Search Documents

By William Glenn

Almost beyond doubt, the most important contribution to the assaying of copper yet made, is that of Mr. Eustis (Bans., xi., 120) on the " Comparison of Various Methods of Copper Analysis," which indicates in a manner for which the assayer cannot but feel grateful, how a copper sample ought to be treated from the moment it enters the laboratory until the copper is finally weighed. Admitting, as the present writer is inclined to do, that this paper establishes, as the official standard, the method of electrolysis, we may note as one of the few details which it does not finally fix, the kind of battery most desirable for precipitating the copper upon platinum. In this respect each assayer appears to be a law unto himself, while all feel more or less " shaky " as to the results. Classsen seems to suggest a remedy when he directs the measuring of the -gases liberated by the battery employed. But, in fact, that measure is not a constant in the Bunsen elements which he prescribes for copper determination. Furthermore, measuring gases necessitates more machinery and labor than the average assayer has a stomach for. It is, however, but just to Classen, to whom we owe so much, to reeall that he wrote more especially for students in the schools.

Jan 1, 1889

By Robert A. Cummings, Francis S. Kendorski

The behavior of the rock mass during block caving affects the production of the mine and dictates the loads and deformations placed on required drifts. Traditionally, the drifts used are massively reinforced and buttressed against very high and erratic mining- induced abutment loads or swell muck loads, resulting from undercut- ting. Extensive field investigations in numerous block caving mines in the porphyry intrusive environment, coupled with models developed for tunneling and longwall coal mining, have allowed the development of a unified hypothesis for ore bodies of various degrees of competence. In general, the hypothesis incorporates several sequential steps in the driftlrock mass deformation history, each with characteristic magnitudes, duration, and areal extents depending on ore body competence. 1. Prior to initiating caving, but subsequent to drift development, the rock mass and drift are in a state of near-equilibrium. Zones of stress concentration have stabilized, as for a tunnel. 2. For a newly undercut panel, the rock mass and drifts directly beneath the undercut respond by dilating towards the void created, and undergo a release of compressive strain that manifests itself as tensile failures. 3. For adjacent areas, the rock mass is compressed as the load is shed from the undercut level.

Jan 1, 1983

By Richard D. Call

In any open pit, some slope instability can be expected, varying from bench sloughing to large-scale slope movement. Major slope displacements are preceded by small, but measurable, displacements and by other indicators of instability, such as tension cracks, rock noise, and changes in groundwater levels. A comprehensive monitoring pro- gram, capable of measuring and assimilating displacement related data, is essential for sound pit operation. The objectives of a pit slope monitoring program are 1) to maintain safe operational procedures for the protection of personnel and equipment; 2) to provide advance notice of instability so that mine plans can be modified to minimize the impact of slope displacement; and 3) to provide geotechnical information for analyzing the slope failure mechanism, for designing appropriate remedial measures, and for conducting future re-design of the slope. Surface displacement measurement using conventional survey equipment and extensometers has been the most widely used method, and it is still the most cost-effective. Tiltmeters and borehole inclinometers are also useful tools, and there are promising developments in micro- seismic monitoring. A monitoring system should have redundancy in both type and number of measurements, and be capable of rapid and effective dissemination of displacement information to those affected.

Jan 1, 1983

By Malcolm C. Bridges

A review of the application of geomechanics to open stope mining in Australia was recently undertaken for the Australian Mineral Industries Research Association (AMIRA). It compiled the current state of geomechanics and its application to open stope mining, and recommended avenues of research which should be supported by the industry. Information was compiled for eleven mines which use the method. This included their geological setting, the performance of the mining and evolution of the method, properties and behaviour of rock and backfill, and techniques for measurement and analysis. Open stoping accounts for about two-thirds of production from underground mines in Australia. In the future this proportion will progressively increase and the method will become more complex. Overall, the method is being sucessfully applied, but its full potential is not being achieved because a range of problems and limitations are evident within the mines. Many of these are common to several or more mines. These include: zones of poor ground conditions that delay access and stope development; crown pillars that are irrecoverable; substantial overbreak from the walls and backs of stopes; and lack of a widely accepted method to design systems of stopes. Generally, geotechnical information and techniques for applying it to mining are well-developed. However, it nee

