Search Documents

By R. L. Perrine

The rise of drain holes drilled from a well to improve productivity is becoming increasingly common. This paper presents data on the productivity increase that may he expected. The data were obtained by use of an electrolytic tank mode1 of a reservoir. Parameter varied in the study to show their effect on productivity include the length, number, and arrangement of drain holes, formation thickness, and damage near the well-hore. The most important results are that very large increases in productivity can be expected only ill damaged wells. The distance, to which drain holes penetrate is of primary importance. Additional length is more effective than increasing the number of drain holes. INTRODUCTI O N In planning the use of drain holes to improve productivity, it is important to he able to estimate the increase in production that can be obtained for a given expenditure. It is also important to know what combination of parameters related to the use of drain holes can he chosen to give the largest production increase. This paper presents data on the productivity increase that may be expected, as obtained by use of an electrolytic tank model of the reservoir. In this study, :! number of parameters were varied to show their effect on productivity. These included the length, number, and arrangement of the drain holes. The presence or absence of a damaged zone of low permeability around the well-bore and the thickness of the producing formation were also considered. The productivity increase that might be expected due to drain holes is presented as the ratio: productivity of a well after drain holes are drilled and completed to the productivity of the same well in an undamaged state without drain holes. The symbol Q/Qo is used to represent this productivity ratio. Thus, the comparison in each case is with a formation of uniform and undamaged permeability. Additional notation includes I;, for the radial extent of the damaged zone, which is assumed to be cylindrical and concentric with the wellbore. Thus the effect of an actual block is approximated by a discontinuous varia-tion in permeability. For purposes of this paper, the permeability within the damaged zone, denoted by kb, is assumed to be 1/25 that in the remainder of the formation, or k. A necessary assumption in making comparative tests using an electrolytic model is that reservoir flow behavior can be approximated by single-phase, steady-\tate flow according to Darey's Law. In addition, the formation must be assumed to be homogeneous with equal horizontal and vertical permeability. The well-hore diameter in this study is assumed to be 11¾ in. and the drainage radius of the well equal to 500 ft. The drain holes are considered to have been completed without damage. THE ELECTROLYTlC MODEL 'She producing formation was modeled by forming a sheet of phosphor-bronze into a cylinder 40% in, in diameter to represent the boundary of the drainage area. This was enclosed in a waterproofed plywood box, and the box filled to an appropriate level with a dilute sodium chloride solution. Solution concentration was adjusted to give a total resistance from

Jan 1, 1956

By P. W. Ramsey, E. J. Boyle, E. A. Anderson

ONLY a few zinc-rich alloys are in commercial use today, and these depend largely upon solid solution effects for their desirable properties. Typical examples are rolled alloys containing about I per cent of copper, with or without additions of elements such as magnesium,1 and die-casting alloys containing about 4 per cent of aluminum with small amounts of magnesium and sometimes copper.2 A number of elements are capable of forming alloys with zinc, which do not enter into solid solution except in limited degree. The present paper considers one such system, zinc-titanium, in which alloys having potentially useful properties in the rolled form were found. ZINC-TITANIUM SYSTEM The zinc-rich portion of the zinc-titanium diagram, as determined by standard methods in this laboratory,3 is shown in Fig. I. The portion of the diagram of significance in the present work extends from 0 to about 0.5 per cent titanium. Gebhardt4 places the eutectic at 0.45 per cent, but the evidence in favor of the composition given in Fig. I is considerable. The solid solubility of titanium in zinc is very low indeed and possibly places these alloys in a somewhat different category from the commercial alloys previously mentioned. ALLOY PREPARATION All of the alloys used in this work were prepared with titanium metal of 98.9 per cent purity. In most cases high-purity zinc (99.99 per cent) was used but sufficient work was done later to show that zinc of about high-grade composition would yield approximately equal results. Best practice in alloy manufacture seemed to be to prepare a zinc-titanium hardener by adding about 4 per cent of titanium metal to molten zinc and holding under a boric acid cover, with frequent stirrings, at 750°C. until the titanium had dissolved. The desired titanium content could readily be obtained in the final alloy by adding the calculated amount of this hardener. The alloys proved to be quite stable in composition, unless overheated, and, with reasonable temperature control, required no cover or flux to prevent loss of titanium content by oxidation. HOT-ROLLING TESTS Three alloys containing, by analysis, 0.05, 0.12, and 0.23 per cent titanium were selected for preliminary study. Slab cross sections revealed a marked grain refinement* (Fig. 2) in the two alloys of highest titanium content. Cast unalloyed zinc has a columnar grain structure similar to that shown for the alloy of lowest titanium content but without the scatter of small equiaxed grains at the center.

