Probably the best documented investigation into applying this idea to drilling was that of Drilling Research Inc. at Battelle Memorial Institute.' Their "annular wing" percussion bit consisted of paired asymmetric chisels oriented so as to produce and move chips to the center of the hole. They predicted that the lowest energy requirement for chip generation would be achieved with a stepped hole bottom having a median angle of 45" to the horizontal. Results from limited tests showed that approximately 50 percent of the rock fragments were large and semi-circular in shape, as would be expected by a chisel impact near an edge. The remaining 50 percent were fine chips produced by the chisels in re-establishing the steps or ledges. Initial penetration rates with this bit were high, but they rapidly decreased. This was the result of excessive tooth wear caused by the constant friction on the gauge surfaces. The basic idea — circumferentially placed asymmetric chisels — still appears to have merit. If the concept could be applied to a rolling cutter bit, two of the shortcomings of the fixed chisel design could be overcome: (1) reduction in tooth friction, and (2) greatly increased cutter surface. Adapting asymmetric chisels to cutters rolling on an inclined hole bottom is restricted by bit geometry. The basic elements of roller rock-bit construction prevents the practical attainment of a 45" hole bottom angle. Nonetheless, experimentally it was considered desirable to investigate the influence of hole bottom angle to at least 40". This paper describes the laboratory studies conducted in evaluating the circumferential-toothed roller cutter rock bit. EXPERIMENTAL APPARATUS AND PROCEDURE BIT ASSEMBLY The cost of constructing a sufficient number of conventional three-cone rock bits to investigate circumferential cutter performance was prohibitive. Instead, a novel two-cone laboratory assembly which used an external bearing system was designed and constructed. The external bearings made it possible to alter the journal bearing angles and thus allow a wide flexibility in cutter configuration. Fig. 1 shows the laboratory bit assembly, the various bearing mount plates and the appropriate roller cutters for drilling shallow holes having hole bottom angles of 0, 10, 20, 30 or 40". The bit was limited to a drilling depth of 1 1/2 in. at the gauge teeth and a hole diameter of 43/4 in. This more or less intermediate size bit was chosen because it gave a more realistic match between bit teeth and the rock than would a microbit. Also, the rock sample size required was convenient and easy to obtain. CIRCUMFERENTIAL CUTTERS The tooth configuration used in our initial studies is shown in the upper half of Fig. 2. All cutters used in this series had the same tooth form — 43" included tooth angle, 2" positive relief angle and a horizontal tooth flat width of 1/32 in. Each cone cuts alternate rows except for the gauge row. The row-to-row spacing in view was 1/4 in. Static loading tests conducted earlier with asymmetrical chisels had been used to establish this spacing. These tests showed energy requirements for chip production increasing rapidly as the distances to the edge increased beyond