Jan 1, 1983

By R. E. Rowlands, I. M. Daniel

An experimental study is discussed of the state of strain, deformation and fracture around lined and unlined cylindrical cavities in rock under biaxial compressive static loading. The specimens were limestone plates 36 in. high, 24 in. wide and 3 in. thick with a 4 in. diameter hole unlined or lined with hydrostone and aluminum liners. The ratio of horizontal to vertical applied stress was one-third. Experimental techniques used were strain gages, differential transformers and photoelastic coatings. Strain distributions were plotted along the horizontal axis of symmetry for various levels of applied stress. The agreement with theory was good at low stress levels but appreciable deviations occurred at higher levels and near the hole. The experimental strain concentration factor was nearly the same, slightly higher and appreciably higher than the theoretical value for the hydrostone-lined, unlined and aluminum-lined specimens, respectively. Failure modes were splitting along a vertical plane for the unlined and hydrostone-fined specimens, compressive (shear) failure for one unlined specimen and splitting with radial cracking for the aluminum-lined specimen. In the latter, a maximum tensile stress of more than three times the uniaxial tensile strength existed at the interface with the liner at the time of fracture,

Jan 1, 1971

By Alan F. Stewart, Douglas R. Piteau, Dennis C. Martin

Three examples of open pits where toppling failure controls the stability and design of the slopes are described. Two examples involve the design of overall slopes in base metal mines. The third example concerns the analysis and design of remedial measures to prevent toppling failure from occurring in a critical slope in a coal mine. The analytical techniques for assessing toppling failure on a rational basis are discussed for the three examples. This includes an assessment of the important parameters which govern the stability for the toppling failure mode. The geological setting and input data for each example are described, as are the important external or limiting factors pertinent to the sites in question. A statistical cumulative technique was used to assess one of the most important input parameters in the two examples involving overall slope design. Both deep-seated toppling failures, involving the entire slope, and shallow bench failures are considered. Results of the stability analyses and their related engineering significance with regard to slope stability and design are discussed. A sensitivity analysis of various parameters is effectively utilized. Design charts are developed and evaluated accordingly. In the example where toppling failure was unavoidable, the rationale for design of stabilization techniques to prevent toppling is discussed.

Jan 1, 1983

By H. G. Papacharalambous, S. C. Sun

Experimental results indicate that wet cyclones could be effectively used for the preliminary classification of the tested synthetic abrasive materials, thus supplementing the currently used sedimentation method. An empirical formula is also proposed on the basis of the test data to calculate the particle size of separation. One of the basic operations in the abrasive industry is the classification of the crushed and ground materials into different sized products. The relatively coarse grains, plus 325 mesh, are commonly sized by dry screening with satisfactory results. On the other hand, however, the currently used grading tank, for classifying grains finer than 325 mesh, is intermittent. Consequently, it is difficult to operate efficiently and keep pace with erratic market requirements. Little success was made in an attempt to substitute air settling and continuous hydraulic settling for the grading tank, because size specifications1 for abrasive powders are very stringent and difficult to meet. Finally, a wet cyclone was chosen for experimentation. Even though wet cyclones have not been extensively used in the classification of abrasives; however, their performance as a classifier has been verified by Driessen2,4 on coal, McCarrel5 with manganese, and Herkenhoff6,7 on iron ore. Experimental work on silicon carbide, boron carbide, and fused alumina has shown that the cyclone

Jan 1, 1963

By H. M. Hobart

THIS paper deals principally with investigations undertaken by the Welding Research Sub-committee of the Welding Committee of the Emergency Fleet Corporation. The general object of the investigations has been to extend the use of welding in the construction of merchant ships and, specifically, to provide a definite basis for obtaining the best economy and efficiency in employing welding in place of riveting in the construction of the hulls of such ships. Composition of Ship-plate Steel The chemical composition of the steel employed in such hull construction varies with the thickness of the plates. Through the courtesy of Mr. H. Jasper Cox of Lloyd's Register of Shipping, the following information may be given concerning the kind of steel plate employed in American Shipyards in 1918 for the hull construction of merchant ships. Lloyd's requirements do not relate to the chemical composition. They require a tensile strength of 58,000 lb. per square inch (40.75 kg. per sq. mm.) for their lower limit and 72,000 lb. per square inch (50.59 kg. per sq. mm.) for their upper limit. For the information of the Committee, Lloyd's obtained from their surveyors at various works data of the carbon content, which is as follows:

