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By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By J. W. Walker, G. J. Heuer, E. W. Hough

An improved apparatus is described for the deterrni-nation of interfacial tension* by the pendant drop method in the pressure range from 15 to 15000 psi and the temperature range from 100º td 280°F. The chief characteristics of this apparatus are reliability and ease of operation. Temperature control was accomplished by means of an electrically heated jacket which could he completely removed while cleaning the apptrratus. The cell was designed so that the camera could he placed about I in, from the window without overheating the carnera lens. Separate "0" rings employed to seal each window and corresponding window backup plate gave very reliable window operation at 10,000 psi. An extra pistorr-cylinder combination was added so that a high compression ratio could he attained when gas was employed as one phase in the pendant drop cell. Other essential parts of the system were similar to an apparatus already described.' The interfacial tension for carbon dioxide and water varies from about 69 dynes/cm at 15 psi to about 19 dynes/cm at 1,250 psi for 100°F. For pressure.r between t,500 and 3,500 psi, the interfacial tension is between 32 and 24 dynes/cm at this temperature. The interfacial tension at 280°F varies from about 50 dynes/cm at 200 psi to about 17 dynes /cm at 10,000 psi. The maximum surface excess for carbon dioxide, assuming the surface excess of water to be zero, occurs at about 1,500 psi jor the 100°F isotherni and Itas a value of about -79 X 1014 mol/sq cm. At 160°F this maximum IS shifted to about 2,000 psi and has a value of about 10 X 1014 111ol/.sq cm. Other maxima, us well as several minima, are present at these and other temperatures. Judging from the data on the solubility of water in carbon dioxide at elevtrted pressures2,3, it appears that the principal maxinza natned are in regions of increasing solubility of the water in the carbon dioxide rich phase. INTRODUCTION AND APPARATUS A pendant drop interfacial tension apparatus which would accommodate an opaque liquid in a gas phase was constructed several ycars ago' for industrial purposes. This apparatus was used as a starting point for the present development. The objective of the present development was to enhance reliability and convenience of operation. Other articles'" have described pendant drop apparatus which could not accommodate a gaseous phase adjacent to the windows. A schematic diagram of the apparatus is shown in Fig. 1. The water used followed the path; A, intro-

By P. E. Queneau

This study confines itself to an examination of the two million square miles of the northern hemisphere which the geographer defines as the terrestrial Arctic, a land region in which the mean temperature of the warmest month is below 50°F-in effect, the area lying north of the tree line. The engineering and human problems there are of a different order of magnitude than is generally true of the sub-Arctic. Whether in Dawson Creek or Matanuska, in Mo i Rana or Skelleftea such problems are of the same general order as in Hibbing or Noranda. The same is not true in Kong Oscar's Fjord or Lancaster Sound.

