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By Grover R. Castle

INTRODUCTION "Project Financing" or "Project Loans" have become increasingly popular in recent years, and commercial banks are being asked to consider more and more of such financing. However, the analysis of this type of loan is quite different from the analysis of a loan to a financially sound corporation based on the company's balance sheet. For this reason Chemical Bank did a study of project loans in an attempt to be more sophisticated in our approach to them. As part of this study, we examined 29 project financings for which information was available. In this article I shall describe project loans and set forth the guidelines we developed, as an aid to credit officers who might have occasion to analyse this type of financing. DEFINITION OF "PROJECT FINANCING" OR "PROJECT LOAN" The terms "project financing" and "project loan" commonly describe the various methods that banks and institutional lenders use to finance the construction of new projects on a basis whereby payout is anticipated from the revenue stream generated by the project. A project financing often involves a loan to a new entity formed specifically to own the project. The analysis of a project loan proposal is quite different from the analysis of other term-loan proposals since it involves a credit decision based on the review of a projection or forecast rather than of historical earnings and/or it involves the reliance on contractual obligations of third parties. Lenders are asked to assume the added risks associated with project loans because: 1. Project financing may permit a company to obtain additional leverage. It is possible for companies to arrange financing on a project basis that could not be arranged as a direct borrowing. For example, a company may not be permitted to borrow more money directly, due to a limitation in a bond indenture. However, a project financing can sometimes be negotiated on a basis not prohibited by the indenture. 2. Often the sponsors of, or the stockholders in, the project are seeking an off-balance-sheet financing. For example, 11 of the 29 projects in our study were arranged on an off-balance-sheet basis and one showed on the balance sheet as a deferred income item. An off-balance-sheet financing, for the purpose of this article, is a financing which does not show as a direct liability on the balance sheet of the sponsors of or stockholders in a project. 3. Projects are often located in a foreign country. The financing is arranged so that the lenders assume the political risk on the loan because many companies rightly believe that this arrangement affords a degree of insulation from political risk not otherwise obtainable. 4. Many projects are jointly owned by several sponsors. This form of financing lends itself well to a situation where a new entity is formed to own a project and do the borrowing. Project loans can be used to finance a variety of activities including development of iron-ore deposits and associated pelletizing plants; development of coal reserves; construction of pipelines, alumina plants, fertilizer plants and refineries; etc. The specific areas of analysis can be quite different, depending upon the type of project being financed. It is important, therefore, to classify the proposal according to the type of project, and also by the nature of the financing - nonrecourse financing, financing covered by a guarantee of completion and financing supported by an undertaking lasting for the life of the financing. I will discuss each of these types in more detail later, but first, I should like to make some

Jan 1, 1985

By Robert Y. Grant

This study outlines the history of metal mining in Japan and the characteristics of the industry as they existed from 1925 to 1945. Mining and milling operations are described together with the role of the Japanese Government. A description of post-hostilities conditions and the present state of the industry is included. MANY of Japan's larger and better known mines date back to the early centuries of the Christian Era. The first stimulus to mining in Japan came through the growth of Buddhism, A. D. 600 to 700, and the attendant need for copper and other metals for temple ornaments and statues. During the Feudal period, 1333 to 1568, mine operations were expanded to meet the demand for ornament metal and for financing of campaigns. After removal of the seat of government from Kyoto to Tokyo, about 1600, the Tokugawa Shogunate placed great emphasis on mining, and many new mines were opened, some of which are still operating. Toward the end of the Tokugawa period, mining had declined sharply from its earlier peak. The easily worked, high grade portions of the orebodies had been exhausted, and the mining techniques then available could not exploit the deeper, lower grade ores. Similarly, extraction of metal from the sulphide ores presented a major problem. With the Meiji Restoration in 1868 and the rapid opening of the country to western ideas came a rejuvenation of the mining industry. Mining, milling, and smelting processes were greatly improved, resulting in the extension of development work into hitherto inaccessible portions of orebodies. The demand for metal during World War I stimulated activity throughout the industry; copper mining, particularly, expanded to a point where Japan ranked second among world producers.* During the depression following the war, mining underwent a severe contraction in activity, recovering slowly during the late 1920's only to undergo a further setback in the worldwide depression which started in 1929. Mineral output declined in 1930, but the beginning of Japanese expansion, 1931 to 1932, brought about an increase in the output of mine products starting between 1932 to 1934. Production continued to rise, the peak output being attained 1939 to 1943 in virtually all commodities. The greatest production of iron ore, chromite, and manganese was not experienced until 1944 when blocked imports, coupled with strong demands for steel, provided the needed incentive. Through necessity, Japan produced much of her mineral needs from her own mines at high cost during World War 11. Taking the 1932 to 1936 period as an average, however, Japanese mines produced only 16 pct of the iron available to industry, 8 pct of the lead, 33 pct of the zinc, and 68 pct of the copper. Nearly all of Japan's output of gold, silver, copper, lead, and zinc between 1925 and 1945 came from 30 to 49 pct of the mines for which production data are available; for example, 66 of 174 gold-silver mines accounted for 98 pct of the output of this group. Further analysis of mine output indicates that a large part of Japan's metal output was derived from a few large mines; about 10 gold-silver, 15 copper, 3 lead-zinc, 5 manganese, and 2 iron mines account for most of the production. Many of these mines have been operated for 200 to 400 years. With the

