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By James C. M. Li, J. Weertman

James C. M. Li (United States Steel Covp.)—The author has discovered a single analytical relation between the minimum, or the steady-state, creep rate and the applied stress confirming a statement made earlier by orn" that such relation should exist and should reduce to the power law at low-stress levels and to the exponential law at high-stress levels. However, as pointed out by the author, all the available theories of creep are not adequate to explain such a single relation. Inspired by such a statement, I have made a suggestion concerning a possible explanation13 of the new relation. This is based on the concept that the rate-controlling step is the cooperative motion of a short dislocation segment. The nature of and the reason for the cooperation have been discussed13 as well as the reason why the motion of the dislocation could be controlled by the mobility of the short segments. A natural short segment has been proposed13 to be the node formed at the intersection of two dislocations. The reason why the node may contain only a few atoms has not been discussed and the application of the proposed model to all the metals and alloys reported in this paper has not been attempted. It seems appropriate to include these in this discussion. The model was partly inspired by the substructure recently observed in the electron microscope on creep specimens. One such example is shown in Fig. 48 in Darken's Campbell Memorial Lecture. The substructure is a collection of dislocation intersections and irregular networks. No pileups have ever been observed in such specimens. A closer look at the network indicates that one set of dislocations is more straight than the other set sug- gesting that the other set may be mobile in the plane of the net. Since, for the network to survive the creep deformation, some dislocation reaction has to take place at the intersection of the two sets of dislocations, the mobile dislocation, even if it can slip in the plane of the net, will have difficulty in moving at these intersections. To illustrate, an idealized network is shown in Fig. 9. The thin lines represent the set of dislocations which are mobile and can slip in the plane of the net except at the nodes which are formed at the intersection of the two sets of dislocations. The other set of dislocations, represented by the thick lines, may have a Burgers vector which is not parallel to the plane of the net, and therefore may be immobile. Because of this nonparallel Burgers vector, the Burgers vector of the node, which is avectorial sum of the Burgers vectors of the two sets of dislocations, will also be nonparallel to the plane of the net. Therefore, the node cannot slip in the plane of the net and the set of mobile dislocations will have to drag the node along as indicated in Fig. 9. Now the problem is how many atoms could be involved in the nodes. Exact calculation of the length of the node is a difficult task especially since the length should be a steady-state length and not an equilibrium length. An estimate of the equilibrium length can be made by balancing the line tension of all the dislocations. The results would be a small fraction of the length 1 between nodes as shown in Fig. 10. In some instances such a calculation shows that the node will not be formed. But, since the calculation is only approximate, it does not rule out the possibility of the formation of a short node. In other instances the equilibrium length of the node is an appreciable fraction of I. Such a node would

Jan 1, 1963

By C. M. WEILD

ATTENTION has been turned recently to the exploration and development of certain large blanket-deposits of brown iron-ore in Cuba. The most conspicuous of these to-day, and the one upon which the most light has been shed, is the Mayari deposit, situated about 15 miles south of Nipe bay. Here the Spanish-American Co. has sole control over 18,500 acres of ore-bearing lands, reported by its engineers to contain 500,000,000 tons of ore; and the necessary plant and equipment, with docks and railways, is now under construction for the early marketing of this ore. A similar deposit, and undoubtedly the next to be exploited, is the ore-field at Moa bay, where 13,000 to 15,000 acres of ore-lands, immediately adjacent to the shores of an excellent harbor, have been generously covered by numerous mining-claims, practically all controlled by four large interests. This deposit is now estimated to contain approximately 350,000,000 tons, on the basis of dried ore ready for shipment, a figure which may be increased when the western limits of the ore-deposit have been more accurately defined. Other deposits of the same type, but smaller and less accessible, are those at Cubitas, situated from 12 to 15 miles north of Camaguey city, and at Taco bay and Navas, points lying a few miles west of Baracoa. The area of the Cubitas deposit is said to be 6,000 acres, and the yield of ore is estimated at 150,000,000 tons. The Baracoa. deposits are less well known, but preliminary estimates have placed their joint ore-reserves at 40,000,000 tons. Accepting the above tonnages as reasonably correct, we conclude that the deposits enumerated give promise of adding about 1,000,000,000 tons of iron-ore to the world's supply; they have, therefore, to be considered in any attempt to fore-