Jan 7, 1961

By A. Mitchell

An approximate phase diagram has been developed for the CaF2-CaC2 system, indicating a eutectic point at 1240°C, Ncac2 = 0.13, and no detectable solid solution in either phase. The liquidus line is shown to correspond to a simple c22- ion in solution. A thermo-chemical study of&apos; the reaction between carbon-saturated Ni-Ca alloys and CaC2-CaF2 liquids indicates that lhe Raoullian activity coefficient of CaC2 in dilute solution in Cap2 al 1500°C lies between 8 and 10. Some effects of the stabilily of Cap2-CaC2 solutions at high temperatures on electroslag remelting praclice are outlined. THE alkaline earth acetylides. MIIC2, have a reasonably high thermochemical stability at high temperature in the solid state,&apos; with the exception of magnesium, which forms an unstable acetylide at low temperatures (-500°C) and a carbide, Mg2C3, in the range 700&apos; to 1000°C. The acetylides of calcium and barium have been shown to have limited solubility in their respective chlorides,&apos; and further these solutions contain the acetylide as a C: ion.&apos; The equivalent magnesium solutions have not been studied. Although calcium "carbide" is used as a desulfuriz-ing reagent in steelmaking. and is possibly present as an acetylide-oxide phase in very basic electric arc practice slags, the acetylide ion appears to be substantially unstable in a silicate slag.* As a conse- *This instability arises from equilibria in the reaction: CaC2 + CO = (Ca0) + 3C where the low intrinsic solubility of CaC2 in silicate lattice, and the low activity of CaO in a silicate solution where CaO/Si02 < 1, combine to give a very small equilibrium concentration of CaC2 in solution in such silicate slags at temperatures in the region of I 500°c, even under carbon-saturated conditions. Under highly basic conditions, a liquid CaO-CaC2 phase may separate from the silicate system quence of this, the possibility that reactions involving CaC2 in silicate solutions are of importance to general steelmaking practice is remote. However, in operations involving a slag primarily based on a halide, or alkaline earth oxide, we must take into account the possibility that CaC2 will appear in quantities sufficient to significantly affect both the chemical and physical properties of the slag. The work outlined below presents a study of the CaF2-CaC2 system intended to provide sufficient data to allow an estimate of the importance of this system to electroslag remelting and welding practice. However, we should indicate at this point that there will be other processes, e.g., heat treatment, flux cleaning of castings, fused salt electrolysis, and so forth, where alkaline-earth halide fluxes are in contact with carbon, graphite, or carbides, and where halide-acetylide solutions must be taken into account. EXPERIMENTAL 1) Structural Studies. In view of the difficulty ex-perienced in handling CaC2 prepared from calcium turnings and propane gas at 700°C, it was decided to use solutions prepared directly in the equilibration apparatus, Fig. 1. The starting materials were: a) Ni-Ca-C alloy, prepared by adding calcium to liquid nickel held under calcium fluoride in an induction-heated graphite crucible; b) calcium fluoride, prepared by fusing calcium fluoride powder (British Drug House "EXTRA PURE") calcium fluoride in an induction-heated graphite crucible, in air, followed by electrolysis between graphite electrodes at 1 amp cm-2 density, for 10&apos; coulombs per g CaF2. This procedure decomposes the CaO produced by hydrolysis during the fusion step, replacing it by CaC2; Ca2+ + 2e-Ca*(l) Ca*(l) + 2C(gr)-(CaC2)caF2 O2- -2e-O*(g) O*(g) +C(gr)-CO(g) This results in a composition of between 2 and 5 wt pct CaC2 in CaF2. Fifty grams (in lumps) of this material were placed in a graphite crucible, together with Ni-Ca-C alloy (averaging 20 wt pct Ca), and the equilibration apparatus assembled. The alloy reacted with the crucible at high temperature to give CaC2, which dissolved in the calcium fluoride solution to give the desired composition. Cooling curves were plotted manually for these liquids, with rapid stirring and CaF2 seeding to minimize supercooling, and using a Pt/Pt 13 Rh thermocouple calibrated on the freezing points of nickel and copper. This gave a reproducibility of ±0.l°C. and an absolute accuracy of the thermocouple of ±l°C. An example curve is shown in Fig. 2, with the CaF2 end of the binary system in Fig. 3. The CaF2-CaC2 ingots were crushed, under dry nitrogen, and sampled for chemical analysis and X-ray examination. Analytical details are given in the Appendix. Powder diffraction data indicated that the only phases present in all samples examined were calcium fluoride and tetragonal (Types I and 111) calcium acetylide,4 with no evidence of solid solutions or compound formation. 2) Thermochemical Studies. The apparatus used to obtain activity data on CaC2 in these systems is shown in Fig. 4. It consists of an arrangement whereby the graphite crucible and its contents (CaF2-CaC2. Ni-Ca-C) can be rapidly cooled without exposure to air. Trial experiments to determine an equilibration time by ap-

Jan 1, 1969

By R. E. Zimmerman, T. W. Guy

IN approaching the problems of sampling coal, a brief statement of certain facts that are more or less taken for granted may be helpful: 1. The coal-mine operator needs reliable data as to the physical and chemical characteristics of his coal in order to plan and control intelligently its mining, preparation, and marketing. The consumer needs such data in order to select the equipment and the coal best suited to meet his requirements, to check the quality of fuel delivered, and the efficiency of its use. Various government control agencies require such data as a basis for classifications and establishment of limits, for use in carrying out the requirements of federal, state or municipal laws. 2. All such data must be obtained by analyses, measurements, or tests made on samples, which are taken to represent the coal tested. It is now becoming generally recognized that, in accordance with statistical laws, test results from samples are not expected to represent the exact qualities of the lot or lots from which they are taken, except within statistical, or "expected" limits. Such limits are definitely specified by some present standards of the American Society for Testing Materials and the British Standards Institution. 3. Samples that give ash within satisfactory limits are usually assumed to be sufficiently accurate for other analyses, except under special conditions such as meeting close specifications for coals showing wide variability in sulphur, fusibility of ash, or other quality. 4. In modern coal sampling the increment is recognized as the basis for taking samples. For a given accuracy the number and weight of increments specified are increased with: (a) the expected ash, and (b) the top size designation of the lot to be sampled. 5. It is extremely important that every sampler recognize that: the specified number and weight of increments are minimums, and that the precautions to be used in order to take them properly are also minimums; that in the reduction of the gross sample the sizes specified for the coal after each stage of the crushing are maximum; that the quantities specified to be taken after each crushing stage are minimum; that any short cuts or failures to meet the requirements specified will reduce the statistical accuracy of the results, although it is possible that one or two checks on a few results may seem to show otherwise.