Jan 1, 1952

By J. H. Carpenter

LMENITE, rutile, zircon, and other heavy minerals are found in small amounts in the sand that covers most of Florida. Small enriched deposits occur on the beaches and coastal dunes. One beach deposit east of Jacksonville was worked during World War I and another near Vero Beach during World War 11. Both ceased operation when the resumption of imports reduced prices. Early in World War II reduction of rutile imports made a domestic source of the mineral necessary to maintain the expansion of armaments. Explorations made near Jacksonville discovered a relatively large body of low-grade ore about 10 miles inland from the beaches. A plant installed by Rutile Mining Co. of Florida using both flotation and tables encountered difficulties because of low plant capacity and organic slimes in the ore. In 1944 Humphreys Gold Corp. solved the problem of concentrating the low-grade ore by using the newly developed Humphreys spiral concentrator and by mining with a hydraulic dredge. This combination of low cost mining and concentration permitted the plant to continue operation in competition with foreign ores when imports were resumed following the war. The success of the Jacksonville operation renewed interest in Florida as a source of titanium. An extensive survey of the state was made by E. I. du Pont de Nemours and Co., Inc., under the direction of J. L. Gillson in 1945 to 1946. Sampling was carried on by drive pipe drilling to depths of 20 to 25 ft. Encouraging values were discovered near the location of the present Trail Ridge mine, 50 miles southwest of Jacksonville, near the town of Starke. The United States Bureau of Mines was interested in exploring for heavy minerals in Florida, and on the recommendation of both the state geologist of Florida and of Du Pont geologists, drilled deeper where marginal indications were found on Trail Ridge. In 1947 it was discovered that sufficiently higher values occurred at depth to make the deposit commercial. The orebody at Trail Ridge is a long sand deposit averaging about 1 mile in width and 35 ft in depth. It is approximately 1 1/2 miles wide at the north end of the portion now being worked, tapering to a blunt point 3 miles to the south. The ore reaches a maximum depth of 65 ft near the center and feathers out into barren sand at the edges. The ground surface is relatively flat and is covered with vegetation including pine, scrub oak, palmetto, and occasionally in swampy areas, cypress. The remain of a dense woody growth underlies and marks the bottom of the Ore 'One. It is difficult to drill through this layer, but in some cases where it is less than 5 ft thick it has been possible to drive through the wood. Sand lying below is coarser than that in the ore zone and contains no values. The wood layer consists of unconsolidated carbonized fragments of branches and other forest trash associated with a considerable amount of ar-

Jan 1, 1954

By G. M. Schwartz, G. A. Thiel

THE first record of the quarrying of dimension stone in Minnesota dates back to 1820 when limestone was quarried locally for part of old Fort Snelling. Limestone quarries were operated at Stillwater, Mankato, and Winona as early as 1854. Granite was quarried first at St. Cloud in 1868, and within a few years thousands of tons were shipped to widespread points. Rough dimension stone for large buildings furnished the first important market, but beginning in 1886 paving blocks were in demand. The largest shipment was in 1888, when 1925 cars were shipped from the St. Cloud area. Quartzite was quarried first at New Ulm in 1859 and somewhat later at Pipestone and elsewhere in southwestern Minnesota: The productive dolomite quarries at Kasota were opened first in 1868 and have continued as large producers of a variety of stone to the present time. At present, the industry is controlled by relatively few operators, and for that reason detailed figures on dimension stone are not released for publication. A general idea may be obtained from the data in the Minerals Yearbook for 1948. The figures for total stone produced in Minnesota are 1,804,000 tons valued at $5,090,652. Probably the largest item in the latter figure is received from dimension stone. A better idea of the situation, in relation to the country as a whole may be gained by using the data for 1930 when more companies were operating in Minnesota, and complete figures were published. In that year Minnesota produced granite valued at $2,668,119 and ranked third among the states in value. Minnesota's production of granite was almost exclusively for dimension stone. In the same year Minnesota produced 300,000 tons of limestone (dolomite) valued at $840,860, and this likewise was mainly dimension stone. In finished limestone Minnesota ranked second among the states in 1930. Sandstone and minor amounts of quartzite are the only other dimension stones that have been produced in Minnesota, but the quarries are now inactive. The commercial stones of Minnesota have been described in two reports by Bowled and by Thiel and Dutton.2 The early history of quarrying in Minnesota and extensive notes on the various rocks are given by N. H. Winchell.3 Small limestone and dolomite quarries were numerous throughout the area of Paleozoic rocks in southeastern Minnesota. Early production was largely dimension stone. With the increased use of Portland cement, most of these ceased production, and today only those at Kasota and Winona remain in operation. In recent years many quarries have reopened and new ones started, but these are devoted to the production of crushed rock and agricultural lime. As the application of modern quarrying and finishing methods increased, small companies in the granite business have dropped out, and the remaining companies have modernized their plants, purchased old quarries, and opened up new ones, thus furnishing a wide variety of granites suitable for most of the customary uses. It is the purpose of this review to present notes on' the geology and operations of each of the quarries now operating within the state. Granites and Related Igneous Rocks The term granite as used in this report includes granites, gneisses, diorites, gabbros, and other igneous rocks. The granites of greatest economic importance are found in three widely separated regions, see Fig. 1. 1-Central Minnesota in the region of the city of St. Cloud, 2-the upper Minnesota River valley region, 3-the northeastern portion of the state, commonly referred to as the Arrowhead region. The St. Cloud Region: The rocks of the St. Cloud region are mainly granites and related rock types such as monzonites and quartz diorites. The stones may be grouped into three major types, namely, pink granite, red granite and gray granite. Most of the pink granite occurs in the area to the southwest of St. Cloud. The rock is best described as stone with large pink crystals set in a finer grained black and white background. The minerals of the matrix occur in remarkably uniform sizes, and the pink crystals are sufficiently uniform in. their dis-

Jan 1, 1952

By M. Garfinkle

LITERATURE data1'3 have suggested that the resolved shear stress necessary to initiate slip in a particular slip system in tungsten single crystals is strongly dependent on the tensile orientation of the crystals. This orientation dependence is contrary to the critical resolved shear stress criterion. Because the Schmid factors for slip on particular {110}( I l l), {112}(Ill), or {123}(111) slip systems in a (100) oriented tungsten crystal are virtually identical to the respective Schmid factors for a (110) oriented crystal, slip should initiate on the same system in both orientations, independent of the values of the critical resolved shear stresses. Thus, it would be expected that, for a critical resolved shear stress model to hold, the proportional-limit stress for these two orientations must be similar. The expectation of similar proportional -limit stresses has not been borne out by reported experimental observations. Rose et nl.' reported that the proportional-limit stress for crystals near the (110) orientation was 92,000 psi, approximately three times that of (100) oriented crystals (31,000 psi). Garlick and probst2 reported greater than a fourfold difference. Most recently, Beardmore and ~ull~ examined tungsten crystals with orientations along the edge of the standard stereographic triangle and showed a gradual increase in proportional-limit stress from 28,000 psi for the (100) orientation to 93,000 psi for the (110) orientation. Again, the difference was more than threefold. As has been emphasized by these investigators, the apparent gross variation of proportional-limit stress with orientation precludes any meaningful analysis of slip mechanics using a simple critical resolved shear stress relation. The purpose of the present communication is to report that, by use of refined strain-measuring techniques, the proportional-limit stresses for the (100) and (110) orientations are quite similar. Obviously, to determine accurately the value of the proportional-limit stress, which is by definition the stress at which nonlinear stress-strain behavior first occurs, the method of measuring strain must be capable of high accuracy. The investigators cited used as the measured elongation the crosshead displacement of the tensile machine. This method, however, introduces extraneous strain contributions from the load train. Because these extraneous contributions are considerable in the initial portions of loading (as has been well-documented in the literature) the proportional-limit stress measurement, dependent on the deviation of a line from linearity, can be significantly affected. During the course of a recent study, room-temperature strain was measured directly on several (100)-and (110)-oriented tensile specimens axially oriented within 5 deg of the desired direction. Each specimen was fitted with two foil strain gages mounted on opposite sides of the 0.08-in.-diam reduced section. The tensile specimens were loaded at a crosshead speed of 0.01 in. per min on an Instron Universal Testing Machine. Strain was monitored through an external bridge circuit in which the specimen strain gages comprised two arms. The bridge output was recorded against the applied load. A strain of 2 x 10"" could be readily detected by this method. Some specimens were subjected to conventional loading while the load for others was cycled between zero and continually increasing values until the first deviation from linearity was observed. The results of these methods were similar, and the stress at which nonlinear behavior occurred was considered the proportional-limit stress. The proportional-limit stresses measured in this study are approximately 5000 and 6500 psi for the ( 100) - and ( 110) -oriented crystals, respectively, a range of values almost a magnitude less than those reported previously. Representative curves are presented in Fig. 1. Because of the nature of the measurements made, the point of departure of a line from linearity is often debatable. While the load-strain curve for the (100) -oriented crystals made a relatively abrupt deviation from linearity, the curve for the (110) -oriented crystal was more gradual, so that the actual point of tangency may be at a lower load than reported. Thus, the difference in values for the proportional-

