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By E. A. Gulbransen, A. Pebler

Pressure-composition isotherms have been determinedfor the systems ZrMo2 -H2 between 0" and 900°C at hydrogen pressures between 10-4 and 760 Torr. Tkese studies plus X-ray diffraction analyses of selected compositions show that these intermetallic compounds form a complete series of hydrogen solid solutions within this temperature and pressure range. The partial molar enthalpies and entropies of solution of hydrogen in the three intermetallic compounds were calculated. The solubility of hydrogen in these Laves phases can be related to their free electron concentration. ThE reaction of hydrogen with inter metallic compounds of zirconium with Laves phase-type structure has both theoretical and practical interest. The in-termetallic compounds have structures different from any of the pure metals. In addition the electron to atom ratio of the intermetallics varies appreciably. In the nuclear materials field, these materials are of interest since intermetallic compounds may exist as precipitates in commercial zirconium alloys with transition metals. From studies on the hydrogen reaction, one can establish the stability of the intermetallic compounds relative to the hydrides of the component metals. The intermetallic compounds may also be used as getters for hydrogen and as materials for hydrogen storage. This paper will present the results of equilibrium and structural investigations of the ZrCr2-H2, the ZrV2-H2, and the ZrMo2-H2 systems for the temperature range of 0" to 900°C and the pressure range of Torr to 1 atm. A complete thermochemical analysis will be made of the measurements. Some of the results have been referred to in a survey paper' covering the types of hydrogen behavior observed in zirconium alloys. LITERATURE ZrCr2 is the only intermetallic phase in the Zr-Cr system.' It exists in two allotropic modifications. Between 900" and 1000°C the hexagonal MgZa (C14) structure transforms into the cubic MgCu2 (C15) structure. Beck4 has previously shown that the intermetallic ZrCrz takes up hydrogen into solid solution up to a composition H/ZrCr2 = 1.14 at room temperature and 1 atm hydrogen. A ZrCr2 hydride was stated to have a fcc structure. The binary Zr-V system has been investigated by williams5 although Rostoker and Yamamoto 6 had given earlier a partial phase diagram. ZrV2 was the only intermediate phase found in the system. wallbaum7 reported earlier that the compound ZrV2 hp the MgZm (CJ4) type structure with a = 5.288A and c = 8.664A. This was not comfirmed by Elliot8 nor by Matthias, Compton, and corenzwit9 who reported that ZrV2 has a cubic MgCua LC15) type structure. The latter authors gave a = 7.429A. Also, several authors do not agree on the temperature of the peri-tectic horizontal. It appears that ZrV2 may exist in several modifications. A high capacity for occluding hydrogen was reported by Beck4 who found H/ZrV2 = 1.38 at room temperature and 1 atm of hydrogen. ZrMoz is the only intermetallic phase in the Zr-Mo system.10 ZrMoa is formed by a peritectic reaction of the melt with a molybdenum-rich solid solution. ZrMo2 has the C15-type structure with a = 7.59A. MATERIALS High-purity chromium, vanadium, and molybdenum were used together with grade 1 crystal bar zirconium to prepare the alloys. Table I lists the chemical analysis and the sources for the metals. Ten-gram alloy compacts were levitated and melted in an inert argon

Jan 1, 1968

By Paul B. Crawford, Melvin B. Burton

A procedure is given which describes how the gelatin model may be-used to study the effect of mobility ratio on areas swept before and after breakthrough in fluid injection programs. Differences in mobility ratio are achieved through the proper selection of electrolytes for the invading and displaced fluids. The progress of the front is followed visually and photographed or traced onto plates (it desirrd positions before and after breakthrough. Example applications to standard flooding pattrrrls, vertically and horizontally fractured reservoirs and the in-situ combustion recovery process ore presentrtl. INTRODUCTION In water flooding, gas cycling and other fluid injection programs, the sweep efficiencies and swept areas after breakthrough are known to depend on the mobility ratio. Previous investigators have described the application of the X-ray technique, stepwise use of the poten-tiometric model and numerical procedures for studying these problems.1,3,4,6 Others have described the application of the electrolytic and gelatin models for studying sweep efficiencies at a mobility ratio near one.2,5,7,8,9 It is a purpose of this paper to describe a procedure for using the gelatin model to study swept areas at mobility ratios other than one. PROCEDURE The technique developed for gelatin model studies is composed of four phases: the construction of the model, the selection and preparation of electrolytes, the running procedure, and the recording of the swept areas. Each phase is discussed independently in order that the over-all procedure will not be confused. Construction of the Model Since some of the advantages of the gelatin model are its economy, and speed, it is desirable to have as small a model as is possihle without creating error through the inability to follow visually the progress of the colored front. For this work, it was found that a distance of 4 to 6 cm between salt bridges is convenient to use. Since the size is relatively small, it follows that the gelatin layer must be thin. For this study, 1/8 in. was used as the gelatin thickness in each case. The model was constructed on a flat 1/2-in. plastic (Lucite) base with boundaries constructed from 1/8-in. plastic strips. The well pattern to be studied was outlined with the 1/8-in. plastic strips on the base with narrow apertures (- - 2 mm) in the boundary to represent the wells. Behind each well opening, a rectangular area of some 8 to 12 sq cm was outlined by additional plastic strips. The plastic strips were fastened to the base by any suitable non-conducting cement so that the boundary system was liquid tight. The electrodes were constructed from sheet copper in a fashion that would allow easy removal. In this work, it was found that by simply forming a large U-shaped clip from a strip of the copper that would slip over the boundary was satisfactory and easily removed. The electrodes should be as wide as one of the sides of the rectangular area behind the well opening. If a fractured pattern is studied, fractures inside the well pattern may be represented by strips of copper of the desired shape mounted in some easily removable fashion. The reason that apertures (or salt bridges) were used for wells instead of metallic electrodes is that the plating of the electroactive ion at the cathode and the introduction of an electroactive ion at the anode has a detrimental effect on the swept area outline if these operations \rere permitted to be carried on within the well pattern itself. The anode may be used within the well pattern