Jan 1, 1950

By D. W. Frommer, M. M. Fine

Mineral dressing research showed that iron concentrates of commercial quality could be produced from the Pea Ridge deposit near Sullivan, Mo. Magnetic separation and flotation, on a laboratory scale, yielded concentrates ranging from 60.0 to 71.4 pet Fe at recoveries of 89.9 to 97.6 pct. Early in 1957 St. Joseph Lead Co. announced discovery of three new centers of iron ore deposition in east central Missouri.&apos; The discovery resulted from exploratory drilling in the vicinity of a magnetic anomaly or high. A deep hole, drilled into the Pre-Cambrian porphyry to determine the cause of anomaly, penetrated a magnetite-rich deposit.&apos; The magnetic surveys that revealed the anomalies were begun by the Missouri Geological Survey in 1929 and were continued into the 1930&apos;s.3 At that time an area in Crawford County known as the Bourbon magnetic high was located. A second anomaly, similar in size and intensity, was discovered about six miles to the northeast in Franklin County in the vicinity of Sullivan. This area was not studied in detail until the early 1940&apos;s. To determine the cause of the anomalies, the USBM drilled four holes at the Bourbon site in 1943-1944.4 The most productive hole penetrated four mineralized zones having a total thickness of 127.5 ft. These zones contained magnetite in rhyo-lite porphyry at depths between 1600 and 2000 ft. Additional iron ore below 2000 ft was considered a possibility at the time. Some years later, the USGS, Missouri Geological Survey, St. Joseph Lead Co., and others cooperated in sponsoring an aeromagnetic survey of the Bourbon-Sullivan area which resulted in discovery of a third high, about eight miles distant at Pea Ridge. This deposit, with an estimated reserve of 50 to 100 million tons of iron ore, is considered the main find, although other orebodies in the same general area are of definite interest.&apos; When this discovery was announced, St. Joseph Lead also revealed plans to exploit the deposit jointly with Bethlehem Steel Co. A new corporation, Meramec Mining Co., was established, and 1962 was set as the target date for completing physical plant.2 Annual production goals of 2 million tons of beneficiated and pelletized iron ore were proposed. Preparation of the site for shaft sinking was begun in June 1957. Orebody and Character of Samples: Drilling to date has established the Pea Ridge orebody as a crescent-shaped pipe about 300 ft wide. Some drillholes were bottomed at 2800 ft in very good iron ore.6 he orebody is predominantly magnetite, although hematite and a mixture of hematite and magnetite occur in the upper areas and peripheral walls. Drillhole cores representing ore from different areas and depths of mineralization were grouped into composites for testing. These composites consisted of: 1) medium grade mixed hematite and magnetite, 2) high grade mixed hematite and magnetite, and 3) high grade magnetite. The medium grade ore came from three holes with depths of i350 to 1900 ft. The high grade mixed hematite and magnetite cores came from the 1790 to 2812-ft interval of one hole. Partial chemical analyses of the three samples, given in Table 1, reveal that all are excessively high in phosphorus and sulfur, and sample 1 is

Jan 1, 1960

By George C. Bateman

I HAVE been introduced in the dual capacity of president of the Canadian Institute and Metals Controller for Canada. There are three particular points of similarity between these two positions. They are both temporary ; they both have to do with the mining industry ; and by a peculiar coincidence they both pay me exactly the same salary. It is difficult to appreciate the background of our present situation without knowing the really tremendous changes that have taken place since the last war. I sometimes think that even among ourselves we are likely to forget the extent to which our great mining industry has been expanded. In 1914 Canada&apos;s gold production amounted to only $16,000,000 and the suggestion was seriously ad¬vanced in Ottawa that the gold mines should be allowed to close down so that their men might be used in more important work. Today with a production at the rate of over $200,000,000 a year no one in Canada would venture such a suggestion because the output of our gold mines is the greatest single factor in producing dollar exchange, badly needed for the purchase of munitions and to maintain Canada&apos;s unbroken record of always meeting its obligations. Even with the severe restrictions now in effect against the importation of nonessentials, our imports for war purposes from the United States are resulting in the biggest adverse trade balance in our history. With us, gold mining ranks as an essential industry.