Jan 1, 1967

By Harold M. Mooney

WHEN apparent resistivity data are taken with the symmetrical Wenner 4-electrode spread, a fixed center position is used and readings are taken for values of electrode separation. Basic data consist of apparent resistivity plotted against separation of adjacent electrodes . The interpreter attempts to infer geologic structure, such as the depth to discontinuities and the nature of subsurface earth materials. An earlier paper' described methods for interpreting resistivity data. All of these involve a severe assumption, namely that the earth in the region of interest consists of horizontal layers, electrically homogeneous and isotropic. The actual earth never satisfies this assumption exactly and may deviate from it so much that none of the above methods can be applied. Attempts in three directions have been made to modify the assumption so that it approaches known geologic complexity more closely. First, curves have been calculated for dipping discontinuities. Stern' and Aldredge hose a few widely separated dip angles. Trudu confined his attention to small dips. Berel'kovskiy and Zubanov computed gradient curves for widely separated dip angles. Unz as given the most complete solution, with a brief attempt to treat the three-layer case. Second, anisotropy can be taken into account. It seems geologically probable that layered materials have different vertical and horizontal conductivities. Cagniard, Maillet, and Pirson et up methods for finding an equivalent hypothetical isotropic medium. Standard interpretation methods can be applied to this, and the actual medium can then be deduced. Belluigi'" discounts the practical importance of anisotropy; Geneslay and Rouget do not agree with his conclusion. Third, the effect of variable resistivity in a layer can be considered. Keck and Colby" examine the mathematics of an exponential increase in a surface layer. Several authors, for example, Stevenson,'' consider a continuous variation of resistivity with depth. The present paper deals with a linear variation of resistivity in a surface layer. Geologically, surface variations should be expected. Unconsolidated materials such as glacial drift show marked irregularities over short distances. The effects of weathering change with depth. The moisture content of material above the water table may vary from a dry sand to a saturated clay, and both of these will be changed by rainfall. Figs. 1 to 6 present apparent resistivity curves to show the effect of a variable surface layer. In all cases resistivity varies linearly with depth down to a depth of one unit. Material beneath this depth has constant resistivity. Electrode separation is plotted in depth units. Insets on each figure show the corresponding cross-sections, plotting true resistivity against depth. To illustrate, consider curve A of Fig. 1. The true resistivity of material at the surface of the earth is taken as 0.4 units. Resistivity increases with depth, reaching a value of 1.0 at 0.5 depth units and 1.6 at 1.0 depth units. Below a depth of 1.0, all the material has very low resistivity (zero, for purposes of calculation). Curve A in the main part of Fig. 1 shows how apparent resistivity varies for this case as the electrode spacing is increased. To illustrate further, curve E of Fig. 4 corresponds to true resistivity of 1.2 units at the surface, 1.0 at a depth of 0.5 units, 0.8 at a depth of 1.0, and 1.5 for all depths greater than 1.0. Apparent resistivity curves have been plotted logarithmically so that the shape of the curves becomes independent of the units, giving the curves wide validity. A certain drift-covered area, for example, shows a gradual decrease of resistivity from 230 ohm-meters at the surface to 150 ohm-meters at the bedrock surface, 275 ft down; bedrock resistivity is 800 ohm-meters. Curve E of Fig. 5 indicates that true resistivity decreases from 1.2 units at the surface to 0.8 at a depth of 1.0, then increases abruptly to a constant value of 4.0 units. Since resistivity and depth ratios are the same, this can be used to predict the field curve. For Fig. 5, multiply true resistivity and apparent resistivity by

Jan 1, 1955

By Gordon M. Yocom

A pRopeR consideration of the subject of this paper should include economic aspects as well as the technical phases of the metallurgy, production, and properties of the product. The metallurgical phases of the processing and properties of the product will be considered only from practical aspects and within the scope of the writer's experience with tonnage production. The Bessemer process was invented 85 years ago and became important because it put steel manufacture upon a larger and less costly basis. In America the Bessemer production has declined for many years and has not maintained its proportionate place with the rapid advances of the open hearth. The achievements in the open-hearth field were attained by the greater number of technical people attracted to that branch of the industry. The antipathy of technical students for the older and less popular Bessemer field gradually weakened the forces defending it and retarded the development of new and better methods. In Europe the economic advantage of the basic Bessemer process has not been overlooked and the tonnage usually is greater than that of the open hearth. The acid process has been the subject of renewed attention in America during the past few years and those who are more familiar with it are striving to show that the method is too valuable to abandon. A considerable tonnage of Bessemer-blown metal, in both molten and ingot forms, used in connection with the open-hearth practice makes it an important auxiliary unit to the industry. This practice aids in modifying the price level of heavy remelting scrap in addition to speeding up the open-hearth operation. The use of Bessemer steel has continued not only because of periodic economic advantages but also because of certain inherent qualities of machinability, weldability and stiffness, which are valuable for many applications. The properties of stiffness and rather high reaction to cold-work require some modification in order to meet the demands of modem methods of processing, which involve cold-reduction and cold-forming. At least one factor contributing to the stiffness of this steel is the relatively high phosphorus content of the acid product. The phosphorus content of the Thomas or basic Bessemer steel of Europe is considerably lower than the normal acid product in America. The American industry has continued the use of the acid process chiefly for the reason that the available ores are more easily adapted to this process from both metallurgical and economic standpoints. In European practice the basic process is necessary with the highly phosphoric ores available and it is sustained to some degree by the sale of the rich phosphate slag as a by-product. The basic process was used in this country at several plants many years ago, but was abandoned for economic reasons. A part of the past history of these trials is given here because the author believes it has not been published and it has some bearing on the subject of this paper. The information is authentic to the extent that he possesses chemical laboratory notebooks