By L. L. Handy

Solvent floods using slugs of solvent have been found to show continuity in behavior from the vapor pressure of the solvent to the critical pressure for the two-component driving gas-solvent system. In the pressure region between the solvent vapor pressure and the critical pressure for the gas-solvent system, the gar and solvent are only partially miscible. Although complete miscibility cannot be obtained at these pressures, complete oil recovery is possible in principle. In two-phase solvent floods the solvent is propagated tllrough the reservoir, primarily, in the vapor phase. The carrier gas requirements constitute a significant factor in the economics of the process. A qualitative theory is proposed for estimating the amount of dry gas required to move the solvent through the reservoir. The theory shows that for two-phase solvent floods the total gas needed is a minimum at the vapor pressure of the solvent and at the critical pressure for the gas-solvent system, and is a maximum at some intermediate pressure. The predictions of the theory are supported by experimental studies using methane, butane and decane or methane, propane and decane in a natural sandstone core. INTRODUCTION Previously, solvent slug processes have been found effective for oil recovery in two pressure ranges. First, conventional miscible displacements are possible at pressures greater than the critical pressure for the gas-solvent system. Second, Jenks, et al,' have shown that, at pressures slightly in excess of the vapor pressure of the solvent, a solvent slug can be propagated through a reservoir by a gas essentially insoluble in the liquid solvent. The solvent bank displaces the oil ahead of it. Both of these processes, at least ideally, are capable of recovering all of the oil in the swept regions. Slug processes for which the gas and solvent are partially miscible have not been considered; that is, those systems for which the solvent and driving gas form two equilibrium phases in which the vapor phase contains a significant amount of solvent and the liquid phase an appreciable amount of the driving gas. Welge and Johnson' have shown that the gas needed to movc a solvent slug through the reservoir increases with increasing pressure above the vapor pressure of the solvent. It will be shown that solvent slug processes can, theoretically, recover all of the oil at any pressure greater than the vapor pressure of the solvent. But the amount of gas required to move the solvent through the reservoir depends very much on the pressure and temperature. In the present study a maximum in the gas requirements was both predicted theoretically and observed experimentally. This result has not been reported previously, and would not have been predicted from the Welge and Johnson model. The gas requirements are a minimum at the pressures corresponding to the vapor pressure of the solvent and again at the critical pressure for the gas-solvent system, and are a maximum at some intermediate pressure. AN APPROXIMATE THEORY FOR TWO-PHASE SOLVENT FLOODING The differences and similarities between conventional solvent floods and two-phase solvent floods are best understood by referring to concepts developed for miscible displacement in which miscibility is generated in the reservoir. In Fig. 1(A), a ternary diagram is shown for a hypothetical gas-solvent-oil system. To be rigorous the three components should each consist of a single molecular species. The pressure for Fig. 1(A) is greater than the critical pressure for the binary gas-solvent system at the specified temperature. Diagrams of this type are the ones most frequently referred to in discussions of enriched-gas drive and miscible displacement. A limiting tie line is shown tangent to the two-phase envelope and intersecting the gas-solvent line at Point A. To obtain generated miscibility with this type system, others have shown that, for an oil of Composition D, a mixture of gas and solvent must be injected which is richer in solvent than that composition indicated by A. An oil repeatedly contacted with a gas phase richer than A changes toward a composition which would be at equilibrium with the injected mixture, that is, a composition lying on a tie line which passes through the injected-gas composition. Since no such tie line exists, the oil is enriched to the point at which it becomes directly miscible with the injected mixture. At pressures lower than the critical pressure for the gas-solvent system, other types of phase diagrams are observed. The ones of interest in this paper are for pressures greater than the vapor pressure of the solvent, but less than the critical pressure of the gas-solvent system. Such a ternary diagram is shown on Fig. 1(B). In this case, two-phase behavior is observed not only for gas-oil mixtures, but also for certain compositions in the gas-solvent system. If a gas of Composition A (a dew-point vapor) is injected, once again the original oil is enriched by successive

