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By R. E. Hurst, D. E. Ramsey, J. M. Moore

The "frac" method of well stimulation has been applied successfully to all producing formations in the Permian Basin area. During the five years since its development, many changes and improvements have been made in treating materials. procedures, and equipie11t. A number of fluid carrying agents, having different physica1 and chemical properties, have been developed to meet variorus well requirements. The current trend is toward larger gallonage treatments, employing higher injection rates. The use of "down-the-casing" techniques has greatly reduced high surface working pressures, attributable to friction losses resulting from injection throrugh tubing. Petrographic studies of various Permian Basin formations, coordinated with laboratory and well log data, have been found a valuable guide in planning frac treat111o1t.s. A knowledge of the extent (and orientation of naturally occurring fractures and planes of weakness in the formation, aid in predicting the ultimate drainage pattern resulting from the frac treatment. INTRODUCTION The South Permian Basin covers an area in Wcst Texas and New Mexico about onc-half the size of the state of Texas, This vast region has been called the "Permian Basin" for so long that the term will he used here. It includes an area south of the Matador Arch. approximately 250 miles wide and 300 miles long. Structural features of importance within the basin are the Northwest Shelf, Eastern Platform, Midland Basin, Central Basin Platform, and Delaware Basin. The principal producing formations include sand, limestone and dolo-mite, with lesser amounts of shale, anhydrite. chert. and various silicates. All of the producing formations in the Permian Basin have responded to some type of frac treatment. Essentially, a frac treatment may be defined as the injection, into a formation. of a fluid carrying agent containing a particulated solid (usually sand), for the purpose of increasing production. The application of this method of well stimulation to many differing Permian Basin reservoirs has necessitated numerous changes and improvements in carrying agents, solids, service equipment. well equipment. and treating techniques. CARRYING AGENTS A number of different types of fluid carrying agents have been developed since the introduction of the frac method of well stimulation. These agents have different physical and chemical properties, and in many cases the extent of production increase derived from the frac treatment depends on the choice of fluid carrier. Unfortunately, due to many different systems of nomenclature used in the oil field, these differences are not always recognized by the oil Operator. In general, carving agents may he divided into the following broad classi-

Jan 1, 1956

By R. H. McLean

Velocity, kinetic energy and shear in crossflow beneath three-cone jet bits may influence cleaning of the bottom of the borehole and the teeth of the bit. Laboratory investigation shows that each of these parameters is a function of the diameter of the borehole and the product of the volume rate of flow and velocity through the nozzles (QVn). Increasing QV, or decreasing the diameter of the borehole increases each parameter. These functions provide means of predicting the magnitude of each parameter and of scaling the cleaning forces. INTRODUCTION In drilling operations using conventional jet-type rock bits, the impinging jels create an important flow mechanism. Called crossflow, this flow mechanism originates in the impact area of the jets, spreads across the bottom of the hole and supplies the principal source of energy to clean the teeth of the bit and most of the bottom.' Besides providing the means of cleaning cuttings from the bit and the hole bottom, crossflow may also have other, less direct, effects on the rate of penetration. The shear stress generated on the bottom by crossflow will inIluence the thickness and permeability of any filter cake of mud solids or crushed material which forms on the bottom.' These factors may affect the rate of penetration. A previous pulblication introduced some fundamental concepts of crossflow.' Crossllow was shown to occur in a thin layer adjacent to the bottom, and to cover the bottom completely. The maximum velocity in the crossflow above any position on the bottom was found to be directly proporlional to the square root of the product of the volume rate of flow and velocity through the nozzles—the jct QV,,—and inversely proportional to the diameter of the borehole. This information indicated that the effectiveness of crossllow in scavenging the bottom can be improved by maximizing the jet QV. The investigation reported herein amplifies the definition of crossflow. Complete velocity profile data above a representative position on the bottom are analyzed. These data better illustrate control of the capacity of crossflow to scavenge the bottom, and also relate shear stress on the bottom to known, controllable parameters. The conclusion reached in the previous publication that maximization of the jet QV. produces the maximunl cleaning beneath current jet bits is unchanged by these new data; rather, it is strcngthened. Data presented here show that the kinetic energy flux above a representative position on the bottom is maximized by maximizing the jet QV. The shear stress on the bottom will also be shown to be maximized in the same manner. Since the functions relating the jet QV. to velocity, shear stress and kinetic energy also involve the diameter of the borehole, means of equating, or scaling, these quantities in different sizes of boreholes will be illustrated. EXPERIMENTAL EQUIPMENT AND TECHNIQUE JET BIT MODEL Data were recorded from the same laboratory model as used in the aforementioned investigation of the flow around a jet bit.' The model consisted of a 43/4-in. three-cone, jet-type rock bit in a smooth, flat-bottomed borehole constructed of lucite. The bit had a shape and nozzle placement closely resembling larger three-cone jet bits commonly used in field operations. Fig. 1 illustrates the impact area on the bottom of a jet from this bit. Details of the orientation of the jets may be found in the previous publication. TECHNIOU'E OF MEASUREMENT Measurements of the crossflow were made by inserting a very small Pitot tube through the bottom of the simulatetl boreholc. Extreme thinness of the layer of crossflow necessitated accurate measurements of the height of the Pitot tube above the bottom to achieve close definition of the velocity profile. A cathetometer, which could be read to the nearest 0.005 cm, was used to make this measurement.

