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By J. P. Hammond, C. J. McHargue, S. E. Adair

Cold-rolled sheet textures have been determined for binary solid solutions of aluminum, columbium, tantalum, and zirconium in titanium. An alloy containing 3.8 pct Al had a (0002) [10101 texture, whereas alloys with the other elements had rotated (0002) [10101 textures similar to that of iodide titanium. THERE have been relatively few studies of the effect of alloying on deformation textures. A second element may be present in the base metal in solid solution and/or as a second phase. The literature offers no satisfactory explanation for the effects of solid solution alloying on textures noted thus far. For example, there is no satisfactory explanation of the difference in the textures of copper and a brass. The most complete study of the effects of solid solution alloying on deformation textures has been that of Brick, Martin, and Angier.¹ These investigators reported that the copper texture was retained by alloys of copper with up to 30 pct Ni, less than 5 pct Zn, less than 2 pct A1 or Co up to the limit of solubility. Copper containing more than 5 pct Zn, more than 2 pct Al, or the maximum soluble concentration of tin, silicon, or manganese showed the deformation texture of a brass. Bakarian² reported that additions of 0.20 pct Ca to 99.98 pct Mg or 2.0 pct Mn plus 0.15 pct Ca to magnesium resulted in entirely different textures than for the pure magnesium. The texture obtained for high-purity magnesium sheet showed the basal plane to be concentrated parallel to the rolling plane. The texture obtained for the alloy containing 0.20 pct Ca had the basal planes concentrated in elliptical areas whose centers were tilted 15" from the center of the pole figure toward the rolling direction. This split basal orientation was even more pronounced in the alloy containing 2.0 pct Mn and 0.15 pct Ca. Fuller and Edmunds" studied the rolled sheet textures in a zinc alloy containing 1 pct Cu and 0.01 pct Mn. The basal pole figure of this alloy contained a region of strong concentration not found in the pole figure for pure zinc.' In the above cases, results were discussed in terms of possible changes in slip and/or twinning systems and critical shear stresses. However, there were no experimental data to relate these speculations with the observed textures. It has been suggested that the deformation textures of titanium, zirconium, and beryllium could be directly ascribed to their low c/a ratios. The complex deformation mechanisms of titanium" also have been suggested to be characteristic of hexagonal close-packed metals with low c/a ratios. The purpose of this investigation was to study the cold-rolled sheet textures in binary titanium-base a alloys in which the c/a ratios were greater than, less than, and about the same as the c/a for iodide titanium. The annealed textures of these alloys will be reported in a subsequent article. Materials and Methods The chemical analyses of the metals used in this investigation are given in Table I. The alloys were prepared as 15 g buttons on a water-cooled copper block in a vacuum arc-furnace. The furnace was evacuated to pressures of the order of 10.' mm Hg, flushed with 99.98 pct pure argon, and melting was carried out in 0.2 atm pressure argon. Each button was remelted until radiographs and chemical analyses indicated complete solution of the solute elements. All buttons were forged and homogenized 72 hr at 500°C. The buttons to be rolled were ground and etched to sizes and shapes suitable for the rolling