Jan 1, 1957

By E. I. Alessandrini, A. U. Seybolt

Selective oxidation (preferential oxidation of a single alloy component) can be an important oxidation mode in the case of alloys such as Si-Fe, Al-Fe, and so on, when heat-treating in atmospheres of low oxygen potential. It was the purpose of this work to identify the oxide films formed on iron containing 31/4 pct Si at low oxygen potentials, and to make some observations on the H2O/H2 ratios required to form them. EXPERIMENTAL METHOD HYDROGEN of varying water content offers a very convenient method of establishing a wide range of oxidizing power, or oxygen potential. The method chosen to provide a desired H2O/H2 ratio was to nearly saturate hydrogen at room temperature by bubbling the gas through water at room temperature, and then to wring out the excess water by passing the wet gas through a long glass spiral immersed in a refrigerated liquid at a desired dew point. After oxidation, the samples were examined by electron diffraction in order to identify any film which might be present. PREPARATION AND TREATMENT OF SAMPLES The samples were prepared from a Si-Fe alloy made in the laboratory using electrolytic iron and 96 pct ferro-silico11, vacuum-induction melted, hot-rolled then cold-rolled to 0.015-in. thickness. After the cold-rolling the samples were annealed at 1000°C. Transmission Laue X-ray patterns showed very little evidence of preferred orientation, but it is likely that a weak texture could have escaped notice. The chemical analysis was as follows: 3.34 Si, 0.01 Al, 0.001 0, 0.006 C, 0.002 N. Before each sample was oxidized, it was polished through 4/0 emery paper, cleaned and dried using benzene, carbon tetrachloride, acetone, absolute alcohol, and ether. The method of oxidizing the samples was as follows: Samples about 1/2 by 1 by 0.015 in. were held in the upper, cool part of a vertical vacuum furnace until the desired temperature was established in the furnace, Fig. 1. The sample was then lowered into the uniform hot zone where it was heated quickly to the desired temperature, and subjected to hydrogen of controlled moisture content (dew point) as mentioned previously. Temperatures from 400" to 1000°C were used, and dew points from room temperature to —78°C were explored. In general, the runs lasted about 6 hr, but a few runs were of different duration, as will be indicated later. After the predetermined period of time had elapsed, the specimens were withdrawn by the hollow stainless steel-quartz holder to a cool zone at the top of the furnace. EXPERIMENTAL RESULTS The results are summarized in Table I. Most of the electron-diffraction patterns were obtained by glancing-angle reflection, but in a few cases it was possible to strip the oxide films from the surface by a total immersion in a 3 pct bromine-methanol solution. Some of the thinner stripped films yielded quite satisfactory transmission patterns. However, both diffraction techniques yielded the same results; the patterns while most frequently showing a (low) tridymite, also showed a (low) cristobalite in some cases. A few patterns showed evidence of both phases. Because of the known nonequilibrium behavior of silica, it is not surprising that both forms of silica could coexist on one sample. It was noted that at fairly low dew points such as —40°C, there was a tendency for diffuse diffraction rings, suggesting a very small crystallite size. Also some subsequent experiments to be reported later show that thin silica films can be amorphous.

Jan 1, 1959

By Wilfred Walker

With the advent of the New Global Tectonics a coherent pattern of geology is emerging. To the economic geologist this is of vital concern because the type of mineralization in particular environments is predictable. Developments in geological reasoning now take their place beside developments in geochemistry and geophysics. Much is known of the worldwide geography of the Alpine orogenic period because it is now ending its 200 million years of existence, starting with the Jurassic, and we can see the mid-ocean rises and the down flow zones, and between them the stable oceanic and continental platforms. The concepts of mantle cells, the spreading sea floor, and continental drift have gained general acceptance. The oceanographers have demonstrated the uprises like that in the mid-Atlantic. In this paper it is suggested that down flows in the oceans are marked by island arcs, like the West Indies; and down flows in the continents are marked by orogens like the American Cordillera. The number and position of mantle cells is controversial: a total of about 16 cells is suggested in this paper. Certain cells expand, and as they carry continents with them give rise to concepts of plate tectonics. Specific types of mineral deposits are associated with the uprises, oceanic and continental platforms, and down flows. The uprises are accompanied by the currently described Red Sea and Salton Sea deposits, the oceanic parts of the platform have the nodular deposits, and the continental platforms have the post-tectonic deposits. However, most economic metal deposits are associated with the down flow zones in which the stage of geosynclinal development controls the type of deposit: (1) In the initial development stage the simatic upper mantle may be tapped and give rise to the volcanogenic massive base metal sulfide deposits and to the ophiolite suite which characteristically carries nickel, chrome, and cupreous pyrite. (2) In the early geosynclinal stage sialic crust is driven down into the simatic magma of the upper mantle and basic to acidic differentiates give rise to stocks accompanied by skarn and hydrothermal deposits. (3) The intermediate stage of geosynclinal development gives rise to tin-tungsten, lithium, and beryllium deposits as the magma chamber rises above the level of the upper mantle and there is no simatic component. (4) The late stage is one of regenerated deposits. The porphyry deposits are not restricted to stages but only by the time of generation of acid magma. As the geosynclinal system dies, the mantle is again the source of magma, giving rise to gabbro and diabase dykes and sills: in this last, post-tectonic, continental platform environment are found the Mississippi Valley type lead-zinc deposits, the Blind River and Witwatersrand type of sedimentary uranium and gold deposits, and also Sudbury's nickel. The key relationship of major ore deposits generated by downflows is depicted herein on a framework of uprises, platforms, and downflows in the Alpine orogenic period. There is evidence for nine orogenic periods, of which the Alpine period is the latest, having taken place from 3500 million years ago to the present. Each period was characterized by its own worldwide mantle cell system and associated uprises, platforms, and down flows. The cycle of geosynclinal development, including corresponding cycles of mineralization, can be precisely defined in relation to each of these orogenic periods. The development of the Alpine orogenic period therefore can be used as a guide to the study of the earlier orogenic periods which comprise well known periods: Kenoran, Hudsonian, Grenville, and Paleozoic; and less well known: Konkian, Aulian, Belomorian, and Elsonian [(Table 1)]. Each name is used for the period as a whole, and not for the main orogenic event.