Jan 1, 1966

By R. E. Mazurak, E. L. Ealy

At the Beckley mine in southern West Virginia, forecasting unstable roof conditions in advance of mining is accomplished by wing a rating system that combines historical information on mine roof failures with known mine geology. Failure frequency rates are derived for each category of roof rock composition, unit thickness, structure, and extraction ratio. In this manner, known geological environments are rated according to instability based on actual experience. Drill hole control and geological interpretation provide the basis for forecasting unstable conditions beyond working faces. The forecasting technique has assisted mine management in reducing fall frequencies by 80% over the past two years compared to the first five years of operation. This reduction in fall frequency was accomplished by modifying the plan of advancing sections to minimize mining exposure to unstable roof conditions.

Jan 1, 1983

By Jerome Strauss, Carl L. Shapiro

THIS is a critical examination of the theory that the amount of carbon necessary to form the iron-carbon (carbide) eutectoid is lowered by the addition of any carbide-forming element. Although this theory has been built up over a long period of years,, it appears, in the light of recent published investigations upon the ternary constitutional diagrams of iron with carbon and other alloying elements, to be no longer tenable. A survey of these new results, summarized below, shows that (as is known) some metals lower the carbon content of the iron-carbon (carbide) eutectoid, whereas others raise it, but (as not heretofore clearly set forth) some first move the eutectoid in one direction and then, at higher concentrations, shift it in the opposite direction. Moreover, these differences in behavior exist even among the common alloying metals classed as carbide formers. PART I INFLUENCE OF BODY-CENTERED CUBIC ELEMENTS The effects of the various body-centered cubic metals (chromium, tungsten, molybdenum, vanadium, columbium and tantalum) are reviewed individually. Iron-carbon-chromium System.-In the monograph on Alloys of Iron and Chromium, Kinzel and Crafts' concluded that the carbon content of the eutectoid is lowered by increasing the chromium content. The quantitative influence of chromium on the eutectoid point of iron-carbon alloys was shown by Monypenny2 (Fig. I) and no data have been forthcoming to refute his findings. Iron-carbon-tungsten System.-Gregg,3 in the monograph on Alloys of Iron and Tungsten, accepted the data showing that tungsten decreases the amount of carbon required to form the eutectoid. The influence of tungsten on the eutectoid percentage of carbon as determined by Oberhoffer and Daeves4 is shown in Fig. a; these results have received general approval. Iron-carbon-molybdenum System.-In the monograph on Alloys of Iron and Molybdenum, Gregg5 reviewed the work of Guillet,6 Swinden,7 and Reed,8 all showing that molybdenum lowered the carbon content of the eutectoid, whereas Takei9 contradicted this conclusion. Svetchnikoff and Alferova,10 a little later, showed that large additions of molybdenum shift the eutectoid to the right. These last-named investigators found that molybdenum, up to 1.2 per cent, shifts the pearlite point and the point of maximum solubility of cementite in the gamma phase only slightly in the direction of lower carbon content; on the other hand, increasing amounts of molyb-