Jan 1, 1954

By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

By E. S. Machlin, C. W. Chen

RECENTLY Chen and Machlin' proposed a mechanism for intercrystalline cracking in metals during high-temperature stressing. According to this mechanism the formation of voids at grain boundaries is primarily responsible for intercrystalline cracking. A model has been provided to demonstrate the initiation of submicroscopic cracks and voids at jogs of grain boundaries where grain boundary sliding is inhibited. Submicroscopic cracks can grow as a result of either further grain boundary sliding or localized tensile stress. In the former case, it is believed that grain boundary sliding produces more voids which link together to produce macroscopic cracks and which may lead to the eventual failure of the metal. Concurrently, Nield and Quarrell2 reported their interesting results obtained in a systematic investigation of intercrystalline cracking in two aluminum alloys under various creep conditions. Their observations are generally in agreement with the above mechanism, especially the conclusion that voids are formed as a direct consequence of grain boundary sliding. On the basis of the volume fraction occupied by voids, they could find no confirmation of vacancy condensation as the mechanism for void growth. Furthermore, an important feature of intercrystalline cracking has been likewise pointed out by them that the majority of cracks are not formed at grain corners. Nield and Quarrel1 meanwhile emphasized the importance of grain boundary migration by designating it as one of two main processes operative in the mechanism of crack formation during creep. The designation seems unnecessary because overemphasis of grain boundary migration only complicates the mechanism of void formation. There are two reasons which militate against the inclusion of grain boundary migration in the mechanism of void formation. In the first place, the formation of intercrystalline voids per se does not require grain boundary migration. Secondly, in addition to grain boundary migration, void formation may be minimized by any other process such as plastic deformation which is capable of relieving localized stresses around jogs. Chang and Grant3 have shown that intercrystalline cracking is prevented in aluminum by lattice bending in high stress regions. The influential role played by grain boundary migration in creep has also been realized in our studies. In several cases, voids did not appear at all in grain boundaries whenever grain boundary migration took place prominently during creep. The purpose of this paper is to discuss the effect of grain boundary migration on the formation of intercrystalline voids and other related rupture properties. Experimental evidence indicates that in an unstable grain structure void formation may be markedly modified by structural changes. The abnormally high ductility and the transcrystalline mode of fracture observed in copper at elevated temperatures reveals that effective grain boundary migration minimizes void formation. Grain boundary migration has long been known as a common high-temperature phenomenon in metals with the grain configuration in a nonequilibrium state. Its effect on ductility and mode of fracture has not been recognized until recently.4 Since the introduction of the term "Equicohesive Temperature," the conventional belief has been that below the equicohesive temperature the ductility of metals increases moderately with decreasing temperature until the ductile-to-brittle transition temperature of fracture is reached. In this temperature range, metals fracture in a ductile mode with a "cup-and-cone" fracture surface. Above the equicohesive temperature, ductility remains invariably low and decreases slightly with increasing temperature. The mode of fracture is strictly brittle and intercrystalline. Typical examples have been shown for a brass and copper in Fig. 1 and 9, respectively, in the paper by Greenwood, Miller, and Suiter.5 The observation in the upper temperature range that ductility of metals is low and insensitive to temperature may be explained in terms of void formation at grain boundaries. It is also in accordance with the findings of McLean6 and Fazen, Sherby, and Dorn7

Jan 1, 1961

By E. E. Thurlow

The Geology Div. of Northern Pacific Railway Co. has adapted to its exploration efforts field procedures for geochemical sampling and semi-quantitative analysis which have been developed through research by the U. S. Geological Survey. The sampling is done in conjunction with reconnaissance geologic mapping on aerial photographs or during field checking of maps which have been prepared largely by photo-geologic interpretation. Stream sediment or soil samples are taken and readily soluble combined heavy metals are extracted with ammonium citrate followed by colorimetric titration with dithizone at the sample site. The effectiveness of this approach has been demonstrated both in positive and negative results, thereby assisting in the elimination of large areas of land from further immediate attention and in providing targets for followup exploration. An occa sional sample is submitted for spectrographic analysis as a check on the possible presence of other elements of economic significance. Field laboratory procedures are also being implemented for determining molybdenum, mercury, and other metals which may be valuable in themselves or useful as pathfinder elements in outlining mineralized areas. A lead-zinc occurrence in Oregon and a copper deposit in Montana were readily detected and outlined by stream sediment and soil sampling and a heavy metal anomaly that lacks obvious interpretation has been found in northwestern Montana. Detailed mapping and additional sampling are followed by other exploration techniques if warranted. Northern Pacific's program of reconnaissance mineral evaluation of company-owned lands and adjoining areas was outlined in a paper presented at the American Mining Congress meeting in Las Vegas four years ago. That report included policies and procedures with respect to mineral development on Railway Co. lands and may be referred to for information on these matters.1 In a sense this paper is a progress report on the use of geochemical prospecting in Northern Pacific's continuing mineral evaluation program. At this time there are positive results but as yet there is no real success story in the form of a minable ore body. GEOCHEMICAL PROSPECTING PROCEDURES The decision to use geochemistry as a reconnaissance exploration tool must be followed by research into sampling and analytical methods and into the interpretation of results. Various analytical methods were tried and evaluated by the Geology Div., including hot and cold acid extraction with and without fusion of the sample, panning and magnetic separation followed by dithizone testing of the magnetite, and cold aqueous extraction of metallic ions followed by indicator tests. Samples were first sent to the laboratory for analysis; later field laboratories were established and now virtually all testing is done at the sample site. It was concluded that, where applicable, the quickest dependable methods for reconnaissance use are the dithizone field tests for readily extractable heavy metals. This involves the simultaneous treatment of a sample, usually of soil or stream sediment, with two immiscible liquids; one a cold aqueous extractant (ammonium citrate) and the other a solution of dithizone in toluene or xylene.2 Dithizone is a colorimetric indicator that reacts quantitatively with copper, lead, zinc, and several other metals to form colored complexes in organic solvents. Results may be expressed in ml of 0.001 pct dithizone that are required to reach the blue end point, or calibration of the test results can be carried out with standard solutions of zinc; conversion factors would then be expressed in ppm, zinc equivalent. Calibration of dithizone solution with zinc standards indicates that 1 ml of 0.001 pct dithizone is equivalent to approximately 0.25 ppm of zinc. An authoritative report on dithizone field tests authored by H. E. Hawkes in the June-July 1963 issue of Economic Geology* states "The appeal of these techniques has been the simplicity and speed of the determinations as compared with more tedious laboratory determinations of trace metals in weathered rocks, soils, or plant materials. This obvious appeal, however, has often been more than matched by misuse of the method in such a manner that the results are