Aug 1, 1909

By George C. Coupland

Ecstall Mining Limited, a wholly owned subsidiary of Texas Gulf Sulphur Company, is the owner and operator of the Kidd Creek Mine including the concentrator complex located near Timmins, Ontario. Canada, approximately 450 miles north of Toronto. The mine, concentrator and Timmins form a triangular arrangement with a 17-mile rail link connecting the mine and concentrator and both of these facilities 18 and 14 miles respectively by road from Timmins. A core drilling program in the spring of 1964 established the presence of a large massive sulphide orebody which was to become the Kidd Creek Mine. Texas Gulf Sulphur had been conducting an intensive search for base metal in various parts of Northern Ontario and Quebec since 1957. Of several thousand anomalies detected in airborne electromagnetic surveys, several hundred warranted ground inspection, but only one of more than sixty drilled became a commercial orebody, the Kidd Creek Mine. The geophysical exploration work has been well covered in a paper written and presented by Van Donohoo, presently a Vice-President of T.G.S., at the American Mining Congress in San Francisco in October 1969. GEOLOGY The orebody lies within a series of overturned rhyolitic flows and pyroelastics with a major peridotite intrusive to the east. The hangingwall and footwall are composed chiefly of intermediate volcanics, andesite and dacite. The southern end of the orebody appears to terminate abruptly against greywacke while the north end is bifurcated and the structure obscured.

Jan 1, 1970

By A. B. Cook, C. J. Walker, G. B. Spencer

Although water will displace oil from a petroleum reservoir to a greater extent than gas will, there are some reservoirs in which gas rather than water should be used for pressure maintenance. This is indicated by the high-percentage oil recovery in the case history reports on the Pickton field1 in East Texas and the Raleigh field2 in Mississippi. In gas cycling, total oil recovery includes vaporized products from the immobile oil in addition to oil produced by displacement. If a large part of the immobile oil is vaporized, total oil recovery may be higher than that obtainable from pressure maintenance by water injection. However, the amount of immobile oil vaporized may range from almost 0 to 100 percent, and no simple and reliable method has been presented in the literature for calculating oil vaporization. Development of such a method was the purpose of this study. Several papers concerning the calculation of oil vaporization have been published,3 6 and each is based on the concept dealing with K values — equilibrium constants for the various components in reservoir oils. (K for a component in a system of vapor and liquid in equilibrium is the mole fraction in the vapor phase divided by the mole fraction in the liquid phase.) This appears to be the most logical approach. Yet, the problem is too great for a perfect solution, even with modem laboratories to analyze oils and high-speed digital computers to perform calculations; the number of components in reservoir oils is too large. Because of their complexity no two reservoir oils are exactly alike. Also, K values change not only with variations in pressure and temperature but also with composition of the reservoir oil. In addition, during gas cycling, the lighter hydrocarbons tend to vaporize first. Thus, the reservoir oil becomes more dense and less volatile as gas cycling continues. Furthermore, the greatest amount of oil vaporization occurs near the injection well. Therefore, a simplified method is required for calculating oil vaporization because a rigorous method is not practical. The present methods of calculating vaporization generally require knowledge of the reservoir oil composition in which the mole fractions of the lighter components through hexanes are given; the remaining oil is described as C, + (heptanes and others of greater molecular weights). Assigning one K value for the C,+ system provides the simplest solution, but this incorrectly assumes that K for C, + does not change as gas cycling continues. This assumption can cause large errors because the K value may become less than a thousandth of the original after a large amount of oil vaporization. Another way to solve the problem is to determine changing K values for C, + according to how much of the C, + has been vaporized. To determine these values a sample of the reservoir oil is injected into a pressure-volume cell, and dry gas is batched in and out of the cell. Appropriate measurements and tests are made to determine K