Jan 1, 1944

By R. M. Goldhoff, H. J. Beattie

The high-temperature properties of a 1 Cr-Mo-V forging steel are described. A series of controlled heat treatments was designed to delineate the effects of austenitizing and tempering treatments, temile strength, and grain size on such properties. Studies indicate that the mechanical properties and their varlations under creep can be described by the initial metallurgical structures and their changes droPirzg exposure, particulavly the carbide reactions. Such structures are described and correlated with the mechanical properties. FOR many years the large steam turbine industry has relied on the 1 Cr-Mo-V type forging steel for critical applications. Because of its adequate heat resistance and relative economy, it is currently in use in the temperature range up to about 1050" to 1075°F. Attempts to understand the large property variations attainable in this steel involve the structural modifications due to the wide latitude in its heat treatment. The heat treatment essentially involves a two-step process which includes solution-ing of carbides in the austenite range followed by a suitable tempering treatment below the critical to adjust the level of properties. The latter step is referred to as "secondary hardening" and is basically an ordinary aging reaction involving carbides. In the commercial heat treatment of large components of such steel, homogenizing and stress-relief anneals may be included and have some importance in determining subsequent properties. Several studies of the engineering properties of this steel as a function of transformation micro-structure have been reported.1 3 However, in this steel the carbide reactions, which are a function of composition and heat treatment, appear to be the property-controlling factor rather than the micro-structure defined as a transformation product. Thus, the tempering resistance of this type of alloy steel is mainly a function of the size and distribution of alloy carbides.4 However, it is also necessary to consider the stability of the microstructure and the effect of dynamic carbide reactions on subsequent properties. It is the purpose of this paper to show the interdependence of properties and corresponding structures, particularly carbide reactions, developed for a limited set of controlled heat-treatment conditions applied to 1 Cr-Mo-V steel. MATERIALS AND PROCEDURE The material for this work came from a large production forging whose chemical composition is shown in Table I. The property data accumulated on this steel as a function of heat treatment were room-temperature tensile and smooth- and notch-bar creep rupture at 1050°F (notch geometry: shank diameter = 0.357 in., depth = 50 pct, radius = 0.005 in.). To achieve controlled structural variations the temperature and time of both austenitizing and tempering were varied in a manner to produce a series of eight steels each at one of two grain sizes and one of two hardness levels in proper combination for valid comparisons. This will be clear upon examination of Table I. Structural studies involved the use of optical and electron microscopy as well as X-ray and selected-area electron diffraction. To reveal the nature of carbide precipitations, electrolytic extraction techniques were used with subsequent analysis of the residue by X-ray diffraction. Weight losses of the steel specimens during electrolysis were measured and successive chemical fractionations of the residues were applied and checked by X-ray examination. The details of fine structural distributions, morphologies, and crystallography of the precipitates as well as dislocation distributions were investigated by examining in the electron microscope three common types of preparation. a) Relief Replicas. Mechanically polished sections were etched in 2 pct nital, replicated with a nitrocellulose film, which was shadowed by chromium vapor deposited at a glancing angle of 20 deg. b) Extraction Replicas. A thin film of carbon was vapor-deposited on the polished and etched surface. The carbon films were then etched off and gathered on electron-microscope supporting grids. The carbides left imbedded in the carbon replica in their original distribution were then examined crystallo-graphically by selected-area electron diffraction. c) Thin Films. Specimens were mechanically ground and polished down to a thickness of 0.001 to 0.003 in. Final thinning was done electrolytically in a "chrome-acetic" electrolyte. When holes began to appear in the foil, the voltage was interrupted and applied in several 1-sec bursts. Sections of the foil between holes were thin enough to pass a 100-kv electron beam that carries an image.