Jan 1, 1964

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 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. E. Powers, J. F. Libsch

THE simultaneous influence of time and temperature upon the tempering process in steel is well known. Hollomon and Jaffe¹ have expressed the effect of time and temperature upon the progress of tempering by a single parameter, T (c + log t); where T is the absolute temperature; t, the tempering time; and c, a constant characteristic of the steel and treatment. It was found that when hardness data for plain carbon and low alloy steels were plotted vs. this parameter, a master tempering curve was obtained which satisfied all the data for a given steel and a given hardening treatment. Roberts, Grobe, and Moersch² successfully applied the tempering parameter to various tool steels, including high speed steel for tempering times ranging from 6 min to 100 hr. The influence of tempering time and temperature upon the physical properties of high speed steel has also been extensively investigated.&apos;" Recently, the use of induction heating for very rapid tempering treatments has received attention. The authors% have shown that tempering treatments of only a few seconds duration may be successfully applied to plain carbon and low alloy steel. However, the influence of such short tempering treatments in high speed steel has not been explored. Since high speed steel is a highly alloyed steel exhibiting physical reactions during tempering that are often relatively slow and large in magnitude, it is an interesting steel for the study of tempering reactions. It was the purpose of the present investigation, therefore, to study the early progress of reactions leading to secondary hardness in high speed steel, type 6-5-4-2, and to determine if induction-tempering treatments of a few seconds duration are able to produce results equal to those of more conventional long-time tempering cycles. Experimental Details The chemical compositions for two different heats of W-Mo high speed steel used in this study are given in Table I. Table II summarizes the heat treatment given various groups of specimens cut 21/2 in. long and centerless ground to ¼ in. diam. Hardening treatments consisted of preheating to 1600°F (870°C) for V2 hr and then oil quenching from 2250°F (1230°C). Heat I was subjected to the high temperature in a salt bath for 3 min, while specimens of heat II were austenitized in a carbon-block muffle furnace for 10 min. Specimens of series E were immediately refrigerated to — 318°F (— 195°C) in liquid nitrogen following the hardening treatment to transform the major portion of the retained aus-tenite. Specimens of series F and G were subzero cooled to — 100°F (-75°C) in a dry ice-alcohol mixture. Induction tempering was performed with a Lepel high frequency converter operating at a frequency of approximately 300,000 cycles per sec. Heating cycles were controlled and recorded for each specimen using a chromel-alumel thermocouple, percussion welded to the surface of the specimen, and a modified high speed instrument with a timer previously used and described.&apos; Temperature oscillation of the specimens, while being held at the tempering temperature, was ± 15°F (8°C). Tempering Treatments: After hardening, specimens were tempered between 900" and 1500°F (480" and 815°C) to study the progress of retained austenite decomposition and secondary hardening. The specimens tempered in salt for 1 hr (series C, G, and I) were considered to represent conventional treatment and are used for comparison with rapid tempering treatments. Several induction-tempering cycles were employed: 1—flash tempering, i.e., induction heating to the tempering temperature and immediately cooling (series A, E, and F); 2—induction heating for 60 sec at temperature (series B); and 3—double-induction tempering by two successive heating and cooling cycles (series D). All specimens tempered by induction were heated at an initial rate of 450°F (250°C) per sec except those of series E, which were heated at an initial rate of 1300 °F