Jan 1, 1973

By E. S. Machlin, Morris Cohen

The isothermal formation of martensite in a 71 pct Fe, 29 pct Ni alloy is found to take place mainly by the nucleation of new plates rather than by the growth of existing ones, and is dependent on the temperature and time of the isothermal hold, the amount of atherrnal martensite present, the state of internal strain, and the application of tensile stress. The conclusion is reached that the isothermal nucleation is activated by thermal fluctuations superimposed on localized regions of very high strain. The reaction-path concept, involving martensite nucleation at strain embryos by athermal activation on cooling, or by thermal fluctuations on holding, reconciles the athermal and isothermal modes of transformation, and offers a unified picture of the kinetics of martensite formation. THE phenomenon of isothermal martensite formation has been the subject of considerable study lately,'-' and its reality has been thoroughly established. The existence of such isothermal transformation has been claimed to confirm the nucleation and growth hypothesis as applied to the martensitic reaction.1 " However, the isothermal formation of a martensitic phase is also compatible with the reaction-pathw escription of the transformation. The purpose of this investigation is to examine the isothermal mode of the martensitic reaction, both theoretically and experimentally, in order to test the likelihood of the above two mechanisms. Material and Methods The alloy used in this study contained about 71 pct Fe and 29 pct Ni. The complete analysis was 29.5 ± 0.2 pct Ni, 0.036 pct C, 0.02 pct N, 0.19 pct Mn, 0.09 pct Si, 0.008 pct P, and 0.006 pct S. The amount of isothermal transformation was determined by electrical resistance measurements using a Kelvin double bridge. The specimens were in the form of rods 1/16 in. diam x 4 in. long. Aus-tenitizing was performed at 1095°C for % hr either in a pre-purified nitrogen atmosphere or in an evacuated Vycor tube, followed by oil quenching to room temperature. After this treatment, the samples were completely austenitic, and the transformation studies were conducted at subatmospheric tempera- tures. Lineal analysis and X-ray determinations of retained austenite were used to calibrate the electrical resistance changes in terms of the percentage of martensite. The martensite range curve for this alloy is given in Fig. 9 of ref. 6. The M, temperature occurs at about -18°C (255°K). Reaction-Path Theory The nucleation and growth description of the martensitic transformation that occurs isothermally has already been given by Kurdjumow.','2 However, no comparable treatment exists using the reaction-path concept." Consequently this section presents the reaction-path description of the isothermal mode of the martensitic transformation. According to the latter theory, there is a reaction path (a strain) which describes the relative motion of the atoms during their transference from the austenitic to the martensitic state. The possibility exists, therefore, that the nucleation of a martensitic plate is accomplished by an embryo that comprises a state intermediate between that of austenite and martensite. This state may be attained within a finite volume by means of a homogeneous strain of the austenitic matrix. There is a free-energy barrier (F.) along the reaction path, corresponding to a critical strain in a critical volume. When activation is achieved, a spontaneous increase in strain and volume of the embryo takes place to generate the full-size martensitic plate. This mode of nucleation is to be distinguished from the more conventional mode involving embryos of the martensitic phase that merely grow in size by an interface motion. There are two ways whereby embryos in the austenitic phase can achieve the critical state of strain for isothermal nucleation: 1—through the formation of internal strains by plastic deformation or by stress; and 2—through thermal fluctuations, preferably superimposed upon existing internal strains. The activation free energy F,, must be supplied either mechanically by internal strains or thermally by energy fluctuations, or by a combination of both.

Jan 1, 1953

By Kenneth E. Gray

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton's equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?' lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.' It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By Christian F. Baiz

INTRODUCTION Industrial minerals can have similar financing requirements to those needs of metaliferrous and coal mining projects. One of the outstanding differences is the understanding of the many different markets that these industrial minerals represent. There are in excess of 30 principal industrial minerals ranging in terms of annual production from the largest quantity such as sand and gravel, to possibly the smallest quantity of production of a legitimate industrial mineral which may be defined as industrial and rough gem diamond. (See Tables 1 and 2) Project finance techniques, analytical methods, and information requirements are covered elsewhere in this Chapter and Chapter 10. Some comments on equity finance aspects follow. EQUITY AMOUNT The amount of equity in a financing transaction provides a cushion to the lender in case the project runs into trouble. Generally speaking, the greater the amount of risk in a project, the more equity a lender will require. The amount of cash equity in a project financing transaction is between 25 and 40 percent. The amount of leverage (debt/equity) is negotiable based on such factors as the strength and extent of the sponsor's undertakings, of the project's economics, and the term of a strong sales contract. Naturally, a borrower seeks to obtain d loan with as little equity required as can be negotiated. Zero percent equity is usually associated with a take-or-pay contract (a hell-or-high- water unconditional commitment under which the purchaser must pay for the commodity as though it were shipped regardless of whether it is actually mined or shipped) with a financially strong corporate entity i.e., the parent company or an end user. As a take-or-pay contract is tantamount to a guarantee of payment, the banker views the credit basis of the loan as being other than the borrower's mining operation and therefore will analyze the creditworthiness of the institution purchasing the commodity on the basis of its corporate balance sheet. Do not confuse a take-or-pay contract with a take-if- tendered or take-and-pay contract. Another means in the United States of obtaining zero percent equity is the carved out production payment financing, typical of coal mine financing. This involves the sale, or conveyance, by the owner of the mineral property of a production payment to a nominally capitalized company. The nominally capitalized company is formed solely to buy the production payment and usually borrows 100 percent of the purchase price from a lender. Equity amounts of 10 to 20 percent generally are found in transactions which employ techniques such as an advance sale or a subordinated lease/loan. These agreements are viewed as quasi equity by most banks for several reasons. First, the proceeds represent a cash infusion early in the project's life - usually prior to the bank lending any funds. Thus, the repayment schedule is "behind" that of the bank debt. In the case of an advance sale, repayment is in the form of a long-term supply contract with favorable terms, usually priced close to the mining operation's costs. There is also usually a requirement that all costs of the project be paid for by the loan or equity, often making the sponsors financially responsible for any cost overruns. Cost overruns are a major risk in any project, large or small, and are often due to unforeseen factors such as wildcat strikes, a piece of faulty equipment, or any event which delays completion, e.g., remote location, weather, etc.. . The question of how overruns are covered can be negotiated. For example, in addition to the original debt/equity ratio of the project, there can also be a cost overrun ratio that will