Jan 2, 1919

By E. Buehler, E. Berry

HE magnetic properties of dilute palladium alloys are of fundamental interest.''' Neutron diffraction studies3 have indicated that a better understanding of the behavior of these alloys could be realized with the availability of high-purity single crystals of palladium. Crucible melts of 99.999 pct pure palladium were found inadequate for such research. In a successful effort to fill this need, floating zone refining of palladium was undertaken. In this note the results of the initial experiments are reported. Zoning was accomplished in an argon atmosphere using 450 kc rf generator for an energy source. Samples 5 to 6 mm in diam were suspended in a gastight quartz envelope which could be moved vertically through the rf coil. A nominal upward traverse rate of 1.5 mm per min was maintained during a pass. Close coupling was found to be essential for stable retention of the liquid in the zone. Single crystals averaging 3.5 cm in length were obtained. Laue photography showed them to be continuous single crystals without gross imperfections. Several criteria were used for evaluation of the purity of the zoned material: magnetic behavior, low-temperature specific heat and residual resistivity ratios. Table I shows the residual resistance ratios obtained for two samples, one subjected to a single pass, the other zoned four times. It is appilrent that palladium can be zone refined with the electrically active impurities being transported toward the tail end. A decrease in susceptibility for zone-melted specimens over any previously measured material from 1.5" to 80'~ has been obserted by H. J. Williams and R. C. Sherwood4 substantiating the residual resistance data. The specific heat measurements are currently being made3 and will be published at some later date. Discussions with J. H. Wernick and S. C. Abrahams are acknowledged. We also wish to thank G. F. Brennert for the residual resistance measure ments.

Jan 1, 1962

By Riki Kobayashi, Donald L. Katz

The dew point of natural gas which has been in equilibrium with gas hydrates has been reported to be lower than that obtained for natural gas in equilibrium with water1,? Hammerschmidt' reports a lowering of the dew point of 13 F for a natural gas in equilibrium with hydrate at 380 F and 525 psi. Records and Seely2 likewise show that the dew point of gas leaving hydrate separators' is as much as 150 F below the separator temperature. This paper presents the reasons for the observed differences between the equilibrium temperatures and the dew point temperatures. Descriptions of the dew point determination by the Bureau of Mines and ASTM tester3 indicate that the dew point is taken as the temperature at which liquid water droplets first begin to appear on the cooled mirror surface even though the temperatures involved are below that required for the formation of gas hydrates or ice. PRESSURE-TEMPERATURE DIAGRAM FOR METHANE-WATEK SYSTEM Fig. 1 presents a schematic pressure-temperature diagram for the methane-water system" for some constant pressure between the critical pressures of pure methane and pure water i.e., pressures frequently encountered in pipeline operations. The possible equilibrium relations are shown by the heavy solid lines. Curve AE represents the saturated water content or dew point of gas in equilibrium with a water-rich liquid solution while curve EF represents the dew point of gas in equilibrium with hydrates. In addition the dotted line DE labelled "metastable dew point" is introduced to explain the apparent discrepancy betwceen the dew point determination and gas-hydrate equilibria. Thermodynamics place certain restrictions on the location of line DE6, namely, that (1) the concentration of water along the line DE be greater than the concentration of water along EF or that the metastable line split the angle formed by the intersection of line GE and EF