Jan 1, 1941

By L. W. Pommier, F. B. Brien

The Rheological properties of pulps are non-Newtonian in character and more than one viscosity parameter is necessary to describe their behavior, therefore, the single term 'apparent viscosity' which has been used in the past may be misleading. The study reported in this paper uses a dimensional analysis based on the Ostwald-de Waele shear stress-rate of shear model for non-Newtonian liquids to develop velocity and resistance equations for falling spheres. An electronic monitoring apparatus was assembled for determining the velocity of metallic bodies as they fall through opaque liquids and suspensions. By means of this apparatus the behavior of the viscosity parameters of the Ostwald-de Waele model and the applicability of the proposed equations were examined for a number of non-Newtonian liquids. The validity of the equations for these liquids was confirmed. Preliminary data collected using solid-liquid suspensions established the validity of the form of the basic equations for these systems. The differential movement of solid particles through solid-liquid pulps and suspensions is very important LO many branches of engineering, such as minerals processing, soil mechanics, ceramic slip processing, oil well drilling-mud technology, materials-handling in pipelines, and many others. There is a dearth of fundamental knowledge on the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The resistance offered by Newtonian liquids to the movement of free settling spheres is well described for laminar and turbulent conditions by Stokes' and Newton's Laws, respectively. However, problems are encountered when attempts are made to extrapolate these simple relationships into solid liquid suspensions. The rheological properties of pulps are such that they are non-Newtonian in character;'" that is, the applied shearing stress and resulting rate-of-shear are related by non-linear functions, and thus, in the simplest case two viscosity parameters are necessary to describe their rheological properties. For this reason the single term 'apparent viscosity' which has been commonly used to explain the flow resistance of suspensions and non-Newtonian liquids may be misleading. It is realized that a rigorous analysis of the rnechanisms of momentum transport of liquid-solid systems is complex indeed. There are many variables that affect the rheological properties of the systems such as density, size, shape, and surface energy of the suspended solid and density and viscosity of suspending liquid, as well as the solid to liquid ratio. However, it was felt that a useful contribution to the knowledge of the behavior of suspensions could be made by examining the systems in terms of the basic fundamentals of nowNewtonian flow. This has led to the development, by means of dimensional analysis, of velocity and resistance equations, using two viscosity parameters to describe the velocity of penetrating bodies and the flow resistance encountered by these bodies, as they pass through non-Newtonian systems. THEORY In order to examine the effects of the rheological properties of solid-liquid suspensions on the movement of immersed bodies it is appropriate to start with non-Newtonian liquids and develop equations, analogous to those of Stokes and Newton, for laminar and turbulent flow respectively, from which quantitative information may be obtained. Further investigation would then be directed at the complex suspension systems, and the effects of the many variables on the velocity and resistance equations. Liquids are classified on a basis of viscosity which may be defined as the relationship between applied shear stress and resulting rate of shear?-'* Pure single phase liquids composed of small light molecules behave as Newtonian liquids, having a single viscosity parameter since the shearing stress and rate-of-shear are related by a linear function. Bingham plastics are similar but have a yield stress. Of particular importance in our investigation are dilatant (shear thickening) and pseudoplastic (shear thinning) non-Newtonian liquids, with and without yield values.

Jan 1, 1968

By F. F. Craig

A series of both welter and gas puttern Hoods was made in the laboratory to study the oil recovery performances of .such operations. These tests were contlrrctt~tl on consolidated sandstone models, using oil. water, and gas. The model floods were scaled to reprotlrrce field performance under gas arid water five-spot injection. X-ray shadowgraphs permitted observation of the gross fluid movement within the models. A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The area1 sweep efficiency. tit breakthrough for dispersed gas drives is much higher than previorsly expected, Iying in the range of 50 to 100 per cent. A method is presented for predictitig the water-oil ratio performance of five-spot pattern water flood., in uniform sands. This method is verified experimentally for the cotidition of 120 free gas initially present and for va1ues of gas saturation normally encountered in fields following depletion operations. Prodrrction perfort?zut~cc for pattern gas injection is also predictable by this method. INTRODUCTION In field pattern hater flooding or dispersed gas injection operations, the displacing fluid (water or gas) is injected and oil is produced through wells which are, area-wise. small openings in a large container or rescrwir of oil. As a result, not all of the area between the injection and producing wells is necessarily contacted by the injected fluid by the time it first reaches the producing wells. The question arises in predicting oil recovery. as to what traction of the pattern area involved is contacted by either the injected water or gas due to the relative position of the injection and producing wells. This is the areal sweep efficiency. It is also desirable to know how well arrangement affects the oil production performance. A solution to this problem has been attempted by many means. Mathematical analysis¹,²,³, and electrolytic models', have been used to establish a breakthrough areal sweep efficiency of 73 per cent for a five-spot pattern in which the ability of the oil to flow ahead of the invading fluid is equal to the ability of the invading fluid to flow in the invaded zone. All of these studies simulate only one of many field conditions. Improved studies of areal sweep efficiency at breakthrough were made using the fluid mapper5, poten-tiometric models" and X-ray shadowgraph techniques. In these it was possible to study the effect of variations in mobility of the injected and displaced fluids, and so to cover a wide range of field conditions. The limitation of these studies is that, with these models, it was not possible to simulate the saturation gradient behind the flood front when oil is displaced by gas or water. In the most recent published technical paperS on the subject, a method was presented for predicting the oil recovery performance after breakthrough in a five-spot pattern water flood. The method involved correlations which were obtained experimentally using miscible fluids. One limitation of this work was that a saturation gradient, usually found in immiscible fluid displacement, was absent in these studies. Also the laboratory studies did not cover the situation of a water flood following oil recovery by depletion drive. as is the situation in most field water floods. The tests reported in this paper were made using oil. water, and gas, thus eliminating the simplifications of former studies. Also reported are laboratory studies on