Jan 1, 1985

By J. S. Brown, A. G. Guy

With the exception of the work of Tammann and Hartmann,1 no published information has been found on the structural changes produced in eutectic structures as the result of heating following plastic deformation. In part this lack of information may be due to the fact that many eutectic structures contain an intermetallic compound as a prominent phase, and as a consequence have been considered to be unworkable. For example, Tammann and Hartmann were able to obtain useful data only on those alloys that they could greatly reduce in thickness by cold rolling. This restriction placed on the investigation of alloys containing intermetallic compounds has been largely removed by the work of Savitskii2 which showed that large deformations of such alloys can be produced by relatively slow compression at temperatures near the melting range. It was possible, therefore, to carry out the present work on a range of binary eutectics including one composed of two intermetallic compounds. The essential results obtained on the alloy systems studied are illustrated by the Pb-Mg eutectic containing 33.2 pct Mg, Fig 1. The cast structure, Fig la, was obtained by melting together magnesium of 99.8 pct purity and chemically pure test lead, casting into a heated, small steel mold, and furnace cooling in the mold from about the eutectic temperature. The fairly coarse eutectic structure thus obtained was too brittle to work at room temperature without cracking. Fig 16 shows the worked structure obtained by compressing a 1/2-in. cube 70 pct in about 15 sec at 550°F and then water quenching. The pronounced changes in the distribution of the two phases produced by heating the worked alloy at 850°F for 1 hr are shown in Fig lc. Recrystallization of both phases appears to have taken place, and the mechanical properties of the cast alloy must have been significantly changed by the working and heat treatment. Similar results were obtained with the Mg-59.5 pet Bi, Mg-36.4 pet Sn, Mg-65.4 pet Cu, and Bi-40 pet Cd eutectics, only the last of which could be worked at room temperature. Tammann and Hartmann reported a thickening and shortening of the needles of the eutectics which they heated about 10°C below the melting range for 1 hr after drastic cold rolling. They found the following eutectics, given the indicated amounts of reduc- tion, to have a granular structure after heat treatment: Sn-9 pet Zn (98 pet); Cd-82.5 pet Pb (60 pet); and Bi-43.5 pet Pb (90 pet). On the other hand the alloy Al-11.7 pet Si (60 pet) showed no change after heating. Tammann and Hartmann observed a distinct shrinking of the needles in unworked eutectics subjected to heat-treatment. In the present work inappreciable change in the eutectic structure was found on heating undeformed alloys. In summary, it appears that eutectic structures can be recrystallized into a "spheroidized" condition by heating near the eutectic temperature after severe deformation. If the eutectic contains one or more brittle phases the necessary deformation can be accomplished by pressing at high temperatures. It is reasonable to expect that this tendency towards equiaxed grains from the plate- or needle-like eutectic structure should be general since the energy relations and mode of growth in recrystallization are so different from those that hold for eutectic crystallization. References 1. G. Tammann and H. Hartmann: Ztsch. Melallkunde (1937) 29, 141-144. 2. E. M. Savitskii: Doklady Akad. Nauk S.S.S.R. (1940) 62, 349-351. Abstr. in Melal Prog. (July, 1949) 56, 126, 128.

Jan 1, 1950

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By C. E. Birchenall, G. Derge

IN studying the kinetics of slag-metal reactions, it has become increasingly apparent that a complete knowledge of all aspects of interface phenomena will be required to clarify these processes adequately. A part of the data required for all oxidizing slags used in the refining of impure iron to steel is the rate of exchange of iron between the slag and metal phases. The simplest equilibrium of this type is that between liquid iron and iron silicate slag when both phases are equilibrated with the silica crucible containing them. In this study, the exchange of iron between the two liquid phases has been measured by using radioactive Fe as tracer. The observed high exchange rate indicates the ease with which such interfaces may be crossed in refining processes. The experiments required for this study involved relatively minor and normal modifications of well established techniques. Melting was accomplished by induction heating in heavy walled, fused silica, rotating crucibles." Rotation was used to minimize dilution of the slag by crucible erosion. The melting stock was ingot iron. Slags were prefused in iron crucibles using chemically pure grade oxide reagents. The special conditions applying to the active iron additions will be described for individual experiments. Suitable precautions were observed with regard to protection against radiation hazards.' Identification of Activity This particular study was initiated several years ago, but held in abeyance because the radioactive iron available at that time contained a foreign activity which concentrated in the slag so as to mask the iron activity and render the results unin-terpretable. With the benefit of experiences from other studies, radioiron of suitable purity can now be prepared. As received from the Isotope Div. of A.E.C., the unit appears to contain Fe + Fe50 and a high activity cobalt. The cobalt and iron are separated by repeated ether extractions, and the purified iron stored for sufficient time for the Fe'7 44 day half-life) to decay to negligible activity, leaving only Fe as the active isotope. This was confirmed by the absorption curves for slag and metal samples from heat No. 1. In Fig. 1 the experimentally measured points for the absorption curves of slag and metal are fitted by the calculated slope of 5.8 mg per sq cm in aluminum, which corresponds to the Mn K doublet emission resulting from the capture of an orbital electron of Fe" by the nucleus. This shows that the radioactive species are the same in both slag and metal and identifies it as Fe55 Description of Individual Heats For the first heat, the radioactive iron was contained in the prefused slag. The active Fe55 had been precipitated with carrier and was added as Fe2O3 during fusion in the iron crucible. The charge of 500 grams of ingot iron was melted, the protective iron sleeve added, rotation started, and a prefused, inactive slag was added to allow the system to approach equilibrium. After about 5 min at temperature, the wash slag was skimmed and the active slag added. Initial slag and metal samples were taken as soon as the slag was molten. Additional samples were taken at indicated intervals thereafter. Slag samples were dipped with a small iron spoon and metal samples were sucked into 1/4 in. ID silica tubes. The slag and metal samples were pulverized and mounted for radioactive counting. The slag samples were analyzed chemically for FeO. Temperature was read after the last slag sample by immersion of a Pt-Pt-Rh thermocouple protected by a fused silica sheath. Since no significant variation of rate with temperature was observed