Jan 1, 1943

By H. I. Aaronson, H. A. Domian, A. D. Brailsford

A current study of the growth kinetics of k (hcp) plates in a Cu-Si (fcc)' has generated a requirement for data 02 the chemical interdiffusion coefficient in a (termed D,) as a function of temperature at the composition of the a/a + k pJase boundary. Rhines and Mehl 2 have determined D, as a function of composition at lower silicon contents by making Matano analyses of concentration-penetration curves. However, the accelerating increase in B, which they demonstrated as the phase boundary composition is approached at constant temperature and the rapidly diminishing accuracy of this analysis as the limiting compositions of a diffusion couple are approached (the silicon-rich component of their couples contained appreciably less silicon than is permitted by the solubility limit) indicate that the required information cannot be safely obtained by extrapolation of their data. Although the quite different method employed in this study is not exact, it will be shown that the approximations made are not serious ones, particularly from the viewpoint of the prgcipal application anticipated for these data. D, was determined from the migration kinetics of the a :k boundaries formed in sandwich-type diffusion couples produced by welding a block of high-purity copper to opposite sides of a cube (* in. on edge) of homogenized high-purity Cu-5.82 wt pct Si alloy. The alloy is pure k in the temperature range employed. The surfaces of the couple components which were normal to the diffusion direction were machined accurately flat and parallel, lightly polished, and carefully cleaned. Welding was then accomplished by means of the vacuum-encapsulated pressure jig technique previously employed.3 Welding was always conducted at the intended diffusion temperature; thus the welding anneal also served as the first diffusion anneal. Subsequent diffusion anneals were performed in evacuated Vycor capsules. Following the welding anneal, one of the surfaces parallel to the diffusion direction was machined, ground, and polished flat; additional material was removed from this surface after each diffusion anneal in order to avoid any effects of composition changes. After etching,4 the average distance between a : k boundaries was measured by means of a traveling microscope with an accuracy (per measurement) of better than 1 p. Satisfactory results were obtained at four temperatures in the range 775° to 655°C; attempts to obtain data at two lower temperatures were unsuccessful, evidently as the result of the interference of surface contamination during the welding process.

Jan 1, 1969

By J. D. Irving

In the summer of 1899 there appeared in the Black Hills Mining Review† a short note announcing the discovery of certain deposits of wolframite in the vicinity of Lead City and Yellow creek, Lawrence co., South Dakota.

Jan 1, 1902

By John Naughton

At the General Electric ResearchLabora-tories, we have been interested in the iron-manganese system and the effect of hydrogen on the properties of these alloys. Dr. H. H. Uhlig previously has presented some of these results.' We wish now to offer some other of the data that have a bearing on the subject of this symposium. In the determination of hydrogen in the iron-manganese system by any heating Method we are presented with the problem of the evaporation of volatile manganese and the consequent adsorption of hydrogen by this evaporated metal. It seems wise. therefore, to extract gas at as low a temperature as feasible. Consequently we chose the vacuum or hot extraction method for the analyses of these alloys. The apparatus used is shown in Fig. I. The design is a modification of the apparatus described by Holm and Thompson. To limit loss of hydrogen, samples are stored in a chamber immersed in liquid air. We recommend this procedure whenever there is a question of loss of hydrogen at room temperature. Thence they are moved to the quartz furnace by means of a small magnet, where they are heated by induction to 700' to 800°C. The extracted gas is removed by the circulating pump and placed in the known volume VI (or V2). The circulating pump has been described.3 It is so designed that in spite of the fact that the outlet portion of the pump is part of the known volume, this volume is affected neither by the speed of pumping nor by the pressure of stored gas. The pump also serves to circulate the gases for analysis. The analytical system consists of a

