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By C. F. Cornell, R. C. Emmett, D. A. Dahlstrom

FOR many years the disk-type and cloth-covered drum filters have found widest application in liquid-solids separation, which uses continuous filters. The disk type is less expensive, occupies less floor space per square foot of filtration area, and requires negligible down time for filter media changing. However, because filter cloth is billowed out by the blowback in the cake discharge, it is very short-lived if the scraper blades are set too close. Consequently cake weight is very important in assisting cake discharge, which normally necessitates a minimum cake thickness of 3/8 to ½ in. Also, the vertical position of the disks eliminates the possibility of efficient cake washing for removal of soluble values. The disk-type filter is generally limited, therefore, to applications that require no cake washing and form relatively thick cakes within the normal range of filter cycle times. The conventional cloth-covered drum filter is a more flexible unit, permitting wider variation in the percentage of cycle time devoted to cake formation, dewatering, or washing, as required by the application. Thinner filter cakes can be discharged because a horizontal line across the filter medium at the location of the scraper blade is equidistant from the edge of the blade at all points. The scraper blade therefore may be set a short distance from the filter medium or, where wire winding is not used, a floating scraper can be utilized so that the contour of the cloth can be followed. The drum filter is generally employed when there are difficult filtering slurries with resultant thin cakes or when cake washing to recover soluble values must be practiced. Difficulties sometimes encountered in continuous filter operation can be summarized in the following four categories: 1) Low filtration and/or washing rates due to blinding of the filter medium. 2) Poor cake discharge resulting from sticky cakes, filter medium blinding, or too thin a cake for the particular type of filter. 3) High filter media costs caused by short life and frequent down times for cloth changing. This results from blinding or from abrasion by the scraper blade when cakes are thin. 4) Blowback of filtrate at cake discharge because not enough air passes through the cake to purge the drainage area and filtrate lines during dewatering. To reduce or eliminate blinding tendencies several modifications have been tried, for example, cover-cleaning showers, blowback under the feed slurry, and snap-blow cake discharge. In many cases, however, this simply retards the rate of blinding, since the filter medium is kept clean at its outer surface only by these methods. As blinding usually occurs within or on the back of the medium, the operator is finally forced either to remove the cloth and scrub the medium intensively with a cleaning solution or acid-rinse it on the filter—all resulting in down time, short cloth life, and additional costs.

Jan 1, 1959

By D. J. Coolidge, H. L. Sheakley

THIS paper does not deal with all sands used in the glass industry in Missouri; it covers only that used in the plate-glass factory at Crystal City. However, it is probably safe to say that other sands, pro- [ ] duced throughout the state for this purpose, are of identical nature. The glass sand used in Missouri is commonly called the St. Peter deposit, which is ascribed to the Ordovician Rock series in the form of sandstone. This St. Peter deposit, aside from a few small outliers, covers a large area of eastern Missouri. It forms, through a broad curve, the northeast margin of the typical Ozark region between Cape Girardeau on the southeast and Mineola, Montgomery County, on the northwest. The belt is extremely irregular, varying from one to ten miles in width; its length is 150 miles in a straight line. [ ] The outcrop near the entrance to the Crystal City mine appears in the form of a sandstone bluff approximately 30 ft. high, running along Plattin Creek (Fig. , I). Above the sand rock an overburden of Joachim limestone appears, which, thickens to nearly 300 ft. and forms the hill commonly called Buck Knob. Test holes, where drilled at various points and the drillers' log indicate that the St. Peter deposit ranges in thickness from 63 to 71 feet. PROPERTIES OT THE ST. PETER SAND From an analysis of the glass sands of the St. Peter formation in Missouri, the follow-

