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By Charles S. Larkey

Numerous papers have been published on the use of graphic methods for determining the best curve for estimating the production decline of oil wells but, as far as the writer has been able to ascertain, nothing has been published showing how curves may be worked out mathematically that will conform most closely to the production data under consideration in any given instance; hence the writer has endeavored to show just how such application can be made. Among the valuation engineers, two types of curves are in current use for the representation of the decline in production of oil wells. One may be represented by the equation, y = krx; this is sometimes known as a percentage curve, for the production for any period is multiplied by a constant rate or percentage to obtain the production for the succeeding period. It appears as a straight line on semilogarithmic cross-section paper. The other curve may be represented by the equation, y = kxn, and is shown as a straight line on logarithmic cross-section paper. In each equation, y represents the number of barrels produced in a given period of time, and x the successive periods of time. The other letters are constants to be determined for each well, or group of wells considered in arriving at the most probable curve to represent the rate of production for a given property. From this the underground reserves may be estimated by extrapolation, or by extending the curve beyond the last known period of production to show the most probable production values for the future. Application to the Burbank Pool Fig. 1 relates to a property in the Burbank Pool, Osage County, Okla. The production is shown as an average per well per month, is plotted to the vertical scale of barrels on the left-hand margin and to the horizontal scale of months at the bottom of the chart. In column y, the number of barrels is listed beginning with May, 1922, as the first month on which to base a decline curve. The type of curve used is of the form, y = krx, or, expressed in logarithms, log y = log k + x log r, in which log k and log r are constants to be determined so that the curve will most closely approximate the production data given.

Jan 1, 1925

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By H. J. Morel-Seytoux

The influence of patten, geometry on assisted oil recovery for a particular dispIacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presents (1) very brieily, the methods and mathematical derivations required to obtain the results of engineering concern, and (2) typical results in the dorm of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston- like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. ,These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M = 1 and the numerical results for non-piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed farm solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-fIood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Jan 1, 1967

By Robert Sisselman

Dramatic changes have been effected since 1955 in the mode of iron ore shipments within the U.S. In 1955, less than one percent of ore consumed in domestic blast furnaces-approximately 125 million long tons-consisted of pellets. Five years later, in 1960, some 94.8 million tons of ore were consumed, 14% in the form of pellets. Projections for 1980 reinforce confidence in this most economic of blast furnace feeds, and set U.S. pellet consumption at 151.2 million tons. In the last decade, pellets caught fire in other countries. By 1969, world production reached 96 million tons. This compares strikingly with present world output of 154 million tons.

Jan 9, 1973

By Adrian C. Dorenfeld

Factorial design is a mathematical method of drawing valid conclusions from a series of tests made in a predetermined pattern. It is applied to flotation ore testing using, in this case, five variables, each varied twice, requiring a total of 32 tests. Representative conclusions are checked by repeat testing.

Jan 12, 1951

By T. Egleston

IF we may characterize the aim of metallurgists twenty years ago by any one point towards which their efforts were especially directed, we should say it was the idea of adapting &apos;&apos; waste products" to some useful purpose, while the energy of to-day seems rather to take the direction of so arranging processes as to have no "waste products." The iron-master of this decade no longer speaks of the waste gases

By T. Prof. Egleston

IF we may characterize the aim of metallurgists twenty years ago by any one point towards which their efforts were especially directed, we should say it was the idea of adapting "waste products" to some useful purpose, while the energy of to-day seems rather to take the direction of so arranging processes as to have no " waste products." The iron-master of this decade no longer speaks of the waste gases

Jan 1, 1873

By C. E. Birchenall, J. R. Stubbles

ThE equilibrium between lead, lead sulfide (PbS), and atmospheres of H2 and H2S has been determined previously by Jellinek and Deubel,&apos; and SudO.&apos; Blbem and Kroger3,4 used Jellinek&apos;s data to calculate the sulfur dissociation pressures of PbS crystals (of