Jan 1, 1941

By A. C. Richardson

Troughs or launders are probably the oldest machines used for ore concentration, and their development was suggested no doubt by the natural segregation and stratification of materials that take place in the bed of a stream. Trough washers for coal cleaning were first used in France and Germany about one hundred years ago and have been used in some form or other ever since. The early launders were intermittent or batch machines, and only comparatively recent developments have made them continuous. The chief disadvantage of early launder systems as applied to coal has been that when a satisfactorily clean coal was produced the loss of good coal in the refuse was excessive. Other disadvantages have been the large quantities of water and the great lengths of troughs necessary to treat moderate tonnages of feed. One of the most widely used types of trough washers is the Rheolaveur, which has been developed in the last 25 years. Fig. 1 shows a more or less standard arrangement for fine coal. In this there are four trouglis placed one below the other and sloped a few degrees from the horizontal. Rheo-boxes or draws are provided at intervals in the bottom of the trough for the removal of material deposited from the stream. These draws are spaced substantial distances apart. Some of the rheo-boxes are provided with upward currents of water to modify the horizontal current stratification. In operation it is the function of the first two troughs to remove all refuse material and permit only clean coal to be discharged over the end. In order to accomplish this, large quantities of coal are drawn through the rheo-boxes. The third and fourth troughs are used to recover the coal discharged through the boxes of the first two troughs as a middling product and to discharge a clean refuse. The middlings are returned to the first launder and are usually about equal to 40 per cent of the raw coal being fed to the launder. In considering launder processes, one would reason that the conditions of extreme crowding under which stratification takes place in a flowing stream should effect complete separation in a single pass down a launder.

Jan 1, 1938

By A. C. Richardson

Troughs or launders are probably the oldest machines used for ore concentration, and their development was suggested no doubt by the natural segregation and stratification of materials that take place in the bed of a stream. Trough washers for coal cleaning were first used in France and Germany about one hundred years ago and have been used in some form or other ever since. The early launders were intermittent or batch machines, and only comparatively recent developments have made them continuous. The chief disadvantage of early launder systems as applied to coal has been that when a satisfactorily clean coal was produced the loss of good coal in the refuse was excessive. Other disadvantages have been the large quantities of water and the great lengths of troughs necessary to treat moderate tonnages of feed. One of the most widely used types of trough washers is the Rheolaveur, which has been developed in the last 25 years. Fig. 1 shows a more or less standard arrangement for fine coal. In this there are four trouglis placed one below the other and sloped a few degrees from the horizontal. Rheo-boxes or draws are provided at intervals in the bottom of the trough for the removal of material deposited from the stream. These draws are spaced substantial distances apart. Some of the rheo-boxes are provided with upward currents of water to modify the horizontal current stratification. In operation it is the function of the first two troughs to remove all refuse material and permit only clean coal to be discharged over the end. In order to accomplish this, large quantities of coal are drawn through the rheo-boxes. The third and fourth troughs are used to recover the coal discharged through the boxes of the first two troughs as a middling product and to discharge a clean refuse. The middlings are returned to the first launder and are usually about equal to 40 per cent of the raw coal being fed to the launder. In considering launder processes, one would reason that the conditions of extreme crowding under which stratification takes place in a flowing stream should effect complete separation in a single pass down a launder.

Jan 1, 1938

By C. S. Barrett

WhEN a collimated beam of protons or other energetic particles is scattered by a single crystal, the emerging particles produce patterns that contain much crystallographic information. Calculations of the trajectories of individual particles can predict with reasonable accuracy the complete pattern (which is related reciprocally to channeling, now studied in detail6) but the task is a lengthy one which has been completed for very few cases. A many-beam dynamic diffraction calculation of the patterns would be even more difficult and in some cases may be invalid. Because of these complexities, simple methods that will predict to a rough approximation the relative intensities of the lines in films of the back-scattering patterns of a given crystal are wanted. I have found a method which, although it is not a valid computation of intensities or of film darkening by either dynamic or kinematic diffraction principles or by trajectory calculations, nevertheless is found to be useful in practice. It has been tested on several crystal types,7 and is here tested on additional ones. The method consists in first calculating the structure factor F(hk1) for the (hkl) plane, of spacing d, by the familiar equation: where the summation extends over the atoms in the unit cell and fj is the atom scattering factor of the jth atom (using tables computed for electron diffraction, preferably those computed without exchange). Then the F values are squared and summed over all the orders, n, for which F2 has an appreciable value, giving a quantity: Finally, I, is expressed as a percentage of Ic for the

Jan 1, 1970

By John Carter Anderson

The theory of a zonal deposition of ores from ascending solutions which were differentiation products of a cooling magma, first propounded by Spurr,l in a measure explained by Lindgren,2 and recently re-emphasized by kemp,3 while perhaps accepted in principle by many mining geologists, so far has not been accepted as capable of practical application in the study and development of ore deposits. From his observations, the writer is convinced that there are laws governing the primary deposition of ores which, when properly worked out, will be of greatest economic value; and that the application of this knowledge to the development of new mines will mark an advance in the mining industry similar to that following the working out and application of the theory of secondary enriehiment. That there has been a tendency to a zonal distribution in the formation of ore deposits, by which the ores of one metal have been precipitated from tile mincralizing solutiolis at a greater distance from the source than those of another, cannot be disputed; and the nature of this zoning in a given deposit or district has been frequently described.4 But that a selection precipitation of the ores of two or more metals, other than lead and zinc, in successive zones may have taken place in a single deposit within limits economically possible of exploration is not generally recognized or admitted.

