Search Documents

By Robert D. Pike

IN November 1939, on behalf of the Harbison-Walker Refractories Co., the author undertook the study of the problem of utilizing the dolomite of northwestern Ohio for the manufacture of calcined magnesia suitable for use in refractories. Grateful acknowledgment is made of the unfailing assistance and encouragement throughout this work from the executive and technical staff of Harbison-Walker Refractories Company. The dolomite of the Niagara formation that is exposed or near the surface of a wide area in northwestern Ohio1 constitutes a vast supply of almost pure dolomite. It offers a virtually unlimited supply of cheap raw material of uniform dependable analysis for the manufacture of magnesia. A typical analysis of dolomite from the vicinity of Luckey, Ohio, follows: [ ] Brines containing magnesium chloride or sea water can be reacted with calcined dolomite to produce magnesia.2,3 In such reactions the MgCl2 of the brine supplies some of the magnesia and the amount of dolomite required is thereby reduced by an equivalent amount, but brines of commercial importance containing magnesium chloride are some distance away from the purest grades of the dolomite of northwestern Ohio. It was decided therefore to concentrate upon the development of a suitable process for separating the lime and magnesia of dolomite, depend¬ing upon the dolomite itself as the sole source of magnesia. This would make it possible to place a plant at the dolomite quarry, thus eliminating the cost of transporting the stone and also rendering the calcined magnesia available at a most convenient production point, considering the cost of delivery throughout the steel industry. The selection of a process depending solely upon the dolomite as a source of magnesia also necessarily entails production of the lime content of the dolomite as a by-product. It was recognized that if such a lime by-product could be produced in a suitable form, a plant location in northwestern Ohio would also be advantageous for marketing the lime. The problem, therefore, was the discovery and development of a low-cost process for separating the magnesia and lime of the dolomite of northwestern Ohio and producing each in a form relatively free from the other, and meeting the respective requirements of established markets. A satisfactory solution of this problem has been found, and it is the

Jan 1, 1947

By Jens P. Nielsen, W. H. Justice

This paper describes an improved acidizing technique which has been applied in acidizing gas wells in the La Gloria Field. Wells acidized in this manner exhibited a much greater increase in deliverahility than wells acidized in the conventional manner. The acid is injected into the well in small slugs separated by a small volume of high pressure gas. The acid and gas are displaced from the tuhing by high pressure gas to reduce the hydrostatic head on the well when the acid is recovered from the well. The well is opened for production as soon as the acid and gas are displaced. This procedure permits a very rapid recovery of the acid which results in large increases in the deliverability of the gas wells. It has been found advantageous in the acidization of gas injection wells to inject the high pressure gas directly after the acid without backflowing the acid out of the well. This practice has made it possible to inject the gas in the injection wells of this field with a much lower pressure differential. This reduces the horsepower required to inject the gas and also decrease:, the number of injection wells required per reservoir. INTRODUCTION The results obtained by acidizing gas wells ill the La Gloria Field have varied considerably in the past. For this reason. a planned study of the acidizing procedure was undertaken in order to obtain more consistent results. The Frio Sands of the La Gloria Field are rather permeable and it was not necessary to acidize many of the wells when they were originally completed. At the completion of an eight-year cycling program in several of the gas reservoirs, it became necessary to recomplete many wells in other reservoirs. It was found that the opan Flow potential of the wells recompleted in different sands was not as large as wells that were originally completted in that reservoir. A study of the drilling records of several of these wells indicated that the sands had originally been subjected to considerable hydrostatic drilling fluid overload while the well was being drilled to the deeper sands of the field. It is indicated that during this eight-year period, the drilling mud and water that were lost into the formation when the well was being drilled had formed a relatively impermeable Eone around the well bore. This impermeable zone around the well bore made it very difficult to obtain high deliverability wells when the original wells are recompleted in other zones. Muskat' has shown that in uniformly permeable and porous formations a zone of partial plugging one ft in radius around the well would drastically decrease the productivity of the well. The analysis for this problem shows that the production capacity of a well is very sensitive to the value of the permeability of the zone immediately surrounding the well bore. This is to be expected in view of the highly localized character of the pressure drop in a radial flow system about the well center. The reduction of the deliverability is not proportional to the thickness of the mud-affected zone as the major portion of the reduction in deliverahility IS caused hy the