Jan 1, 1970

By G. F. Butterworth

The metallographic structures most frequently encountered in rifle barrels, and which are illustrated by the accompanying photomicrographs, fall naturally into two groups, distinguished by the method used to, produce in the stock a physical condition having the requisite properties. The fist group consists of "rolled" barrels; that is, barrels subjected to hot working by rolling in or near the critical range. In the second group, the stock, which is smaller in diameter than the first, is upset to form the butt end and is then heat treated by giving it a quench and a draw. These barrels will be referred to as " heat-treated " barrels. The structure of the rolled barrels resembles closely that of the same steel after annealing. There is the same network of excess ferrite outlining the grain boundaries, but the grains themselves are composed of sorbite rather than pearlite. The grain size is closely related to the rolling temperature. The critical-point curves of this grade of steel, which is approximately 0.50 to 0.60 per cent. of carbon and 1.00 to 1.30 per cent, of manganese, show a single very pronounced point between 1300" and 1350" F. (704" and 732" C.). Barrels rolled within this temperature range give an exceedingly fine grain, shown in Fig. 1. In fact, the grains may be so fine that, at a low magnification, they may be confused with the heat-treated structure shown in Fig. 6. A magnification of 500 diameters, however, will always resolve a rolled barrel into the characteristic structure shown in Fig. 2. As the temperature is increased, the grains are found to be larger. If, on the other hand, the rolling temperature is below the critical range, the structure previous to rolling will not be obliterated, the only effect of rolling being to elongate the coarse sorbite grains in the direction of rolling, Fig. 3. This distortion is greatest at the muzzle. Heat-treated barrels are quenched in oil from above the critical range, which should give a martensitic structure, Fig. 4, but the presence of some troostite in the martensite is frequently noted when the quench has not been sufficiently drastic, Fig. 5. The structure brought about by the subsequent draw is not so striking, though quite as typical. It is sorbitic or sorbito-pearlitic, and under a low magnification appears almost homogeneous, as in the case of fine grains of pepper and salt well mixed together, Fig. 6. This structure is substantially the same for all

Jan 1, 1920

Jan 1, 1963

By Marius R. Campbell

VARIOUS classes of coals are recognized in this country at the present time. These classes depend largely upon physical characteristics rather than upon chemical composition, and consequently they cannot be accurately defined. The divisions into anthracite, semi-anthracite and semi-bituminous are fairly satisfactory; but the term bituminous embraces so large a variety of coal that it is of little value, and the term lignite is so loosely applied that it has little or no place in a scientific classification. At present there is no way of accurately defining the vari¬ous classes of coal, because no adequate scheme of classification, which applies to lignites as well as bituminous coal and anthracite bas been proposed. The object of this paper is to present such a scheme, which is based upon data obtained dur¬ing the past year by Prof. N. W. Lord,1 in charge of the chemical laboratory of the United States Geological Survey coal-testing plant at the Louisiana Purchase Exposition, St. Louis. All the classifications of coals proposed prior to 1877 were based either on physical characteristics or on proximate analyses, including all of the impurities. These schemes were illogical and highly unsatisfactory, for the physical properties of a coal give little indication of its true composition; and impurities, such as ash and sulphur, are largely the results of acci-

Sep 1, 1905

By Paul M. Tyler, Colin G. Fink

THE field of rare metals is so broad that progress can be reported upon many important fronts. Not satisfied with the 92 elements that Mendeleeff and his followers have accepted as legitimate, scientists are trying now to complicate matters by making new elements. Enrico Fermi announced the fabrication of "Element 93". Uranium, instead of being allowed to disintegrate slowly according to its normal habit, was bombarded with neutrons until some of them seemed to have stuck in the nucleus. To understand just what is alleged to have happened all one has to do is to line up the elements in their usual order of ascending atomic weight and imagine, as physicists do, that each atom is a little solar orbit comprising a central mass or planet about which other masses revolve like satellites. Ordinary hydrogen, being very light, consists of only one positively charged proton center, with only one positively charged electron revolving about it. Other atones are progressively more complicated until we come to uranium, which has a relatively big center and 92 particles revolving around it.

