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By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By David B. Reger

Widespread wildcatting for new supplies of natural gas and the beginning of importation from the southwest characterized the petroleum industry of West Virginia during 1944. Within the state, drilling for oil did not increase but. more gas wells were completed than in any previous year since 1937. Out of 40 wildcats drilled there were 25 gas discoveries and 15 dry holes. No commercial oil was found in the 40 wells. The proved limits of several oil pools were slightly extended by marginal drilling, resulting in 1300 acres of new oil territory, although no distinctly new pools were found. At least four new gas pools were assuredly discovered and various successful wildcats indicate future pools or wide extensions. The new proved gas territory, in definite new pools and definite extensions, is about 34,000 acres. A considerable net decline of proved oil has occarred and probably a slight decline of proved gas reserves. The account of operations, as gathered from trade journals and other reporting services, shows that 918 new wells were drilled, resulting in 71 oil wells with 613 bbl. of daily new production; 577 gas wells with 305,372,000 cu. ft. of daily open flow, and 142 dry holes. Also, 107 old wells were drilled to deeper sands, with 22 bbl. and 12,327,000 cu. ft. of added production. On the new wells the oil average was 8.6 bbl. per well per day, and the gas average was 529,241 CU. ft. per well per day. On new wells the ratio of dry holes to completions was 15.47 per cent. On deeper drilling the ratio of failures was 19.63 per cent. Production of oil for the year was estimated by the Oil Weekly as 3,069,000 bbl., as compared with 3,349,000 bbl. in 1943. Production of natural gas for the year is estimated by the author as 200,000, 000,000 cu. ft., as compared with the U. S. Bureau of Mines final figures of 223,789,000,000 cu. ft.t in 1943.

Jan 1, 1945

For the year ending February, 1919 PRESIDENT SIDNEY J. JENNINGS NEW YORK, N. Y. PAST PRESIDENTS L. D. RICKETTS NEW YORK, N. Y. PHILIP N. MOORE ST. Louis, Mo. FIRST VICE-PRESIDENT C. W. GOODALE BUTTE, MONT. TREASURER GEORGE D. BARRON NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER W. RAYMOND, NEW YORK, N. Y. SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 1, 1919

By B. F. Tillson

Mining may be defined as a general term for the working of valuable deposits of minerals, either organic or inorganic in origin, for their removal from the crust of the earth. Besides subsurface excavations, mining generically includes opencuts, clay pits and stone quarries, oil wells, sulphur wells, salt wells, placers, coal stripping, and the leaching of ore bodies. The origin of the word "mine" or "mining" is a matter of conjecture. A Celtic origin has been suggested since the Irish word mein, or the mwyn, meant ore, but it seems to have come from an olf French verb mineor, which meant to excavate, to make an underground passage as in the military appraoch to a fortification, sometimes called ?sapping.?

Jan 1, 1949

By Gerhard Derge, Harold Markus

The introductory paper1 of this series described the potential behavior of tin in sodium carbonate and bicarbonate solutions whose pH ranged from 8.4 to 11.2 and demonstrated that significant and reproducible results could be obtained by proper attention to experimental technique. In examining the corrosion of tin under such conditions, it is desirable to know the effects of anions, aside from carbonate, that are likely to be present in commercial materials packaged in tin. Therefore, in this paper the potential behavior of tin in carbonate solutions to which sodium fluoride, chloride, bromide, iodide, sulphate, nitrate, monobasic phos-phate, dichromate, perborate and acetate have been added will be dcscribed. For most of the additions, solutions containing 0.001 and 0.01 moles of the added material were studied. The experimental procedure was exactly the same as that described in the first paper; the pH of the electrolyte was controlled by adjusting the ratio of carbonate to bicar-l,ol~ate as follows: pH 0.1 M NaHC0............................................ 8.4 2 parts 0.1 M XaHCOr, 1 pa.rt 0.1 M NaZCO?................. 9.5 1 part 0.1 M NaHCOs, 2 parts 0.1 M iVa.,C03. ................ 10.0 0.1 M Na2C0............................................. 11.2 The reagents used were all of C.P. grade. The anions studied may be divided into three groups: (1) anions that had little or no effect upon the potential curves—sulphnte, nitrate, and acetate; (2) those that helped to prevent corrosion at low pH only -fuoridc, chloride, bromide, and iodide; (3) those that helped to prevent corrosion at high pH also—phosphate, pcrborate, and chromate. Potential Measurements f The time-potential curves represntative of group 1 are shown in Fig. 1. These are the curves for 0.005 M sulphate ion and their similarity