Jan 1, 1956

By J. J. Scott

This investigation utilizes three dimensional photo-elastic techniques to determine the stress distributions in the pillars and the roof of a room and pillar mine model. Castolite plastic was used for the construction of the model in which a stress pattern was developed by the stress freezing process. Analysis of the stress pattern was accomplished by observation of points in slices from the model with a polariscope and solving the data thus obtained by the shear-difference method. Slices through the centerline, edge of pillar and centerline of span were investigated. The results of this work provide information on the overall stress distribution in points of stress concentration in compression, shear and tension, show relative magnitude of stress throughout the model and indicate directions of the most important stress values. A generalized roof bolt pattern is developed for room and pillar mines based on the stress distribution. A digital computer was used in the reduction of data and proved to be extremely useful for investigation of this type. Underground excavations disturb the equilibrium of the earth's crust and a core of fracture, or altered stress distributions exists around the openings. This fact is well known by mining operators and investigators in the rock mechanics field. Analysis of the stress distribution in the areas around mine workings is a most difficult problem and one which has no simple and direct solution. Some of the approaches used by investigators in attempts to study stress distribution around mine openings involve mathematical analysis, photoelastic techniques, statistical analysis, model studies on brittle materials and observation of fracture patterns. Models involving imbedded strain gauges, gelatin models using imbedded strings to show internal movement, and many other unique laboratory techniques are employed. Work is also being done in mining operations where load cells, strain gauges, photostress material, convergence plugs, dynamic plugs, etc., are used to measure strain which can in turn be used to obtain stress. Some of these devices measure strain from which stress may be derived. All approaches to the solution of stress distribution are hampered by the fact that the earth is not a homogeneous, isotropic and elastic media. Geologic faults, fractures, bedding planes, vugs, variations in material composition, variations in grain size and structure, etc., make it extremely difficult to obtain results which can be universally applied to mining operations. The purpose of this investigation will be to demonstrate the use of three-dimensional photoelastic techniques to obtain the stress distribution in the pillars and roof of a room and pillar mining operation. This method utilizes full analysis of interior points, and thus it may be that small tensile or shear stresses found in the investigation will prove to be of greater significance than the more obvious points of stress concentration found by two-dimensional techniques. A digital computer was employed to simplify and to shorten the time necessary to obtain final results. Application of the computer to problems of this type may enable future investigators to attempt more elaborate analyses than have been previously considered feasible. THEORY Three Dimensional Stress Analysis-Shear Difference Solution:' Photoelastic studies are based on the fact that an optically isotropic transparent solid becomes optically anisotropic when subjected to forced deformation; the degree of optical anisotropy being proportional to the deformation of the material. There are two fundamental laws which govern photoelasticity: 1) Light is polarized in the directions of the principal stress axes, and is transmitted only on planes of principal stress. 2) The difference in principal stresses is proportional to the difference in the indices of refraction along the planes of principal stress. One method used in three-dimensional photoelastic work is to examine a slice of the object by normal incidence and oblique incidence. In normal incidence,

Jan 1, 1964

By C. G. Dunn

WITH respect to theories of recrystallization in metals plastically deformed, it has been said that the present status of this subject is far from satisfactory.1 It may also be said that before any mechanism of recrystallization for metals and alloys can be set forth in a satisfactory manner, there must be made available considerable data on orientation changes that occur during the deformation and recrystallization processes. Although extensive data have been published on recrystallization in single crystals and in polycrystalline specimens, more results of a type that can be classified according to simple orientation changes would be desirable in this complex field. It might even be said that before classifications are made according to types of orientation changes, it may be possible to classify a considerable amount of data into certain kinds of orientation states if groups of common or nearly common orientation occur. Methods for computing the probability of occurrence for various types of groups have been published2 and it has been pointed out in particular that it should be possible to analyze orientation data for high-order twin relationships between old and new grains even when agreement is not at all exact. In this connection, work on recrystallization in silicon ferrite reported in a paper concerned with complex groups of annealing twins' indicated that some data were consistent with primary nucleation occurring according to a second-order or a third-order twin transformation. However, further work in this latter direction was definitely needed. It is, therefore, the purpose of the present paper to report data and analyses for primary nucleation in silicon ferrite following small deformations that have been carried out at the Pittsfield Works' Laboratory of the General Electric Co. Analyses have been made with the aid of standard groups of twins that are reported elsewhere .4 PREPARATION OF SPECIMENS AND EXPERIMENTAL PROCEDURE The material used in the present investigation was taken' from the same heat of steel as that used in a prior report.3 The finished strip in both cases was made by the Allegheny-Ludlum Steel Corporation according to methods that produce a high degree of preferred crystal orientation. Samples with large grains had the following composition: 3.45 per cent Si, 0.003 C, 0.008 P, 0.020 S, 0.075 Mn, 0.031 Al and 0.072 Cu. Thickness of specimens was 0.012 inches. Plastic deformation was produced by cold-rolling the samples on a mill with

Jan 1, 1945

By I. Lowthian Bell

THERE has been probably no improvement introduced into the manufacture of iron which created more surprise in the minds of practical smelters and of scientific men than Neilson's discovery of the hot blast. In 1829, Messrs. Dunlop & Co. consumed at the Clyde Works, near Glasgow, nearly 79 tons of coal to make a ton of pig iron, of which about 20 cwts. was employed under the boilers of the blowing engines, leaving nearly 7 tons for the consumption of the furnace itself. In the year 1833, by heating the air to 612' F. (322' C.), they redoccd the 79 tons to 3 tons by the mere burning of 8 cwts. of coal in the apparatus for raising the blast to this temperature. The statenlent just given is strictly true in a commercial sense, but when we come to consider the question as one of physical science, it is necessary to eliminate some of the conditions which conduced to so extraordinary a result. Anterior to Neilson's time the fuel employed in smelting iron was coke, and it was supposed at that period, erroneously, however, that coal in its raw state, when burned with cold air, was totsally unfit for the purpose in question. This mineral, as it was obtained from the Lanarkshire coal-field, contained about 35 per cent. of volatile matter, but the process of charring it was performed in so unskilful a manner that instead of receiving 88 cwts. of coke from 135 cwts. of coal, 60 cwts. only was the product of the operation. Again, the reduced colisumption of carbon in the furnace itself was accompanied by a corresponding diminution of blast, and this was followed by an economy of half a ton in engine coal. After making a proper allowance, however, for all these collateral circumstances, we are within the mark when we admit that in actual coke, which is really the form the fuel has to assume before it is burnt in the blast-furnace, not less than 30 cwts. was saved by heating the blast to 615° F. (322° C.). This unexpected economy, be it remembered, was obtained by the combustion of the 8 cwts. of coal, somewhat wastefully applied in the hot-air apparatus. Numerous have been the opirlions advanced by different authorities in the scientific world to account for the apparent anomaly, bat none,