Jan 1, 1954

By J. Chipman, J. B. Gero, T. B. Winkler

D. C. Hilty—This paper is a useful and timely addition to our store of quantitative data relating to manganese distribution between slag and metal in steel-making processes. For some time, many of us have suspected that the values of Kmn derived by Körber and Oelsen might be too low, and this paper now appears to confirm that suspicion. Application of the new constant to openhearth data should prove interesting. The manganese deoxidation curves of fig. 4 agree fairly well with direct measurements of isothermal solubilities of oxygen in liquid iron containing manganese that have recently been made at the Union Carbide and Carbon Research Labs., Inc. According to the solubility data just mentioned, however, the curves for 1550" and 1600°C lie much closer to each other than the authors have indicated. In other words, the solubility measurements suggest that the logarithm of the oxygen solubility is not a linear function of the reciprocal of the absolute temperature, as the authors have assumed for their calculations. It seems possible that this discrepancy may be due in part to the authors' use of the distribution coefficient, L,,, obtained from Taylor and Chipman's curve for the solubility of oxygen in iron as shown in fig. 2. Taylor and Chipman gave the equation of this curve as —6320 Log % 0 - ---T + 2.734 Their data, however, can be fitted equally well by a curve having the equation: 13.23 x104 1.18x10" Log % O = 36.350 -13.23x10 Moreover, this curve also fits the authors' oxygen distribution data somewhat better than does the linear curve of Taylor and Chipman. Its use in the derivation of Lo for calculation of the deoxidation curves by the authors' eq 15 causes the effect of temperature on the calculated curves of fig. 4 to agree quite well with the temperature effect that has been observed. An experimental determination of the temperature coefficient of the manganese reaction appears to be desirable. J. E. Stukel—Because the authors have done such an excellent job, my comments will be confined to additional information. Very shortly Professor T. L. Joseph and I will publish the results of a study of the reaction between molten manganese and silica. It was found that electrolytic manganese, melted in silica crucibles, reacted with the silica to form a silico-manganese alloy containing 18 pct silicon (1500°C) and a silica saturated MnO-SiO, slag. Therefore, the presence of silicon and its oxides in the Fe-Mn-0 system will affect the equilibrium. Carbon is also an important factor. The higher the carbon content of the iron the less ability manganese has to reduce silica. As a matter of interest, recently a study of the manganese equilibrium in carbon saturated iron and blast furnace slags was completed at Carnegie Institute of Technology. As a comparison to the present study, 2 to 5 hr were required to reach equilibrium and temperature was a much more important factor than slag composition in determining the (Mn)/(MnO) ratio. These results will also be published in the near future. It can be seen, therefore, that the results of this paper cannot be applied directly to openhearth studies without a degree of flexibility. J. Chipman (authors' reply)—With regard to the effect of silicon on the manganese constant, this effect is, of course, known. Much more data is needed in order to establish it accurately, and I hope we can look forward to having some accurate data on that. Mr. Hilty suggests that a three-term expression for the Taylor-Chipman solubility of oxygen in liquid iron might fit a little better than the two-term equation. I think that it would be too great a compliment to the precision of the data to employ a three-term equation, and I would still recommend the simple, two-term expression.

Jan 1, 1951

By P. M. Aziz, I. Markson, C. S. Barrett

The abnormal after-effect in twisted wires that occurs when untwisting is interrupted by etching con be brought under control and used to study the mechanical properties of thin surface films and how they are effected by reagents and heat treatment. Results are given of studies of oxide films on high purity aluminum. IF a wire is subjected to plastic deformation by torsion and then released, it untwists in the normal after-effect, but under certain circumstances the untwisting is abruptly lessened or reversed by the application of an etchant to the wire.1,2 This abnormal after-effect may occur, for example, if there is a coherent oxide film on the surface of the wire which is removed by the etchant. Following a suggestion of A. H. Cottrell that predicted this effect, it is attributed to dislocations that had piled up beneath the oxide layer and represents the rapid release of residual stresses caused by these dislocations. When the layer is removed, the stress relief may be by escape of piled-up dislocations from the metal, or by an activation of latent sources of dislocations located at the surface, together with rebalancing of elastic stresses to compensate for the loss of stressed material, as in a residual stress analysis determination, these mechanisms acting singly or in combination.' The slower the attack of the reagent, the more gradual is the stress relief and the smaller the change in strain rate when the reagent is applied. A study has been made of the factors that influence the magnitude of the normal and abnormal after-effects with the object of developing techniques suitable for a quantitative investigation of the influence of various surface films on dislocations in wires, and of the rate and extent of the attack on the films by different reagents. It was found that reasonable sensitivity and reproducibility could be achieved if a suitable choice of variables was made and if these variables were held constant through a series of experiments. The method was then applied to a study of oxide films produced and treated in different ways on the surface of high purity aluminum wires, and to a study of the damage to these films caused by various reagents. Experimental Procedure The material used throughout this work was prepared from 99.9968 pct Al. This high purity aluminum was melted, cast into 1/2 in. diameter ingots, and then swaged and drawn without intermediate annealing to 0.040 in. diameter wire. A sketch of the apparatus employed for twisting is shown in Fig. 1. The test wires were mounted into the apparatus by cementing one end of the wire to the beaker and the other to the tube with laboratory wax of high melting point. The length of the wire between the waxed joints was 4.2 & 0.2 cm. Extreme care was taken during mounting to avoid cold-working the wire. The wire was twisted through 335" in 2 to 4 sec by rotating the pinion on the gear box until the vertical post on the rotating table, which was initially touching the horizontal stop, was arrested by the stop. All the tests were conducted with apparatus and reagents at the same temperature (about 25°C). In all tests, except those where the duration of the initial torque was investigated, the torque was applied for a period of 2 min. At the end of this time the table was rotated back a few degrees away from contact with the stop and the wire allowed to untwist. The after-effects were measured by reflecting a beam of light from the mirror shown on the apparatus. After the wire had untwisted for 6 min, a reagent was carefully poured into the beaker and thereby applied to the surface of the wire.. In some tests the liquid in the beaker was removed after a few minutes and replaced by an-