Jan 1, 1956

By Kenneth Cottingham

The year 1941 brought a considerable increase in drilling activity in Ohio. In 1940, the total of wells completed was 1228, whereas in 1941 it was 1561, or an increase of approximately 27 per cent. Of the 1561 wells, 333 were oil wells, 701 gas wells and 527 dry holes. The completions for the past five years are shown in Table I; the number of productive oil or gas wells for the year 1941, arranged by producing formations, are given in Table 2; the number of wells, oil, gas or dry, completed in each county in 1941, in Table 3, and wells by sands in Table 4. The production of oil increased by about 500,000 bbl. in 1941, nearly all of the increase being in Pennsylvania grade. In 1940, the total production was 3,052,000 bbl. from 25,500 wells. In 1941 the total production was 3,547,534 bbl. from 24,801 wells. The increase in production is chiefly due to the Clinton pool in Clayton township, Perry County, which is briefly men- tioned later in this review. The number of oil wells, by grades of oil, and the total quantities produced are shown in Table ;. Annual oil production for five years is listed in Table 6. The average prices paid for crude in 1941 were slightly higher than in 1940 These 1941 prices, with dates of change, are shown in Table 7. The maximum production of natural gas in Ohio was in the year 1915, when the total was just under 80 billion cu. ft. The maximum consumption occurred in the year 1916, and was approximately 169 billion cu. ft. For the past several years, Ohio has ranged from eighth to eleventh, in order of gas production for the different states, being in tenth place in 1940. In the matter of consumption, however, Ohio remains in fifth place. Preliminary figures for 1940 indicate that production of natural gas increased II per

Jan 1, 1942

By Kenneth Cottingham

The year 1941 brought a considerable increase in drilling activity in Ohio. In 1940, the total of wells completed was 1228, whereas in 1941 it was 1561, or an increase of approximately 27 per cent. Of the 1561 wells, 333 were oil wells, 701 gas wells and 527 dry holes. The completions for the past five years are shown in Table I; the number of productive oil or gas wells for the year 1941, arranged by producing formations, are given in Table 2; the number of wells, oil, gas or dry, completed in each county in 1941, in Table 3, and wells by sands in Table 4. The production of oil increased by about 500,000 bbl. in 1941, nearly all of the increase being in Pennsylvania grade. In 1940, the total production was 3,052,000 bbl. from 25,500 wells. In 1941 the total production was 3,547,534 bbl. from 24,801 wells. The increase in production is chiefly due to the Clinton pool in Clayton township, Perry County, which is briefly men- tioned later in this review. The number of oil wells, by grades of oil, and the total quantities produced are shown in Table ;. Annual oil production for five years is listed in Table 6. The average prices paid for crude in 1941 were slightly higher than in 1940 These 1941 prices, with dates of change, are shown in Table 7. The maximum production of natural gas in Ohio was in the year 1915, when the total was just under 80 billion cu. ft. The maximum consumption occurred in the year 1916, and was approximately 169 billion cu. ft. For the past several years, Ohio has ranged from eighth to eleventh, in order of gas production for the different states, being in tenth place in 1940. In the matter of consumption, however, Ohio remains in fifth place. Preliminary figures for 1940 indicate that production of natural gas increased II per

Jan 1, 1942

By C. M. Ball

The very considerable progress made during the past three years in the crushing and concentration of ores, lends special interest at the present time to any means of a more efficient character than such as are already generally known and in use, for the rapid and regular reduction of large quantities of the harder and heavier grades of mineral-bearing rock. Such means are of exceptional importance in connection with the preparation of iron-ore for separation by the magnetic process, since in this operation the capability of dealing with large volumes of material and of securing by ready means of adjustment, a granulation of the material under treatment to any required mesh or fineness, is of the greatest possible value. With these, however, must be coupled the further considerations of the amount of power expended for the work done, and the wear and tear, represented in the cost for renewal of parts of the crushing machinery, per ton of material reduced to a given degree of fineness. In general terms it may be stated that the operation of a crushing train, capable of reducing an ore-rock of average density and hardness, from the condition of mine lumps to pass 1/16-inch screenopenings at the rate of 20 tons per hour, should not call for an expenditure of more than 125 horse-power, and that the wear and tear of the crushing machinery, all told, should not exceed 2 cents per ton. In the design of a crushing-train for an ore-dressing plant, there are, moreover, considerations of great importance which relate to the simplicity or complexity of construction and arrangement, the wear and tear of few or many elements, the easy ability or difficulty of maintaining the working adjustment of the various elements of the train, and the number of hands required for the operation of the system. With these points in view, it is thought that the Cummings ore-