By Thomas A. Read

The internal friction of single crystals of metals is affected markedly by a variety of factors, which, according to the literature, are without influence on the internal friction of polycrystalline metals at strain amplitudes less than 10-5. For example, the internal friction of a suitably oriented zinc single crystal is multiplied by a factor of ioo when the vibration amplitude is slightly increased, and the internal friction of a copper crystal is markedly increased by the application of a stress of 30 lb. per sq. in. for one minute. In this paper it will be shown that these, together with the other phenomena associated with the damping of mechanical vibrations in metal single crystals, can be satisfactorily explained, at least qualitatively, in terms of an atomic mechanism that has been proposed for quite another purpose—that of accounting for slip in metals. The extraordinary agreement between the observed behavior of the metal single crystals and the behavior that could be predicted on the basis of this atomic mechanism leads to the belief that the latter is probably essentially correct. If this is so, it follows that valuable information about the slip process in metals may be gained from measurements of internal friction on single crystals. In this paper the results of the only study to date on the damping of mechanical vibrations in single crystals of metals mill be presented. Experimental Procedure The internal friction of a material is a measure of the rate at which the energy of mechanical vibrations is converted into heat. The measure of internal friction used in the present paper is the decrcment A, which is defined as the fraction of the energy of vibration lost per half cycle. The measurements described here were made for longitudinal oscillations at a frequency of 33.5 kc. for the copper crystals, and at a frequency of 39 kc. for the zinc crystals. The method used is that of the composite piezoelectric oscillator. The single-crystal specimens are in the form of circular cylinders M in. in diameter and I 1/2 to 21/2 in. long. The crystal rods are waxed in a V-block and sawed to the proper length with a fine jeweler's saw. The ends of the specimen are ground flat, and one end is cemented with a very thin film of beeswax and rosin to the end of an x-cut quartz rod which is 1/4 in. in diameter and 3 in. long. The length of the specimen rod is determined by the condition that its natural frequency for longitudinal vibration be the same as that of the quartz rod, within 0.5 per cent. The lengths of the specimens are thus different for different orientations of the cylinder axis with respect to the crystallographic axes. When the specimen and quartz rods are thus matched in frequency the adhesive is at a node of stress, and it has been shown experimentally that under these circumstances

Jan 1, 1941

By A. P. Pipilen, M. Weintraub, W. F. Hosford, A. A. 230-000-000-006 Orning

In a study of the principal factors affecting the transport of coal-water mixtures through a centrifugal pump and a pipeline, the interrelation between solids concentration, velocity, and pressure drop was established for a minus 2-in. bituminous lump coal in concentrations up to 48% by weight. Optimum concentrations were found to exist for maximum capacity of a given pipeline and for minimum energy requirements per ton of coal. Coal size degradation by particle fracture took place in the pump; abrasion and attrition to form fines took place in both pump and line. A novel system of studying flow of solid-liquid mixtures in pipelines by the determination of relative sound intensities was developed. The hydraulic transport of minerals is in part an established art and in part a relatively new field of industrial technology. The established art developed especially where the mineral was under water, where water was used in hydraulic mining, or where large quantities of water had to be pumped from the mining site to expose the mineral. Power requirements and limited life of pumps and pipelines, under such conditions, were relatively unimportant. Examples may be found in dredging, and in hydraulic mining and transportation of phosphate rock.' In the design of a coal pipeline the most needed information relates to flow characteristics, power requirements, pressure drop, size degradation, and size segregation as a function of solids-water ratio and size distribution of the mineral. A considerable amount of information has become available concerning pressure drop and energy requirements.2'3 These topics were therefore not studied intensively. Coal degradation, however, has not been clearly delineated. Lammers and coworkers4 showed that coal may be severely degraded in size but did not distinguish between degradation produced in the pump and in the line. It is the primary purpose of this paper to outline techniques used to acquire some of the much needed design data. A full report of the investigation is to be published by the Bureau of Mines at a later date. APPARATUS AND PROCEDURE The apparatus for circulation tests (hereafter referred to as Type III tests) consisted essentially of a loop and a centrifugal solids handling pump, with attendant instrumentation, and coal weighing and feeding equipment. It also included an adequate water supply, as shown in Fig. 1. The selection of 6-in., schedule 40, carbon steel pipe was based on the top size of coal to be used. Assuming that the top size of coal should not exceed 1/3 the inside diameter of the pipe, a 6-in. pipe would accommodate 2-in. coal, a realistic size for transport from the mine face. An 872-ft loop was constructed first. Later a few tests were made with a lengthened circuit of 1361 ft by superimposing an additional loop on the original one. All bends used were of 3-ft radius. A noisemeter microphone, taped to the pipe at various points, but generally about 50 ft downstream of the pump, was used to sense segregation of the coal and the length of slugs of coal in water. To measure the stream velocity, radioactive sources were encapsulated in plastic cubes. The specific gravity of the blocks was adjusted to 1.3 and 1.8 to simulate low ash and high ash coal particles. Their passage through the pipeline was detected by a Geiger counter. Because the repeated circuits of the Type III tests did not permit coal degradation in the line to be distinguished from that produced by the pump, the two