Jan 1, 1942

By J. Moore, D. Gault, R. V. Lugn

Impact of small projectiles with velocities between 0.9 and 7.3 km per sec on basalt produce craters chiefly by the ejection of fragments. Weight-size distributions of the ejecta are linear for part of the size range of the fragments. Cumulative weight-size distributions of the ejecta from different craters vary because of erratic formation of large fragments and a large percentage of ejecta below 0.1 mm. In the range of velocities studied, the crater depth is approximately proportional to the 0.75 power of velocity of the projectile. This relationship may represent a transition regime between the fluid impact regime and the undeformed projectile impact regime. The volumes per unit of projectile energy of the craters produced are comparable to those reported for lower speed projectile impact and drill bits. An experimental investigation of projectile impact on rock is being conducted jointly by the Ames Research Center of the National Aeronautics and Space Administration and the U.S. Geological Survey. Projectiles are launched with light-gas guns at the Ballistics Range of the Ames Research Center. The craters and ejecta produced in these experiments are being studied by the U.S. Geological Survey. Steel, aluminum and polyethylene projectiles weighing from 0.25 to 0.015 g were accelerated to velocities of 0.88 km per sec (2,900 fps) to 7.3 km per sec (24,000 fps) with a light-gas gun, using hydrogen as the propellant medium. Projectiles impacted the targets normal to plane rock surfaces in an atmosphere of air with a nominal pressure of 25 to 50 mm of mercury. The metal projectiles were mounted in supporting four-piece nylon sabots, which guided the projectiles down the launching tube. After launch, aerodynamic drag acted to separate the sabots from the projectiles. Impact velocities were determined with time measurements and spark photographs of the projectiles in flight. Ejecta were collected in lucite and aluminum containers placed around the target block. A small hole in the containers permitted projectile entry. Impact of projectiles of the size employed produced craters in the rock targets chiefly by ejection of fragments. The craters are small, roughly conical depressions with crushed and intensely fractured rock at the bottoms of the depressions. The ejecta are composed of pieces of the projectile and rock fragments ranging in size from a few tenths of a micron or less to several centimeters in maximum dimension. In this paper, the structural features of the craters, the weight-size distributions of the recovered ejecta, and crater depth and crater volume relationships are described. DESCRIPTION OF CRATERS Typical craters (Fig. 1) produced by experimental projectile impact in basalt are shallow, wide base

Jan 1, 1963

By G. R. St. Pierre, A. J. Wilhelem

In connection with the reduction of hematite or magnetite to metallic iron, it appeared desirable to study the rate of reduction of each oxide to the next lower oxide under conditions which excluded all other condensed phases. For this purpose, pellets of Fe,O,, Fe,O,, and oFeOo were prepared. A gas train for the preparation of Ar-Hz-H20 mixtures was employed to establish a continuous flow of a controlled atmosphere over a pellet suspended on a balance. In this manner the following individual reduction steps could be studied: For example, pellets of hematite were reduced solely to magnetite by adjusting the gas atmosphere such that it was oxidizing to wustite. In other words, the reaction was complete when the hematite pellet had been totally converted to magnetite. The pellets were prepared from Baker Chemical ferric oxide. The ferric oxide powder was moistened and handrolled. Air sintering at 950°C produced Fe,0, pellets with a density of 3.65 g per cm3. The pellets ranged in size from 0.6 to 1.2 cm diam. The magnetite and

Jan 1, 1962

By Charles R. Fettke

In connection with the gathering of data for a report on the geology of the Humacao district of southeastern Porto Rico during the summer of 1916, under the auspices of the Scientific Survey of Porto Rico and the Virgin Islands, conducted by the New York Academy of Sciences, the writer had an opportunity to make a brief examination of the magnetite deposits of the eastern portion of the island. Inasmuch as these deposits have attracted some attention as possible future sources of iron ore, and as there is only scanty reference made to them in literature,' a short description based on this reconnaissance survey was deemed to be worthy of record. The magnetite deposits of eastern Porto Rico occur in association with a belt of limestone, trending approximately S 53° E, which begins 11/2 miles east of Juncos and can be traced for about 6 miles toward the coast. Four outcrops of magnetite were observed, which are designated as Nos. 1, 2, 3, and 4, respectively, on the map shown in Fig. 1. Others are probably present, but escaped notice on account of the thick mantle