Jan 1, 1952

By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data

By C. F. Baes, H. H. Kellogg

The effect of dissolved sulphur on the surface tension of liquid copper has been measured by a sessile-drop method at 1120°C. Sulphur is highly "surface active" in liquid copper; the surface tension lowering is about 650 dynes per cm for a sulphur content of 0.6 pct. The degree of adsorption of sulphur on the liquid copper surface has been calculated, and various models of the surface layer have been tested against the results. THE science and technology of surface chemistry and physics at room temperature are relatively advanced, and the engineer possesses a background of information that allows him to predict and control many phenomena—such as frothing, emulsifica-tion, wetting of solids by liquids, flow through capillaries, adsorption, mineral flotation, penetration of porous bodies by liquids—which are related to the behavior at interfaces. Surface phenomena in high temperature systems are probably of equal importance to the metallurgist and ceramist, but at present are incompletely understood. Frothing of liquid slags, penetration of refractories by liquid metals and slags, infiltration of powder metallurgy "skeletons" by liquid metals, bonding of metals to ceramic oxides in the manufacture of "cermets," wetting of one metal by another for purposes of soldering and welding, are but a few of the many phenomena of metallurgy that are controlled by surface behavior. Concerning the most elementary of surface properties—the gas-liquid surface tension—the existing data on liquid metals are inadequate. For the surface tension of "pure" metals the results of different investigators differ by 10 or 20 pct. The role of surface-active agents in liquid metals is relatively unknown, and it is not unlikely that the discrepancy in the values for the surface tension of pure metals is due to the presence of traces of surface-tension-lowering impurities in the samples. Based on analogy to room-temperature systems, the highly surface-active impurities in liquid metals should be elements or compounds of limited solubility in the liquid metal and possessing considerably weaker in-termolecular bonding forces than the metal itself. The nonmetals of the V, VI, and VII groups of the periodic table might be expected to act in this way. The experimental work in this paper represents a study of the surface tension of pure liquid copper in hydrogen at 1120°C, and the effect of dissolved sulphur (which is a strongly surface-active agent in liquid copper) on the surface tension of copper. The Gibbs equation has been applied to the results and an attempt made to correlate the surface tension behavior with two models of the interfacial layer. The sessile-drop method for surface-tension measurement at high temperatures which was used in this investigation has been described by several investigators.1,2 It involves the measurements of the dimensions of a stationary liquid drop on a horizontal surface. From these dimensions and the liquid density, the surface tension of the liquid may be calculated either by means of various approximate formulas, or more accurately by means of the Bash-forth and Adams tables.- or liquid drops which exhibit a contact angle greater than 90°, by far the simplest dimensions to measure are those indicated in Fig. 1, i.e., the diameter of the maximum horizontal cross section (2X) and the maximum height (Z) above this plane. In order to calculate the contact angle and the volume of the drop, the diameter at the base of the drop (2a) and the total height (h) also must be measured. Upon investigation of the literature, the authors failed to discover a concise statement of the accuracy of the method when used in conjunction with the Bashforth and Adams tables, hence a careful examination of the tables was made and the curve shown in Fig. 2 was constructed. The "error factor," plotted as the ordinate, is the factor by which the

Jan 1, 1954

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

By L. D. Jaffe

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

Jan 1, 1956

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas&apos;-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller&apos;s results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By L. M. Yokum

Tremendous strides have been made in front end loaders in the last 15 years. Fifteen years ago a 21/4-cu-yd front end loader was the largest standard machine you could purchase. Today there are two commercially available 15-yd front end loaders and many 10-yd loaders. The estimated total worldwide market for all front end loaders over 1 cu yd has increased to over 30,000 units yearly. The trend for front end loaders, in general, and for the mining market, in particular, is to larger and larger loaders. Today there are 18 and 24-cu-yd front end loaders in prototype form. It is not inconceivable that within another 15 years there will be front end loaders in the 50-cu-yd class with design features quite different from today&apos;s. These larger loaders are being designed at the demand of the mining industry, and the design criteria are being directed at this market area. The costs of these larger loaders may be greater per unit of capacity, but it is the intent of the various manufacturers that they will be more reliable, be easier to service, give greater availability, live longer, and cost less to maintain, than previous loaders. It is also the intent of the manufacturers to compete directly with the large mining shovel as the front end loaders become appropriately larger and more reliable. There has been some trend in this direction in the past with smaller shovels and loaders. In Table 1 are data for U.S. production of front end loaders (5 to 6-cu-yd class and 10-cu-yd class) and U.S. production of cable-operated, crawler-mounted power shovels, draglines, and cranes (11/z to 5-cu-yd class) for the years 1965 and 1970 (Source: Bureau of Census, U.S. Department of Commerce). Many believe that the decline in shovel production, in particular, is due at least in part to the acceptance of the front end loader as a primary production tool. However, the foregoing comparison is for a smaller shovel class than for front end loaders. It has generally been a rule of thumb that a front end loader is competitive on a cost and production basis with a shovel when it is approximately twice as large as the shovel. This same relationship may not hold true with the larger 10 to 15-cu-yd electric shovels, but at some point, direct competition will probably occur. Current Trends There are many trends today that are significant. One major usage trend in large front end loaders involves load and carry operations. This application is defined as "performing the functions of loading, hauling and dumping with one machine over distances within its economical limits." Many people are using front end loaders to transport material as well as load it. It is estimated that nearly half of all 10-cu-yd front end loaders sold in 1970 went into primary load and carry work. Many times, significant savings result from using the load and carry system, instead of small truck and shovel operations, for distances in excess of 1000 ft. Strip mining in coal utilizes great numbers of front end loaders in this manner. In-pit crushing of limestone is developing on an ever-increasing level, especially in Europe, and this stimulates interest in load and carry operations. In Table 2 is a cost example for 10-cu-yd front end loader in a limestone quarry. More than likely, load and carry use will continue to increase over the next few years. While some types of mining do not lend themselves to load and carry in the pit, such areas as surge piles are applicable and should be studied. In the area of machine operating cost reduction, there