Jan 1, 1954

By J. J. Taber, W. K. Meyer

Experiments on consolidated sandstones have shown that a variety of conditions are responsible for the wide range of behavior observed when oil and water are displaced simultaneously by a solvent which is miscible with both. The type of displacement is influenced most strongly by the relation between the plait point of the ternary phase diagram and the composition path followed by the system as it achieves mis-cibility. Neglecting viscosity, the displacement becomes less efficient as the distance between the composition path and plait point is increased in either direction so that a very wide spectrum of displacements is possible with different alcohol, oil and brine systems. It is possible by choosing various composition paths as miscibility is achieved to exercise some control over the actual displacement mechanism. Control over the composition path is exercised by adding oil or water in specific amounts to the alcohol prior to its injection into the porous medium. This technique apparently makes it possible to obtain piston-like displacements with systems which are usually characterized by the efficient displacement of only one of the two phases i.e., either oil or water, while the other phase lags behind. However, the simultaneous displacement of oil and water is not as efficient as other miscible displacements at a similar mobility ratio. The evidence indicates that both oil and water "leak" into the alcohol "piston" in compensating amounts. With oils of low viscosities the displacement is inefficient because the low oil saturation in the stabilized bank causes oil to be trapped by water before miscibility is attained. INTRODUCTION The simultaneous displacement of oil and water by solvents such as alcohol has been investigated in the laboratory and in the field. The laboratorv workers investigating all-liquid miscible systems have recognized the great importance that the nature of the traingular phase diagram exerts on the efficiency of the miscible displacement. Gatlin and Slobod pointed out that displacement efficiency will be improved if miscibility can be retained for long periods and that this behavior tends to be followed if the applicable phase diagrams have very low binodal curves. In their unconsolidated sand tests the alcohol was considered an ideal miscible piston displacing both oil and water phases. Later workers have pointed out that an important feature of the phase diagram as far as oil recovery is concerned is the location of the plait point. This is particularly true in the case of consolidated Sandstone.3 Since the original discussion of this effect, the importance of plait-point location has been confirmed and discussed by other author The early workers394 recognized that the position of the plait point could be altered by changing the oil or the alcohol used in an experiment. In addition, recent work has demonstrated that the plait point can be shifted by altering the nature and concentration of dissolved salts in the aqueous phase. However, the entire scope of the relationship between displacement and plait point has not been discussed previously and a technique for changing the composition path as miscibility is achieved in a particular ternary system, i.e., oil, water and solvent, has not been demonstrated. * The importance of oil viscosity on the efficiency of oil displacement by alcohol has not previously been observed, probably because the range of viscosities used in earlier experiments was too restricted. It is the object of this paper to describe the relationships between the ternary phase diagram, fluid properties and the displacement achieved. A technique for controlling the nature of the displacement is also presented. THEORY AND DEFINITIONS PISTON-LIKE THEORY The theory of alcohol flooding has been discussed in some detail.2-4 The concept was advanced that

Jan 1, 1965

By B. A. Kulp, R. R. Reeber

Lattice parameters for the wurtzite form of' CdS mere measured by powder X-ray diffraction techniques over the temperature range 26° to 1000 K'. A negative thermal -expansion coefficient was determined parallel and perpendicular to the c axis below 13.5°K. Near 808°K, the curves of the a, parameter, the differential thermal expansion, and the resistivitv vs absolute temperature exhibited a reversible discontinuity. j\. direct determination of the lattice parameters of CdS over an extended temperature range is of particular use in interpretation of the effects of high pressure on the band structure of semiconductor materials. For example, Langer' has studied the effects of pressure on the absorption edge of CdS from 77°K to room temperature. In order to properly interpret his results it is necessary to know the change in lattice constants as a function of temperature for the wurtzite, zincblende, and rocksalt2 modifications of this material. Thermal-expansion measurements for CdS, wurtzite phase, have previously been determined over a limited temperature range.s74'5 The zincblende phases, of other compounds with similar bonding, have been investigated by Novikova et a! .'' Previous thermal-expansion measurements for metals with hexagonal symmetry have for the most part used bulk sample techniques for low-temperature result. Most X-ray measurements at low temperature have been on materials with cubic symmetry.'jQ The use of X-ray powder-diffraction techniques offers a convenient and accurate method of measurement over a wide temperature range. The X-ray method, besides measuring unit cell size, also provides information about change in structure type and the nature of some of the stacking defects present. I) EXPERIMENTAL PROCEDURE The thermal expansion was measured by X-ray powder-diffraction techniques. Lattice parameters for the range 300" to 1000°K were determined in a 19-cm Unicam camera. From 26" to 300°K a 34-cm back-reflection camera with the Van Arkel" film arrangement was used. The sample was bonded to a copper cold finger below a helium, hydrogen, nitrogen, oxygen, dry ice, or ice brine bath in a metal cryistat. che inner bath was surrounded by another one for radiation shielding. Nitrogen was used in this outer bath for the very low-temperature runs while dry ice and acetone was used for the 195°K point. CuKa X-rays, filtered with a nickel foil, entered the cryostat through a 0.001-in.-thick aluminum window. During a typical 9-hr exposure the sample was continuously rotated through a 30-deg arc. Heat losses from the sample holder limited the minimum temperature attained to 26°K with helium in the inner dewar. Temperature calibration between 25" and 125°K was determined with an Allen Bradley 300-ohm carbon resistor. The resistor was attached to the back of the copper finger with a thin layer of silicone grease. Liquid He, HZ, N2, and O2 baths were used to calibrate the resistor. Temperature variation is estimated to be *2"K with a slightly higher uncertainty at room temperature and 264°K. The thermal expansion of high-purity germanium from 373" to 900°K was measured as a calibration for the Unicam camera. This value was compared with the known value1' for the thermal expansion. A discontinuity in the thermal-expansion coefficient of the CdS a, parameter was observed. Similar discontinuities in the resistivity and differential thermal analysis at the same absolute temperature indicate that the temperature error is *5°K in the temperature range above 500°K. Temperature errors in the Unicam camera below 500°K are appreciably higher due to large gradients in the resistance furnace. II) SAMPLE PREPARATION The CdS was Eagle Picher ultrapure grade. The crystallite size range of the as-received powder

Jan 1, 1965

By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By A. W. Schlechten, C. M. Hsiao