Jan 1, 1924

By S. A. Hovanessian

The method of characteristics which reduces the Buckley-Leverett mnlineur, partial differential equation to two first-order, linear differential equations is applied to the solution of a waterffood recovery problem for multiple lines of producing wells and one line of injection wells. The application of the method is described by a numerical example, and a brief theoretical background is given. From the results of this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple sets of producing wells. INTRODUCTION In this paper, the method of characteristics is applied to the solution of a waterflood recovery problem with multiple lines of producing wells and one line of injection wells. The application of the method to this type of recovery problem considerably simplifies the procedure of obtaining a numerical solution. It differs from the method described by Kern1 because it eliminates the need for integration in obtaining saturation fronts. In addition, the saturation history at any location within the field is obtained from a single diagram (time vs distance with saturation as a parameter)'. The paper includes a brief theory of the method of characteristics and its application to the solution of oil recovery problems. A numerical example is worked out, and the cumulative oil recovery-vs-time curve for a system with multiple sets of producing wells is obtained. This curve is then compared with the recovery curve of a system with only one set of producing wells. From this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple lines of producing wells. However, the recovery time is considerably longer for multiple sets of producing wells.

By R. C. Neavel

One of the most important requirements to be met by any coal producer is delivery of size consists tailored to specific applications. Generally these specifications include a minimum as well as a maximum size limit. The customers of a major Indiana coal producer noticed that some shipments of sized coal contained a large proportion of undersize pieces. Also, in these shipments, the pieces which remained within the specified limits were cracked and, when handled, crumbled readily. The producer, certain that these shipments had been properly sized at the tipple, suspected that degradation had occurred in transit. The Indiana Geological Survey was requested to examine the coal from one of these shipments to attempt to determine the cause of breakage. Two basic facts about coal and coal seams led to the employment of petrographic techniques in this investigation. First, all coal seams consist of accumulations of diverse organic and inorganic constituents; and second, most coal breakage, either desirable or undesirable, can be attributed to the inherent weakness of some of these constituents or to poor adhesion between certain constituents. Analyses of degraded coal Sampling: Samples were secured from 2 stock piles of 2-by 4-inch coal in a dealer's yard. The coal in both piles had received the same treatment from mining to storage, although it had been mined and shipped on two different days. The size consist of one pile, however, appeared smaller than that of the other. The sample from the degraded pile is referred to as the slack sample, and the other is called the unslack sample. Size analyses: In order to determine the actual size consist, the samples were screened, with a minimum of rough handling, on square 2-inch, 1-inch, 1/2-inch, and 12-mesh screens. It is assumed that 100 percent of the 2-by 4-inch coal is retained on a 2-inch round screen at the tipple. Analyses of several loads at the tipple indicate that approximately 26 percent of the 2- by 4-inch coal, 100 percent of which was assumed held on a 2-inch round screen, passed through a 2-inch square screen. Twenty-six percent may be taken as the normal difference between round and square screens. Results of the analyses of stockpile coal are shown in Table 1. Cumulative percent versus size are plotted on a Rosin-Rammler chart as Figure 1. Both samples approximately follow normal size distribution; this indicates that breakage is not size preferential and also that the samples are representative of the stockpiles. Although both samples exhibit the same general size distribution, the median size of the slack sample is considerably smaller than that of the unslack sample. Fifty-five percent of the unslack sample was undersize (29 percent greater than the normal 26 percent difference), and 83 percent of the slack sample was undersize (57 percent greater than the normal 26 percent difference). Both piles contained a greater percentage than normal of undersize coal; this indicates that they were both affected by degradation, but to a different degree. Bedding-plane analyses: Coal, because of its laminated nature, will break preferentially along bedding planes, especially where adjacent constituents are poorly cemented to each other. Subsequent breakage perpendicular to the