Jan 1, 1964

By Brown, R. W., G. H. Neill, R. G. Loper

All facets of ball sealer behavior must be known and understood to design for their optimum use in well treatments. The down-hole factors including the inertial forces, drag forces and holding forces have been discussed. Equations have been developed and presented for these forces. The use of these equations in this process will contribute to the most efficient use of an economical and proven ball sealer process. The urocedure presented has been used to successfully analyze field results indicating problems involving the use of ball sealers. These problems have been isolated and corrected in future treatments by using the procedure presented to revise the perforating program, the injection rate, the design of ball sealer stages and/or the type and size of ball sealers. The procedure presented also indicates that dislodgement of ball sealers occurs primarily in ultra slim-hole completions. INTRODUCTION The perforation sealing process has been proven highly successful and economical since it was introduced to the oil and gas industry in early 1956.' Since it has proved so successful in multistage fracture treatments at a much lower cost than conventional packers, the ball sealer process has become a byword in well completions.' Not only has it changed the design of fracture treatments, it has changed the concepts of selectively perforating and has greatly aided the success of the single-point and limited-entry techniques." Yet with all the advantages, there are still facets of ball sealer behavior that are not widely recognized. These must be known and understood to better design and execute the optimum ball sealer treatment. The down-hole behavior of ball sealers is influenced by a number of factors including an "inertial force", a "drag force" and a "holding force". These are considered in two phases—the initial seating of the ball and the forces tending to unseat the ball after contact has been made (see Fig. 1). This paper presents a theoretical study of these factors and formulas for predicting their influence. The authors acknowledge the fact that the flow equations presented herein describe the behavior of Newtonian fluids and do not cover the so-called power-law fluids. The assumptions made, however, are reasonable and well within practical limitations of the conditions encountered during field application. For example, it is assumed that the perforations are round with a discharge coefficient of 0.82. While this may not be exactly true, it has been verified within practical field limitations.' The discharge coefficient would not vary significantly even if the perforation size or configuration varied pronouncedly. The approach of assuming uniform perforation size is not as strained as it might first appear. Normally, a perforator contains charges equally spaced with the same number in each vertical (or horizontal) plane. If the perforating gun is not centralized, the holes in one plane will be smaller than average, while the holes in opposing planes will tend to be larger than average. The net result is that the two effects tend to balance. FACTORS AFFECTING CONTACT WITH PERFORATlON Ball sealers are injected into well treating fluids for the purpose of contacting and sealing those perforations which are accepting the fluid flow. The efficiency of the sealers is primarily influenced by: (1) the velocity of the balls down the pipe, and (2) the fluid velocity through the perforations. To divert the sealer to the perforation, the inertial force of the ball must be overcome by the drag force created by the fluid velocity through the perforation. BALL VELOCITY The final, or stable, velocity of the ball is the sum of the actual fall velocity and the fluid velocity. This will be

By C. F. Floe, N. J. Grant, A. Joukainen

A CCORDING to Guertler,¹ Smith and Hamilton were the first to study the Cu-Ti alloy system, but because of the presence of large amounts of impurities their data are inconclusive. Hensel and Larsen² in 1930 and Kroll³ in 1931 determined the high copper end of the diagram. In 1939 Laves and Wallbaum,4 in a short summary of compound determinations in titanium binary alloys, mentioned the existence of a face-centered cubic compound, Ti2Cu, with 96 atoms per unit cell, and also a compound, TiCu3, which was said to have a deformed hexagonal close-packed structure in which ordering had been observed. The existence of a compound, TiCu, was also found but the crystal structure was not determined. Craighead, Simmons, and Eastwood determined the effect of copper on the allotropic transformation in titanium. The investigation was limited to alloys containing from 0 to 5 pct Cu, using titanium of fairly high impurity content. Experimental Procedure The methods used for determination of the diagram included metallographic examination and X-ray and thermal analyses. The system was first worked out using the higher purity "Process A" sponge titanium and oxygen-free copper. The high titanium region was next determined more accurately using iodide titanium and vacuum-melted, oxygen-free copper. Preparation of Alloys: The alloys were prepared by arc melting under prepurified helium atmos- pheres in water-cooled copper crucibles. The high purity iodide titanium alloys were prepared by melting three compositions along with a specimen of unalloyed titanium in a single charge. A multiple crucible was used which consisted of a copper plate with four cup-like depressions. The unalloyed titanium was melted first and acted as a getter for any oxygen and nitrogen in the melting chamber. Since these elements harden titanium, the hardness of the standard specimen was an index of the highest probable contamination of the alloy melts. The sponge titanium alloy melts weighed from 100 to 200 g each and the iodide titanium melts from 20 to 25 g. In order to insure greater homogeneity most of the alloys were melted, turned, and remelted twice. The larger buttons made from sponge titanium were sectioned or crushed before remelting. These alloys up to 30 pct Cu were further homogenized by forging at 925°C. They forged readily up to 20 pct Cu but numerous cracks were formed in the alloys containing from 20 to 30 pct. Above 30 pct Cu the sponge titanium alloys were homogenized by heating for 200 hr at 850°C under prepurified helium. Similarly, the iodide-grade titanium alloys containing up to 3 pct Cu were homogenized at 1000°C for 24 hr and all others at 880°C for 200 hr.

Jan 1, 1953

By C. J. Ramsburg

THE construction and operation of by-product coke-oven plants in America are essential to strong national defense and of the greatest importance to many widely diversified undertakings as well as to safety and health. CARBONIZATION PROCESS Coal used under a boiler or in a locomotive is consumed by combustion. Coal used in a by-product oven is distilled or carbonized, meaning that heat is applied to the coal, out of contact with air, causing a distillation that removes the volatile matter in the coal in the form of gas and vapor, leaving coke as a final product. From the gas and vapor distilled from the coal, many valuable substances can be secured, known as by-products. Hence the name "by-product oven." The simplest example of this principle can be shown by means of an ordinary clay pipe. If powdered coal is placed in the bowl of the pipe, the opening of the bowl is plugged with clay, and the bowl placed in a flame, the bowl will become hot, transferring the heat through the wall of the bowl to the coal within. When this coal attains a temperature of about 950°F., gas will begin to pour out of the pipe stem, and this gas may be lighted. A black liquid also will exude from the stem of the pipe. This is tar mixed with certain other products. What remains in the bowl after distillation is coke. A coke oven corresponds to the bowl of the pipe. A modern oven of the latest type is a refractory brick chamber approximately 42 ft. long and 14 ft. high, averaging 18 in. in width. The oven is filled with coal through closable charging holes in the oven top. Each end of the oven consists entirely of a self-sealing door, the removal of which permits the finished coke to be discharged by means of a power-operated pusher machine. The ovens are built in batteries, and the heating is effected by gas burned in vertical flues in the oven walls, each set of flues heating the walls of two adjacent ovens. Such ovens carbonize a charge of approximately 18 tons of coal in 18 hr., or have a daily throughput of 24 tons per oven, producing about I 7 tons of coke. In times of need, the output may be increased by raising the temperature of flues, thus shortening the coking time. There is one great essential difference in principle between distillation in a clay pipe and in a coke oven. In the 18-in. oven, the distillation proceeds from two parallel walls held at a high temperature (over 2000°F.) and instead of all the coal being heated at once, the distillation is a progressive one creeping inward. The average travel of this heating is 1/2 in. per hour from each vertical wall, and as the volatile products are formed progressively they must push away from the interior toward the wall through the previously formed hot coke, then up the walls and over the top of the coal charge, finally escaping through the outlet pipe. This results in a cracking of the components into many different and valuable substances not formed when the carbonizing temperature is low.