The apparent vapor pressures of a number of metal sulphides were determined by measuring their rate of weight loss when they were heated under vacuum. The calculated pressures are due in some instances to the volatility of the sulphide and in others to the decomposition pressure. FIE direct reduction of metallic sulphides, as in the precipitation method for lead or antimony, is not a widely used process today. However, it might be employed for the production of a number of metals if the operation were carried out under reduced pressures. Two general procedures are possible; the reducing agent could form a stable nonvolatile sulphide from which the valuable metal could be removed by volatilization or liquation. The other approach would be to choose a reducing agent which would form a sulphide that could be volatilized away from the valuable metal. A vacuum operation would serve to protect the sulphides and metals from oxidation and would increase the evaporation rates. A related process is the separation of metallic sulphides by selective volatilization either at atmospheric pressure or under vacuum. This procedure is already used commercially for the elimination of lead and cadmium as PbS and CdS from zinc calcines; it might well have other applications. To predict such processes it is necessary to know the relative volatilities of the metallic sulphides and to know whether they volatilize as sulphides or whether the predominant weight loss is due to decomposition. Such data would also be of value in studying problems such as the use of sulphides for refractories, as described by Brewer,] or in the evaluation of the theory of ore deposition from the vapor state, as proposed by Brown.' Qualitative statements concerning the volatility of metallic sulphides can be found frequently in the literature and are well summarized by Mellor, but accurate determinations of rates of evaporation or vapor pressures are very scarce. Kelly" lists vapor pressure data only for PbS; his reference being to the work of Schenck and Albers,4 who measured the vapor pressure of PbS by a dynamic method between 850" and 995°C. More recently Veselovskii5 has determined the vapor pressures of the sulphides of antimony, lead, cadmium, and zinc at temperatures ranging from 360" to 1000°C using Knudsen's method. A second Russian worker, Pogorelyi,6 determined the vapor pressures of CdS and ZnS at temperatures from 900" to 1250°C. The results obtained by these workers are shown in subsequent graphs in comparison with the data of this paper. Brewer and coworkers1 have studied some of the metallic sulphides to determine their suitability as refractories in vacuum. Veselovskii's determinations on PbS checked well with those of Schenck and Albers, and his determinations of CdS check almost exactly with Pogo-relyi. For the vapor pressure of ZnS the data of Veselovskii and that of Pogorelyi are in fair agreement, as shown in Fig. 1, but it should be pointed out that Lumsden7 has discovered that the equation given by Veselovskii for the vapor pressure of ZnS: - 14,200 log P9.495 is in error by a factor of ten when compared to the experimental data. In contrast with the scarcity of data on vapor pressures, the decomposition pressures of many metal sulphides have been determined and are summarized by Smithells.8 Theoretical Considerations The experiments described in this paper consisted of determinations of the rate of weight loss of certain metallic sulphides under very low pressures at different temperatures. These data plus observation and analyses of the products reveal the mechanism of the weight loss and also provide a basis for the calculation of the vapor pressure or apparent vapor pressures of the sulphides.

Jan 1, 1953

By G. W. Doepel, W. P. Sibley

A three-dimensional, multilayer, mathematical model has been developed for predicting performance by mis-c.ible displacement. Areal and vertical coverage, total gas-oil ratio, propane-oil ratio and oil-recovery factor for the multilayer system are computed as functions of hydrocarbon pore volumes of solvent injected. The technique has been programed for use on the IBM-7090 digital computer and was used in calculating perfortnance for continuous miscible displacement of a five-spot, 50-layer .system. Results reported are based on the use of published laboratory data for a single, uniform five-spot layer. However, the technique is sufficiently generalized to calculate performance of any system of layers of any pattern configuration and mobility ratio, provided data are available to describe perfortilance of a single layer. The technique has also been adapted for predicting oil recovery resulting from various gas-driven slug sizes. The results presented for both continuous and slug-type injection show, that permeability variation has 0 significant effect on oil recovery but that solvent composition, within the range studied, has a lesser effect on oil recovery. INTRODUCTION Experience from many of the miscible-phase displacement projects currently in operation indicates that the injected solvent flows preferentially through the more permeable zones in the reservoir. This preferential solvent flow in the high-permeability streaks results in a reduction of vertical coverage (C,) and an attendant decrease in oil recovery. The multilayer technique presented in this paper uses areal coverage (C.,) data for a single layer from the literature and from laboratory measurements of displacement efficiency (herein referred to as microscopic coverage, C,,) to calculate areal coverage (C,) and vertical coverage (C,) for the multilayer system. Oil recovery for the multilayer system is obtained as the product of (Ca) (Cm) (Cv). It is assumed that C, in a single layer is 100 per cent; therefore, (C,) (Cm) is a measure of oil recovery from that layer. Data presented in the literature for a single layer generally deal only with areal coverage and/or microscopic coverage —but seldom specifically with oil recovery. Nevertheless, this technique is flexible in that either Ca and C,, of an individual layer or a direct measurement of oil recovery for the layer may be used. In developing this technique, the problem arose concerning a method of determining the relative amounts of solvent that will enter each layer during any increment of solvent injected. To solve the problem, a dimensionless equation was derived for expressing solvent injected into each layer as a fraction of total injection. A finite-difference method was applied in integrating the equation to determine oil recovery for the system of layers as a function of pore volumes injected. The technique subsequently was programed for solution on a digital computer. The method was applied to predict performance of a deep California reservoir under continuous miscible displacement and has been extended for calculating oil recovery as a function of slug size for gas-driven slug injection. The technique may be applied to any petroleum reservoir that can be adequately represented as a layered system, by considering permeability variation,1-3 permeability range and average permeability. Each layer is then assigned its appropriate permeability, porosity and hydrocarbon saturation. RESERVOIR VOLUME CONTACTED BY SOLVENT It has been recognized for some time that high microscopic coverage (C,) can be obtained by injecting a miscible agent, such as propane, into an oil reservoir. These high values of C,,, have been demonstrated in the laboratory and are normally between 80 and 100 per cent, depending on solvent and reservoir oil composition as well as on reservoir temperature and pressure. In miscible-phase displacement, because there is no interface between solvent and oil, effective permeability to solvent is the same as that to oil. (This assumes that oil saturation has not changed and that water is immobile.) Consequently, mobility ratio (M) simply reduces to that of viscosity ratio . Perrine4 and Habermann5 have shown that large