Jan 1, 1961

By G. F. Butterworth

The metallographic structures most frequently encountered in rifle barrels, and which are illustrated by the accompanying photomicrographs, fall naturally into two groups, distinguished by the method used to, produce in the stock a physical condition having the requisite properties. The fist group consists of "rolled" barrels; that is, barrels subjected to hot working by rolling in or near the critical range. In the second group, the stock, which is smaller in diameter than the first, is upset to form the butt end and is then heat treated by giving it a quench and a draw. These barrels will be referred to as " heat-treated " barrels. The structure of the rolled barrels resembles closely that of the same steel after annealing. There is the same network of excess ferrite outlining the grain boundaries, but the grains themselves are composed of sorbite rather than pearlite. The grain size is closely related to the rolling temperature. The critical-point curves of this grade of steel, which is approximately 0.50 to 0.60 per cent. of carbon and 1.00 to 1.30 per cent, of manganese, show a single very pronounced point between 1300" and 1350" F. (704" and 732" C.). Barrels rolled within this temperature range give an exceedingly fine grain, shown in Fig. 1. In fact, the grains may be so fine that, at a low magnification, they may be confused with the heat-treated structure shown in Fig. 6. A magnification of 500 diameters, however, will always resolve a rolled barrel into the characteristic structure shown in Fig. 2. As the temperature is increased, the grains are found to be larger. If, on the other hand, the rolling temperature is below the critical range, the structure previous to rolling will not be obliterated, the only effect of rolling being to elongate the coarse sorbite grains in the direction of rolling, Fig. 3. This distortion is greatest at the muzzle. Heat-treated barrels are quenched in oil from above the critical range, which should give a martensitic structure, Fig. 4, but the presence of some troostite in the martensite is frequently noted when the quench has not been sufficiently drastic, Fig. 5. The structure brought about by the subsequent draw is not so striking, though quite as typical. It is sorbitic or sorbito-pearlitic, and under a low magnification appears almost homogeneous, as in the case of fine grains of pepper and salt well mixed together, Fig. 6. This structure is substantially the same for all

Jan 1, 1920

By F. Haessner, M. Wilkens, U. Jakubowski

ThOUGH at present there is a wide range of possibilities for the quantitative determination of preferred orientations, pole figures of identical specimen material have not been determined by different methods as yet.''' In this paper a comparison of (Ill), (200), and (220) pole figures is presented which were obtained from a 95 pct cold-rolled high-purity cop- per sheet (99.9998 pct Cu), by three different methods. The three methods are: a) The combined X-ray reflection-transmission technique of plane samples by schulz3 and Decker, Asp, and Harker. 4 A Siemens texture goniometer was used. The experimental details are described elsewhere. 6 b) The X-ray reflection technique of spherical samples by Jetter and Boric.' A Siemens texture goniometer with some modifications was used. The samples were prepared by sticking 140 polished sheets together with an adhesive and machining a sphere (20 mm diam).* Additional

Jan 1, 1967

By R. E. Gilchrist, R. F. Nielsen

When a gas is displaced by mother in a porous medium, and there is a relative immobile liquid present. there is a transition zone in which the gas composition varies from essentially that of the original gas to that of the injected gas. The change in extent of this zone with time may be governed by a mixing process in the direction of flow and by the rate of establishment of gas-liquid equilibrium, if the gases are appreciably soluble in the liquid. The relative importance of these two factors in deterri~ining the growth of the transition zone is discussed, with appropriate equations and experimental data. INTRODUCTION The various solution methods of oil recovery involve a transfer of the components of a mixture, whether within a single phase or between a liquid and gas. The similarity of a natural porous medium to systems used in separation and chromatographic processes makes it seem reasonable that certain concepts used by chemical engineers in "mass transfer" might be applicable to petroleum reservoirs. One approach, the HETP (height equivalent to a theoretical plate), involves a distance or length of time over which equilibrium might be con. sidered as established. Another approach involves direct use of a rate of mixing or rate of establishment of equilibrium. The latter approach has been preferred in relation to production problems. DISCUSSION AND PROCEDURE When a gas or liquid in a porous medium is displaced by one of different composition but miscible with it there will be set up a transition zone in which the composition varies from cssentially that of the original fluid to essentially that of the injected fluid. If the fluid being displaced is a gas, and there is a relatively immobile liquid present, the transition zone may be