Jan 1, 1935

By C. K. Leith

GENERAL GEOLOGY OF THE LAKE SUPERIOR IRON-BEARING AND COPPER-BEARING SERIES. THE geology of the Lake Superior region is of general interest, both from an economic and a scientific standpoint. The presence of large and rich iron- and copper-deposits has made a knowledge of the geology of the region necessary for purposes of exploitation and exploration. The ores of the region are contained in rocks of pre-Cambrian age, 'pith for most of the country up to recent years have usually been referred to as « crystalline schists " or " crystalline complex;" and regarded principally as metamorphosed basement-unit upon which the sedimentary rocks, beginning with the Paleozoic, were laid down. In the Lake Superior re¬gion this pre-Cambrian complex presents an unusual variety of rocks with determinable relations. It has been possible, with the large expenditures which-the magnitude of the iron-mining industry warrants, to work out their stratigraphy to a larger extent than has been possible in almost any other area of pre-Cambrian rocks. The real complexity of Lake Superior geology, the confusion of names and the multiplicity of reports covering small parts of the region, are such that interested persons, other than. geologists directly engaged in the work, may well hesitate to attempt to comprehend the geology of the region as a whole. The following paper is a somewhat elementary outline of the geology of the Lake Superior region with special reference to new developments not yet covered in published reports. Geological information concerning the region has been gath¬ered by mining companies, and by the geological surveys of Michigan, Wisconsin, Minnesota, Ontario, Canada, and the United States.. Perhaps in no other part of the country have the mining men themselves spent such large sums in purely geological work. This has made possible the publication of ,reports and maps by the State and Government surveys in much less time and at far less cost than would have been otherwise possible. The. U. S. Geological Survey is the only organization which has covered all of the region on the United 'States side of the boundary, and as its reports include the in¬formation gathered by the mining companies and State organi

Mar 1, 1905

By B. M. Larsen, J. W. Campbell

Several articles have recently been published discussing the conditions necessary for accurate measurements of temperatures in the open-hearth steel furnace. In the course of a study of refractories service conditions in steel furnaces, the present writers have taken temperatures in several open-hearth shops in the Pittsburgh district. The conclusions, as to conditions necessary for accurate measurements of temperature, are somewhat at variance with those of other investigators. The subject is closely connected both with the close control of steel-making and the prevention of overheating of the silica refractories used in roofs and walls. It is becoming more and more important to obtain furnace temperatures of fairly definitely known accuracy. At present, the most useful instrument for such measurements is the disappearing-filament type of optical pyrometer. This method of measurement has formed the basis of most other discussions on the subject and was also used by the writers. Previous Investigations In 1916, Burgess' made perhaps the first systematic series of measurements in steel furnaces. The emissivity figures of 0.40 for liquid steel and of 0.53 to 0.65 for liquid slags had been determined by the Bureau of Standards and were used by Burgess in this work. These correction factors are still being used and are regarded as fairly accurate, so that the tapping and teeming temperatures on metal streams given by Burgess should be very nearly correct. Most of his temperatures of furnace roofs and slag surfaces were taken while flames were present in the furnaces and include a few roof temperatures above 1700' C. (3100' F.).