Jan 1, 1974

By W. M. Reilly, Martin E. True, O&apos

A technique, equipment, and a compound have been developed and field tested for sealing tubing joint thread leaks without removing the tubing from the well. This eliminates the necessity of killing the well with possible damage to the producing formation, which could result if it were exposed to drilling mud. A thread sealing compound, developed and tested in the laboratory, is introduced into the tubing and squeezed into the joint to eliminate the leak. A high percentage of successful field applications have eflected an appreciable cost reduction in repairing leaking tubing strings in East Texas and in the Louisiana Gulf Coast area. INTRODUCTION In producing oil and gas wells the industry has been plagued with a never ending problem of tubing connection leakage. This situation is becoming increasingly more significant as more gas wells are placed on production and as higher pressures are encountered at greater depths of current drilling. Substantial progress has been made in minimizing thread leaks by careful handling and cleaning of joints and by the use of improved sealing compounds in combination with controlled makeup. But even with the use of the best known methods and sealing materials during initial makeup, occasional leaks through tubing joint threads appear inevitable. In some instances, tubing joints in high-pressure gas wells have been found to leak gas at relatively less pressure than that at which the tubing had been tested satisfactorily using liquid. Many expedients have been employed to prevent the physical replacement of tubing when leaks have developed. Perhaps the most commonly used is the sodium silicate treatment in which the solution is lubricated into the tubing to form a crystalline plug in the leak. Generally, any benefit realized is of a temporary nature. In addition to field studies on handling and makeup of tubing, extensive laboratory work has been undertaken on the development and testing of thread dopes.&apos; Also, substantial effort has been devoted to testing tubing joints using high-pressure gas as a pressure medium.&apos; The results of this work have emphasized that tubing joints are susceptible to occasional leaks, especially when subjected to relatively high differential pressures. To cope with the problem of leaking connections, an extensive investigation was undertaken to devise means of sealing leaks without removing the tubing from the well and without reducing the inside diameter of the tubing. The purpose of this paper is to present a technique, together with the associated equipment and compound, which have been developed for effecting a seal of leaking tubing in place. DISCUSSION Work was initiated simultaneously on two ventures: (1) to develop a satisfactory leak sealing compound and (2) to develop tools necessary to find the leak and place the compound. Leak Sealing Compound In the development of a sealing compound, tests were conducted on those compounds commercially available which include: (1) conventional thread lubricants, (2) thermo-setting resins and (3) other materials which held promise of effecting a seal. Although none proved completely satisfactory in their available form, two commercial compounds proved nearly equally effective in sealing leaks during laboratory tests after proportioned quantities of graded silica had been added. Field usage has indicated that the preferred compound is one prepared of an aluminum-stearate base thinned to the proper constituency and carrying a mixture of fine mesh graphite and graded silica. The compound developed by Humble Oil & Refining Co. is designated as Tubing Thread Leak Sealant 800. Placement Tools and Technique In developing tools to detect joint leaks and to place the sealing compound, work was done initially on wireline equipment. Preliminary designs were completed of a tool somewhat on the order of a pressure bomb to test individual joints with gas at high pressure to determine if the joint was leaking. An entirely different tool equipped with opposed packers was intended for placement of the sealing compound at high pressures in each leaking joint. The application of these tools