By K. P. Fournier

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus:

Jan 1, 1966

By E. T. Turkdogan

Jan 1, 1962

By F. A. Forward, A. H. Ross, J. Halpern

Application of the carbonate leaching process to carno-tite ores has often been limited by the difficulty of obtaining simultaneous high recoveries of uranium and vanadium. The chemical aspects of this problem are discussed and the effect of prior roasting procedures on this discovery is described. IN treating carnotite ores by carbonate leaching it is often necessary to subject the ore to a prior roast. Among the advantages that may result from roasting are: 1) improvement in settling and filtering characteristics of the ore; 2) destruction of carbonaceous impurities that would otherwise contaminate the leach solution and consume carbonate reagent; and 3) substantial increase in extraction of vanadium, which is usually low when the un-roasted ore is leached. Recovery of vanadium may be an important factor in processing carnotite ores, and the fact that vanadium is usually recovered in good yield by acid leaching has often been an economic advantage over results obtained with carbonate leaching. It has been found that response of an ore to carbonate leaching, following roasting, depends primarily on its composition and on the conditions of the prior roast treatment, particularly with regard to the roasting temperature, the atmosphere maintained above the charge during roasting and cooling, and the presence of certain reagents. These factors, especially the last, virtually determine the extractions of uranium and vanadium attainable by carbonate leaching, as well as the reagent consumption on leaching, whereas adjustment of the leaching conditions has only a limited influence. These variables were examined systematically to elucidate roasting and carbonate leaching of carnotite ores and to establish a treatment yielding high recoveries of both uranium and vanadium. Tests were conducted on samples of four different Colorado Plateau ores, described in Table I. Roasting Procedure: The roasting tests were conducted in an electrically heated furnace in which the temperature was controlled to ±15°C. The ore (usually a 500-g charge) was ground to —100 mesh, mixed with the desired reagent, and spread in a silica tray to a bed depth of about 1/2 in. During the roast the charge was rabbled at intervals of 15 min. To provide free access of air the furnace was usually ventilated; however, in a few experiments a controlled atmosphere such as carbon dioxide or hydrogen was maintained above the charge. Leaching Procedure: The pulp, generally comprising 500 g of ore and a 2000-cc solution containing 80 g per liter of Na2CO8 and 20 g per liter of NaHCO3, was agitated in an autoclave at 120°C, under 30 psi 02. Samples were withdrawn periodically, and the solution and ore residue were analyzed. Under the conditions employed, maximum attainable extractions were generally achieved in 4

Jan 1, 1959

By H. W. Fleming, R. R. Brooks

The Clearwater Deposit, a small occurrence of massive-sulphide mineralization enclosed in an envelope of disseminated-sulphide mineralization, was discovered as a result of an aeroelectromagnetic survey in New Brunswick in 1955. Subsequently, additional flights were made over the deposit and various ground follow-up methods were employed to ascertain the nature of their response. All methods proved to be capable of indicating the occurrence with varying degrees of precision. This paper is a presentation and a discussion of the magnetic and electromagnetic data, both airborne and ground, and the self-potential data obtained over this deposit. The attention of Canadian mining exploration companies was initially focussed on New Brunswick by the discovery, in 1953, of the Brunswick ore body. Ground electromagnetic surveys were of considerable assistance in locating and developing this deposit. In the following year, 1954, the Heath Steele base-metal deposits were discovered by employing an airborne electromagnetic device and ground electromagnetic surveys to follow-up the airborne indications. These discoveries demonstrated clearly that both airborne and ground electromagnetic techniques were applicable for locating the near-surface deposits of massive sulphides present in this region. Airborne electromagnetic equipment became available on a contract basis through Aeromagnetic Surveys Limited early in 1955 and was used extensively thereafter throughout a large portion of northern New Brunswick. It was as a result of one of these surveys with Aeromagnetic Surveys Limited equipment in the summer of 1955 that the Clearwater Deposit was detected. The airborne anomaly was located on the ground by means of an electromagnetic survey using a Swedish Slingram unit. During 1956, the region was investigated more thoroughly- in the hope that other sulphide bodies might be located. Airborne electromagnetic coverage was extended and the Clearwater Deposit itself was used as a testing ground for the various methods and types of equipment currently in use in New Brunswick. In this paper com prative data are presented for the airborne magnetic, airborne electromagnetic, ground magnetic and ground electromagnetic surveys over this deposit. The ground electromagnetic instruments used were the McPhar vertical-loop unit and the Slingram and Boliden horizontal-loop units. Self-potential surveys were carried out with a McPhar unit. From the geophysical point of view, all ground electrical methods employed indicated the presence and the extent of the massive-sulphide mineralization with a good degree of accuracy. The horizontal-loop methods however, defined the contacts more precisely as is to be expected when dealing with a flatly-dipping