Jan 1, 1945

By J. Marvin Weller, M. King Hubbert

Preliminary investigations were undertaken with a Megger Ground Tester in 1931 by Hubbert to determine whether the faults in Hardin County, Illinois, could be located by earth-resistivity surveys. The results of these investigations, which were in part presented before this Institute in 1932,1 were sufficiently promising to warrant a more extensive field program in the same general area the following summer. During the second season an apparatus of the Gish-Rooney type was employed because of its greater sensitivity and to avoid the troublesome correction for resistance of potential electrodes necessitated by the use of a Megger instrument. The discussion of earth-resistivity traverses which constitute the main part of this paper is based entirely upon the results of the second season's work. All of the traverses were made with a constant electrode spacing of a equal to 100 ft., and the four-electrode technique was employed. Successive stations in these traverses were spaced at intervals of 100 ft. and the line of electrodes was carried parallel to the line of traverse. The graphs of resistivity profiles presented here (Figs. 1 to 3) are plotted with resistivities in ohm-centimeters as ordinates and with distance divided into stations at 100-ft. intervals as abscissas. After the traverses were run by Hubbert the results were computed, the profiles plotted, and tentative interpretations were made by him. These curves and interpretations were then taken into the field by Wellcr, who made a careful geological examination along the lines of traverse for the purpose of checking and supplementing Hubbert's interpretations. Weller then constructed a geologic cross-section extending along the line of each traverse. The accompanying diagrams graphically illustrate the correlation that can be made between earth resistivity and geology in this area.

Jan 1, 1934

By J. J. Mulligan, F. F. Colcord, E. F. Kern

The electrolytic separation of silver and gold has been practiced by the refineries in the United States for a good many years, and probably because of frequent visiting between officials of plants and the consequent exchange of views, operations in the various silver and gold refineries are very similar. We find, for instance, they practically all use electrolytes of approximately the same composition, which, no doubt, is more the result of experience than of studies of electrolytes. At the new electrolytic parting plant of the U. S. S. Lead Refinery, Inc., East Chicago, Ind., considerable attention has been given to the composition of electrolytes, especially to their conductivity and their effect on the character of the silver deposit. We are not aware that anything has been recently published on this subject and are, therefore, presenting such data as we have with the idea that, although it will not be wholly new, it may stimulate interest in the subject. Effect of Copper Content on Conductivity The first work was to determine the specific conductivity of silver nitrate and copper nitrate solutions. Concentrated solutions of silver nitrate and copper nitrate were prepared by dissolving analyzed chemically-pure salts in distilled water, and determining the silver and copper in each. Definite amounts of the concentrated solutions were taken, mixed and diluted to a definite volume. The silver and the copper were determined in each of these solutions and the conductivity was then determined. The plotted results are shown in Figs. 1 and 2. The effect of increasing quantities of silver and copper is readily seen. A comparison of the two sets of curves shows conclusively the benefit of holding the copper content of the electrolyte above 5C g. per liter, as its effect is to increase greatly the conductivity in an approximate propor-

Jan 1, 1926

By E. E. Bach

The administration of industrial organization today embraces more than the cost of production and selling prices. Competition is deeper seated than mechanical devices, overhead charges, and a shrewd manipulation of the markets. Despite the " down-to-the-minute " equipment and the "last word in organization," it is quite evident that "capacity production" will be an unknown quantity until the workman is considered as a producer, in relation to his home, as he is now considered in relation to industry. Whether or not a man shall do an honest day's work is as much a psychological condition as it is a matter of physical strength or skill. His attitude toward his work each morning is determined, to a large degree, by the environment of his home. Whether this attitude, good or bad, obtains the day through will depend entirely upon the one fact as to whether the corporation which employs him does or does not differentiate between the mechanical factor and the human factor in industry. To be more specific, sociological work, under whatever name, should be of such a character as to influence the life of a workman in such a manner as to establish a cooperative interest in his work, foster within him a spirit of contentment in his home, lead him so to employ his leisure time that he will not lower his efficiency as a workman, destroy his domestic happiness, or endanger his standing in the community as a citizen. While no fixed rules of procedure can well be formulated for the development of the work, yet definite lines of activities will readily present themselves as applicable to the individual needs of a community. This is especially true where community influences and agencies pertaining to general welfare are easily correlated. Any definite work attempted must be determined by the type of the