Jan 1, 1952

By R. Simon, L. Yarborough

This paper presents a correlation for predicting the critical pressures of gas-solvent-reservoir oil systems of the type encountered in gas and solvent injection processes. Experimental data from 14 systems were used to develop the correlation which expresses critical pressure as a function of composition, C7+ mol weight, and C7+ characterization factor. Critical pressures predicted by the correlation for the 14 gas-solvent-reservoir oil systems have an average deviation of 2.8 per cent of the experimental values. The correlation war used to study a wide variety of other hydrocarbon mixtures reported in the literature whose critical conditions are in the range of interest in oil recovery work (100 to 280F and 2,000 to 6,000 psia). Critical pressures predicted by the correlation had an average deviation, expressed as per cent of experimental value, of 5 per cent for 20 miscellaneous mixtures from the literature, and 6.4 per cent for I7 methane-butane-decane mixtures reported by Sage and Lucey. INTRODUCTION Predicting critical points of hydrocarbon mixtures is an important part of phase behavior calculations. If the critical point can be predicted for a specific mixture, the separation between the bubble-point and dew-point regions will be defined, and physical properties of the mixture can be calculated by using the principle of corresponding states. Numerous correlations for predicting critical points of hydrocarbon mixtures have been published. Six of these correlationsl-8 were for light hydrocarbons, and two correlations7,8 ere for high boiling-point petroleum distillates. Organick9 And Eilerts" presented correlations which combined the published data from both light and heavy mixtures, and these correlations became the only available methods for predicting critical pressures for wide boiling range mixtures. In the course of the authors' work on secondary recovery by gas and solvent injection, experimental data were obtained for 14 mixtures of dry gas, ethane-propane-butane solvents, and various reservoir oils. The critical pressures and critical temperatures of these gas-solvent-reservoir oil systems were in the range of 1,900 to 4,800 psia and 180 to 265F. The critical pressures predicted for the 14 mixtures by the correlations of Organick and Eilerts had an average deviation from the measured values of about 13 per cent. The authors felt that it was necessary to develop a better correlation for engineering calculations and the resultant correlation, which is presented on Figs. 1 and 2, predicts the critical pressures of the 14 mixtures with an average deviation of 2.8 per cent. The validity of the correlation was tested by applying the correlation to other hydrocarbon mixtures reported in the literature. This subject is discussed later in the paper. The authors feel that there is also a need for an improved critical temperature correlation for gas-solvent-reservoir oil systems. However, developing a critical temperature correlation is a significant study in itself and is not included in this paper. EXPERIMENTAL DATA The compositions and critical points obtained by the authors for 14 gas-solvent-reservoir oil mixtures are shown on Table 1. The methane concentrations in these mixtures varied from 20 to 63 mol per cent. The intermediate hydrocarbon group, consisting of ethane, propane, and butane, varied from 20 to 64 mol per cent, and the concentration of the C,, fraction from 10 to 20 mol per cent. The physical properties of the C,, fraction covered the range from light, paraffinic, nonasphaltic (Mixtures 5, 6, 7, 8, 9 and 10) to heavy, aromatic, and asphaltic (Mixtures 13 and 14).

By A. G. Weber, H. J. Welge

A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. INTRODUCTION The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature.1-3 When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well's limit of drainage. Calculations can be made for the producing history both before and after cone breakthrough. A typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). Vertically, the blocks are bounded by horizontal planes located at different depths through the

Jan 1, 1965

By S. Vela, R. M. McKinley, L. A. Carlton

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.' The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measzcrement of the re.rulting pressure changes at an adjacent well with a very sensitive differential pressure gauge. This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusivity, trans-missibility and storage. The primary objective in presenting these data is to demonstrate the potential of the methcid for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (I) pulse-test data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data: (2) pulse-test values for permeability are comparable with core va1ue.s; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should. The pulse-testing technique by Johnson et al.' is an ideal source of data for purposes of reservoir description, for it provides a measurement of formation storage S = +ch, hydraulic diffusivity 91 = k/+cp and transmissibility T — This paper describes an application of this method in a producing oil field. Results were analyzed to give numerical values for the parameters 7, T and S. These values were compared with oil-water production data (for the effect of fluid saturation), with core data and with data from an interference test. The reservoir in which the pulse-test survey was run is the result of a structural trap formed by a fault along the east side of a north-south trending anticline. A down-structure aquifer providcs a natural flank water drive for the pool. The producing formation is a dolomitic lime- stone having mainly vugular permeability; the formation oil has a gravity of 29" API with negligible dissolved gas. The field contains 19 wells, all on pump, arranged on 40-acre spacing along the top of the anticline. Fig. 1 shows the location of all these wells except two at the south end of the field. The dashed line on the right-hand side of the figure represents the approximate location of the fault with respect to well positions. Pulse-Test Survey and Analysis of Data A pulse-test requires a pulsing well and a responding well. In the field, changes were made in the rate of flow at the pulsing well by stopping and starting the pump periodically and measuring the corresponding pressure