Jan 1, 1965

By C. W. Crispell

The four nomograms presented in this article were designed to simplify and make more rapid the calculations connected with the compression and transmission of air. The formulae involved are rather complicated, but the graphic solutions are simple; their use requires an ability to follow explicit directions and to interpolate values on a logarithmic sca1e. † For the sake of convenience, the nomograms will be divided into two classes, and the purpose and accuracy of each will be discussed. Power foR CompREssion It is frequently desirable to determine the horsepower necessary to compress a given amount of free air from atmospheric pressure to a certain final pressure. The nomograms in Fig. 1 and 2 present a rapid method of calculating the horsepower required to compress 1 cu. ft. of free air per minute by single or two-stage compression. The general formula for the horsepower required to compress air adiabatically is: S X 144 PVn [(P')n-1/sn -1 (1) where: P = absolute atmospheric pressure at compressor, in pounds per square inch. P' = final absolute pressure of compressed air, -in pounds per square inch. V = volume of free air compressed per minute, in cubic feet. S = number of stages. n = exponent of the compression curve.

Jan 1, 1918

By C. W. Crispell

THE four nomograms presented in this article were designed to simplify and make more, rapid the calculations connected with the compression and transmission of air. The formulae involved are rather complicated, but the graphic solutions are simple; their use requires an ability to follow explicit directions and to interpolate values on a logarithmic scale. ? For the sake of convenience, the nomograms will be divided into two classes, and the purpose and accuracy of each will be discussed. Compression It is frequently desirable to determine the horsepower necessary to compress a given amount of free air from atmospheric pressure to a certain final pressure. The nomograms in Figs. 1 and 2 present a rapid method of calculating the horsepower required to compress 1 cu. ft. of free air per minute by single or two-stage compression. The general formula for the horsepower required to compress air adiabatically is: HP = S X 144/33,000 PVn/(n-1) [(P'/P) n-1/Sn -1] (1) where: P = absolute atmospheric pressure at compressor, in pounds per square inch. P' = final absolute pressure of compressed air, in pounds per square inch. V = volume of free air compressed per minute, in cubic feet. S = number of stages. n = exponent of the compression curve.

Jan 6, 1917

By W. K. Hardy, H. H. Stadelmaier, L. J. Huetter

The ternary system Co-Sn-C was studied in the cobalt-rich region. The liquidus projection ulas established and two fonr -phase reactions were found. An isothermal section at 950°C was worked out. In the region studied the following phases were observed: cobalt-rich solid solution, graphite, binary compound y -cobalt-tin, and a ternary compound. As a result of the limited solubility of carbon in liquid cobalt-tin alloys, the investigation was limited to the cobalt-rich region. Tin contents up to 32 at. pct were studied. Cobalt of 99.99 pct purity, tin of 99.97 pct purity and synthetic graphite of 99.93 pct minimum purity prepare the alloys. Carbon determinations of all alloys were obtained by gas volumetric analysis. Samples were investigated microscopically and by X-ray diffraction using CoK, and FeK, radiation. Cooling curves were obtained with a number of alloys to determine the temperature of the four-phase reactions. The thermocouple was calibrated with the melting points of high-purity silver and copper. In the region studied the following phases were observed: Cobalt-rich solid solution (face-centered cubic) Graphite. Binary compound y (solidifies congruently at composition Cop~n)'. Ternary compound k which is face-centered cubic with superlattice and nonferromagnetic.' In Fig. 1 the fields representing the projections of the liquidus surfaces were determined by microscopic investigation and are labled by their primary phase. In the field labled C graphite is the primary phase. During solidification in this field much of the primary graphite was expelled through the surface of the melt. It could not always be established microscopically whether the remaining graphite was primary or purely eutectic. Therefore it was not possible to determine accurately the boundary curve which drops from the binary eutectic el at 1309 "~~ to the point of the four-phase reaction at F. The ter-nary carbide is the primary phase in the field labled k. To the right of this field the primary graphite is consistently nodular whereas flake graphite is observed at tin contents somewhat below F. The ternary carbide does not appear to solidify congruently. The graphite is attacked in a peritectic reaction along the boundary between k and C. Thus no graphite is observed in alloys in the k field. In alloys right of the boundary between k and C the graphite nodules are located in the center of the k crystallites, further documenting the peritectic nature of the reaction with the graphite. A four-phase reaction was found at F and 1120 &3"C. The most likely reaction is L+ CY-Co + C — k. Below the temperature of the binary eutectic ez at 1112" a second four-phase reaction was observed at E and 1100 lt3"C. It is the ternary eutectic L — CY-Co + k + y. Figs. 2(a ) to (e) show microstructures of the ternary alloys in the as-cast condition. Fig. 2(a) shows the eutectic a-Co + C (with some primary graphite) with the carbide k in the grain boundaries. Fig. 2(b) shows primary cobalt (dark areas) and the eutectic a-Co + k which is formed along F-E.