Jan 1, 1958

By W. D. Robertson

SINCE the comprehensive paper of Moore, Beckin-sale, and Mallinson,&apos; little consideration has been given to the mechanism of mercury stress cracking of copper-base alloys, apart from extensive work on metallurgical and fabrication variables employing mercurous nitrate as an evaluation test. However, with the phase diagrams now available and the recent considerations of interfacial tension at grain boundaries, developed by Smith,2 it appears that the elements of a detailed solution to the problem are available. The facts that require explanation are: 1—Pure copper is not embrittled by mercury, with or without an applied or residual stress. 2—Cu-Zn and other copper-base alloys, in excess of some undefined solute concentration, are embrittled provided an external or residual stress is acting; cracking is not observed in the absence of stress. 3—The path of fracture is invariably intergranu-lar. 4—Copper and copper-base alloys do not dissolve readily in mercury at room temperature.&apos; Consideration of the Cu-Hg phase diagram% hows that, at room temperature, solution of copper in mercury is probably limited by the formation on the surface of a microscopically thin layer of inter-metallic compound, CuHg, having a very limited range of solubility which effectively restricts diffusion of copper and mercury. But, above 150°C (the highest peritectic temperature) copper solid solution is in equilibrium with a liquid Hg-Cu solution and, consequently, copper should dissolve freely in a large volume of mercury with the formation of an equilibrium dihedral angle at grain boundaries in contact with the liquid phase. Depending on the magnitude of this angle, mercury will or will not penetrate the solid phase along grain boundaries and spread over grain faces. Thus the measurement of the dihedral angle of grain boundaries in equilibrium with the liquid phase above 150°C should indicate whether copper is intrinsically resistant to embrittlement by mercury. In view of the fact that mercury is appreciably soluble in copper, it may also be anticipated that diffusion of mercury will take place at higher temperatures in the absence of the intermetallic compound and possibly at a more rapid rate along grain boundaries than through the grains, resulting in a Cu-Hg alloy of unknown properties. In the case of brass, the ternary system Cu-Zn-Hg is involved and, from the resistance of brass to general solution in mercury at room temperature, it is probable that a compound of limited solubility range also exists, similar to the binary Cu-Hg sys- tem. Also, compared with copper, a change in the dihedral angle at grain boundaries in contact with mercury may be expected to result from the addition of zinc to copper. The preceding generalizations appear to be confirmed by the following experiments. Experimental Results Oxygen-free copper wire, annealed at 700°C for 3 hr in copper foil, was immersed in mercury at 170°C, with and without an applied stress. After 24 hr immersion, specimens which were spring loaded to a nominal stress of 10,000 psi had not failed, and there was no apparent embrittlement as indicated by a 180" bend around a diameter approximately equal to the diameter of the wire (0.125 in.) : General solution of the surface had taken place, indicated by a change in diameter of the wire, and the resulting structure of the surface is shown in Fig. 1. It is apparent that angles have developed at grain boundaries and examination at a high magnification indicates that the angle is in excess of 120°, completely excluding penetration of mercury. In view of the measurements made by Smith n the

Jan 1, 1952

By P. J. Root, J. E. Warren

An idealized model has been developed for the purpose of studying the characteristic behavior of a permeable medium which contains regions which contribute significantly to the pore volume of the system but contribute negligibly to the flow capacity; e.g., a naturally fractured or vugular reservoir. Unsteady-state flow in this model reservoir has been investigated analytically. The pressure build-up performance has been examined in some detail; and, a technique for analyzing the build-up data to evaluate the desired parameters has been suggested. The use of this approach in the interpretation of field data has been discussed. As a result of this study, the following general conclusions can be drawn: 1. Two parameters are sufficient to characterize the deviation of the behavior of a medium with "double porositym from that of a homogeneously porous medium. 2. These parameters can be evaluated by the proper analysis of pressure build-up data obtained from adequately designed tests. 3. Since the build-up curve associated with this type of porous system is similar to that obtained from a stratified reservoir, an unambiguous interpretation is not possible without additional information. 4. Differencing methods which utilize pressure data from the final stages of a build-up test should be used with extreme caution. INTRODUCTION In order to plan a sound exploitation program or a successful secondary-recovery project, sufficient reliable information concerning the nature of the reservoir-fluid system must be available. Since it is evident that an adequate description of the reservoir rock is necessary if this condition is to be fulfilled, the present investigation was undertaken for the purpose of improving the fluid-flow characterization, based on normally available data, of a particular porous medium. DISCUSSION OF THE PROBLEM For many years it was widely assumed that, for the purpose of making engineering studies, two param- eters were sufficient to describe the single-phase flow properties of a producing formation, i.e., the absolute permeability and the effective porosity. It later became evident that the concept of directional permeability was of more than academic interest; consequently, the degree of permeability anisotropy and the orientation of the principal axes of permeability were accepted as basic parameters governing reservoir performance. 1,2 More recently, 3-6 it was recognized that at least one additional parameter was required to depict the behavior of a porous system containing regions which contributed significantly to the pore volume but contributed negligibly to the flow capacity. Microscopically, these regions could be "dead-end" or "storage" pores or, macroscopi-cally, they could be discrete volumes of low-permeability matrix rock combined with natural fissures in a reservoir. It is obvious that some provision for the inclusion of all the indicated parameters, as well as their spatial variations, must be made if a truly useful, conceptual model of a reservoir is to be developed. A dichotomy of the internal voids of reservoir rocks has been suggested.7,8 These two classes of porosity can be described as follows: a. Primary porosity is intergranular and controlled by deposition and lithification. It is highly interconnected and usually can be correlated with permeability since it is largely dependent on the geometry, size distribution and spatial distribution of the grains. The void systems of sands, sandstones and oolitic limestones are typical of this type. b. Secondary porosity is foramenular and is controlled by fracturing, jointing and/or solution in circulating water although it may be modified by infilling as a result of precipitation. It is not highly interconnected and usually cannot be correlated with permeability. Solution channels or vugular voids developed during weathering or burial in sedimentary basins are indigenous to carbonate rocks such as limestones or dolomites. Joints or fissures which occur in massive, extensive formations composed of shale, siltstone, schist, limestone or dolomite are generally vertical, and they are ascribed to tensional failure during mechanical deformation (the permeability associated with this type of void system is often anisotropic). Shrinkage cracks are the result