Jan 1, 1918

The total crude production from the Dutch East Indies, and the British Protectorates of Sarawak and Brunei for 1932 is given in the following table: Production, which had shown a rapid increase from 1921 to 1929, has since been reduced. Exploitation drilling in the majority of the larger fields was suspended and existing production kept within predetermined limits by beaning. Most of the smaller fields were shut down entirely. The depth of producing levels varies widely in the different fields. Shallow fields with drilling depths to 500 meters (1650 ft.) are still numerous as well as those with depths between 500 and 1000 m. (3300 ft.). A few of the newer fields reach greater drilling depths up to 1600 m. (5250 ft.). The deepest exploration well drilled to date (Djambi field, South Sumatra) reached a, depth of 2332 m. (7650 ft.) before abandonment in March, 1930. The specific gravities of the various crude oils produced range between 0.65 (86.2° A.P.I.) and 0.95 (17.5° A.P.I.). The lighter crudes have a high gasoline content and fuel oils are derived from the heavier crudes, which usually are rich in paraffin. Producing companies are: De Bataafsche Petroleum Maatschappij (Royal Dutch-Shell combine in Dutch territory); The Anglo-Saxon Petroleum Co. Ltd. (Royal Dutch-Shell combine in British territory); De Nederlandsch-Indische Aardolie Maatschappij (De Bataafsche Petroleum Maatschappij-Dutch East Indian Government combine); De Nederlandsche Koloniale Petroleum Maatschappij (Standard Oil Co. of

Jan 1, 1933

By H. A. Schwartz

THE spheroidal form of the temper carbon nodules in malleable cast iron and of the graphite mottles of "mottled" cast iron suggests that in both all the graphite in a given mottle or nodule grew from a single center of crystallization or nucleus. ? There is, however, a distinct metallo-graphic difference between the mottle and the nodule; the area of mother metal impoverished in combined carbon by the crystallization of graphite in a mottle is practically coextensive with the ramifications of the graphite, while the impoverished zone of metal corresponding to a given nodule is always larger, and usually much larger, than the approximately spherical mass of graphite crystals forming the nodules. Furthermore, the mottle probably is formed during freezing and the nodule almost always at a considerably lower temperature. Assuming that the nodules or mottles can be used as a measure of the existing nuclei (capable of germination) we propose to record certain observations as to the graphitizing reaction in the light of the number and habits of growth of these nuclei. The present authors, in cooperation with others1-7, have reported upon various cognate aspects of the problem. The fact that temper carbon is a mass of flakes and not a solid granule has become well recog-nized since the introduction of an improved polishing technique8,9,10 for cast iron. The problem of deriving from the circular planar intercepts

Jan 1, 1936

By H. A. Schwartz

THE spheroidal form of the temper carbon nodules in malleable cast iron and of the graphite mottles of "mottled" cast iron suggests that in both all the graphite in a given mottle or nodule grew from a single center of crystallization or nucleus.? There is, however, a distinct metallo-graphic difference between the mottle and the nodule; the area of mother metal impoverished in combined carbon by the crystallization of graphite in a mottle is practically coextensive with the ramifications of the graphite, while the impoverished zone of metal corresponding to a given nodule is always larger, and usually much larger, than the approximately spherical mass of graphite crystals forming the nodules. Furthermore, the mottle probably is formed during freezing and the nodule almost always at a considerably lower temperature. Assuming that the nodules or mottles can be used as a measure of the existing nuclei, (capable of germination) we propose to record certain observations as to the graphitizing reaction in the light of the number and habits of growth of these nuclei. The present authors, in cooperation with others1-7, have reported upon various cognate aspects of the problem. The fact that temper carbon is a mass of flakes and not a solid granule has become well recog-nized since the introduction of an improved polishing technique8,9,10 for cast iron. The problem of deriving from the circular planar intercepts