By Herman Dykstra, Irving Fatt

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 A. G. Metcalfe, A. Siede

The hardening of annealed copper during fatigue testing appears to be independent of the applied stress and to occur largely within the first 4000 cycles. Copper hardened by fatigue is more resistant to annealing than copper hardened by static means, and softens by a multistage process. Creep studies at 300°C show that copper hardened by fatigue also has greater resistance to creep than statically hardened copper. Some theoretical explanations are discussed. RECENT interest in the behavior of metals subjected to fatigue stems from observations of phenomena which could not be explained by current theories of the structure of metals. In 1953 Bullen et al.l showed that the hardening caused by fatigue at low stresses did not cause severe bending of the lattice as did hardening by static methods. This was later confirmed by Wood, 'and Broom and Ham.3 Clarebrough et al4 showed that as the stress level used in fatigue hardening was increased, bending of the lattice was introduced, eventually approaching that of metals deformed by conventional cold-working methods. The type of hardening introduced by fatigue has other interesting characteristics. Kemsley5 showed that copper fractured by fatigue at low stresses resisted annealing as compared to copper hardened an equal amount by static means. The work of Clarebrough etal, shows that the manner of energy release during annealing differs for fatigue-hardened and statically hardened metal in both magnitude and temperature range of release. In addition to hardening of the lattice, fatigue has been shown to cause softening in materials previously hardened by static methods,5 and also in age-hardened alloys.7 The superposition of a small fatigue stress on the static loading of high-temperature alloys has been shown to increase their resistance to creep.' The present work was an attempt to determine the relationship between fatigue hardening, resistance to annealing, and the creep properties of pure copper. EXPERIMENTAL PROGRAM The program described here was designed to answer three questions: 1) Can stress-cycle combinations well below the failure values give significant increases in hardness? 2) Does hardening, under different stress-cycle combinations, give increase resistance to annealing? And if so— 3) Does superior resistance to annealing confer superior creep properties over statically hardened material? Three-quarter hard OFHC copper was annealed in vacuo at 550°C for 1 hr to produce a strain-free material having a fine grain size and uniform hardness. (The standard deviation of the mean hardness of the annealed samples was less than + 1.9 Dpn). Annealing was performed after machining the fatigue specimens so as to avoid work-hardened surfaces. Jigs were used to avoid distortion. The fatigue properties of the annealed copper were determined using an accurately aligned Baldwin-Sonntag SF1-U machine operating at 1800 cycles per min. This limited the minimum number of cycles which could be examined to about 4000 stress reversals. Since failure resulted in specimen damage, hardness increase with number of cycles was measured by testing specimens fatigued to different fractions of the failure values. The results are shown in Fig. 1, and are superimposed on the S-N curve of the copper in Fig. 2. The resistance to annealing of fatigue-hardened material was compared to that of material hardened by uniaxial tensile straining. Specimens hardened to equal values by both methods were progressively annealed for 1 hr at temperature in vacuo. After each annealing treatment the hardness was measured using a Leitz Durimet hardness tester with a 500-g load. At least five tests were made for each hardness determination. The standard deviation for individual specimens varied from 0.26 to 1.48 hardness points. The results are shown in Figs. 3 to 5. The discontinuous nature of the annealing process has been brought out by drawing idealized curves through the data points. This can be justified by the consistency of the results as well as by general agreement with results of Kemsley.5 The creep resistance of fatigue-hardened and

Jan 1, 1960

By Harvey T. Kennedy, Erasmo T. Guerrero

In this investigation, the effects of the surface tension of brine and the interfacial tension between oil and brine on the recovery of oil by water flooding of Woodbine sand were studied. Variation of the surface forces was obtained by the addition of small amounts of commercially available chemicals, which did not appreciably change the surface tension of the oil. Fourteen surface-active agents, which were found to be effective in lowering the surface and interfacial tensions, were further investigated to determine the extent of their adsorption by the Woodbine Sand cores. It was found that adsorption was sufficient in all cases to prevent any substantial concentration of chemical at the flood front. The flow system was, therefore, brought to equilibrium with definite concentrations in the flood water by circulation before each test. The data thus have no relation to the results obtainable by using the chemicals in full-scale water floods, but should be helpful in predicting the performance of surface-active chemicals which are not lost by adsorption, if such can be found. Flow tests were made on various concentrations 01 six chemicals selected from the 14 investigated for surface activity and adsorption, with and without the presence of gas in the core. It was found that lowering the interfacial tension had a tendency toward reducing the recovery of oil and that the reduction of the surface tension of the brine had little or no effect. A substantial beneficial effect, however, resulted from the presence of gas in the cores. INTRODUCTION The movement and distribution of crude oil in a porous medium are governed by such factors as surfacc and interfacial tensions, viscosity of the oil, pore size configuration, and wetting characteristics of the medium. The knowledge of the part played by each of these factors is limited. If the oil is assumed to be distributed in droplets whose movement is restricted only by the pore openings, the following equation may be applied: ?P= 2r(1/r1-1/r2) .......(1) In this equation ?P is the pressure drop necessary to force an oil droplet through the construction, r is the oil-brine interfacial tension, r1 is the radius of curvature at the forward and smaller end of the deformed droplet, and r2 is the larger radius. This equation neglects the effects of viscosity, as a static or near static condition is assumed. It would apply equally well for a bubble of gas in liquid if r were taken as the surface tension of the liquid. This relation shows that droplets can be more easily displaced if the interfacial tension is decreased. The displacement of oil from the surface of a sand particle may also be considered from the basis of selective wetting assuming that the oil droplets are smaller than the pore constructions and that the sand surfaces may be considered as planes. A relation of the forces involved can be derived from Dupre's equation to give: Wos = row (1 +Cos?)........(2) where Wos = Work of adhesion between the sand and the oil row = Oil-water interfacial tension 0 = Contact angle ros = Oil-solid interfacial tension This equation would indicate that the displacement of oil from a sand surface is more readily obtained when the water-oil interfacial tension is reduced provided the contact angle remains constant. Evidently. however, the values of Cos 0 may vary along with the water-oil interfacial tension due to changes in the other surfaces of the system. The above theoretical considerations suggest that perhaps even the static behavior of a dispersed oil phase in a porous medium is considerably more complex than may be inferred by the simple systems

Jan 1, 1955