Jan 1, 1960

By R. G. Ward, John Henderson

It has been shown1 that the observed density1-&apos; of liquid iron silicates in contact with solid iron depends upon whether nitrogen or argon is used to protect the experimental system from oxidation. These densities have been measured by the maximum bubble-pressure method, in five different labora-

Jan 1, 1965

By C. G. Rhodes

A technique for producing etch pits in uranium monocarbide has been developed. The pits, which are assumed to be associated with dislocations, appear individually and as arrays delineating sub-boundaries, as seen in Fig. 1. The samples used were single crystals prepared by the technique described by Nadler.* Uranium

Jan 1, 1963

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemisorption.

Jan 5, 1950

By T. O. Breitling

Two significant problems In mill design are environmental control and cost reduction. Environmental control is predicted to be 5-10% of total plant costs in some parts of the U.S. Operating and design companies will assign this new "unit operation" a place in the early flow sheets. More advanced environmental control will add to both capital and operating costs, so mill designers will strive to reduce other costs.

Jan 1, 1970

By James A. Burns

The challenge to designers of bulk materials handling systems is to apply the existing technology in areas where it has not been used and to foster better, cheaper and safer job performance. The Dashaveyor Co., a subsidiary of The Bendix Corp., built and tested a pilot system at Copper Range&apos;s White Pine mine. Based upon this success, a prototype system development was begun in 1967 to test the concepts in a full-scale, realistic environment.

Jan 11, 1973

By C. Baldwin Sawyer

J. S. Vanick,* Washington, D. C. (written discussion).—To those who have been confronted with the study of the gas-metal reactions, this paper is a most welcome contribution. My personal interest in work bearing upon this general problem, stimulated by an appreciation of the difficulties inherent to problems of this type, prompts a few words of discussion. Table 2 of the paper shows a gradual increase in the nitrogen content with an increase in pressure, and an interpretation follows in which nitrogcn is used as the compressed medium when the conditions admit that cyanogen gas could be active as a contaminating ingredient. Fusions of electrolytic iron made in the induction furnace in an atmosphere of deoxidized nitrogen and out of contact with contaminating materials have shown no microscopic evidence of -a nitrogen increase; using a refractory-lined graphite crucible in the furnace under the same conditions or admitting air often resulted in the occurrence of nitride needles in the solidified melt. These results suggested that a nitrogenous compound served as a vehicle for the introduction of nitrogen and that such compound was not available when the pure gas and carbon-free refractory were used. The fusion of pure iron in pure nitrogen is perhaps a matter of theoretical interest. The author&apos;s work serves a more practical purpose when applied to steels rather than iron. Table 2 reports the absence of nitride needles in melts made under pressure of one atmosphere, although the quantity of nitrogen present would seem to exceed microscopically detectable percentages. In some recent work29 on carburized iron, nitride needles have been observed in areas analyzing as low as 0.015 per cent. nitrogen. This low percentage of nitrogen would indicate that the solubility limit is less than 0.030 per cent. for hypoeutectoid steels. There is the possibility that the areas of pearlite which exist in a hypoeutectoid steel restrict the distribution of nitrogen and limit its presence to the ferritie fields. In view of this work and the references quoted by the author, I am led to expect that the value for the solubility of nitrogen in solidified iron may approach

