Search Documents

By Alfred H. Bell

Drilling activity increased in Illinois in 1935. There were 34 com-pletions as compared with 26 in 1934 and 18 wells were drilling at the end of 1935. Some large blocks of acreage were leased in Marion and Clay counties near the central part of the Illinois structural basin. Production of oil in the state totaled 4,305,000 bbl., a decrease of 4 per cent from that of 1934 There was some curtailment of production in the early part of 1935 but none after April 30 as shown in the following table. Percentage Pro-duced of Potential ProductioN (USING September 1934 Period as BaSis) Jan. .l-Feb. 20............................................ 79 Feb. 21-Feb. 25............................................ 85 Feb. 26-Feb. 38............................................ 79 Mar. 1-Mar. 11............................................ 85 Mar. 12-Mar. 31............................................ 100 Apr. 1-Apr. 9.......................................... 80 Apr. 10-Apr. 30............................................ 86 May 1-Dec. 31........................................... 100 This is equivalent to an average curtailment throughout the year of 5 per cent. The price of Illinois crude oil at the wells remained constant during 1935 at $1.13 per barrel. A small amount of oil was sold at a 1ower price, notably from the Dupo field, but to arrive at a value for the state's production there would be little error in assuming an average price of 81.13, giving a total value of $4,864,465. The following table shows production in Illinois by moths in 1935, according to the U.S. Bureau of Mines. Jan............. 332,000 May.......... 382,000 Sept ,............. 370,000 Feb............. 295,000 June. ........... 858,000 Oct.............. 391,000 Mar............ 370,000 July............ 377,000 Nov............. 369,000 April............ 338,000 Aug............. 379,000 Dec............ 344,000

Jan 1, 1936

By Northcutt Ely, Charles F. Wheatley

This chapter deals with the systems of laws by which governments regulate the exploration for and production of the minerals within their jurisdictions. It is a summary, restricted by necessary space limitations, of material assembled by the author for a forthcoming publication of the United States Bureau of Mines, "Summary of Mining and Petroleum Laws of the World." (Information Circular, 1959.) The present study is organized in three parts, dealing with (1) the historical background of these legal systems, (2) laws of the United States, and (3) laws of other countries of the world. The reader's attention is invited to the acknowledgments at the end of the chapter, which inadequately express the appreciation due those who have assisted in the collection of this material. Part I. Historical Development of Major Western Systems of Land Tenancy with Respect to the Ownership and Control of Minerals The use of metals in primitive societies was largely confined to the manufacture of weapons for self-preservation. The ruler's control over copper, then brass, then iron, was essential to maintenance of his own ascendancy at home and his group's position against neighbors who had access to similar metals. Ancient societies were thus characterized by the ruling group's ownership of minerals and metals. The Egyptian civilization, which emerged in the fourth millenium B.C. upon the agricultural subjugation of the lower valley of the Nile, was responsible for extensive development of the upper valley as a source of mineral wealth. The production of gold during the height of that civilization has been estimated at $30,000,000 per year, thus equaling the early placers of California and Australia. The mines of Egypt were the property of the Pharaohs and were controlled at their direction. Greek mining developed a different scheme of land tenancy which more closely resembled modem concepts. Development of mineral resources was

Jan 1, 1959

By R. J. Stokes

S. Floreen (international Nickel Co.)— One fairly simple way to differentiate between em brittle me nt due to surface microcracks or due to a dislocation barrier effect might be to load a brittle rock salt crystal in tension to some stress just below the fracture stress and then immerse the loaded crystal in water. If a surface film is retarding plastic flow then one should observe some plastic deformation of the rock salt as

Jan 1, 1962

By Thomas T., Read

THE decades immediately before and after the end of the nineteenth century (1890-1910) were a period of increased activity in mineral industry education. One reason for ,this, undoubtedly, was the rapid increase in mineral production in the decade 1880-1890; pig iron and copper production tripled; coal, lead, and zinc output more than doubled. Most of the other mineral substances followed the same general trend. Aluminum production began in 1886; petroleum output, which in 1888 was less than it was in 1882, almost doubled in the next three years. Gold alone showed no appreciable change until its discovery at Cripple Creek in 1891, followed by the Klondike in 1896, brought to boiling a public interest in minerals that had been simmering for some years previously. The first cyanide plant in the United States was erected at Bodie in 1893, and the first chlorination plant at Cripple Creek* the next year. Silver- lead smelting had already greatly developed, and the metallurgy of copper was almost transformed. The hearth area and smelting capacity of copper reverberatory furnaces more than quadrupled between 1878 and 1894; matte converters were first erected at Butte in 1884. Copper production of the United States in 1899 was 30 times that of 1872. While it was the increased technology used in mineral production that really made the field attractive for educated young men, undoubtedly they did not realize that, and were impressed mainly by the quantitative increase in output. Another factor was the increased general interest in engineering education; three times as many men took engineering degrees in the United States in 1890 as in 1880; 1893 showed almost a 56 per cent increase over 1890. Industry had come to recognize that technical training was worth while. The mineral industry lagged somewhat at first; the total number of mining degrees