By Rudolph G. Wuerker

Charles T. Holland (Head, Dept. of Mining Engineeri*, Virginia Polytechnical Inst., Blacksburg, Va.) Mr. Wuerker has presented a very interesting discussion of the use of triaxial test methods for investigating the strength properties of rocks. Such methods, no doubt, eventually will develop considerable information of interest to those concerned with the design of mine layouts, particularly in the field of pillar design. From his discussion of my recent article, "Cause and Occurrence of Coal Mine Bumps" (Holland Mining Engineering 1958, p. 933-1002), it is evident that in one place at least I did not make my meaning clear to him and perhaps others. To clear the matter up I think it best to quote from the article, somewhat more fully than did Mr. Wuerker, as follows: "4) In actual operations — because rocksare not perfectly elastic, homogeneous, nor isotropic and because local yield does occur — the maximum stress as demonstrated by Phillips (Ref. 22, pp. 64, 65) and indicated by much experience in mining, does not occur at the walls of the opening but at a short distance inside the pillar. Furthermore, the maximum stress does not reach as great a value as theoretical considerations and laboratory experimental methods indicate.* Actual distance inside the pillar, measured from the wall, at which the maximum stress exists, has not been determined. Observations in many mines, however, indicate that this distance could have a mini-value of one to six or eight times the bed thickness and that it is probably affected by width and height of the opening, depth of cover, and relative values of the elasticity and plasticity of materials comprising the roof, floor, and coal seam. The actual value of the stress produced probably lies between the theoretical maximum and the average stress concentration that would be produced if the weight of the strata above the unsupported opening were evenly distributed over the pillars for a distance equal to the opening width." The footnote reference in the above quotation referred to the following: "*For example, the Pocahontas No. 4 coal bed in southern West Virginia is mined under cover up to 1800 ft thick. Development openings are driven 18 to 20 ft wide, and the bed is about 6 ft thick. According to the work of Panek, the tangential wall stress at mid-bed height under these conditions would reach values between 4000 and 5000 psi. Actual tests of 3-in. cubes of this coal show its compressive strength would be much less than this, perhaps as low as 400 psi. Yet the pillars usually show no evidence of failure in these headings. In this same bed at a depth of 800 ft, the author has seen an opening 225 ft between supports lying between two old groves approximately 1100 ft apart. According to the theoretical considerations, the stress in the pillar walls would have been about 18,000 psi, yet the pillar showed little or no evidence of weight. In view of these observations, it is clear that the wall stress does not attain the maximum values indicated by theory." (Underlining added to original wording.) By referring to Fig. 2A of my paper it will be noted that theoretically the maximum pillar stress would occur at the pillar wall, i.e., at the passageway surface of the pillar. Obviously this cannot be correct in the cases of stress ranging from 4000 to 18000 psi since the coal at the surface of the pillar is under no constraint and cannot have a strength much greater than 400 or 500 psi. Hence, my conclusion that the maximum stress does not occur at the wall but back in the pillar some distance from the wall. Since these stresses are pushed back in the pillar from the wall, it is also obvious that the loads transferred to the pillar from the opening will be spread over a greater area and hence Pillar stresses will not rise to the values postulated by theory and photoelastic experiment. Further since to visual inspection the coal along the pillar wall did not appear to be failed the conclusion was reached that the stress shift was caused by local elastic or plastic yield and by difference in the elastic modulus of the rocks composing the mine floor, mine roof, and coal bed. Later on under the heading "Strength of Mine Pillars" (pages 1000-1002) the effects of constraint is briefly described. Also a formula taking into account constraint is developed relating pillar strength to the uniaxial strength of coal and the L/T ratio of the pillar. Since my paper was written, reports of experiments conducted in South Africa (Denkhaus, et. al., 1959), in Sweden (Hast 19581, and in Canada (McInnes, et.al., 1959) reveal that the conclusion expressed relative to the existence of a low stress area existing around the edges of pillars and solid faces as described above is generally correct. But it seems possible that where the wall stress developed is less than the unconfined strength of the rock composing the pillar and where the roof, floor, and pillar

Jan 1, 1961

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

By W. C. Merrill, P. G. Nahin, A. Grenall, R. S. Crog

A progress report of an experimental investigation into the role of clay in reservoir performance is presented. The Paper gives some of the reasons for considering clay as a significant component and outlines the objectives of a broad field of stud) which it is intended to pursue. Descriptions of the analytical methods used are given; these include X-ray diffraction. elec tron miscroscopy, thin section petrography, infrared spec-troscopy, and cation exchange analysis. A suite of the more important clay minerals has been assembled and characterized l~y these methods for use as standards in core analysis. From the data obtained it appears that although no one method of analysis is diagnostic for all of the clay minerals the infrared technique shows considerable promise in this direction. For the present, one or more supplementary methods should be used to confirm the clay mineral identifications. The methods of analysis are applied to field cores taken from repesentative and widely differing strata especially as regards their susceptibility to damage by fresh water. well.; completed in the stevens and Gatchell zones in San Joaquin valley are I,articularly clear-cut examples of this behavior with stevens zone wells being more adversely affected by fresh water. cores from these zones have been studied and are discussed. It appears that differences in this behavior can be ascribed to differences in the nature of the contained clays. The value of the infrarecl spectra of the clay fractions in establishing the identity of the predominant clay minerals is given particular emphasis. INTRODUCTION It is a challenge to the technical resources of the petroleum industry that when the economic limit of production is reached, from 40 to 70 per cent of the oil in California reservoirs remains unproduced even by use of the best presently known methods of recovery. The magnitude of this abandoned volume of oil can be appreciated when it is considered that to 1950 in excess of 8 billion bbll has been produced from California reservoirs with estimated economically recoverable reserves in known fields and pools totaling nearly 4 billion bbl.24 If for every barrel of oil produced there is at least another barrel still in place, it is evident that the revenue obtained from the recovery of only a .few per cent of this volume would repay the cost of the required research manyfold. From well completion experience. production behavior, and a growing body of laboratory data it now appears certain that the mineral composition of a producing stratum has an important bearing on the productivity and ultimate yield. In addition to the organic component and water, the cores con,ist of gravel, sand. silt, and clay" in diverse variety of (a, composition and (b) texture. It is the composite effect of these two factors which is probably responsible in large measure for the way in which the oil flows to the well. The role of the clay and fine-size accessory minerals is not clear but there is a growing opinion, based on their physical and chemical properties, that it is a significant one. of particular importance are the prime facts: 1. The silt and clay fractions of the reservoir matrix possess the highest surface area per gram, and 2. The silt and especially the clay fractions are the most chemically reactive of the inorganic constituents present. Only within the last few years has the knowledge of clay mineralogy and the techniques of identifying the clay minerals reached such a stage as to enable reliable inquiry into the composition of argillaceous sediments.2,8,10,11,12,16,26 It is the purpox of this and succeeding papers to add to the fund of information on the role which these materials play in the production of petroleum from California formations by correlating their presence and associated properties with observed reservoir behavior. In the present paper attention is directed to their possible influence on damage by fresh water. OBJECTIVES The attack on this problem divides naturally into two broad phases: 1. Determination of the nature of the clays and their relationships to the other mineral components, and 2. Determination of the physico-chemical relationships between the clays and the interstitial fluids. In the work described in this paper the emphasis has been on phase 1, which stems logically from the necessity of identifying and understanding the materials to be dealt with in Phase 2. Based on the authors' present opinion that not all of the minerals which occur in oil-bearing formation are of equal importance in their effects on the flow and recovery of oil, it was decided to focus attention first upon the clay minerals content and then. later perhaps. work into the field of the normally larger size non-clay minerals and fractions. The