Jan 1, 1923

By John Carter Anderson

The theory of a zonal deposition of ores from ascending solutions which were differentiation products of a cooling magma, first propounded by Spurr,l in a measure explained by Lindgren,2 and recently re-emphasized by kemp,3 while perhaps accepted in principle by many mining geologists, so far has not been accepted as capable of practical application in the study and development of ore deposits. From his observations, the writer is convinced that there are laws governing the primary deposition of ores which, when properly worked out, will be of greatest economic value; and that the application of this knowledge to the development of new mines will mark an advance in the mining industry similar to that following the working out and application of the theory of secondary enriehiment. That there has been a tendency to a zonal distribution in the formation of ore deposits, by which the ores of one metal have been precipitated from tile mincralizing solutiolis at a greater distance from the source than those of another, cannot be disputed; and the nature of this zoning in a given deposit or district has been frequently described.4 But that a selection precipitation of the ores of two or more metals, other than lead and zinc, in successive zones may have taken place in a single deposit within limits economically possible of exploration is not generally recognized or admitted.

Jan 1, 1923

By J. S. Aronofsky

The first step in a quantitative analysis ot the mechanism of oil displacement by water in a fractured reservoir is usually conceded to be the solution of the differential equation describing the saturation distribution of two immiscible fluids flowing in a porous medium, where the capillary pressure is taken into account. In such a system the production mechanism may consist of displacement of oil both by the flow of water due to natural or artificially imposed pressure gradients and by imbibition, which implies a flow of water not due to external pressure gradients. Owing to the presence of the two oil displacement mechanisms, the mathematical model given by the differential equation intended to describe the system may not properly represent the behavior of the physical system. In fact, in the reservoir the rate of water advance may be very slow, and in the case of a fractured reservoir with a great number of large fractures, the pressure difference determining the flow of water through the matrix may be much less than 1 lb/&apos;psi over lengths of a few feet. In such a case, imbi-bition (the exchange between oil in the matrix and water in the fractures resulting from capillary forces) may become, with time. a significant element of the production mechanism. It occurred Lo the authors, however, that without going into a physical analysis of the process of production, it might be possible by means of simple abstract reasoning to throw some light on the variation of recovery with time under conditions occurring in a highly fractured oil reservoir with rising water table. The object of this paper is to present both the reasoning and its application to a reservoir of the highly fractured type. Specifically, the analysis given here was undertaken to try to explain the increase of recovery (as defined later) with time as observed in this reservoir, without having to assume unlikely variations in the reservoir parameters with depth. This attempt has been successful as will become clear upon comparison of the computed recoveries with the actual field data. ABSTRACT MODEL Let us consider a small volume. of porous matrix saturated with oil at time, t = 0. Let the process of oil displacement by water start at time, t = t,,. At some time, t, the process will have terminated. Then a volume of oil equal to or smaller than the original oil contained in the matrix will have been produced. The first basic assumption that describes the model and guides the forthcoming reasoning is that the oil production from the small volume. dv, is a continuous monotonic function of time and that it converges to a finite limit. Such an assumption is not inconsistent with the results of laboratory waterflood tests as well as with results of imbibition tests where this is, in fact, observed. The second basic assumption is that none of the properties which determine the rate of convergence change sufficiently during the process to affect this rate or the limit. Let it be assumed that the form of the function of time relative to production from the matrix volume. dv, is given by where V,(t) is the volume of oil produced up to that time t. R is the limit toward which the recovery converges, A is a constant giving the rate of convergence, and V,(t) is the volume of oil originally in place in the volume, dv. It should be noted that recovery at time I will be understood here to he It follows that r. tends to R as t tends to infinity. CONSTRUCTION OF RESERVOIR FROM ABSTRACT MODEL Let the reservoir consist of a series of identical blocks of porous matrix stacked vertically and separated by fractures. Let each of these blocks satisfy the conditions of our abstract model. These conditions are: (1) that recovery is a continuous mono-tonic function of time converging to finite limit, and (2) none of the properties that determine the rate of convergence change sufficiently to affect the rate or the limit. Let water be rising in fractures so that oil production from any part of the block starts when the water comes in conLact with it. TOTAL RECOVERY FROM THE RESERVOIR COMPARED TO RECOVERY FROM A SINGLE MODEL ELEMENT As stipulated in Eq. 1, in the case of the abstract model,