Jan 1, 1961

By H. J. Modi, D. W. Fuerstenau

pH effectively regulates the flotation of corundum through its control of the surface charge. Since collector ions function as counter ions in the double layer, the collector must be anionic when corundum is positively charged and cationic when it is negatively charged. Even a long-chained xanthate will float positively charged corundum. Association of the hydrocarbon chains of the adsorbed collector ions gives rise to increased adsorption and increased rate of flotation. Because of this phenomenon, neutral organic molecules aid flotation although the unionized collector cannot promote flotation independently. Na2SO4 was found to depress the flotation of corundum with animic collectors through ionic competition whereas the same salt activates corundum for flotation with cationic collectors. A close connection between ion association, electrokinetic behavior, and floatability is suggested. As part of the increasing interest in the physical chemistry of flotation, strong experimental evidence has been obtained which indicates that organic ions are adsorbed as counter ions by non-metallic oxide minerals mainly because of the electrical forces which exist at interfaces(1-3). Thus flotation of such minerals without activation should then be appreciable only when the mineral and the collector are oppositely charged. Since only limited work has been reported on the effect of surface charge upon flotation behavior(3) this general hypothesis on the flotation of insoluble oxide minerals has not been tested thoroughly. Investigating the flotation of a mineral for which extensive electrokinetic data exist yields a way to test this hypothesis more extensively. The electrokinetic behavior of corundum in solutions containing both organic and inorganic electrolytes has been studied quite thoroughly' Electro-kinetic measurements have shown that in the case of corundum, simply by controlling pH the solid surface can be charged either positively or negatively. For this reason corundum was chosen for study. The object of this paper is to present a study of the flotation of corundum and to explain the results in the light of our knowledge of adsorption mechanisms gained from streaming potential investigations. This paper is concerned mainly with the effect of surface charge on flotation with anionic and cationic collectors, but in addition such flotation phenomena as collector hydrolysis, Van der Waals attraction between hydrocarbon chains, ionic competition, and activation are discussed. While the present paper is confined to a reporting of the data obtained and some of the more immediate conclusions, it will be seen that the results, in combination with those on other systems, do promise a

Jan 1, 1961

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By E. H. Boswell, E. M. Cushing