Jan 1, 1951

By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By K. E. Brown, F. W. Jessen

By utilizing an 8,000-ft experimental field well equipped with 10 gas-lift valves and 10 Maihak pressure recorders, gas-lift tests were conducted with port sizes ranging from 5/16 through I in. The well was equipped to provide accurate means of measuring surface pressures, temperatures, quantity of injection gas and fluid production. The tests were conducted in 2%-in. OD tubing, and the well was making 95 per cent water. A complete evaluation of gas-lift-valve port sizes shows the relationship of per cent recovery, gas-liquid ratios, minimum pressure created at the operating valve and horsepower requirements for each port. The length of time necessary for the fluid in the tubing to reach equilib.rium conditions after each cycle was recorded. Fallback of fluid at depths of 477, 969, 1,685, 2,493 and 4,290 ft was noted. For each port size, pressure loads of 2.50, 300, 350, 400 and 450 psi were lifted with a valve operating at approximately 550 psi at 6,000 ft. Gas-liquid ratios for each load were varied from excess gas to a gas volume per cycle whereby the load failed to reach the surface. Numerous curves are presented in evaluating the accumulated dara. The results show a 1-in. port to be the most efficient under all conditions. The production of intermittent liquid slugs against different-sized surface chokes was evaluated. These tests were conducted from a 7/16-in. ported valve at 4,072 ft. Tests indicate that, when possible, a %-in. in diameter choke or larger should be used at the surface. In the past few years most of the advancement in gas-lift operations has been made in continuous-flow operations. Yet, it is estimated that at least 70 per cent of the wells on gas lift in the United States are of the intermittent type. Since the term "slug flow" is sometimes used in both intermittent- and continuous-flow operations, it would be well to distinguish between the two types of flow. Continuous-flow gas lift is defined as a method whereby the fluids are produced at a continuous rate at the surface. This generally requires a continuous injection of gas through a surface choke; however, various other control devices sometimes are installed to eliminate freezing, to shut-off gas during natural flow periods, etc. The actual flow of fluids in the tubing may be of the slug type (one of many flow patterns known to exist in continuous flow). Intermittent flow is defined as a method of gas lift whereby the liquid is produced in separate piston-type slugs. Perhaps this type of flow could best be thought of as a ballistic-type flow where the liquid leaves bottom as a piston, propelled by a slug of expanding gas. Gas generally is injected through some type of control at the surface at predetermined intervals. However, the valve may have characteristics whereby gas can be injected through a small choke and still result in a ballistic-type flow. The purpose of the experimental work was to evaluate the most efficient port size to be used on the operating valve for the ballistic type of lift and, in addition, to establish the importance of utilizing a surface choke large enough to allow slugs to be produced without detrimental effects. This work is part of a compre- hensive study of both intermittent-and continuous-flow gas lift, representing a joint project conducted by the Ohio Oil Co., the Sun Oil Co., Otis Engineering Corp, and The U. of Texas. The problem of evaluating port sizes has been given little previous attention. Some work undoubtedly has been done which has not been published to date. Some tests were conducted when the wireline, mechanically-opened valve (Nixon) first came on the market. This valve was capable of utilizing full tubing area as its port size. It is known that this was a very efficient valve, but to the authors' knowledge the results of tests have never been published. EXPERIMENTAL EQUIPMENT These tests were conducted on an actual field well, the Ohio-Sun Unit Well No. 2-E, in the North Markham-North Bay City field, Matagorda County, Tex. The well incorporated 23/8-in. OD tubing and produced 95 per cent water. Since the running of equipment was to be quite elaborate and expensive, a well was selected in which both intermittent- and continuous-flow tests could be conducted. This particular well was capable of producing in excess of 1,000 B/D of liquid (95 per cent salt water), yet with a 3/64-in. in diameter bottom-hole choke, production was controlled to 82 B/D. Most of the intermittent tests were conducted at this low rate. Figs. 1 and 2 show all the surface and down-hole equipment. As can be seen, every attempt was made to insure that ample equipment was available for reliable testing procedures. Fig. 1 shows the surface testing equipment. The input gas was controlled first by a regulator, then