Jan 1, 1939

By Harold Markus, Gerhard Derge

The introductory paper1 of this series described the potential behavior of tin in sodium carbonate and bicarbonate solutions whose pH ranged from 8.4 to 11.2 and demonstrated that significant and reproducible results could be obtained by proper attention to experimental technique. In examining the corrosion of tin under such conditions, it is desirable to know the effects of anions, aside from carbonate, that are likely to be present in commercial materials packaged in tin. Therefore, in this paper the potential behavior of tin in carbonate solutions to which sodium fluoride, chloride, bromide, iodide, sulphate, nitrate, monobasic phos-phate, dichromate, perborate and acetate have been added will be dcscribed. For most of the additions, solutions containing 0.001 and 0.01 moles of the added material were studied. The experimental procedure was exactly the same as that described in the first paper; the pH of the electrolyte was controlled by adjusting the ratio of carbonate to bicar-l,ol~ate as follows: pH 0.1 M NaHC0............................................ 8.4 2 parts 0.1 M XaHCOr, 1 pa.rt 0.1 M NaZCO?................. 9.5 1 part 0.1 M NaHCOs, 2 parts 0.1 M iVa.,C03. ................ 10.0 0.1 M Na2C0............................................. 11.2 The reagents used were all of C.P. grade. The anions studied may be divided into three groups: (1) anions that had little or no effect upon the potential curves—sulphnte, nitrate, and acetate; (2) those that helped to prevent corrosion at low pH only -fuoridc, chloride, bromide, and iodide; (3) those that helped to prevent corrosion at high pH also—phosphate, pcrborate, and chromate. Potential Measurements f The time-potential curves represntative of group 1 are shown in Fig. 1. These are the curves for 0.005 M sulphate ion and their similarity

Jan 1, 1939

By R. G. Wheeler, J. W. Goffard

The Larson-Miller parameter was used to correlate time, temperature, and indentation creep of magnesium, aluminum, and some of their alloys. In the temperature range 300" to 450°C, the short-time Meyer hardness of pure magnesium was less than that of the magnesium alloys tested, but for long times the pure magnesium has greater indentation creep resistance. Aluminum (1100 alloy) had 1.5 to 2.5 times more indentation creep resistance than magnesium at 300" and 450oC, respectively. Hardening of aluminum with a dispersion of Al2O3 was effective in the time and temperature ranges studied. New technologies have required the development of new materials and the utilization of the more familiar materials for new and unusual applications. The use of magnesium and aluminum and some of their alloys, because of their desirable nuclear characteristics, light weight, low cost, and ready availability, has been extended to the 300" to 450°C temperature range. In this temperature range the basic consideration of these materials must be their rate of plastic flow rather than offset yield strengths. The indentation testing reported here arose from a need for design data for the load-holding ability of supports made of these materials. Test Procedure—Hardness indents were made with a 0.275-in.-diam quartz indentor and a 10.65-lb load. The indentor was made by fire-polishing a spherical surface on the end of a fused quartz rod. The samples were held at temperature in a graphite crucible controlled to ±2°C. A thermocouple was attached to the sample and test temperatures were recorded. The diameter of the spherical indentation was measured at the end of a test period and the compression stress (Meyer Hardness) was determined by: H___________load__________ m = projected area of indent Samples were 1 in. in diam and at least 1/4 in. thick. It was observed that at the higher temperatures and longer times, the quartz indentor would stick to the magnesium sample. The quartz indentor was, therefore, frequently inspected and fire-polishing repeated when necessary. The area of sticking was always a small fraction of the area of indent and was therefore considered to have an insignificant effect on results. Correlation of Hot-Indentation Test Data with Time-Temperature Parameter—Sherby and Dorn' have correlated creep or tensile data of a' solid solutions of aluminum with a temperature and strain-rate parameter suggested by Zener and Holloman. underwood2 used this parameter to correlate creep properties of some steels with hot hardness, and upon the basis of this correlation a means of obtaining creep properties from short-time (and inexpensive) hot hardness tests has been demonstrated. Since the validity of the correlation of creep properties with a time-temperature parameter and the correlation of creep properties with hot hardness have been shown, it follows that hot hardness may correlate with the time-temperature parameter. The hot-indentation data obtained was expressed as Meyer hardness, and was shown to be time and temperature dependent. Correlation of Meyer hardness, time, and temperature with the parameter was made using the relationship: Hm = Meyer hardness t = time, hours T = absolute temperature, OK K = constant A value for the constant K was calculated by equating In l/t + K/T at different temperatures and times but at the same hardness. The correlation was tested by plotting Hm vs the parameter, In 1/t +K/T. Since materials are being sought which have high hardness at low indentation creep, i.e., a high Meyer hardness for long time at high temperatures, low values of the parameter are ofthe most interest. TEST RESULTS Magnesium—Pure magnesium (99.98 pct) cut from extruded rod was indentation tested perpendicular to the rod axis at temperatures of 300°, 350°, 400°, and 450°C for times ranging from 6 sec to 112 hr. Fig. 1 shows the time dependency of Meyer hardness at the four constant temperatures. Fig. 2 shows the correlation of the Meyer hardness of pure magnesium with the time-temperature parameter using a K of 22,720 in Eq. [I]. At the bottom of Fig. 2, the effect of doubling the time of indentation t2 = 2(t1), on the abscissa for any time is shown graphically. This effect is of constant magnitude. Also shown graphically are the magnitudes of the effects on the