Jan 1, 1927

By FRABK HERVEY PETTINGELL

THE stock exchange and its functions is about as well understood by the average individual as the fourth dimension. What is a stock exchange? Divested of the rules and regulations by which it is governed, and the facilities it provides for the convenient handling of securities, it would be in its nude state nothing more or less than a meeting place for brokers. The stock exchange in America dates back to 1752, when a group of merchants of New York established a meeting place at the foot of Broad Street for the purpose of dealing in meal and slaves. The first definite orgarization, however, had its beginning in 1792 when 24 New York brokers signed an agreement not to buy or sell public stock for less than one quarter per cent. commission. From this small group has grown by gradual degrees, the greatest organized security market in the world, namely, the New York Stock Exchange. At the present time there are 27 stock exchanges in the United States and 5 in Canada. Based on the volume of business transacted, the Los Angeles Stock Exchange ranks 6th among them. This is attributable to the fact that strictly speaking Los Angeles has never been a stock exchange town, like some other large cities. Take for instance San Francisco, which supported one stock exchange from 1862 to .1882 and has since supported two. No city, by the way, should tolerate two stock exchanges at the same time. It is an economic folly and a senseless duplication that can be compared with rival telephone companies or competing street railway systems, paralleling each other's lines and always leads to trouble and confusion, and sooner or later one or the other falls by the wayside. While Los Angeles has had stock exchanges of one kind or another since 1896, none of them attracted much attention until 1899 when the present exchange was organized and it did not get well under way until along in 1906.

Jan 1, 1925

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By William E. Greenawalt

IN these days of special legislation for the benefit of various industries one might well consider one branch of human endeavor intimately associated with engineering-that of patents and patent litigation. It is estimated that 85 per cent of all industries in the United States are based directly or indirectly on patents. Most inventors are engineers, and most patent litigation pertains to the engineering industries. It is fitting, therefore, that engineers should be vitally interested in discussing patent affairs, particularly as inventors are not a professional group, and invention is mostly a transitory phase incident to the development of specific industrial problems.

Jan 1, 1937

By A. B. Parsons

Jan 1, 1971

By K. W. John, L. Mueller

The rock mechanics approach to stability problems of steep rock slopes dealt with in this article has particular reference to the concept and methods of analysis developed by the Salzburg, Austria, school of rock mechanics. These theories are based on the principal postulate of the anistropy of the technological properties of in-situ rock masses. The present approach, which is more in line with geological engineering concepts, differs distinctively from the soil mechanics and engineering geological concepts commonly practiced in the United States. PRINCIPAL ENGINEERING APPROACH TO GEOTECHNICAL PROBLEMS AVAILABLE ENGINEERING CONCEPTS At the present time two different concepts are available for engineering analysis of underground structures and foundations in different earth material: soil mechanics and rock mechanics. Of these two branches, soil mechanics is, after 40 years of initially revolutionary and more recently evolutionary development, well established. Its principal concept of replacing in-situ soils or rock masses by perfectly homogeneous substitues has resulted in many practicable methods of analysis which, if applied with judgement, have resulted in successful applications throughout the world. Conversely, rock mechanics is still in the early stages of revolutionary development. Few, if any, standard concepts or methods of analysis have been established. Opinions vary widely. At present the professional background of an investigator very often determines the engineering concept to be applied to a particular problem, rather than its actual requirements if considered objectively. This paper stresses the rock mechanics or geological engineering point of view advocated by the Salzburg group. A review of the soil mechanics concepts is considered beyond the scope of this paper. THE "SALZBURG APPROACH" TO ROCK MECHANICS The rock mechanics concept as outlined here was initiated by Stini, based upon work by sander.1 Since

Jan 1, 1963

By Lewis Robert M.

The importance of phosphate in feeding the people of the world has been recognized by mining companies as they continue their search for new ore deposits and ways of improving phosphate production. An extensive phosphate-recovery research project involving investigation of beneficiation variables by batch testing, flotation pilot-plant processing of the major portion of the ore, gravity separation of the coarse fraction, and recovery of byproduct heavy minerals of a North Carolina phosphate deposit has been completed. Data obtained through batch tests enabled the development of an economical flowsheet which proved successful for the efficient recovery of a good quality phosphate concentrate in a pilot plant.