By H. H. Reamer, B. H. Sage

Attempts have been made to predict the volumetric and phase behavior of naturally occurring hydrocarbon mix-turesl-6 but these methods have not been extended to the higher pressures and tem-peratures that are currently encountered in some producing formations. Furthermore, the methods of prediction at present avail-able have not been tested in a sufficient number of cases to ensure their applica-bility to all naturally occurring hydrocar-bon mixtures, even at the lower pressures and temperatures. For these reasons the behavior of a number of hydrocarbon mix-tures from a field in which the subsurface pressures are above 4500 lb. per sq. in.t and the temperatures are in the neighbor-hood of 250°F. was investigated. Method The objective of this program was to determine the volumetric behavior of ma-terial as it existed in the reservoir as a function of pressure, temperature and com-position. Strictly speaking, this cannot be accomplished in any simple fashion. How- ever, the variations in composition that are encountered within a producing reservoir may be approximated roughly by means of mixtures made up of two arbitrarily chosen constituents. Experience indicates that the liquid and gas phases from a high-pressure gas trap afford a simple source of material for this purpose. Throughout this discus-sion the samples of the gas phase and liquid phase from the production trap will be called the "trap-gas sample" and the "trap-liquid sample," respectively. The volumetric behavior of both of the trap samples was determined throughout the temperature interval between 100" and 250°F. at pressures up to 5000 lb. per sq. in. In addition, the behavior of eight different mixtures containing varying proportions of the two trap samples was studied throughout the same temperature and pressure intervals. The experimental results yielded information concerning the specific volume of the material as a function of pressure, temperature and the relative quantity of the trap samples. The relative amount of each of the paraffin hydrocarbons of lower molecular weight than n-hexane was determined for each of the trap samples. In addition, the specific weight, viscosity and average molecular weight of the hexanes-and-heavier fraction of the trap-liquid sample were determined as well as similar information for each of five fractions separated from this material by distillation. From these data the weight fractions of each of the components from methane through pentane were determined for the trap samples and eight systematically chosen mixtures. Materials The gas and liquid samples were obtained from the production trap of a well in the Rio Bravo field in California during the fall of 1939. Information concerning the condi- 70

Jan 1, 1941

By H. H. Reamer, B. H. Sage

Attempts have been made to predict the volumetric and phase behavior of naturally occurring hydrocarbon mix-turesl-6 but these methods have not been extended to the higher pressures and tem-peratures that are currently encountered in some producing formations. Furthermore, the methods of prediction at present avail-able have not been tested in a sufficient number of cases to ensure their applica-bility to all naturally occurring hydrocar-bon mixtures, even at the lower pressures and temperatures. For these reasons the behavior of a number of hydrocarbon mix-tures from a field in which the subsurface pressures are above 4500 lb. per sq. in.t and the temperatures are in the neighbor-hood of 250°F. was investigated. Method The objective of this program was to determine the volumetric behavior of ma-terial as it existed in the reservoir as a function of pressure, temperature and com-position. Strictly speaking, this cannot be accomplished in any simple fashion. How- ever, the variations in composition that are encountered within a producing reservoir may be approximated roughly by means of mixtures made up of two arbitrarily chosen constituents. Experience indicates that the liquid and gas phases from a high-pressure gas trap afford a simple source of material for this purpose. Throughout this discus-sion the samples of the gas phase and liquid phase from the production trap will be called the "trap-gas sample" and the "trap-liquid sample," respectively. The volumetric behavior of both of the trap samples was determined throughout the temperature interval between 100" and 250°F. at pressures up to 5000 lb. per sq. in. In addition, the behavior of eight different mixtures containing varying proportions of the two trap samples was studied throughout the same temperature and pressure intervals. The experimental results yielded information concerning the specific volume of the material as a function of pressure, temperature and the relative quantity of the trap samples. The relative amount of each of the paraffin hydrocarbons of lower molecular weight than n-hexane was determined for each of the trap samples. In addition, the specific weight, viscosity and average molecular weight of the hexanes-and-heavier fraction of the trap-liquid sample were determined as well as similar information for each of five fractions separated from this material by distillation. From these data the weight fractions of each of the components from methane through pentane were determined for the trap samples and eight systematically chosen mixtures. Materials The gas and liquid samples were obtained from the production trap of a well in the Rio Bravo field in California during the fall of 1939. Information concerning the condi- 70