Jan 1, 1960

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By D. J. McAdam

In a series of papers the author and associates have discussed the influence of temperature on the tensile properties of metals.11-18 These papers present much information about the influence of temperature and the stress system on the conventional indices of mechanical properties, with special attention to the fracture stress. A recent study of the data, however, has revealed much additional information about the influence of temperature on the fundamental factors involved in the flow of metals. The present paper presents results of this study. Attention will be confined almost entirely to results derived from tension tests of unnotched cylindrical specimens at strain rates a little slower than those used in ordinary tension tests. According to a concept first presented by Ludwik and elaborated in recent papers by others,8,9,22,23 the mechanical state of a metal depends on the total plastic strain, but not on the temperature during straining, provided that the only structural changes are those essential to plastic deformation. In the summer of 1948, however, the author made the previously mentioned study of results of a general investigation by the author and associates and reached the conclusion that the mechanical state depends not only on the total strain, but also on the temperature during the straining. A number of diagrams were then prepared. These conclusions were presented without diagrams in a discussion last October of a paper by Dorn, Goldberg and Tietz.2 The metals used in the investigation on which this paper is based were Monel and oxygen-free copper. The Monel was supplied by the International Nickel Co. through the courtesy of Dr. W. A. Mudge. The copper was supplied by the Scomet Engineering Co. through the courtesy of Dr. Sidney Rolle. The data to be presented are based on results of tests at temperatures ranging between 165 and — 188°C. Description of the apparatus and methods of test are given in previous papers.1011&apos;1"2 The present paper is the first part of the general discussion of the influence to temperature on the stress-strain-energy relationship for metals. The next paper will deal with metals that are subject to structural changes other than those induced solely by plastic deformation. Influence of Temperature and Plastic Strain on the Flow Stress of Monel and Copper For a study of the influence of temperature on the stress-strain relationship, flow-stress curves obtained with annealed metals at various temperatures will be compared with curves obtained with the same metals after cold drawing or cold rolling at room temperature. Diagrams thus obtained with Monel and copper are shown in Fig 1 to 8. Fig 1 to 7 show the variation of the flow stress with temperature and plastic strain; Fig 8 is a diagram of a different type, derived from Fig 4 to 7. In Fig 1 to 7 strain is expressed in terms of A0/A, in which A0, and A represent the initial and current areas of cross-section. Since values of Ao/A are represented on a logarithmic scale, abscissas are proportional to true strains; moreover, the true strains representing prior plastic deformation and those representing subsequent strain during a tension test are directly additive. Fig 1 shows flow-stress curves obtained with annealed Monel. Five of the curves are based on results of tension tests. Between yield and the maximum load, the flow was under longitudinal tensile stress; between the maximum load and fracture, the local contraction induced transverse radial tensile stress. The portions of curves designated F, therefore, represent flow with increasing radial stress ratio, the ratio of the transverse stress S3 to the longitudinal stress Si. Curve Fo is based on the ultimate stresses of specimens taken from bars that had been cold drawn various amounts.17 Since the tensile stress at the maximum load is unidirectional, curve Fo represents the course that a flow-stress curve would take if the stress during an entire tension test could be kept unidirectional. The flow-stress curve F obtained at room temperature (Fig 1) has been established accurately by numerous measurements of the diameter of the specimen during the extension from yield to fracture.17 At the time of the experiments, however, no apparatus was available for measuring the diameter during tension tests at low temperatures. Nevertheless, curves have been established to represent with sufficient accuracy the flow at low temperatures. Each flow-stress curve must be tangent to a curve U, which starts at a point representing the ultimate stress of annealed metal. Since the ultimate stress is based on the area of