Jan 1, 1969

By Edgar R. Kendall

A knowledge of the fundamental principles of locating, sampling, testing and evaluating materials is essential in prospecting for mineral aggregates. In this discussion, mineral aggregates will be considered sand, gravel, crushed stone and slag that are used as materials of construction. The quantity of mineral aggregates produced in the United States during the year 1935 for such purposes was roughly 165,000,000 tons, about 60 per cent of which was sand and gravel, 37 per cent crushed stone and 3 per cent crushed slag. The total value of this material was approximately $100,000,000. It is apparent therefore that the prospecting for suitable mineral aggregates is of considerable economic importance. In prospecting for mineral aggregates, the methods employed are the same whether the organization is large or small. In the large organization there may be available geologists for locating sources of supply, a land acquisition department to arrange for the necessary options or permits, engineers to do the sampling, a laboratory for testing, and a board of consulting materials engineers to make the final selection. Even small organizations must follow the same general procedure, though the responsibility for the selection of aggregates may rest with one man, who may or may not be an engineer, but who must depend entirely upon his own judgment. Locating the Supply The initial step in prospecting for mineral aggregates is the locating of suitable, adequate and economic sources of supply for the project in mind. Commercial plants in the vicinity should be investigated and a survey made of the existing structures that have been built of aggregates from these sources. If the structures are rather old and show no signs of deterioration, it is fairly good evidence that the aggregate is satisfactory. If materials of the proper quality can be obtained from commercial sources in sufficient quantity, and delivered to the job economically, it

Jan 1, 1942

By Edgar R. Kendall

A knowledge of the fundamental principles of locating, sampling, testing and evaluating materials is essential in prospecting for mineral aggregates. In this discussion, mineral aggregates will be considered sand, gravel, crushed stone and slag that are used as materials of construction. The quantity of mineral aggregates produced in the United States during the year 1935 for such purposes was roughly 165,000,000 tons, about 60 per cent of which was sand and gravel, 37 per cent crushed stone and 3 per cent crushed slag. The total value of this material was approximately $100,000,000. It is apparent therefore that the prospecting for suitable mineral aggregates is of considerable economic importance. In prospecting for mineral aggregates, the methods employed are the same whether the organization is large or small. In the large organization there may be available geologists for locating sources of supply, a land acquisition department to arrange for the necessary options or permits, engineers to do the sampling, a laboratory for testing, and a board of consulting materials engineers to make the final selection. Even small organizations must follow the same general procedure, though the responsibility for the selection of aggregates may rest with one man, who may or may not be an engineer, but who must depend entirely upon his own judgment. Locating the Supply The initial step in prospecting for mineral aggregates is the locating of suitable, adequate and economic sources of supply for the project in mind. Commercial plants in the vicinity should be investigated and a survey made of the existing structures that have been built of aggregates from these sources. If the structures are rather old and show no signs of deterioration, it is fairly good evidence that the aggregate is satisfactory. If materials of the proper quality can be obtained from commercial sources in sufficient quantity, and delivered to the job economically, it