Jan 1, 1941

By John E. Carr

A bewildering variety of continuous thickeners and clarifiers are used in mineral industries and other heavy industries. General topes arc: ? Conventional thickeners ? Thickeners with flocculating feedwells ? Solids contactors ? Tray thickeners ? Lamellas ? Conventional thickeners with Lamellas ? High flow, fluid bed thickeners These units must be adapted to varied applications. They must provide operating flexibility to meet process needs. Such factors multiply the decisions which must be made prior to the selection of a thickener. The seven types of thickeners listed above, with their variations, share design concepts which limit their application and which can be used to evaluate their performance. Some of these arc: ? Feed velocities must be limited and/or controlled. ? Natural or reagent flocculation is necessary. ? Horizontal settling area is the basis for capacity. ? Overflow velocities must be limited and. or controlled. ? A controlled underflow is necessary. Thickener selection is the application of these needs to the basic process concepts. The basic function of a thickener, in the minerals industry, is the separation of a thickener sludge containing fine solids from water. In addition to this primary separation function, others include: ? Separation of solids from water ? Separation of flocculated solids from slimes ? Storage of solids ? Control of percent solids ? Storage of water ? Process control by absorbing fluctuations in feed ? Process control by increase in head clue to the depth and percent solids of the thickened sludge. Most thickener designs, suitable to minerals applications, are based on the separation of minus 65-mesh, 2.7 specific gravity solids containing slimes. These designs are routinely adapted to coarse and or denser materials. Materials of lower specific gravity such as coal, wood, char, some chemical precipitates and organics act Hike slimes if a thickener is used. Perhaps the most conservative approach to sizing and application is the use of comparative data from similar plants or similar industries. Thickeners are-routinely used in a great number of industries from which there is good historical information available. In the minerals industry, thickeners are used in: clay sizing, coal refuse, heavy media, copper concentrates, copper tailings, gold flotation concentrates, and countercurrent decantation for cyanidization in gold and CCD in uranium. Concentrate and tailings thickeners are used in iron ore plants, and concentrate and tailings units in lead-zinc plants. In addition, there arc thickeners designed to handle lime mud; limestone concentrates and tailings; phosphoric acid; potash; and rutile concentrates. Thickeners are, in addition, widely used in gravel plants for water reclamation. This gives excellent data on clay settling in some cases. Thickeners are used extensively for slurries generated by flue dust from wet scrubbers. Thickeners in flue dust applications are operating with considerable variations, treating blast furnace dust. BOF flue dust, and wood char. Similar applications are met in the power industry with fly ash and SO2 scrubber systems. Even though field data is preferred, such data has limitations as listed: ? Flowsheets are seldom identical. ? Data is often incomplete or limited. ? Ores vary significantly. ? Operating needs are changing. For these reasons, mathematical and theoretical methods are needed for application of field data to a specific project. In addition, laboratory data for similar projects and, if possible, laboratory data on a representative sample should be used to specify the thickener. There is a great volume of thickener literature. The references for this paper, along with their references, and past AIME papers provide excellent background. Older literature can be reviewed in light of current methods. It is interesting to note that the requirements for higher flow rate designs, more extreme flocculation systems, etc., can be logically introduced by reading Gaudin&apos;s Sections on Flocculation and Thickening, which was written before field installations could illustrate all of his ideas. The problem, then, is to select hardware which will take into consideration the functions of flocculation, separation of the solids, water clarity, control of the underflow, and control of the overflow. Reliable operation and simple control are customary.

Jan 1, 1979

By Arthur Baker

The orebodies are long bedding-plane lenses of chalcopyrite and sphalerite, associated with garnetite masses. Most of the orebodies are within a 50-ft thickness of Cambrian limestone; other Paleozoic limestones and dolomites are locally metamorphosed but only slightly mineralized. Pre-mineral faults are numerous, but shallow folds were the main ore-localizing structures.

Jan 12, 1953

By Willard S. Morse

The ores of the district are treated at this mill by the lixiviation process, consisting of drying, crushing, chloridizing-roasting and lixiviation by hyposulphite and Russell solutions. Gas is used as fuel for both drying and roasting, The gas-plant consists of two- Taylor revolving-bottom gas-producers, one 6 feet in diameter for the ore-dryers, the other 7 feet in diameter for the Stetefeldt furnace. The producers were made by Messrs. R. D. Wood & Co., Philadelphia, who also furnished the