Jan 1, 1935

By W. Rostoker

PART of a program of research on the Ti-A1 system1 involved a study of the lattice parameters of the titanium-rich a solid solution, which has a hexagonal close-packed structure. For this work, a 14 cm Debye-Scherrer powder camera and filtered CuK, radiation was used. For each pattern, the parameters were calculated by a least squares solution of the five strongest high angle lines. This provides an accuracy of i0.005A or better. The results are shown graphically in Fig. 1. It will be seen that an unusual change of slope occurs in the curve for the C parameter at high aluminum contents. Such anomalous changes in slope have been recorded by RaynorV or several magnesium-rich solid solutions. The effects were interpreted in terms of a special contribution to the lattice distortion due to factors of electronic origin predicted by Jones." Jones' theory, in substance, suggested that an unusually large expansion of the lattice would begin when the electron per atom concentration in the alloy was increased to a value at which an overlap just began from one Brillouin zone to another. Con-

Jan 1, 1953

By Edwin Chance

EDWARD H. Coxe, Knoxville, Tenn. (communication to the Secretary*).-Mr. Chance has omitted to mention one very important use for the chemist in connection with the preparation of coal, and that is in connection with coal washing. Efficient coal washing, and especially of the finer sizes, can be accomplished only under the supervision of a chemist, as the proper regulation of the washer can only be had by frequent sampling and analysis of the raw and washed product and the refuse, say at least semi-weekly; and only in this way can a check be kept on the quality of the product and the amount of good coal wasted in the refuse. In large operations, frequently enough coal can be saved from going to the refuse pile to more than pay the salary of the chemist.

Jan 12, 1916

By J. S. Falcone

Soluble sodium silicate materials have well known applications in flotation for desliming, selective depression and corrosion control. Recent advances in the understanding of the complex polymeric nature of silicate solutions using NMR spectroscopy, combined with our studies of the effects of polymeric silicate anions on metal ion activities in solution, oxide mineral surface charges and surfactant adsorption on clays are related to beneficiation processes. The results of these studies indicate the sodium silicates can be used to cause a solution chemistry and particle surface charge characteristics favorable to enhanced effectiveness in typical ore beneficiation systems.

Jan 1, 1983

By Fred T. Agthe, Fred C. Bond

When some materials are ground dry in a ball mill, a stage of comminution is reached at which the finely divided particles begin to adhere to the balls and to the mill lining. As grinding progresses, a coating accumulates upon the grinding media, which tends to cushion the impacts and thus retard reduction of the material. and finally becomes so thick that all grinding ceases. At this stage, the characteristic noise produced by the grinding media during normal mill operation changes to a dull, muffled sound. In most instances, the formation of the coating marks the practical limit of size reduction. Industrial requirements for fine grinding frequently meet with this obstacle, and the tendency in many commercial operations to grind materials to a higher degree of fineness than formerly makes the solution of this problem an important one. The phenomenon is of far greater importance, therefore, than the limited amount of research and technical discussion devoted to it implies. In order to learn more about the coating of different materials when ground dry to a high degree of fineness, certain laboratory tests were made from which it was found that different materials form coatings at widely different size distributions. It is probable that most materials will coat if they are ground fine enough; the exceptions have inherent lubricating qualities, like coal and graphite. In general, the softer materials tend to coat at coarser sizes than the harder or more brittle materials. Limestone, as an example, will coat more readily than quartz, even though limestones of different- texture and composition exhibit great differences in coating potentialities. Various materials were tested in the laboratory to show the variation in coating qualities. It was found that in most tests quartz must be ground to a fineness that would permit it to pass through 325 mesh before coating became markedly detrimental to the grinding operation. Siliceous rocks, however, tend to coat more readily than quartz. Granite, which is composed essentially of feldspar, quartz and mica, has been found to start coating at about 92 per cent through 200 mesh, and feld-spathic minerals alone usually show a tendency to coat at the same fineness. Barite has been ground in the laboratory to a fineness of 99 per cent through 325 mesh without showing serious coating of the grinding media. Gypsum coats readily. Apatite and phosphate rock usually tend to coat. Hematite usually coats, although when mixed with charcoal it does not do so. In testing the carbonate rocks and minerals, it has been found that burned magnesite, dolomite, and dolomitic limestone coat, whereas calcite and calcined calcite do not coat so readily. It has been found that commercial glass, slate, talc, steatite and coke have little tendency to coat. The relative tendencies toward coating during grinding operations, exemplified by