Jan 1, 1893

By S. R. B. Cooke, Iwao Iwasaki, Hyung Sup Choi

John Dasher (Materials and Processes Engineer, Crucible Steel Co. of America, Pittsburgh, Pa.) The authors are to be congratulated for their excellent work, dramatic results, and persuasive explanation on the neglected subject of the temperature variable in soap flotation. The explanation includes why heat is helpful in conditioning and why heat is helpful in flotation. This is a fine start, but I hope the work will be continued to show which is the major effect. In the work of Noman and Dash er(1) it was found that substantially all the benefit of heat came from the conditioning step, and that results were much better if a thick pulp was conditioned hot and then diluted with unheated (or less heated) water for flotation (or agglomerate tabling) than if the same quantity of heat was used to condition and float at some intermediate temperature. In other words, heat for conditioning gives a Rood return, but additional heat for dilution water is near or beyond the point of diminishing return. Strathmore R. B. Cooke, lwao lawsaki, and Hyung Su0p Choi (Authors' Reply) Mr. Dasher'skind comments on our paper are appreciated. In view of the relative simplicity of empirical investigationsof the temperature variable upon conditioning and flotation, it ispuzzling why the subject is so neglected. Our work, being sub sidiary to the main investigation of the effect of structure of fatty acid collectorsupon iron ore flotation, was quite restricted, but we intend to return to the subject as soon as possible. Mr. Dasher's point, that given a certain number of calories it is better to invest them for conditioning in a thick pulp rather than to spread them out for both conditioning and flotation operations, is well taken and cannot be argued. On the other hand there is no question that high temperature during the flotation of iron ores induces superior frothing characteristics, and, in particular, greatly augments the rate of flotation and markedly decreases the time required for "difficult" particles to float.

Jan 1, 1961

By Fred W. Gordon

The North Chicago Rolling-Mill Co., of Chicago, have four furnaces at South Chicago, built during 1881. Each furnace is 20 feet diameter of bosh, and 75 feet total height, the hearth being 11 feet diameter, and the top 15 feet 4 inches. They are blown through seven 7-inch tuyeres placed 5 feet 6 inches above the hearth level. Cubical contents, 15,000 cubic feet. Each furnace is supplied with 2 blowing engines, 84-inch blowing cylinder, and 36-inch steam cylinder, and 54-inch stroke. These two have one jet-condenser worked by an auxiliary pump. The blast for each furnace is heated by the aid of three Whitwell fire-brick stoves, each 21 feet diameter and 60 feet high. In the batteries of boilers furnishing steam for four furnaces there are 36 double-length boilers, 76 feet long, 48 inches diameter and 16,000 square feet heating-surface. The plant was designed to produce 3600 tons per week, or 900 tons for each furnace, and was fitted as above with such engines, boilers, and hot-blast stoves as were thought requisite for that production ; hence, calculated from the present make—not the least remarkable feature is the economy of construction—there are less engines, less boilers, and less hot-blast power for the iron made than at ally plant within my knowledge, or it could to-day be duplicated for less money per ton of iron made per week than could any plant now in existence, whether using fire-brick or cast-iron stoves for heating the blast. This is a practical demonstration of my assertion in a paper on fire-brick stoves, read before the Institute," that the application of fire-brick stoves in construction really lessens the first cost. In view of the statements just made, I must be most emphatic in assuring the members that nothing is strained or overburdened.