Jan 1, 1942

By D. V. Carter, F. M. Hackbusch

Beginning the year 1938, the East and East Central Texas district comprised 48 counties, which is equivalent to the Texas Railroad Commission districts 5 and 6. At the close of the year there were 46 oil and gas fields in this district. Eight other fields, seven oil and one gas, have been abandoned. Exploratory Drilling During the year, 113 exploratory wells were drilled. Nine discoveries were made, five of which proved to be oil fields, three distillate, and one gas. Completions for the district were 2043 oil wells (distillate wells included), 36 gas wells and 163 dry holes. Exclusive of the East Texas field, the Marion County extension of the Rodessa field led the district in the number of completions during the year. Production and Proration All fields in the district produced a total of 182,369,484 bbl. of oil, a decrease of 12.57 per cent compared with the 208,594,453 bbl. produced during 1937. The East Texas field produced 148,189,913 bbl., which was 81.6 per cent of the district's production for 1938. November daily average oil production for the East and East Central district was 469,102 bbl. The estimated cumulative production to Jan. 1, 1939, for this district was 1,753,894,802 bbl. It is estimated that the East and East Central district produced 38.9 per cent of the state's total production for the year, which was 468,781,632 barrels. The decrease in 1938 production, as compared to that of 1937, in this district was partly due to the Saturday and Sunday shutdowns, 71 days for the year, which is equivalent to 19.45 per cent of the year. All fields in this district were affected by shutdowns except the Texas portion of the Rodessa field, which was shut in only during January and February. Certain wells were exempt from these shutdowns because of special pro-

Jan 1, 1939

By D. V. Carter, F. M. Hackbusch

Beginning the year 1938, the East and East Central Texas district comprised 48 counties, which is equivalent to the Texas Railroad Commission districts 5 and 6. At the close of the year there were 46 oil and gas fields in this district. Eight other fields, seven oil and one gas, have been abandoned. Exploratory Drilling During the year, 113 exploratory wells were drilled. Nine discoveries were made, five of which proved to be oil fields, three distillate, and one gas. Completions for the district were 2043 oil wells (distillate wells included), 36 gas wells and 163 dry holes. Exclusive of the East Texas field, the Marion County extension of the Rodessa field led the district in the number of completions during the year. Production and Proration All fields in the district produced a total of 182,369,484 bbl. of oil, a decrease of 12.57 per cent compared with the 208,594,453 bbl. produced during 1937. The East Texas field produced 148,189,913 bbl., which was 81.6 per cent of the district's production for 1938. November daily average oil production for the East and East Central district was 469,102 bbl. The estimated cumulative production to Jan. 1, 1939, for this district was 1,753,894,802 bbl. It is estimated that the East and East Central district produced 38.9 per cent of the state's total production for the year, which was 468,781,632 barrels. The decrease in 1938 production, as compared to that of 1937, in this district was partly due to the Saturday and Sunday shutdowns, 71 days for the year, which is equivalent to 19.45 per cent of the year. All fields in this district were affected by shutdowns except the Texas portion of the Rodessa field, which was shut in only during January and February. Certain wells were exempt from these shutdowns because of special pro-

Jan 1, 1939

By Frederick Laist, H. J. Maguire

The ore from the Butte mines of the Anaconda company is quite siliceous; that is, it contains considerably less iron than is needed for the fluxing of the silica. The direct smelting of this ore, therefore, requires the addition of considerable fluxing material. The only flux available in sufficient quantity at Anaconda is limestone containing no metallic minerals. This necessarily makes the direct smelting of the ore so expensive that it is more profitable to subject the ore to a preliminary treatment by concentration. However, as the losses in the concentrator were very high, compared with the losses in the blast furnaccs, it was found, by calculation, more profitable to send ores containing more than a given percentage of copper to the blast furnaces, in spite of the higher costs of treatment. The dividing point was dependent on various factors, the chief of which was the prevailing market price of copper. It was customary, therefore, to segregate the ore as mined into two classes. Ore in the first class generally contained 5 per cent. or over of copper; this was sent directly to the blast-furnace department. Second-class ore contained less than 5 per cent. of copper, and averaged around 3 per cent.; it went to the concentrating department. With the introduction of the flotation process, it mas found possible to maintain an average recovery, as concentrates, of 96 per cent. At the same time, the cost of reverberatory smelting was very materially decreased by the use of pulverized coal. These two changes in practice made the blast furnaces unable to compete with the reverberatory furnaces on a cost basis. The distinction between first- and second-class ore was therefore abandoned, and the ore was treated by concentration. Obviously, on ores as high in iron as the Butte ores, the concentrator produces a product that is self-fluxing; in fact, it is possible to produce a concentrate containing more iron than is necessary to flux the silica. Under these conditions, the amount of basic fluxing materials required for the smelting operations became very srnall and the converter slag lost its former value as a blast-furnace flux. For this reason, a less expensive method of recovering the copper, silver, and gold contained in it than smelting in blast furnaces had to be found. It was not feasible