Jan 1, 1943

By Fred C. Bond, Fred T. Agthe

When some materials are ground dry in a ball mill, a stage of comminution is reached at which the finely divided particles begin to adhere to the balls and to the mill lining. As grinding progresses, a coating accumulates upon the grinding media, which tends to cushion the impacts and thus retard reduction of the material. and finally becomes so thick that all grinding ceases. At this stage, the characteristic noise produced by the grinding media during normal mill operation changes to a dull, muffled sound. In most instances, the formation of the coating marks the practical limit of size reduction. Industrial requirements for fine grinding frequently meet with this obstacle, and the tendency in many commercial operations to grind materials to a higher degree of fineness than formerly makes the solution of this problem an important one. The phenomenon is of far greater importance, therefore, than the limited amount of research and technical discussion devoted to it implies. In order to learn more about the coating of different materials when ground dry to a high degree of fineness, certain laboratory tests were made from which it was found that different materials form coatings at widely different size distributions. It is probable that most materials will coat if they are ground fine enough; the exceptions have inherent lubricating qualities, like coal and graphite. In general, the softer materials tend to coat at coarser sizes than the harder or more brittle materials. Limestone, as an example, will coat more readily than quartz, even though limestones of different- texture and composition exhibit great differences in coating potentialities. Various materials were tested in the laboratory to show the variation in coating qualities. It was found that in most tests quartz must be ground to a fineness that would permit it to pass through 325 mesh before coating became markedly detrimental to the grinding operation. Siliceous rocks, however, tend to coat more readily than quartz. Granite, which is composed essentially of feldspar, quartz and mica, has been found to start coating at about 92 per cent through 200 mesh, and feld-spathic minerals alone usually show a tendency to coat at the same fineness. Barite has been ground in the laboratory to a fineness of 99 per cent through 325 mesh without showing serious coating of the grinding media. Gypsum coats readily. Apatite and phosphate rock usually tend to coat. Hematite usually coats, although when mixed with charcoal it does not do so. In testing the carbonate rocks and minerals, it has been found that burned magnesite, dolomite, and dolomitic limestone coat, whereas calcite and calcined calcite do not coat so readily. It has been found that commercial glass, slate, talc, steatite and coke have little tendency to coat. The relative tendencies toward coating during grinding operations, exemplified by

Jan 1, 1943

By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the 'drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By C. Laird, C. E. Feltner

IN previous workif2 we have shown that the steady state cyclic stress response of pure copper tested in the low cycle fatigue range was determined only by the plastic strain amplitude and the test temperature. hus, copper, at any given temperature, has a unique cyclic stress-strain curve independent of prior history. Cu-7.5 wt pct Al, however, showed a stress response for a given plastic strain amplitude and temperature which depended sensitively on prior history. From this work we predicted that all wavy slip mode materials, typified by copper, would have a unique cyclic stress-strain curve; whereas all planar slip mode materials, typified by Cu-7.5 pct Al, would not. This prediction has now been tested for a number of materials of widely varying crystal structure and slip character. Wavy slip mode materials studied include: Fe. Al, Cd, disordered FeCo-V, and Cu-3 pct Co (quenched and aged). Planar slip mode materials investigated include: Fe-3 pct Si, ordered FeCo-V, disordered Ni3Mn, ordered Ni3Mn, and Zn. The treatment and properties of these materials are listed in Table I. Cyclic stress-strain curves were determined by controlled plastic strain tests (see Ref. 1 for details) at room temperature for all materials in both the initially annealed and cold worked conditions. The results obtained for iron and Fe-3 pct Si are typical of wavy and planar slip mode materials, respectively. The cyclic stress-strain curves for these materials are shown in Fig. 1 and it can be seen that iron has a unique cyclic stress strain curve while Fe-3 pct Si does not. Aluminum, Cu-3 pct Co, and disordered FeCo-V showed a behavior like that for iron, while Ni3Mn in both the disordered and ordered condition behaved in the same manner as Fe-3 pct Si. These results therefore support the general conclusion drawn in Refs. 1 and 2 that. for wavy slip mode materials, a cyclic mechanical equation of slate it =t.(hcp, i. T) is approximated in which the satura-

Jan 1, 1970