Jan 1, 1975

By L. T. Stanley

A method is described whereby the behavior of the front is approximated when gas is injected into a thick reservoir having reasonably homogeneous properties. The method is applied to the Abqaiq field of Saudi Arabia. The producing member is the Arab-D, a high-permeability calcarenite which has no continuous betlding planes. Field performance indicates the injected gas to be partially miscible with the reservoir oil because gas volume factors experienced are lower than those predicted by the gas law. Eqlrilibril~m calculations confirnz ihis and also show that the volume factor may vary appreciably, depending on the relative quantities of oil and gas in contact in the reservoir; consequently, volutnetric balances are made for the purpose of determining the behavior of the gas volume factor during injection history. The effect of gravity segregation on position and shape of the gas front is approximated by dividing the producing section into three zones vertically and tracing the movement of the average interface in each zone, with counterflow of oil and gas taking place betweell zones behind the front. This results in a gas front that advances more rapidly along the top of [he formation than along the base, producing an "umbrella" effect in cross section that becomes more pronounced as the front progresses. The calculations cover the gas-injection period of Abqaiq field history through 1958, and the position of the gas front is plotted at one-year intervals. Finally, some comparisotls between the calcrlated fronial position and the gas-oil contact as Measured by neutron logs are made. INTRODUCTION Fig. 1 is a structure contour map of the Abqaiq field. For analytical purpcses, the field has been divided into two areas designated A and B, as shown on the map. Gas injection into Area A was begun in early 1954 into two wells located near the crest of the structure on the north-south axis of the anticline. During the period covered by this paper, the average injection rate has been 122 MMscf/D with a maximum sustained rate of 160 MMscf/D. The reservoir pressure has been maintained at 2,450 psig since start of gas injection. The reservoir originally was undersaturated but, prior to pressure maintenance, the pressure was drawn below the bubble point in most of the Area A section, creating an in-place free-gas saturation of 8 per cent at the crest of the structure. The average critical gas saturation is 13 per cent established by laboratcry core tests. That the entire reservoir remained below critical gas saturation prior to gas injection is borne out by the fact that none of the crestal wells have exhibited high gas-oil ratios during production history. The Area A reservoir is a carbonate section about 200-ft thick having average porosity and permeability of the order of 22 per cent and 500 md, respectively. The productive horizon is the Arab-D member of Jurassic age and is encountered at an average depth of

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969

By C. C. Miller, A. R. Belyea, C. H. Herty, E. B. Burkart

The removal of sulfur from steel has been studied by many investigators, but the quantitative relationships between the factors involved have not been determined. This is undoubtedly due to the number of variables encountered in practice, an attempt to study any one reaction or relation being affected by other reactions the relative importance of which cannot be estimated. The factors that affect the extent of removal of sulfur in the basic open-hearth process are generally considered to be: 1. Basicity of the slag: (a) Iron oxides in the slag; (b) carbon in the metal or carbide in the slag; (c) temperature. These factors affect the reactions: FeS + CaO = CaS + FeO FeS + CaO + C = CaS + CO + Fe. 2. Amount of sulfur in the gas. 3. Amount of manganese in the metal. The factors which affect the rate of removal of sulfur include, in addition to these: 4. Fluidity of the slag: (a) Normal changes in fluidity with temperature; (b) changes in fluidity because of the addition of special reagents such as fluorspar. 5. Agitation of the bath. Within the past two years, two papers have been presented dealing with the influence of sulfur in the gas on slag and metal. Nead' has shown that if a gas high in sulfur be used for heating, the metal and slag will absorb sulfur. Whitely2 concluded from his experiments that if a

Jan 1, 1925

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970