Jan 1, 1921

By Albert D. Brokaw

THE accompanying chart was devised to provide a rapid and simple method of correcting for temperature and compressibility (deviation from Boyle's law) of gas under relatively high pressures and temperatures, such as are encountered in many deep reservoirs. The chart was prepared by interpolating for the desired values in the experimental data of Burke and Keyes1 and Kvalnes and Gaddy2 on the compressibility of methane, after adjusting their results from 0°C. to 60°F. and combining the correction factors for compressibility and temperature into a single multiplier, which, applied to the product of pressure and reservoir volume, gives at once the volume at one atmosphere (14.7 lb. per sq. in. abs.) and 60°F. The relationship 0f this multiplier to the compressibility factor Z, as used in most discussions, is simply: [Multiplier = 460° + 60°ZT –] where Z is the compressibility factor and T the absolute temperature (Rankine). Fahrenheit temperatures are shown on the vertical axis and pressures in pounds per square inch absolute on the horizontal axis. Correction factors or multipliers at intervals of 0.05 from 0.55 to 1.40 have been plotted on the chart and are calculated t0 give volume of gas at one atmosphere pressure (14.7 lb.) and 60°F. The operation is as follows: The reservoir volume, times the number of atmospheres pressure, times the multiplier, gives the volume of gas measured at one atmosphere (14.7 lb. per sq. in.) and 60°F. For example, a reservoir is estimated to have a volume of 10,000,000 cu. ft., bottom-hole pressure is 2940 lb. per sq. in. and temperature is 184°F To make the correction for methane, follow the 184° line horizontally to the 2940-lb. pressure line. The intersection lies between the 0.85 and 0.90 correction lines, and by interpolation we may estimate the multiplier at 0.863. The computation is simply: [ ] Using the chart for methane prepared by Prof. G. G. Brown3 and his associates, the multiplier is found to be 0.867. Details 0f computation are as follows: Correction factor to apply to PV to correct for deviation from Boyle's law and adjust to measurement basis of 60°F.: [ ]

Jan 1, 1941

By Richard Moldenke

AmonG the things that will always remain to the credit of the foundry-industry is the circumstance that nearly all the research-work of practical value in daily routine was done by active foundrymen, and the results were freely given by them to the world. Moreover, while consumers felt that to them was due a more systematic and exact method of work, the foundry-men again were the first to act in the establishment of specifications under which their product should be sold. To come to more recent times, the American Foundrymen's Association has not only made an elaborate series of tests on cast-iron, and adopted tentative specifications based upon them, but, in addition, it has urged the International Association for Testing Materials, through its American representatives, to make the testing and specification of cast-iron a distinct issue. The half-hearted support first granted was greatly augmented by the rapidly-growing recognition accorded to the enormous iron-casting industry; and when the president of the American Society for Testing Materials was instructed to ask for a special commission for this purpose, Europe was ready to cooperate. During the Buda-Pesth congress, at, which America was represented by Prof. Howe, Mr. Wood and myself, it was decided to add five members to the general committee on steel and iron, whose special duty should be to conserve the interests of the cast-iron branch of the industry. America took up the work at once, and enlarged its committee to 67 members, all of whom were actively concerned in the manufacture or study of cast-iron in all of its branches. At the organization-meeting in Philadelphia, April 25, 1903, Mr. Walter Wood was elected chairman, and myself secretary; and, within a week thereafter, the sub-committees were appointed and became active at once. The scope of the work was naturally limited to those branches of the iron-casting in-