Jan 1, 1942

By L. D. Jaffe

From data found in the literature, a method has been derived for calculating hardenability of titanium alloys from their composition. A single graph gives the contributions of each alloying element. These are simply added to a base hardenability for unalloyed titanium. Results agree satisfactorily with measured harden-abilities. RECENTLY the importance of hardenability of titanium alloys in permitting attainment of high strength and hardness has become apparent. If a titanium-base alloy has adequate hardenability for the section size and quenching practice used, it can generally be heat treated to high strength and hardness either by simple quenching or cooling from temperatures near the ß transus, by quenching and tempering (aging), or perhaps by direct isothermal transformation of ß1,2 If the hardenability is inadequate, high strength cannot be attained. Preliminary charts translating hardenability requirements for shapes quenched in various media into terms of Jominy end quenched hardenability specimens or ideal round sizes are now available for titanium alloys." The method proposed in 1942 by M. A. Grossmann for calculating hardenability of steels from composition has proved to be of great practical value.' It appeared worthwhile to see whether, using information available in the literature, a corresponding method for calculating hardenability of titanium-base alloys could be derived. Data No systematic experimental study of the hardenability of titanium-base alloys has yet been made. There is available, however, a considerable quantity of scattered data bearing on hardenability. Some investigators determined Jominy curves on one or several alloys. Others reported as-quenched hardness for specimens of a few alloys cooled at various rates or in various media. Still others gave the as-quenched hardness for systematically varied composition, using one or several cooling mediums. The measurements utilized in this work were limited to hardness. Strength measurements were not used because a low strength may reflect high hardness combined with brittleness. Since, in general, the hardness of titanium alloys goes through a peak as the cooling rate is varied from extremely fast to extremely slow, the cooling conditions at which peak hardness was found were taken as the measure of hardenability.1,2 When as-quenched hardness was found to drop as the content of an alloying element (believed to increase hardenability) was raised, this was taken as an indication that the cooling rate was faster than that giving peak hardness; otherwise, the hardness should go up because of solid solution hardening. Also, if the hardness increased on tempering at low temperatures, this was again taken to indicate that the cooling rate had been faster than that giving peak hardness. Many of the data did not indicate precisely the cooling conditions for peak hardness but merely set a maximum or a minimum bound, or a bracket. Since the sizes of specimens quenched and the location of the hardness readings were not always given, it was occasionally necessary to estimate reasonable limits for them. Only the nominal compositions were available in some cases. As quenching from below the ß transus is equivalent to starting with a mixture of a and ß phases, whose individual composition would differ from the overall composition of the alloy, only measurements after quenches from above the ß transus were used. Hardness measurements on samples heated during metal-lographic mounting were also discarded. Because of their bulk, the data used will not be reproduced. They have been or will be published elsewhere.5-22 Approach All data were first translated into terms of ideal round size. For conversion from Jominy or quenched round or sheet, the author's graphs were used." For a few furnace cools or helium quenches where cooling rates were given, conversion was made on the basis of equal cooling coefficient.23 Plots of ideal round size for peak hardness against percentage of alloying element were next made for

Jan 1, 1956

By Donald A. Brobst

The minerals barite (BaSO4) and witherite (BaCO3) are the chief sources of the element barium and its compounds needed for many industrial processes and products. Barite, the principal ore mineral, is found the world over and is abundant and widely distributed throughout the United States.3 Witherite is much less common than barite, though more desirable in many ways as a raw material for the production of barium chemicals. England is the chief producer of witherite. Witherite is not mined in the United States at the present time, but it has been mined with barite from a deposit at El Portal, California. Barite is also called barytes, tiff, cawk, or heavy spar. Ordinarily it is a heavy mineral that crystallizes in the orthorhombic system. It is colorless, white, or gray, and transparent to opaque. In some deposits barite is black, yellow, brown, red, green, or blue because of included impurities. The streak is white and the luster vitreous to resinous or pearly. The specific gravity of pure barite (65.7 pct BaO and 34.3 pct SO3) is calculated to be 4.5, but inclusions and impurities in natural barite may reduce this value considerably. Well-formed crystals are generally tabular and have three cleavages. The barite of many deposits, however, has an uneven fracture and an apparent cleavage caused by separation along planes between successively deposited layers. The hardness is 2.5 to 3.5 on Mohs' scale. Commercially the terms "hard" and "soft" are used to refer to ease of grinding. Barite is relatively insoluble in water and acid, and thus can be used as a chemically inert material. Witherite, the natural carbonate of barium (77.7 pct BaO and 22.3 pct CO2), crystallizes in the orthorhombic system. The fracture is uneven and the luster is vitreous to resinous. The hardness is 3 to 3.5. The specific gravity of the pure mineral is calculated to be 4.29. It is transparent to opaque. The color is ordinarily white, gray, yellow, brown, or green. Geology and Distribution of Deposits Workable deposits of barite are widely distributed throughout the world in many geologic environments in sedimentary, igneous, and metamorphic rocks. Most deposits can be classified into three main types: (1) vein and cavityfilling deposits; (2) bedded deposits; and (3) residual deposits. 1. Vein and cavity-filling deposits are those in which barite and associated minerals occur along faults, gashes, joints, and bedding planes, and in breccia zones and solution channels. They also occur in various collapse and sink structures in limestone. Sharp contacts of the veins and cavity fillings with wall rocks are common. Barite cements fault and collapse breccia by replacement of the matrix or by filling voids. Large-scale replacement of the wall rocks beyond ore-controlling structures is rare. Barite in vein and cavity filling deposits is generally dense, "hard," and white to gray. Associated minerals are fluorite, calcite, ankerite, dolomite, quartz, and many sulfide minerals, especially pyrite, chalcopyrite, galena, and sphalerite. Gold, silver, and rare earth minerals occur with barite in some deposits in the western United States. Barite is also a gangue mineral in metallic ore deposits but production as a byproduct from such deposits will be affected by many economic factors. The host rocks are igneous, sedimentary, and metamorphic rocks of pre-Cambrian to

Jan 1, 1960

By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy's law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.