Jan 1, 1941

By C. G. Cheriton

The Bathurst mining district is located near the town of Bathurst on the north shore of the province of New Brunswick in eastern Canada. This region is the northeasterly extension of the Appalachian mountain system. The area is heavily forested and covered with a fairly uniform layer of glacial gravels and boulder clay. The relief is low, increasing to a few hundred feet in the north west and several hundred feet in the extreme southwest. Thus, rock outcrops are scarce and occur mostly along streams and ridges. These factors made conventional prospecting difficult and resulted in the district becoming an excellent place for the application of regional geological studies, air photo techniques, airborne and gound geophysical methods and soil sampling. Late in 1952, The Brunswick Mining and Smelting Company discovered a very large base metal sulphide body presently known as their No. 6 orebody. Early in 1953, another and even larger sulphide body was discovered and is known as the No. 12 ore body. Mining exploration was very active thoughout 1953 and in 1954, The American Metal Company discovered the orebodies which have been developed into The Heath Steele 'Mines. The location of these deposits is shown on figure one. In the latter part of 1954, The Anaconda Company became interested in the district and decided to make a geological study of this new and promising base rrietal area. The following paper presents the story of the application of modern geological and geophysical techniques, leading to the discovery of a large sul-nhidp liodv. The Bathurst district is generally underlain by the Tetagouche group of Middle Ordovician rocks.

Jan 1, 1961

By E. Northcott, I. M. LeBaron

Before describing the electrostatic processing of feldspar, it might be well to review some of the basic definitions and terminology of feldspars. The feldspar minerals constitute a group of alumino-silicates of potassium, sodium, and calcium. Barium feldspar sometimes occurs naturally but is very rare. Hardness varies between 6 and 6.5 and specific gravity between 2.5 and 2.8. Color is generally white or pale shades of red, yellow, or green. The approximate chemical composition of the principal feldspars is given in Table I. The albite (sodium aluminum silicate) and an-

Jan 1, 1959

By Cyril Wells, Paul E. Busby, Donald P. Hart

EARLY workers in the field have established that the diffusion of nitrogen follows normal diffusion laws. Concentration-penetration data from layer analyses of reasonably pure iron specimens nitrided in an atmosphere of CO-NH, are given in the literature,' and were utilized to calculate diffusion constants for nitrogen. The diffusion of nitrogen in y-iron may be represented approximately by the equation D - 1.07x10-' e-:".'m'"'r The diflusion coefficients, D, given by this relation represent mean values, since carburization occurred simultaneously with nitriding. The rate of diffusion in a-iron has been determined from calculations based on data obtained by measuring the internal friction of samples at each of several frequencies and temperatures.' The expression for the diffusion of nitrogen in a-iron derived from these experiments is D= 1.4x10-1 e-it tudent Increasing carbon content decreases the diffusion of nitrogen in a-iron.3 Oxygen, either dissolved or combined, has been shown' to exert a marked influence on the diffusion of nitrogen from a nitriding atmosphere. D values increase rapidly with increasing amount of dissolved oxide in the metal, but diffusion is completely inhibited if preliminary oxidation has produced the slightest trace of iron oxide on the surface. Diffusion coefficients have also been calculated from permeability and solubility data,' but these values are of questionable accuracy since the boundary conditions assumed may not actually exist. Experimental Method The method selected for determining the diffusion coefficient of nitrogen in a-iron in the present investigation was the so-called fractional saturation method. This method consists of heating the specimen in an atmosphere of H2-NH8 mixtures of known composition for a predetermined time. Following this treatment, the specimen is analyzed for nitrogen; and the diffusion coefficient is calculated from a known relationship of the fractional saturation, time of diffusion, and dimensions of the specimen. This relation is based on a solution of Fick's second law and assumes that the surface of the specimen immediately reaches a given concentration which remains constant during the diffusion anneal. Tabular solutions are available4-5 and provide the relationship between fractional saturation and the quantity \/Dt /a, where D is the diffusion coefficient in cm2 per sec, t is the time of the diffusion anneal in seconds, and a, in the present experiments, is the half-thickness of the slab specimen in cm. The method is adequately discussed elsewhere.9-10 Material The material for this study consisted of 3/32 in. thick (0.24 cm) carbonyl iron plate. The major impurities in this iron are oxygen and carbon, which are readily removed by long time high temperature treatment in an atmosphere of purified hydrogen. In order to reduce the diffusion anneal time for saturation runs, some of this material was rolled to a thickness of 0.015 in. (0.038 cm) prior to the hydrogen treatment. Hydrogen treatments were carried out in a hydrogen-purified Armco iron tube heated in a global