The Mississippi embayment east of the Mississippi River is part of a vast geologic and hydrologic province. The abundance of water available is largely responsible for the agricultural history of the area and is perhaps the key factor in the rapidly accelerating trend toward industrialization. The multiple artesian aquifer systems that underlie the region and the alluvial aquifer along the Mississippi River are virtually undeveloped sources of fresh water in that they are yielding only a fraction of the water available. The potential yield of the 12 aquifer systems is estimated to be about 25,000 mgd (million gpd) of which only about 600 mgd is presently being withdrawn. The amount of water in storage in these systems is about 1600 trillion gal. Ground water having a dissolved-solids content of less than 500 ppm is generally available at depths of less than 1000 ft, and water having a dissolved-solids content of less than 1000 ppm is available in some places to depths of more than 3000 ft. Iron is the most common troublesome chemical constituent in the ground water. Water in varying amounts is also available from streams within the region. The amount of water which originates within the region and which leaves it as streamflow during a year averages about 50 million acre-ft (about 45,000 mgd). An additional 375 million acre-ft (about 340,000 mgd), which originated outside the region, leaves the region as streamflow during an average year. Some streams have considerable flow during periods of no precipitation and the water during these periods generally has a low dissolved-solids content. Large quantities of water from streams and waterbearing sands (aquifers) are available in the Mississippi embayment east of the Mississippi River. Most of the region is underlain by aquifer systems that will yield large quantities of water to wells, making ground water the most readily available source of fresh water. About 90% of the water used in the region is obtained from wells. Streams have been used primarily to dispose of, and dilute, wastes that have been dumped into them. The Mississippi, Ohio and Tennessee rivers, and the lower parts of the Tombigee and Yazoo rivers also serve as a means of transportation. This nominally water-rich region receives from 48 to 56 in. of precipitation in average years and is crossed by several large rivers. The largest, the Mississippi River, is the western boundary of the region discussed in this paper. The economy of the region is basically agricultural, but industry has become increasingly important since World War 11. The diversification and mechanization of agriculture have resulted in a surplus of manpower, most of which is being absorbed by the expansion of industry. Further industrial expansion probably will occur because of the available manpower, natural resources and economical transportation. Increasing demands on available water supplies will be made and the future economic growth of the region will be largely dependent upon wise utilization and management of the water resources.

Jan 1, 1969

By A. Timur

Fluid flow properties of porous media have long been of interest in such varied disciplines as geology, geophysics, soil mechanics, and chemical, civil, and mechanical engineering. This interest has resulted in numerous models of porous media that have been proposed, tested, and found to be useful under, at best, only special circumstances. A critical review of most of these models is given by Scheidegger. 1 The application of each new tool to the study of porous media has helped to test some of the existing theories and to form new ideas based on the new parameters being measured. In the application of nuclear magnetic resonance (NMR) techniques to the study of the properties of fluids in porous media, the theoretical studies of Korringa et al.2 resulted in a model for the relaxation of spin polarization of protons in a hydrogenous fluid in a pore of a solid. Seevers3,4 verified this model, established a method for measuring the surface-to-volume-ratio distribution in a porous medium, and proposed a technique for determining specific permeability in sandstones. In the present investigation, the uses of NMR methods are extended and a simple model of porous media is developed from an analysis of pulsed NMR measurements. In this model, the pore spaces of a porous medium are divided into three groups on the basis of their surface-to-volume ratios. To evaluate predictions of the NMR model, laboratory measurements of spin-lattice relaxation time, porosity, permeability, and residual (irreducible) water saturation were conducted on more than 150 sandstone samples obtained from four oil fields in North America. Applications are discussed for estimating the volume of movable fluid, ?p, and the specific permeability, k, of sandstone samples. The former parameter, which can be considered as producible porosity, is expressed by ?p = [1 -- (Swr/100)]? , .... (1) where + is porosity in percent of bulk volume and Swr is the residual (irreducible) water saturation in percent of pore volume at a capillary pressure of 50 Psi. Fast, nondestructive laboratory methods are described for determining porosity, movable fluid, and permeability of sandstone samples from measurements with a pulsed NMR (spin-echo) apparatus. Procedures are given for adapting these methods to samples of irregular shape and small size. Theory General In the Korringa, Seevers, and Torrey2 (KST) model the observed decrease in the spin-lattice relaxation time, T1, of protons of a hydrogenous liquid contained in the pore spaces of a porous solid is attributed to an increase in the correlation time for the random motion of the water molecules and to the presence of paramagnetic centers at the liquid-solid interface. This KST model predicts the observed relaxation time of a hydrogenous liquid in a pore of a solid through