Jan 1, 1905

By A. G. Guy

IN the course of a research on steady-state diffusion it became necessary to make diffusion calculations for a finite solid. This problem was found to be sufficiently different from the corresponding problem for the semi-infinite solid for an entirely new approach to be necessary in obtaining a useful solution. The assumption of an exponential variation of the diffusion coefficient with concentration' was no longer a practical necessity, so that the new solution offered the possibility of handling diffusion in semi-infinite solids for arbitrary variations of the diffusion coefficient with concentration. In discussing the principle on which this method of calculation is based, it is convenient to consider the relatively simple problem of one dimensional diffusion into a matrix that initially contains none of the diffusing substance. The solution of the set- ond Fick Law,?C/?t=D0?2C/?x2, for diffusion into a semi-infinite solid is3 C/C=1-F(x/2vD0t [1] where C is the concentration of the diffusing substance at a depth x cm below the surface after dif- A. G. GUY, Member AIME, and M. GOLOMB are Professor of Metollurgicol Engineering and Professor of Mathematics, respectively, Purdue University, Lafayette, Ind., A. S. YUE, formerly with Purdue University, is now with the Research Laboratory, Dow Chemical Co., Midland, Mich. TP 4505E. Manuscript, July 18,1956. fusion has occurred for t seconds; C, is the concentration of the diffusing substance at the surface of the matrix; Do is the diffusion constant, expressed in sq cm per sec; and + represents the Gauss error function. The corresponding solution for diffusion into a finite solid of thickness, 1, is conveniently written for the change in concentration, C+, at a point midway through the matrix and for times, t, great enough for the following equation to be used4 c1/2/C1=(1/2-2/?e-?2D0t/l2) [2] In Eqs. 1 and 2 the diffusion coefficient is represented by the symbol Do (rather than by D) to emphasize that these equations are valid only for constant values of D. To understand how these equations can be modified to take account of actual variations of D, such as that shown in Fig. 1, first consider the fact that for a given time of diffusion theconcentration at a given point is determined, not by the D value alone, but by the ratio x/vD0 in Eq. 1 and by a similar ratio, l2/D0 in Eq. 2. Even though in fact D varies, it is possible to keep this ratio constant by using a special coordinate system, x,, that varies with D in the appropriate manner. The necessary character of this special coordinate system can be easily visualized by imagining that

Jan 1, 1958

By Ove Sandberg, Olav Bowitz

The operational characteristics of the Soderberg vertical spike anode are briefly discussed stressing the importance of the flow properties of paste in the fluid zone, the thermal shrinkage in the carbonizing zone, and the surface disintegration in the consumption zone. The requirements for paste recipe and binder quality are combined with design and operation of cell. A low temperature susceptibility of viscosity and low thermal shrinkage of paste together with a low microporosity of the binder coke are important properties. PRACTICAL application of Soderberg's idea of a selfbaking carbon electrode proved successful just before 1920. Shortly after, experimental work was started with the aim of developing a continuous electrode that could be adopted as anode in aluminium reduction cells. The intermittent operation of a large number of small prebaked anodes made the idea of developing a continuous anode for electrolytic production of aluminium especially tempting. Moreover, the electrode consumption in this process, even on a theoretical basis, is very high. Many installations were carried out in the 1930's and during the Second World War. During the tremendous post-war expansion of the aluminium industry, the Soderberg electrode has been steadily more widely adopted. Thus, today more than 60 pct of the Western World's output of aluminium is produced in cells with selfbaking anodes, see Big. 1. The quality of the anode paste of Sfiderberg elec- trodes is considered a major factor influencing the specific carbon consumption. The purpose of this paper is to survey the fundamental requirements which must be met in order to obtain good anode operation. We have limited this paper to a discussion of Elektrokemisk's research on the vertical spike type anode. I) FUNDAMEKI'TALS OF ANODE CARBON PERFORMANCE A) Brief Introduction. The only practical method for producing a conductive carbon anode of the size required is to form and carbonize a mixture of a carbonaceous binder and a precalcined dry aggregate coke. In the Soderberg electrode, the forming and carbonization take place in the electrolytic cell

Jan 1, 1962

By W. A. Wood, W. H. Reimann, Maria Ronay

The basic mechanism of fatigue is studied in annealed a brass subjectecl to alternating torsion at room temperature, 100°, 200°, 300°, and 400°C, and in air. It is shown that the slip-zone micro-cracking which characterizes fatigue damage produced by small amplitudes at room temperature is progressively replaced by grain boundary cracking at elevated temperatures, replacement being complete at 400°C. Replacement occurs not because slip activity decreases hut because slip movements at elevated temperatures cease to concentrate in narrow zones and instead disperse. Decrease of amplitude at 400°C through permitting longer lives of specimens before fracture actually causes in- MOST studies of fatigue at elevated temperature have been concerned with data for design. Observations on the basic mechanism of fatigue have been largely incidental, though they have led to the interesting inference that this mechanism has features in common with that of creep.' This paper is concerned primarily with the mechanism itself. Advantage has been taken of mater- crease in pain boundary damage, an anomaly attributed to the greater difficulty at elevated tempwature of starting and propagating a crack. Surface corrosion was most pronounced along slip bands but since at elevated temperatures the slip hands showed no cracking the surface corrosion did not appear to influence onset and early spread of fatigue damage. Similarly the type of fatigue damage produced at room temperature by cyclic strain at large amplitudes, characterized by irregular mi-crocracks at zones between disoriented regions in a grain, was also replaced by mainly grain boundary cracking at elevated temperature, though not so completely. ials and procedures known to show readily how fatigue affects the microstructure of a metal at room temperature, so that direct comparison might be made with what the same procedures show when the material is subjected to fatigue deformation at higher temperatures. 1) MATERIAL This was 70/30 a brass, used extensively in previous studies at room temperature.' Specimens were turned from extruded rod to have parallel test portions 1-1/4 in. long and 7/32 in. diameter, annealed to a grain size -1/10 mm, and electro-