Jan 1, 1886

By R. E. Whippo, B. L. Murowchick

The commercially exploited sedimentary apatites exhibit a number of variable lattice substitutions which affect their chemical composition. Carbonate is a major diluent of phosphorus values in sedimentary apatites. Substantial amounts of water as hydroxyl, hydronium, and tetrahedral hydroxyl ions substitute for fluorine and oxygen, calcium, and phosphate, respectively. Calcium is also replaced by several other divalent and monovalent cations. The structural formula demonstrates the substitutions in the lattice of the sedimentary apatites studied in view of the crystal-chemical relationships which have been postulated for the isomorphous apatite series. The lattice constant a. varies from 9.29 to 9.40 A for the apatites studied. Quantitative relationships between this constant and lattice substitution are complicated by the interaction of multiple substitutions whose influence is non-additive. The mineral apatite, the principal raw material source of phosphorus for agricultural and industrial applications, offers a wide area for investigation. Considerable research effort has been expended in the study of apatite crystal-chemistry by medical, biological, and earth scientists. Few of these studies deal directly with the sedimentary apatites from the major occurrences which are widely exploited for commercial uses. It is the purpose here to present chemical analyses of several sedimentary apatites and discuss their chemical composition in relation to the structural and crystalchemical principles which have been postulated for the apatite isomorphous series. THE STRUCTURE OF FLUORAPATITE The atomic structure of fluorapatite was described, independently, by Ngray-Szabd and Mehmel in 1930 and has been accepted as presented, with only minor changes,4 since that time. The hexaogonal unit cell with dimensions of a = 9.37 0.01 A and c = 6.88 0.01 A contains two molecules of the composition "There are six (PO4) groups in the cell, four calcium ions on the trigonal axes, surrounded prismati-cally by six oxygen ions and six calcium ions surrounded by an irregular polyhedron of a fluorine and five oxygens. Fluorines are at the comers of the reflexion planes, touching three calcium ions each".l7

Jan 1, 1968

By E. M. Boatman, S. J. Pirson, R. L. Nettle

More than a decade ago some theoretically derived relationships were proposed that permitted the prediction of the relative ability of reservoir fluids (oil, gas, water) to flow simultaneously within the porous structure of rocks. While many successful predictions of fluid-flow ratios from wells have been made from electric logs, the theoretical deductions have not been subjected to laboratory verifications. For the relative permeability to liquid and gas, simultaneous flow of water and air was used, employing the familiar external-gas-drive technique. While in the process or water desaturation, the resistivities of the test cores (Woodbine sand) were measured. Their permeabilities varied from 10 to 280 md. The laboratory results indicated the need for changing the values of exponents in the theoretically derived formulas, whereas the form of the functions of resistivities and saturations remained as derived by theory. For the relative permeability to oil and water, the three-core dynamic technique was used on six cores. In this case it was found that the formulas were valid with but slight modification as derived by theory, to a sufficient degree of accuracy for engineering use and for well productivity prediction from electric logs. INTRODUCTION Conventional quantitative well log interpretation generally stops after reasonable values for formation porosities and water saturations have been established. Yet such in formation is insufficient to predict either the outcome or the desirability of well tests and completion, let alone the economic aspect of producing oil- and gas-bearing sections which might have been established by conventional log analysis. To give an engineering answer to such questions, it is necessary to predict the expected fluid flow ratios, the productivity index and the ultimate recovery from potentially productive wells. This problem requires in part for its solution a determination of the relative permeability characteristics of the potentially producing formations, both to oil (or water) and gas, and to oil and water.

Jan 1, 1965

By C. D. Rubert, W. J. Parton

LARGE quantities of fine anthracite with associated impurities are discharged with the waste water from the coal-cleaning plants in the Pennsylvania anthracite region. Furthermore, for many years this fine material has accumulated and formed silt banks. The difficulty of removing the impurities from the fine material and the lack of adequate markets are responsible for the waste of this material. In view of a larger demand for fine coal, mainly for pulverized fuel, the Lehigh Navigation Coal Co. Inc. decided to investigate the froth flotation process for recovery of fine coal from these waste solids. A test plant was constructed and operated for six months during 1942 in order to determine the practicability of recovering coal from the waste water of a cleaning plant (breaker) by froth flotation, and to obtain operating data for designing a commercial plant if the results were favorable. PRELIMINARY INVESTIGATION Before the pilot plant was constructed information was obtained by field and small-scale laboratory tests to serve as a guide in the design and operation of the pilot plant. Size and ash analyses of a representative sample of the material discharged in the wash water from a cleaning plant are given in Table I. [ ] The refuse content increases progressively as the size of the particles decreases. The larger particles (+35 m.) are low in ash content and could be marketed without cleaning. Since these solids are discharged from the breakers with 90 to 95 per cent water by weight, the first step in the recovery of the coal was that of reducing the quantity of water so that water in excess will not have to be handled. Furthermore, it was found that the removal of most of the minus 200 mesh high-ash material was desirable to permit the most efficient flotation of the coal. Classification tests were run and showed that a hydroseparator overflow rate of 12 ft. per hour was sufficient to eliminate much of the minus 200-mesh material while allowing the coarser material to settle and be thickened.