Jan 1, 1957

By T. F. Witheree

The Fletcherville Furnace was built in 1864 and 1865, making its first blast from August until October of the latter year, when it was blown out to prevent its " bunging-up." Repairs were made in time to enable it to be blown in again December 12th, 1865, the blast ending October 7th, 1866. Total product 1921.15 tons iron, an average of 6.8.2.5 tons per day, from ores yielding 44.8 per cent. Consumption of charcoal 223.2 bushels per ton of iron. The furnace journal up to this time shows no record of furnace dimensions, or temperature of the blast, but as near as can be ascertained, they were as follows, viz.: Height of stack, 42 feet. Diameter of bosh, 11 feet. Angle of bosh, 71/2 inches to 12 inches rise, about 58°. Diameter of open tunnel head, 42 inches. Number of tuyeres 3 ; each 3 inches in diameter. Dam 15 inches high. Tuyeres 24 inches high. Tymp 224 inches high. Diameter of steam cylinder, 20) inches. } Diameter of blast cylinder, 64 inches. } Stroke 5 feet. The engine is direct-acting horizontal non-condensing. December 26th, 1866, the furnace was again put in blast, having been considerably altered in the crucible; the height of stack, bosh, and tunnel head remaining as before. Six tuyeres were put in, three in each of the side arches. The hearth or crucible was rectangular in form, 3 feet wide x 31/2 feet long x 64 feet high. Inclination of bosh 58°. Height of tuyeres 26 inches; nozzles 21/4 inches diameter. Temperature of blast estimated to be about 500°.

By Wilbur S. Burbank, Robert G. Leudke

The impressive western San Juan Mountains of Colorado were carved by Pleistocene and Recent erosion from a thick blanket of Tertiary volcanic rocks that rests upon a basement of metamorphic, sedimentary, and igneous rocks ranging in age from Precambrian to Tertiary. These rocks record a long, complex, and fairly complete sequence of geologic events that have affected the region through much of geologic time. The geologic history of the region includes several periods of deformation, erosion, and igneous activity; closely associated with two of these periods were two periods of mineralization. The older of these was related to Late Cretaceous-early Tertiary (Laramide) intrusive activity, and its deposits occur in the older sedimentary units. The younger, of later Tertiary age and related to the widespread middle Tertiary extrusive and intrusive activity, is the chief concern of this paper. Tertiary volcanism built a great plateau surrounding the San Juan volcanic depression, a complex of subsided crustal blocks in the vent areas. The Silverton and Lake City cauldrons, nested within the larger depression, were domed by resurgent magma that created keystone grabens along the distended crests of the domed floors and many postcauldron radial and concentric fractures, dikes, and intrusive plutons within and marginal to the cauldron sites. The postvolcanic evolution of large quantities of gases, chiefly carbon dioxide and water, propylitically altered the rocks in and around the volcanic depression prior to the younger period of ore deposition. The ore deposits, localized mainly in the radial and concentric fractures about the cauldrons and in the associated graben faults, include fissure veins, chimneys, replacements, and disseminations in volcanic and underlying basement rocks. Fissure veins, constituting the major economic source, yielded precious- and basemetal ores. Most veins are compound with sphalerite, galena, and chalcopyrite; some veins contain silver-bearing arsenical sulfosalts and free gold. These minerals occur in predominantly quartz gangue. However, gangues composed of several manganese silicates and carbonates and relatively· barren of metals are abundant locally and probably originated by alteration of rocks at roots of faults and fissures during evolution of carbonatic solutions. The bulk of the ores are hypogene and probably had their source in deep parent magmas of the shallow eruptive rocks. Total production since the early 1870's has exceeded half a billion dollars in recovered metals, with a ratio of precious- to base-metal values of about 3 to 2. Since 1930, improvements in metallurgical treatment and mining techniques have increased the base-metal yield.