Jan 1, 1965

By D. V. Carter, Dan C. Williams, Franklin M. Hackbusch

During 1939 little of consequence happened in East and East Central Texas in the way of oil discoveries. At the end of the year, there were 47 oil and gas fields in the district. Twelve other fields, 11 oil and one gas, have been abandoned. The ranking fields in order of the number of completions for the year were East Texas, Talco, and Rodessa (Texas portion). There were 511 oil wells (distillate wells included), 32 gas wells, and 257 dry holes completed in the district. Exploration, Discoveries and Extensions During the year, 113 exploratory wells were drilled, the same number as in 1938; four oil fields and one gas-distillate field were discovered. Perhaps the most important discovery, which has been named Barron field, was that of M. Samuel et al., No. 1 Barron in Limestone County. The wells in this field are of the gas-distillate type. Other than the Talco and Sulphur Bluff fields, which produce oil from the Paluxy sand (Upper Trinity), this is the first field on the Corsicana-Mexia fault zone to obtain commercial production from deeper Trinity strata. This "pay" is the Petit lime of the Lower Glen Rose of the Trinity group. The four oil discoveries were: Redland, Angelina County; Bazette, Henderson County; Rowe and Baker, Henderson County; and Marion County Shallow in Marion County. It is believed that the Bazette field, Navarro County, represents an extension of the Flag Lake field. For details concerning discoveries, extensions and important wildcat wells drilled during 1939 see Table 2. Production and Proration The district produced 175,053,729 bbl. of oil (distillate production included) which is a decrease of 4.0 per cent from the 182,369,484 bbl. (distillate production included) produced during 1938. The district's production for the year 1937 was 208,594,453 bbl. The East Texas

Jan 1, 1940

By D. V. Carter, Dan C. Williams, Franklin M. Hackbusch

During 1939 little of consequence happened in East and East Central Texas in the way of oil discoveries. At the end of the year, there were 47 oil and gas fields in the district. Twelve other fields, 11 oil and one gas, have been abandoned. The ranking fields in order of the number of completions for the year were East Texas, Talco, and Rodessa (Texas portion). There were 511 oil wells (distillate wells included), 32 gas wells, and 257 dry holes completed in the district. Exploration, Discoveries and Extensions During the year, 113 exploratory wells were drilled, the same number as in 1938; four oil fields and one gas-distillate field were discovered. Perhaps the most important discovery, which has been named Barron field, was that of M. Samuel et al., No. 1 Barron in Limestone County. The wells in this field are of the gas-distillate type. Other than the Talco and Sulphur Bluff fields, which produce oil from the Paluxy sand (Upper Trinity), this is the first field on the Corsicana-Mexia fault zone to obtain commercial production from deeper Trinity strata. This "pay" is the Petit lime of the Lower Glen Rose of the Trinity group. The four oil discoveries were: Redland, Angelina County; Bazette, Henderson County; Rowe and Baker, Henderson County; and Marion County Shallow in Marion County. It is believed that the Bazette field, Navarro County, represents an extension of the Flag Lake field. For details concerning discoveries, extensions and important wildcat wells drilled during 1939 see Table 2. Production and Proration The district produced 175,053,729 bbl. of oil (distillate production included) which is a decrease of 4.0 per cent from the 182,369,484 bbl. (distillate production included) produced during 1938. The district's production for the year 1937 was 208,594,453 bbl. The East Texas

Jan 1, 1940

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

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 F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.