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By J. Chipman

There is no better way of paying tribute to the memory of a scientist than by developing and carrying forward those ideas which he has contributed to science and which are for us the very essence of his immortality. For a lecturer who has not had the great privilege of stdying under Professor Howe or 'ven of knowing him in person, these ideas must be transmitted through the printed word. It is our great good fortune that Professor Howe left to us a rich heritage of publication, not only in his classic monograph on the "Metallography of Steel and Cast Iron" but in a wealth of earlier hooks and papers in the transactions of this Institute arid of other scientific and engineering bodies. An outstanding characteristic of this published record is the great breadth of interest and of vision which it portrays. His was riot a narrow specialization in only the scientific aspects of ferrous metallographg. On the contra1y many of his important contributions had to do with a far broader field of metallurgicial endeavor. He insisted that his students be well grounded in 1 he fundamentals underlying the whole field and not led into the narrow groove of specific applications. Among his first major publications we find papers on copper smelting, extraction of nickel, the efficiency of fans and blowers, thermic curves of blast furnaces, the cost, of coke, and the manufacture of steel. These are the papers of a metalhurgical engineer and it was among engineers that Henry Marion Howe made his early and well-merited reputation. These early engineering contributions display very clearly the strongly sctientific inclination of their author. The classic work on "The Metallurgy of Steel" published in 1890 contains a thorough and critical discussion of all that was known at the time concerning the alloys of iron and of what we would now call the physical metallurgy of steel. In addition it describes steel-making processes in use and some that had become obsolete, and points out in critical fashion the reasons for success and failure. Steel mill design and layout were included as well as some pertinent discussion of refractories. The book is indeed an embodiment of one of Howe's outstanding characteristics—breadth. It is both the science and the engineering of steel production as known in that day. One of Howe's earliest technical papers was entitled "What is Steel?" That was nearly seventy-five years ago when many new processes and new kinds of steel were being developed. The time was ripe for such a question and the answers which Howe was able to give were helpful in understanding the phenomena of heat treatment. Twenty-five years ago Professor Sauveur repeated the question as the title of the first Henry Marion Howe Memorial Lecture. It seemed to him that this question, "What is Steel?," had served as Howe's motto throughout the remainder of his life. Today I shall present for your consideration a question of another sort: "What is Sletallurgy?" Perhaps it is not too much to hope that in the answer we may obtain a clearer and possibly broader view of the nature of our science and our profession. The time is ripe for giving careful consideration to what we mean by metallurgy. If our Metals Branch is to become in fact an American institute of Metallurgical Engineers, it is essential that we understand what is meant by metallurgical engineering. I am convinced that the best interests of the profession have not been served by a narrow interpretation of these terms. We must now place emphasis on the breadth of metallurgy as a science and as an engineering profession. With its usual brevity and wit. Webster's dictionary definesmetallurgy as "the science and art of extracting metals from their ores, refining them and preparing them for use." I shall riot assume that the words "science" and "art" and "metal" are so well understood as to require no defining but others among our contemporaries are better qualified than either your lecturer or the dictionary to present the broad meanings of these terms. When we say that metallurgy is among the oldest of the arts we are not classing it with painting or sculpture or music but rather with the making of tools or weapons or the building of bridges or chariots or cathedrals. In short we are saying that metallurgy is among the oldest of the engineering professions. The question " What is metallurg ? " has been one of rather more than ordinary concern to those of us who have the task of developing a curriculum for the education of students in this field. This development has been going on in a number of universities over a period of some years. but there seems to be as yet no unanimity as to what such a curriculum should contain. I believe there is fairly complete agreement that it must be founded upon sound