Jan 1, 1924

By J. Morgan Clements

PETROLEUM has been known in Japan since at least 668 A. D., for a picture shows the presentation, during that year, to the Emperor Tenchi (Tenji) of "burning water" and." burning earth" by his subjects from Echigo Province, which today is the largest producer of petroleum in Japan. The burning water was doubtless petroleum and the burning earth either bituminous shale or oil-soaked earth or rock from near the oil seepages. The early methods of getting the oil were simple and similar to methods used today in Japan and in China. Where the seepages occurred, trenches or shallow wells were dug along the seepages and allowed to fill with oil which was then bailed out; in some cases, they filled with oil and water and overflowed. During the 300 years following 1500 A. D:, the use of petroleum in Echigo Province seems to have increased considerably, as compared with earlier centuries, and records show that in 1818 the depth of the wells had been greatly increased. Doubtless, they passed through the seepages and tapped the shallow oil-bearing strata; probably some of these deeper wells were dug before that time. The real value of petroleum was not recognized until early in the Meiji era, which began in 1868, when the Japanese learned that the kerosene that was being imported was derived from petroleum. Guided solely by information obtained from books, they refined the oil and increased the depth of their wells in order to increase the production. The deepest well, dug by hand, about this time was 894 ft.1 (273 m.) and by 1874 the recorded production reached 3499 barrels. In 1876, Benjamin Smith Lyman prepared geological maps of the Echigo oil field, which were the first. of such geological maps made in Japan, and based on these a more enlightened development of the oil fields began; the. Japanese, however, still dug the wells by hand. Toward the end of the &apos;80s, an American well-drilling outfit was secured, but the efforts to use it failed from lack of experience by the operators. In 1888, a complete well-drilling outfit was, purchased and American oil-well

Jan 7, 1922

By J. Morgan Clements

Petroleum has been known in Japan since at least 668 A. D., for a picture shows the presentation, during that year, to the Emperor Tenchi (Tenji) of "burning water" and (&apos;burning earth" by his subjects from Echigo Province, which today is the largest producer of petroleum in Japan. The burning water was doubtless petroleum and the burning earth either bituminous shale or oil-soaked earth or rock from near the oil seepages. The early methods of getting the oil were simple and similar to methods used today in Japan and in China. Where the seepages occurred, trenches or shallow wells were dug along the seepages and allowed to fill with oil, which was then bailed out; in some cases, they filled with oil and water and overflowed. During the 300 years following 1500 A. D., the use of petroleum in Echigo Province seems to have increased considerably, as compared with earlier centuries, and records show that in 1818 the depth of the wells had been greatly increased. Doubtless, they passed through the seepages and tapped the shallow oil-bearing strata; probably some of these deeper wells were dug before that time. The real value of petroleum was not recognized until early in the Meiji era, which began in 1868, when the Japanese learned that the kerosene that was being imported was derived from petroleum. Guided solely by information obtained from books, they refined the oil and increased the depth of their wells in order to increase the production. The deepest well, dug by hand, about this time was 894 ft.&apos; (273 m.) and by 1874 the recorded production reached 3499 barrels. In 1876, Benjamin Smith Lyman prepared geological maps of the Echigo oil field, which were the first of such geological maps made in Japan, and based on these a more enlightened development of the oil fields began; the Japanese, however, still dug the wells by hand. Toward the end of the &apos;80s) an American well-drilling outfit was secured, but the efforts to use it failed from lack of experience by the operators. In 1888, a complete well-drilling outfit was purchased and American oil-well

Jan 1, 1923

By J. Morgan Clements

Petroleum has been known in Japan since at least 668 A. D., for a picture shows the presentation, during that year, to the Emperor Tenchi (Tenji) of "burning water" and (&apos;burning earth" by his subjects from Echigo Province, which today is the largest producer of petroleum in Japan. The burning water was doubtless petroleum and the burning earth either bituminous shale or oil-soaked earth or rock from near the oil seepages. The early methods of getting the oil were simple and similar to methods used today in Japan and in China. Where the seepages occurred, trenches or shallow wells were dug along the seepages and allowed to fill with oil, which was then bailed out; in some cases, they filled with oil and water and overflowed. During the 300 years following 1500 A. D., the use of petroleum in Echigo Province seems to have increased considerably, as compared with earlier centuries, and records show that in 1818 the depth of the wells had been greatly increased. Doubtless, they passed through the seepages and tapped the shallow oil-bearing strata; probably some of these deeper wells were dug before that time. The real value of petroleum was not recognized until early in the Meiji era, which began in 1868, when the Japanese learned that the kerosene that was being imported was derived from petroleum. Guided solely by information obtained from books, they refined the oil and increased the depth of their wells in order to increase the production. The deepest well, dug by hand, about this time was 894 ft.&apos; (273 m.) and by 1874 the recorded production reached 3499 barrels. In 1876, Benjamin Smith Lyman prepared geological maps of the Echigo oil field, which were the first of such geological maps made in Japan, and based on these a more enlightened development of the oil fields began; the Japanese, however, still dug the wells by hand. Toward the end of the &apos;80s) an American well-drilling outfit was secured, but the efforts to use it failed from lack of experience by the operators. In 1888, a complete well-drilling outfit was purchased and American oil-well