By M. T. Simnad, C. E. Birchenall, M. H. Davies

THE marker movements observed by Davies, Simnad, and Birchenall during the growth of magnetite on wustite have been misinterpreted. It is the purpose of this note to correct the original interpretation. In that investigation wustite specimens were prepared by oxidizing pure iron disks in water vapor until the iron was consumed. Argon was used as a carrier gas for the water vapor and on the complete conversion of the metal to its oxides (&apos;FeO&apos; plus a small amount (10 pct) of surface Fe3O) the water supply was bypassed and the specimens were annealed in argon alone in order to equilibrate the wustite with the overlying magnetite. After cooling, the magnetite was ground off, a crude magnetic test being employed to determine its complete removal. Radioactive silver streaks were then applied to the surface and the specimen was oxidized completely in water vapor to prevent hematite formation. After complete oxidation the markers were found to enclose about 80 pct of the magnetite with the other 20 pct lying outside the markers. This observation was interpreted to mean that oxygen transport was four times as great as iron transport during the growth of the magnetite. The conclusion would have been correct if, as in the case of wustite growing on iron, all the iron had started from one side of the marker and all the oxygen from the other side initially. Actually a material balance is required. For simplicity, take wustite to be exactly FeO, and magnetite to be Fe3O,. Then at the start of the reaction 3 FeO + O -> Fe,O., All of the iron and three-fourths of the oxygen of the final product will be within the marker inter- faces. The other fourth of the oxygen is in the gas phase outside the marker. From the experimentally determined final position of the markers simple calculation shows that one-fifth of the total iron has crossed the marker interface, while one-twentieth of the total oxygen has crossed in the reverse direction. The simplified result favors iron transport in the ratio four to one. However wiistite is not stoichiometric FeO. At 900°C, the temperature of the measurement, the composition is about FeO When the material balance for the same experimental result is repeated, assuming the product will be 1 mol of Fe3O4, it is found that 0.6 gram atoms of iron and 0.19 gram atoms of oxygen must have passed the marker in the same direction. (This is readily apparent from the reaction to form 1 mol of Fe3O4 SFeO The total oxygen supplied from the atmosphere is 0.61 gram atoms, but the iron which passes the marker interface, i.e., 0.6 gram atoms, requires 0.8 gram atoms of oxygen to convert it to Fe,O,.) If all the transport during magnetite growth is due to iron ion diffusion, then the marker would enclose about 85 pct of the final magnetite and the original measurement is in error by about 5 pct. This error is probably less than the uncertainty in locating the markers by autoradiography. The possibility also exists that the starting wustite was not quite saturated with oxygen and underwent further enrichment with consequent envelopment of the marker before magnetite caught up with the marker interface. In any case it appears that these measurements actually favor iron ion diffusion in magnetite overwhelmingly as the factor controlling its growth, although further experimental measurements are needed to eliminate the error in material balance described. Such studies are planned.