Jan 1, 1950

By J. W. Snavely

WITH all the advantages of handling bulk materials by means of belt conveyor also go some problems, one of the most persistent being that of cleaning. When sticky materials are being carried; the build-up of material on the return idler rolls results in difficulty of belt training. Much attention has been given to the problem of cleaning conveyor belts, and a great variety of cleaning devices have been developed. Even the best involve troublesome maintenance, and none can completely remove the fine particles imbedded in the belt cover, which cause rapid wear of the return idler rolls, and at the same time, of the belt cover as well. One of the major rubber companies has been promoting a two-way belt system, in which the conveyor belt is given two successive 90" twists at each end to enable it to carry material in both directions simultaneously. For many years the flat belt transmission industry has installed quarter-turn and half-turn twists in countless numbers of instances. While quarter-turn and half-turn twists in transmission belts is a familiar application, the 180" twist apparently has never been previously attempted with a conveyor belt. About a year ago, two officials of the National Iron Co. of Duluth, Lester and Lewis Erickson, proposed twisting the return run of a conveyor belt on an installation that they were designing for one of the major iron ore producers. Since then the soundness of the idea has been demonstrated, both in theory and by practical test, with the result that the installation of two conveyor belts involving the twisting of the return run is now under way. These two installations are designed to have the return run of the conveyor belt twisted 180" as it leaves the snub pulley at the head drive. The clean underside of the belt is thus placed against the idlers on the return run as well as on the carrying run. Just before it enters the tail pulley, the belt will be twisted an additional 180°, restoring it to its normal position. Because this twisting of the return run of a conveyor belt is a radical departure from accepted practice, an elaborate and extensive test was conducted early in 1950 to demonstrate that this twisting of the return run could be done successfully, also to establish application data for accomplishing this twisting, and to determine if any special equipment would be required. In studying this concept of twisting the return run of a conveyor belt, a number of problems need to be solved, primarily the ones brought about by deliberately introducing an unequal distribution of stress across the conveyor belt and controlling that maldistribution of stress, while confining it to the return run portion. The tension conditions existing in the return run of a conveyor belt are clear to all designers. First, the return run carries the initial or slack side tension of the conveyor belt, the tension that must be supplied to the return run to provide proper frictional contact between the belt and the driving pulley so that the necessary power can be transmitted from the driving pulley to the belt without slippage. This slack side tension is supplied to the belt by means of takeups, either of the gravity type, which can be vertical or horizontal, or by means of the screw type. With inclined or declined belt conveyors the slope tension also must be considered, which is the tension imposed by the weight of the belt hanging from the top pulley. This slope tension frequently can furnish part or even all of the initial tension required. The maximum value of the slope tension will be at the top pulley, and it decreases in direct proportion to the length. In addition to the foregoing, it frequently is desirable to impose arbitrarily additional slack side tension to provide sufficient tension at the loading point at the tail, so that the belt will adequately support its load between the carrying idlers. Design Conditions for Twisting A number of design conditions exist, which must be satisfied successfully to accomplish the twisting of the return run without exceeding normal working limits in any portion of the conveyor belt. It is obvious that the belt edge, in its relation to the center of the belt, must stretch in making a twist, because as the twist is accomplished, the belt edge travels through a longer path than does the center of the belt. It is further obvious that if the edge of the belt is stretched, a redistribution of stress in the belt is required to allow this edge stretching. Moreover, this stress will be unequal across the width of the belt, having a maximum value at the edges, with a minimum value at the- center of the belt. With correct initial tension in the return run of a conveyor belt, the existing slack side tension will be unequally distributed when a twist is introduced. A condition then exists in which the edge stresses,