Jan 1, 1970

By T. R. A. Davey

The fundamental principles by which bismuth may be removed from lead by pyrometallurgical processes are enumerated. Qualitative discussion of the phase diagrams concerned is followed by presentation of quantitative diagrams. Brief mention is made of the practical aspects. Data presented show how chemical lead (<0.005 pct Bi) may be produced by the Jollivet, Dittmer, and Kroll-Betterton processes. BISMUTH is an element whose properties are very similar to those of lead, and its minerals are associated to a greater or lesser extent with nearly all the major lead ore deposits of the world. In consequence, the lead produced contains bismuth unless a special debismuthizing process is practiced. There does not appear to be any published comprehensive review of the effect of bismuth as an impurity on the properties of lead, and there is some uncertainty as to the beneficial or detrimental effects of small amounts of bismuth in lead used for particular applications. Standard specifications of most countries stipulate a maximum bismuth content of 0.005 pct for chemical lead. With one exception, this specification is met only by lead producers whose ores are relatively bismuth-free, or whose refineries are electrolytic. In lead for certain applications a higher bismuth content is preferred by some fabricators.&apos; In contrast to the refining for silver, copper, and antimony, the refining for bismuth does not usually result in a large overalil economic gain from the sale of byproduct. Thus, debismuthizing is customarily practiced only if market conditions demand a lead with a bismuth content lower than that produced by classical refining; i.e., softening, desilverizing, and zinc refining. Until this century, debismuthizing was carried out only a:; an incidental result of desilverizing, as later described. This century has seen the development of the Betts electrolytic process—the only successful one of many electrolytic processes proposed and patented —and a number of precipitation processes based on the pioneering work of Kroll,&apos; although only one of these, the Kroll-Better ton process,&apos; is in wide commercial use today. It is proposed in this paper to deal only with the pyrometallurgical processes, excluding those based on aqueous electrolysis. Historical Background Prior to 1833 silver (and incidentally bismuth) could not be removed from lead. To recover silver from rich bullion, the only course available to lead refineries was to cupel the bullion, forming a slag of litharge. The first slag tappings or skimmings, on reduction, yielded soft lead of very low silver and bismuth contents. Intermediate skimmings yielded a lead of somewhat higher silver and bismuth contents, which could if desired be recupelled. The last skimmings yielded a litharge very high in bismuth, which could by successive oxidation and reduction cycles be separated into high purity bismuth, and lead returns. This oxidation reduction process, with modern operating techniques, can still be used today to produce a portion of a lead refinery&apos;s output of very low bismuth content, as discussed later. In 1833 Pattinsone discovered that lead bullion could be purified of silver and bismuth by fractional crystallization, the primary lead crystals formed by partial freezing being purer than the melt. Repeated processing in pans produced a lead containing as little as 0.02 pct Bi. The simple explanation of this

Jan 1, 1957

By . M. Muskat

A THEORETICAL consideration of the mechanics of various water-flooding systems with the viewpoint of comparing their relative merits involves the study of two fundamental properties of such systems. On the one hand, it is important to determine the efficiency of the flood as measured by the percentage of the total area that is swept out by the encroaching water before water actually reaches the output wells. This is really a measure of the regional tendency of the water to "bypass" the oil. On the other hand, the various systems must be compared from the viewpoint of their resistances which determine the rate of fluid production obtainable for given pressures maintained at the water input wells. The first of these questions has been studied and very definite answers have been obtained by means of simple electrolytic models.1 These models showed that, in an ideal system, the percentages of the areas flooded out before water reaches the output wells are about 57 per cent for the direct line-drive flood (the input and output wells being equally spaced and placed in alternate parallel lines), 74 per cent for the regular five-spot network, and 79 per cent for the seven-spot network. With respect to the efficiency of the usual flooding arrangements, they are, therefore, given quite accurately by the above numbers. With regard to the resistances of the flooding networks, electrical conduction models have also been used successfully2 and are well adapted to the problem of determining experimentally the pressure distribution and streamlines, or over-all resistances of specific flooding networks. However, such models do not permit readily a study of the effect of changing dimensions or configuration within a network, since a new model must be made up for each set of dimensions considered.

Jan 1, 1933