Jan 1, 1968

By Don K. Smith

The Reclamation Program for the Northern Zone of the Indus Plains in West Pakistan involves the construction of 30,000 irrigation wells to serve 20 million acres with an annual pumpage of nearly 40 million acre-ft. Detailed hydrologic studies indicated that mild steel would be satisfactory for casing; however, within two years after construction, about 10% of the wells began to fail due to encrustation and corrosion of the casing. A search to find a noncor-rosive substitute for the steel casing disclosed that only fiberglass-reinforced plastic pipe satisfied all requirements. The results of initial use of fiberglass have been highly satisfactory and have resulted in a lower over-all well cost. Advances in technology pomise further reduction in prices and improvement in performance. The northern zone of the Indus Basin comprises a vast area of essentially level land in West Pakistan which is irrigated by means of a complex system of canals that distribute more water to more land than any other irrigation system in the world. In spite of the development of this extensive irrigation system, production of food and fiber has not met the requirements of the country. The major reasons that crop production has not reached anticipated levels are the lack of adequate irrigation supplies and effective subsurface drainage. As a result, yields per acre are among the lowest in the world for areas where irrigation is practiced, and many thousands of acres of valuable crop land have been removed from production or seriously affected by salinity and waterlogging. To rectify the problems of irrigation supply and drainage the Government of Pakistan has undertaken a program of Salinity Control and Reclamation which is being administered by the Water and Power Development Authority. The Authority retained Tipton and Kalmbach, Inc., of Denver, Colo., as engineers for the program in the northern zone of the Indus Basin. This program consists of the construction of about 30,000 irrigation wells to provide drainage for waterlogged lands and full irrigation supplies, including leaching requirements, for all cultivated lands. The program will ultimately ensure the productivity of 20 million acres and involve an annual pumpage from groundwater storage of nearly 40 million acre-ft of

Jan 1, 1970

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

By Francis T. Freeland

In the West many precious-metal mines are worked in patches by lessees, under conditions which closely resemble those of what is called " tribute-work" in Cornwall.* The company has its own foreman or inspector, and usually employs the engineman, blacksmith, pumpman, and perhaps other general workmen. As an inducement to work on a new piece of ground, where no ore is in sight, the company may advance a " footage"

Jan 1, 1896

By Carroll Forbes

INTRODUCTION MANY different shapes of drill bits are in use with hammer drills, but little definite information is available whereby to judge which one of these shapes is the best. The following investigation was undertaken in order to determine what effect, if any, the shape of the cutting edge has on the cutting speed and wearing qualities of drill bits. The bits tested were those in common use, namely, the 4-point or cross bit, the 6-point bit, the Z bit and the "Carr" bit. The rock in which the tests were made was the red granite from southeast Missouri. It is a coarse crystalline granite containing an unusually large amount of quartz and is extremely hard, and on account of its uniform texture is admirably adapted to this work. While tests in other rocks might show somewhat different results, nevertheless it is the opinion of the authors that the relative cutting quality inherent in the shape of the bits would be the same in all rocks. Other qualities, such as mudding freely, freedom from fitchering, etc., might make one bit more desirable than another in softer rocks. DESCRIPTION OF BITS TESTED The 4-point bits were the usual shaped bits commonly made on the Leyner sharpener with 14° taper on the wings and a 90° angle between cutting edges. Some tests were run at 85 lb. pressure with a 4-point bit made with a 5° taper on the wings. This was made by using the Carr bit die. The 6-point bits were the usual shaped hits made on, the Leyner sharpener. The Carr bits were made with a 5° taper and an angle of 100° between cutting edges.