Jan 1, 1952

By J. Chipman, G. G. Hatch

T. ROSENQVIST*—It is a pleasure to see the excellent way in which the experimental part of this work has been handled. There seems to be little doubt that the distribution data obtained corresponds most closely to thermodynamic equilibrium under the prevailing reducing conditions, namely equilibrium with graphite and one atmosphere CO pressure. The desulphurization curves in Fig 10 show the same general feature as the curves given by Holbrook and Joseph, but the distribution ratios are from 20 to 40 times greater—undoubtedly due to a closer approach to true equilibrium. In the theoretical discussion, the authors calculate a theoretical distribution (S) ration -jg-. which they find to be about 50 times greater than the experimental. The deviation is so great that the basis for their calculation needs a more thorough examination. The authors base their thermodynamic calculation on free energy expressions where diluted solutions of FeS and CaS are used as standard states. (The activity coefficient in diluted solutions is taken to equal unity.) Such a standard state will change when the nature of the solvent is changed. Taking the free energy of the reaction [FeS] ? (FeS), Eq 2, which is derived from the distribution of sulphur between an iron and a FeO-melt, it is very unlikely that the free energy of this reaction will be the same for a distribution between pig iron and a calcium silicate slag. Therefore a more fundamental basis for the thermodyuamic calculations seems needed, where all thermodynamic equations are referred to unambiguously defined standard states. The most natural standard states for CaO and CaS are the pure solid substances at the same temperature. As standard state for sulphur in iron, pure liquid FeS can be used. This rules out Eq 2 [FeS] ;=s (FeS) because ?F° = 0. The standard equation will then be: FeS, + CaO6 + Cgraph ?Fei + CaS8 + CO. vFo1773 = 25,000 cal It would be more universal and also simpler to refer the escaping tendency of sulphur in liquid iron to the corresponding H2S/H2 ratio which can readily be determined experimentally. As standard state a gas mixture H2S/H2 = 1/1 can be used. (This corresponds at the temperature of liquid iron closely to one atmosphere S2 vapor.) Thus the standard equation for the sulphur reaction can be formulated as follows: H2S0 + CaO3 + Cgraph ?H2o + CaS8 + COg The standard free energy of this reaction has been calculated from the best available data to AF°m3 = —35,000 cal. This gives for the equilibrium constant at 1500°C Now, the solubility of CaS in blast furnace slags has been determined by McCafferey and Oesterle* and corresponds at 1500°C to about 10 pet S (varying somewhat with the composition of the slag.) If the activity of CaS is assumed linear between 0-10 pet as curve 1, (see Fig 11), then acaO = 0.1 (S); (S) being wt. pet sulphur in the slag. For a diluted solution of sulphur in an iron melt saturated with carbon, the ratio H2S/H2 is, according to Kitchener, Bockris and Liberman,f about 0.01 [S], [S] being wt. pet sulphur in iron. Substituting these values in the expression for Kp we find The value 2.103 is only 4 times greater than the experimental coefficient found by Hatch and Chipman, but the value is very sensitive to a small error in AF°. A better agreement with the experimental distribution coefficient can be obtained if one assumes the activity of CaS to run like curve 2 (Fig 11). This (S) will give a lower theoretical W, value, a value which varies with (S) exactly as Hatch and Chipman learned. Such a shape of the activity curve, which corresponds to a positive deviation from Raoult's law, is actually to be expected from the fact that liquid silicate and sulphide phases usually show incomplete miscibility. A closer agreement between experimental and theoretical data can not be expected before we have more complete data for the individual activities of CaS and CaO in the slag. The activities acaS and Ocao referred to the solid phases as standard states, are exact defined quantities contrary to the somewhat undefined expression "free lime," and they are independent of any theory for the constitution of liquid slag. J. CHIPMAN (authors' reply)—The authors wish to thank Mr. Rosenqvist for his very interesting and useful thermodynamic addition. Curve 2 of his figure offers the needed basis for explaining the increase in the ratio (S)/[S] with increasing sulphur content. Attention is called to an error in the printed paper: Fig 2 and 3 are reversed. M. TENENBAUM*—In the figures showing the relationship between excess base and sulphur distribution (Fig 6, 7 and 9) the slope of the curve tapers off in the negative basicity range. Somewhat the same thing is observed with open hearth slags. In that case, the fact that some sulphur distribution between slag and metal is obtained with negative basicity is interpreted as indicating some dissociation of the lime silicate compounds whose existence in oxidizing basic slags has been used to explain various observed phenomena with regard to other slag-metal reactions. In the case of the blast furnace slags, the reduced slope of the sulphur distribution curve with decreasing excess base is attributed to the amphoteric effect of alumina. Has the possibility of other explanations been investigated ?

Jan 1, 1950