Jan 1, 1923

By E. W. Davis

Iron-ORE beneficiation methods are determined largely by blastfurnace requirements. There are still many millions of tons of direct furnace ore in the Lake Superior district and blast furnaces are designed and operated for the most efficient use of this material. Beneficiated ore must be so prepared that existing furnaces may use it without alteration in design or radical changes in practice. Many attempts have been made to develop new furnaces or processes for smelting iron-ore concentrate not suitable for blast-furnace use, but these processes have gained little importance. It is, therefore, the endeavor in beneficiating iron ore to make a product that will give at least as good results as direct furnace ore in existing blast furnaces. The term "beneficiation," as applied to iron ore, does not necessarily mean concentration, but more accurately means "dressing up" the ore so that it is more acceptable to the blastfurnace operators. In modern blast-furnace practice the structure of the ore is quite as important as the chemical analysis. Certainly, the higher the iron content and the lower the silica, phosphorus and sulfur, the more desirable the ore bccomcs; but if the structure is bad, that is, if the blast-furnace gases can penetrate the charge only with difficulty, the ore is undesirable regardless of its analysis. This means that the ore should be as uniform in size as possible and free from fines, and also that the individual particles of ore should be pervious to the reducing gases of the furnace. Structure and purity are the primary requirements for a furnace ore and structure is just as important as purity. Iron-ore beneficiation processes can be divided, therefore, roughly into two main classifications: (1) processes that primarily improve the structure, and (2) processes that primarily improve the chemical analysis. During the past 10 years approximately 25 per cent of the ore shipped from the Lake Superior district has been beneficiated. Of this about half has been crushed and screened, a simple operation that primarily improves the structure but in some cases also improves the analysis slightly. The other half of the shipment of beneficiated ore, amounting to an average

Jan 1, 1935

By G. E. McElroy

Changes in existing airway and fan-installation conditions offer the most common opportunities for effecting economical operation of mine-ventilating systems, but the largest possibilities for securing this result lie in the original design of the main airways for efficient service. Formulas, and charts for their graphical solution, are presented herewith for the determination of the elements of airways design when the conditions of service are known or may be roughly approximated. Although the analyses are made with particular reference to metal-mine airways, there is no essential difference between main airways in metal and coal mines, and the methods presented are applicable to both. Little attention is paid to designing airways for maximum economy in the ventilation of metal mines. Most of the openings used as main airways are originally designed and used for transportation and other operating purposes. Even where openings are made primarily for ventilation, the possibility of their future use for other operating purposes, or even custom alone, usually results in the selection of a size and shape similar to those of existing openings. Natural conditions, such as heavy ground, often seriously limit the size of opening that can be maintained without excessive expense; and various operating factors, such as velocity limitations on traveling roads, often dictate size requirements in excess of those required for economy in ventilation only. In metal mines the main airways are, as a rule, too small rather than too large for economic service, with the general result that the quantities in circulation are often less than the mine&apos;s proper requirements over long periods, even though excessive amounts of power are applied in an effort to remedy conditions. Increasing the area of an airway increases the cost for excavation and lining practically proportionately but at the same time affects a very rapid decrease in power requirements. The balancing of these two factors of the expense to give a minimum total yearly operating cost for ventilation is mainly a matter of proper original design of the main airways of the mine, since the large volumes handled through these parts of the system involve large power costs and thus present opportunities for effecting large savings through proper design. Many of the factors

Jan 1, 1932