Jan 8, 1917

By W. A. Krivsky, R. Schuhmann

Jan 1, 1962

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By P. G. Hallof

Only recently has the term Induced Polarization found its way into geophysical literature. Schlumberger first mentioned the possible use of the induced polarization effect in one of his early papers. Later, induced polarization was the subject of several university theses, such as Seigel's at the University of Toronto and Bliel's at the Michigan School of Technology. In addition, a group at the New Mexico School of Mining and Technobgy has done work on induced polarization. There is very little to be found in print on the subject of induced polarization. Several papers have been presented at meetings, the 1958 AIME and SEG* conventions, for instance, on laboratory measurements of the effect and theoretical considerations useful in the interpretation of field results. This paper is the first attempt to present actual field results which show the usefulness of induced polarization as a prospecting technique. There are several phenomena that can cause polarization when electrical current is passed through the ground. In a paper presented at the 1958 SEG* meetings Professor T. R. Madden of M. I. T. demonstrated that only two of these gave rise to appreciable effects. The first is a result of the membrane and diffusion effects in a sandstone that contains appre- ciable amounts of clay minerals. The unbonded charges associated with the clay mineral forma material that passes positive and negative ions with different mobilities. When current is passed through such a system for some period of time, polarization results. The second phenomenon, which gives rise to very much larger polarization effects, is the one used in the new prospecting technique. These effects are a result of the blocking action or polarization of metallic or electronic conductors in a medium of ionic solution conduction. This electrochemical polarization, called "the over-voltage effect" by electro-chemists, occurs whenever electrical current is passed through a volume of rock which contains metallic minerals such as base metal sulphides. This polarization at metallic interfaces in ionic solutions depends upon the chemical energies necessary to allow the ions to continue the flow of current by giving up or receiving an electron from the metallic surfaces. The energy stored in this reaction isanalogous to that stored when a condenser is charged. If a d. c. current flowing through such a system is interrupted, the polarization can be detected as a small, decaying current that flows after the applied current is discontinued. The decaying potential measured is a result of the current flow caused by charges returning to their equilibrium positions from the positions they assumed under the applied potential field. Because of the polarization, there is an excess of change at each metallic interface. There is an alternate method of measurement of the induced polarization effect. The electrical

Jan 1, 1961

By Sherwin F. Kelly

One of the most succinct and illuminating perspectives of the field of geophysical exploration to appear in recent years is an article by E. A. Eckhardt, in the magazine Geophysics for October 1949. Although his review covers the year 1948, many of the data presented are apropos to a review of 1949, and form a pertinent background for a consideration of current progress. He presents charts of the world-wide distribution of gravimeter and seismograph activity in oil exploration, which show that surveys in the United States accounted for practically 68%; of all gravity work and 80%; of all seismic activity. Canada ranked second, with a proportion of roughly 6%, in each case; South America accounted for about the same percentage of seismic work, and double that amount for gravity surveys. Within the United States, Texas and Louisiana were the scenes of the greatest activity, both claiming about 60% of all surveys by each method.

Jan 1, 1950

By Arthur L. Hall

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

Jan 10, 1957

By B. A. Eaton

The subject of many discussions and technical papers in the last 20 years has been the prediction of the well-bore pressure gradients that are required to induce or extend fractures in subsurface formations. The subject merits this attention because of the frequently recurring problems that arise from an inability to predict fracture pressure gradients. Encountered in several common types of operations in the oil industry are problems associated with the prediction of formation fracture pressure gradients. When wells are being drilled in both new and old fields, lost circulation is often a very troublesome and expensive problem. Complete loss of circulation has been disastrous in some cases. Many times, such disasters could have been avoided if techniques for calculating fracture pressure gradient had been employed in the well plans, and if casing strings had been set, and mud weight plans had been followed accordingly. In areas of abnormally pressured formations, the prediction of fracture gradients during the well-planning stage is extremely important. In fact, it is as important as the prediction of formation pressure gradients, which has received a great deal of attention in recent years. There are several published methods used to determine fracture pressure gradients. However, none of these methods appears to be general enough to be used with much reliability in all areas. In 1957, Hub-bert and Willis published a classical paper that included the development of an equation used to predict the fracture extension pressure gradient in areas of incipient normal fau1ting.l Overburden stress gradient, formation pore pressure gradient and Poisson's ratio of rocks were the independent variables that were shown to control fracture pressure gradient, the dependent variable. In 1967, Matthews and Kelly published another fracture pressure gradient equation that is different from that of Hubbert and Willis in that a variable "matrix stress coefficient" concept was utilized.3 Later the same year, Costley wrote about a similar idea.5 Goldsmith and Wilson used a least-squares curve-fitting technique and field data from the Gulf Coast area to correlate fracture pressure gradient with formation pore pressure gradient and formation depth.' They noted that the fracture pressure gradient increased with increasing depth while the pore pressure gradient remained constant. In each of these cases, the problem for which a solution was sought was to determine the bottom-hole pressure gradient required to initiate or extend a fracture. Results of the previous work show that fracture pressure gradient is a function primarily of overburden stress gradient, pore pressure gradient, and the ratio of horizontal to vertical stress. There is argument for a fourth variable in that in many cases breakdown fracture pressure gradient is greater than the fracture extension pressure gradient. However, if the fracturing fluid is able to penetrate the formation through the pores or existing cracks, there is very little

Jan 1, 1970