Jan 1, 1954

By J. B. Agan, R. J. Fernandes

This paper utilizes the layered-system approach, modified to include areal sweep efficiency, to determine the miscible-slug size required and to predict the perfort7zance of a miscible-slug process in a highly stratified reservoir having a permeability variation of 0.76. The slug size in each layer was determined from theoretical calculations and laboratory data which showed that, to maintain miscibility in the reservoir, the slug size had to be 8.2 per cent of the floodable hydrocarbon pore volume. Economic considerations, however, such as the value of the miscible product injected, the cost of injection and the cost of reprocessing the miscible product, limited the amount of miscible product which could be injected into the lower-permeability layers. This resulted in subjecting only 60 per cent of the reservoir to a slug size sufficient to maintain miscibility. Utilizing the relationship of producing gas-oil ratio and areal sweep efficiency as a function of pore volume injected (as obtained from data published by Dyes, Caudle and Erickson2), the theoretical performance was determined. This prediction is compared with actual performance to date. Actual performance reflects an increasing percentage of tniscible product in the produced fluid to a particular level, which remains static for a short period and then increases again to a higher level. This performance suggests that the reservoir has performed as a layered system. It is concluded that the layered-system approach can be used to predict performance in a highly stratified reservoir and that economic consideration is a limiting factor in determining the amount of the reservoir which can be miscibly swept. INTRODUCTION The Paloma zone in the Paloma oil field, Kern County, Calif., is comprised of several sand members separated by siltstone, shale and/or cherty sections. Rapid facies changes within the zone indicate that the sediments were deposited in a "near shore" environment. As a result, the Paloma sands have a high permeability variation, and the Paloma zone is comprised of several sand reservoirs. Since one of the sand reservoirs containing crude oil was not receiving the benefits of gas injection, consideration was given to recompleting certain wells to isolate the sand in order to perform a miscible-phase injection project and, thereby, to increase its ultimate oil recovery. Before proceeding with the project, a review of the literature was made to determine the miscible-slug size that would be required to maintain miscibility throughout the displacement process. Although the review showed that considerable information was available for homogeneous systems, insufficient information was available to determine slug-size requirements and to predict performances for a highly stratified reservoir. This paper has been prepared to describe the method used to determine the miscible-slug-size requirement and to predict the performance of the miscible-phase injection project initiated in the Paloma oil field. Although the Paloma project has only been in operation since Aug., 1958, sufficient production history has been obtained so that a comparison can be made with the predicted performance. DESCRIPTION OF RESERVOIR The reservoir in which the miscible-phase project was initiated in the Paloma field is shown on Figs. 1 and 2. Reservoir properties are as follows: average sand thickness, 43 ft; porosity, 19.1 per cent; water saturation, 47.2 per cent: oil viscosity, 0.328 cp; reservoir temperature, 250°F; reservoir pressure, 3,500 psi: gas saturation, 21.2 per cent at time of miscible product injection; and total net hydrocarbon pore volume, 19,993,000 reservoir bbl. LIMITATIONS The method described herein utilizes a layer-system approach, where injection into and production from each layer is assumed to be proportional to the layer&apos;s fractional capacity. The effects of increased fluid mobility on injection and production rates, in layers which have had breakthrough, are not reflected in this method. There has been considerable controversy over the slug size necessary to maintain miscibility throughout the displacement process. In this method, the slug-size

By Larry J. Tucker

INTRODUCTION The orebody at Pea Ridge strikes NE-SW and dips at about 800 to the SE. The ore and surrounding rocks are Pre-Cambrian in age. These rocks are usually very competent. Locally strong jointing has caused problems and toward the hangingwall dikes have caused particular problems during or after the open stoping phase of production. About 396 m of sediments lie over the ore. The shape and mineral content of the orebody has been fairly consistent so far with production areas lying from the 1375 to the 2475 levels. The deeper limits of the ore- body haven&apos;t been found yet. The ore is high grade magnetite with a strike length of over 600 m and a maximum width of over 180 m on some levels at the center of the orebody. Production at Pea Ridge for the first three years of operation came from two types of open stopes. The original stopes were recovered with horizontal production rings being drilled and blasted from vertical raises. Later a more typical sublevel stoping method using vertical production rings from one or more drilling sub- levels was used. There were a number of reasons for the selection of open stoping as the initial production method at Pea Ridge. First, it was judged that the ore was not of a block cave quality. After fifteen years of production, this assumption can be verified. There was some concern during the planning days for the potential for high flow rates of water into the mine from aquifers in the sediments lying over the orebody. Dewatering wells from surface and underground were put in as a precaution and nothing came of this potential problem. Open stoping and its resulting pillar structure put off this problem by supporting the sediments a few years longer. For a moderate investment in level development some production from open stoping was quickly realized. The first open stopes were brought in on what was then the bottom mine production level (2275), near the shaft pillar and situated on the footwall. This production practice of stoping on the heels of development from shaft pillar westward and from footwall to hangingwall continued through the open stope phases of production at Pea Ridge for many years. From the standpoint of mine efficiency and pillar stability, this would not seem to be a recommended mining practice. 74 570 w electric slushers, using 1.37 m dippers, pulled the open stope ore out into 18 ton bottom dump cars. Ordinarily five of these cars made up a train, which was pulled to the dump area by a trolley powered electric locomotive. Open stoping had the disadvantage that 100% of the recoverable portions of the orebody had to be developed in order to recover 33% of the ore. 67% of the ore was left behind in a large pillar system. For many years we had no planned method for recovery of these pillars. Mining methods are of course, limited by the existing technology. Advancing technology, coupled with the limited production capabilities of open stoping, low efficiencies and high relative cost early in the history of the operation recommended that other mining methods be looked at. In Sweden, considerable practical experience, coupled with a large amount of theoretical work had become available on sublevel caving. To Pea Ridge it offered the apparent benefits of: 1) The flexibility of diesel powered trackless haulage. 2) The efficiency of two machines to one operator on longhole drilling. 3) A multilevel production picture with a large number of drawpoints for ore recovery. 4) 100% recovery of the mineable portion of the orebody in one production pass, with no pillar recovery problems left behind. This paper outlines the experiments and experiences which Pea Ridge has gone through with sublevel caving from 1967 to this date.

Jan 1, 1981