Jan 1, 1893

By S. F. Urban, G. Derge

AT the time this investigation was initiated variations were observed in the quality of different heats of basic electric-furnace steels, although they had been made under purportedly similar conditions. This indicated that these variations were related to normally unobserved variations in the character of the bath, especially during the "refining" period. Although the slags used for this operation are commonly referred to as "reducing" slags, and are regarded as having a "deoxidizing" action on the bath, no reliable measurements of this action were available. It was decided, therefore, to study the behavior of oxygen in the metal for a large enough number of heats to learn its normal variations and to relate these variations to regularly observed conditions [f] operation. The most important general conclusion reached was that the time a heat is held under a reducing slag should be reduced to a minimum, which was about an hour and a half under the conditions studied. Beyond this time no observable beneficial effects are obtained from the reducing slags, insofar as oxygen and sulphur content of the bath are concerned. It is likely that added time may increase hydrogen content as well as heat costs. The oxygen content of the bath is never reduced below the amount in equilibrium with the carbon. Concurrently with this work, J. S. Marsh1 presented data that supplement and support many of the results of this paper. PROCEDURE The work was done in two different electric-furnace shops of the same plant. The selection of heats was made primarily with regard to the convenience of heat schedules. Companion slag and metal samples were taken just prior to slag-off and throughout the refining period for an initial set of 17 heats, and before slag-off and near tap for an additional 13 heats. Slag sampling presented no particular problem; a spoonful of slag was poured onto a metal plate and when sufficiently cool was sealed in an airtight container. Sampling the metal for oxygen presented a more complex problem. Because of the lack of previous experience in sampling electric-furnace baths, a number of methods were compared. Chilled Wedge Samples2 An unkilled metal sample is removed from tie furnace in a well-slagged carbometer spoon and poured immediately into a heavy copper mold designed to provide rapid freezing. Three different types of molds were used to determine the optimum for electric-furnace heats. The Big Wedge Mold (a) was a 4 by 4 by 4-in. split copper mold, yielding a wedge-shaped casting 1 in. wide, 1 ½ in. long, and ¼ in. maximum thickness, and was finally adopted as the most satisfactory design. The Long Wedge Mold (b) was a 2 by 2 by 5 ¼ -in. split copper mold, yielding a wedge-shaped casting 1 in. wide, 2 ¾ in. long, and ¼ in. maximum thickness. The Small Wedge Mold (c) was 2 by 2 by 4-in. split copper mold, yielding a wedge-shaped casting 1 in. wide, 1 ½ in. long, and ¼ in. maximum thickness.

Jan 1, 1947

By F. F. Aplan, P. H. de Bruyn

The adsorption density of hexyl mercaptan was measured at the gold-solution and the gold-vapor interfaces. This collector is strongly adsorbed at low concentrations, a monomolecular layer being formed at the gold-solution interface at concentrations as low as 2 x 10&apos;6 moles per liter. A maximum contact angle of 83 ± 3° is observed. From a thermodynamic analysis of the experimental data the changes in surface tension at the gold-gas and gold-solution interface are calculated. The data also suggest that the adsorption density of mercaptan at the gold-gas interface exceeds that at the gold-solution interface. In the equilibrium state, a simple flotation system consists of three phases, the solid to be floated, air, and an aqueous solution in stable contact along a line. During the process leading to this final state, a solid-gas interface is created at the expense of a portion of the liquid-gas and solid-liquid interfaces. This change of state is achieved by addition of a collector and, if necessary, suitable modifying agents to the system. By a combined application of the Gibbs Adsorption and the Young Equations, de Bruyn, Overbeek and Schuhmannl were able to show theoretically that the equilibrium distribution of the collector at all three interfaces determines the magnitude of the contact angle. Their analysis led them to conclude that the equilibrium adsorption density of the collector at the solid-gas interface exceeds its density at the solid- liquid interface. This paper succeeded in focussing attention on the neglected role of the solid-gas interface in flotation. In recent years the application of radiotracer, infrared, electrochemical and electro-kinetic techniques to studies of the solid-liquid interface2-5 enhanced our understanding of adsorption processes at this interface. Except for the measurement of contact angles, the solid-gas interface received no attention in fundamental flotation studies. In an attempt to apply the analysis of de Bruyn, Overbeek and Schuhmann to a simple flotation system, an investigation of the adsorption of hexyl mercaptan onto gold was undertaken. Gold was chosen as the solid phase in order to keep the number of dissolved chemical species in the solution phase to a minimum. Hexyl mercaptan (1 - hexanethiol) was selected as collector because its relatively high vapor pressure at room temperature makes it possible to obtain adsorption measurements at the solid-gas interface. This flotation system consists, therefore, of a pure solid phase (gold), an aqueous solution of a weakly dissociated collector (1 -hexanethiol), and a gaseous phase, nitrogen saturated with respect to both water vapor and mercaptan vapor. EXPERIMENTAL MATERIALS AND METHODS Materials: Liquid 1-hexanethiol (C6H13SH) was obtained from Distillation Products Industries and was further purified by double distillation. The purity of the final product was established by boiling point and refractive index measurements. For the adsorption studies from aqueous solution, the radiotracer element, sulfur-35, (half life 87.1 days, 0.169 Mev beta ray) was synthesized into the mercaptan by Tracerlab Inc., Boston, Mass. A close boiling fraction of the synthesized compound was used in the adsorption studies. The specific activity of the radioactive compound was 10 millicuries per gram.

Jan 1, 1963