Jan 1, 1950

By Thomas M. Plouf

Getting optimal performance from flotation cells can, in many cases, be critical to a project&apos;s economic viability. Simple testing procedures can sound early warning signals as well as maintain optimum recoveries from the flotation cycle. The materials required for a simple testing laboratory include: (1) pH meter or pH paper, (2) bottles of reagents used in plant flotation, (3) stop watch, (4) calibrated eye droppers. (5) laboratory flotation machine (1000-g tank, open impeller), (6) froth collection pans, (7) magnifying glass, (8) sizing screen sufficient to retain 10% of the flotation feed coarse fraction, (9) sizing screen for the size particles at which desliming of the plant flotation feed is to take place, and (10) a set of screens covering the complete range of feed particle size.

Jan 4, 1978

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Jan 1, 1910

By J. D. Vincent, Pierre R. Hines

INTRODUCTION OF FROTH FLOTATION INTO THE UNITED STATES "The introduction and development of the flotation process have proved to be of such momentous importance to the mining industry of the United States that they deserve to be considered historically ." T. A. Rickard l James M. Hyde installed the first froth flotation process in the U. S., about Aug. 1, 1911, at the Basin Reduction Co. plant, Basin, Mont., which was then under lease to the Butte and Superior Copper Co.2 Two months later, the Minerals Separation Ltd.. filed suit in the U. S. District Court of Montana against Mr. Hyde char& him with infringement of their Patent 835, 120/1906. The U. S. District Court decided in favor of Minerals Separation Ltd. on July 28, 1913. This decision was reversed by the Ninth Court of Appeals in San Francisco on May 4, 1914. Then the U. S. Supreme Court, on Dec. 11, 1916, upheld the patent on three counts only but restricted it to &apos;the use of less than one percent of oil.” The Miami Copper Co. was sued by Minerals Separation on Oct. 10, 1914, for infringement of Patents 835,120 and 962,678, and 1,099,699. The Miami Copper Co. was operating under John M. Callow&apos;s froth flotation process Patent 1,104,755/~uly 23, 1914. Miami lost this suit in the District Court of Wilmington, Del., and appealed to the Court of Appeals, Third Circuit, Philadelphia. The Third Court of Appeals decided against Miami, May 24, 1917. The case was referred to a Master and hearings to determine profit and damages were not settled until 1923. Nevada Consolidated Copper Co. was sued Sept. 9, 1919, and Magma Copper Co. was sued Jan. 10, 1920. Thus, the first ten years of froth flotation in the U. S. were beset by patent litigation. This litigation suppressed the free circulation of new discoveries or useful information that might be cited in a patent suit against the originator; it accounts for many of the blank spaces in the historical record. T. A. Rickard3 has reviewed the history of flotation and has given the chain of discoveries, patents, and processes that resulted in froth flotation. He has re- ported also on the patent litigation beginning in 1911 and ending in November 1923, when Minerals Separation&apos;s Patent 835,120 expired. He comments on

Jan 1, 1962

Jan 1, 1885

By C. W. EICHRODT

NUMEROUS requests for the suspension of publicity make difficult the preparation of the annual review of copper metallurgy for 1934. In the United States, sales allocations indirectly have set restrictions on the scope of activities of producers and refiners, and necessitated closer cooperation between secondary and primary producers. However, the feeling exists that preparations for a return of intense competition should not he neglected, and careful investigations are being conducted for ways and means of improving industrial positions and production methods. In all probability, efficiency in technique and equipment will prove of far greater importance in the near future than production capacity, and many important developments in copper metallurgy later will be found to have been born during the current year.

Jan 1, 1935

By Moshe Sheinkin, Douglas E. Julin

Large tonnage operations face many problems in adequately planning ahead for future years production. In order to maintain desired levels of production, such problems as source of tonnage, man- power and equipment requirements, tailings disposal and water requirements must be anticipated. Of course, before any of these problems can be analyzed, daily tonnage requirements and its source must be determined. Looking ahead for one year or even two or three is usually not sufficient time to adequately prepare an area for production. Because of the sequence of mining and the multilevel nature of the 42,000 tpd Climax mine in Colorado long-range planning must be on a ten-year basis. By using a ten-year base, adequate time is allowed to gain access and prepare a new level for production. Usually eight years will be required for this phase of the initial mine preparation. Once production has been started on a level and access to the area is available, three years is usually sufficient to prepare a new block for production as long as it follows in the normal sequence of mining.

Jan 4, 1967