Jan 1, 1944

By John C. Calhoun, Raymond G. Loper

Theoretical calculations for the decline of pressure and the variation of instantaneous producing gas-oil ratio with increased cumulative production have been made for reservoir systems under various producing drawdown values and for various spacings. These variables have been included by a modification of previously Published techniques. This consists essentially of utilizing a radial system flowing gas and oil in a succession of steady state calculations. The results of the calculations do not show any variation in the predicted behavior of the internal gas drive reservoir when either the drawdown or the spacing are changed. The prediction of performance on an internal gas drive reservoir has been presented by various authors. ',"' These predictions are in the form of a pressure decline and an instantaneous producing gas-oil ratio as a function of cumulative oil withdrawal. In making these predictions a basic assumption has been that the saturation of the reservoir is uniform throughout at any time, or that the pressure differential imposed on the reservoir system is zero. Because of these assumptions the validity of such predictions has been questioned. Their application to actual systems, where saturations are not uniform and where producing differentials exist, has been a hazardous procedure. The authors cited have used different methods of approach to the derivation of equations for making their predictions and for arriving at a solution of both equations, but basically the same relationships are utilized in each case. In all instances the instantaneous producing gas-oil ratio is calculated from the equation: In utilizing this equation an average reservoir pressure and an average reservoir saturation must be known, the former to define ß, v, s, and uo/ug and the latter to define kg/ko. Predictions can be made, therefore, only for the conditions of a uniform reservoir saturation and a uniform reservoir pressure. This restriction of requiring a uniform oil saturation can be resolved by applying two-phase steady state flow for the radial system to the reservoir's history. Radial steady state flow is defined when the ratio of phases flowing,

Jan 1, 1949

By John C. Calhoun, Raymond G. Loper

Theoretical calculations for the decline of pressure and the variation of instantaneous producing gas-oil ratio with increased cumulative production have been made for reservoir systems under various producing drawdown values and for various spacings. These variables have been included by a modification of previously Published techniques. This consists essentially of utilizing a radial system flowing gas and oil in a succession of steady state calculations. The results of the calculations do not show any variation in the predicted behavior of the internal gas drive reservoir when either the drawdown or the spacing are changed. The prediction of performance on an internal gas drive reservoir has been presented by various authors. ',"' These predictions are in the form of a pressure decline and an instantaneous producing gas-oil ratio as a function of cumulative oil withdrawal. In making these predictions a basic assumption has been that the saturation of the reservoir is uniform throughout at any time, or that the pressure differential imposed on the reservoir system is zero. Because of these assumptions the validity of such predictions has been questioned. Their application to actual systems, where saturations are not uniform and where producing differentials exist, has been a hazardous procedure. The authors cited have used different methods of approach to the derivation of equations for making their predictions and for arriving at a solution of both equations, but basically the same relationships are utilized in each case. In all instances the instantaneous producing gas-oil ratio is calculated from the equation: In utilizing this equation an average reservoir pressure and an average reservoir saturation must be known, the former to define ß, v, s, and uo/ug and the latter to define kg/ko. Predictions can be made, therefore, only for the conditions of a uniform reservoir saturation and a uniform reservoir pressure. This restriction of requiring a uniform oil saturation can be resolved by applying two-phase steady state flow for the radial system to the reservoir's history. Radial steady state flow is defined when the ratio of phases flowing,

Jan 1, 1949