Jan 1, 1961

By Carl H. Samans

In their recent complete review of the subject of age-hardening,' R. F. Mehl and L. K. Jetter classify the main types of precipitation-hardening alloys under two headings, depending upon the nature of the precipitate and the character of the precipitation. In the alloys falling under the first heading, which display "continuous precipitation" and are typified by the aluminum-copper alloys, "precipitation seems to occur without much regard to grain boundaries and apparently at much the same rate at every point," although an acceleration in regions plastically deformed has definitely been established.2 In the second type of alloys the precipitation is "discontinuous," as in the copper-silver system for example, and "seems to start in restricted regions, primarily those contiguous with the grain boundaries, and to spread inward in an advancing wave." The reasons for the occurrence of these two greatly different types of precipitation are unknown, as are those for many other reactions that take place in the solid state. In the present paper only the first or "continuous" type of precipitation will be dealt with, for which a complete crystallographic mechanism has been worked out for the process of precipitation from a supersaturated solid solution of copper in aluminum. Based upon this mechanism, an explanation of the various property changes found experimentally will be developed in the second paper of this series. In later papers ('discontinuous precipitation" in copper-silver alloys will be explained, and an effort will be made to rationalize the two processes and types of precipitation. Crystallography of the Precipitation Process Through the extensive investigation by R. F. Mehl, C. S. Barrett and F. N. Rhines3 on the Widmanstätten structure in aluminum-rich copper

Jan 1, 1940

By Carl H. Samans

In their recent complete review of the subject of age-hardening,' R. F. Mehl and L. K. Jetter classify the main types of precipitation-hardening alloys under two headings, depending upon the nature of the precipitate and the character of the precipitation. In the alloys falling under the first heading, which display "continuous precipitation" and are typified by the aluminum-copper alloys, "precipitation seems to occur without much regard to grain boundaries and apparently at much the same rate at every point," although an acceleration in regions plastically deformed has definitely been established.2 In the second type of alloys the precipitation is "discontinuous," as in the copper-silver system for example, and "seems to start in restricted regions, primarily those contiguous with the grain boundaries, and to spread inward in an advancing wave." The reasons for the occurrence of these two greatly different types of precipitation are unknown, as are those for many other reactions that take place in the solid state. In the present paper only the first or "continuous" type of precipitation will be dealt with, for which a complete crystallographic mechanism has been worked out for the process of precipitation from a supersaturated solid solution of copper in aluminum. Based upon this mechanism, an explanation of the various property changes found experimentally will be developed in the second paper of this series. In later papers ('discontinuous precipitation" in copper-silver alloys will be explained, and an effort will be made to rationalize the two processes and types of precipitation. Crystallography of the Precipitation Process Through the extensive investigation by R. F. Mehl, C. S. Barrett and F. N. Rhines3 on the Widmanstätten structure in aluminum-rich copper

Jan 1, 1940

By T. R. A. Davey

A Survey of current and recent research and developmental work is supplemented by predictions for processes which should be developed over the reminder of this century.

Jan 1, 1970

By Frederick N. Rhines, William A. Anderson

The investigations of Wymanl have demonstrated that copper deoxidized with several of the commonly used agents that confer immunily to ordinary hydrogen em-brittlement can still be embrittled if it is annealed alternately under oxidizing and reducing conditions. During the oxidizing cycle, oxygen diffuses into the copper and frequently deposits a subscale composed of the oxide of the residual deoxidizing agent. Upon subsequent reduction with hot hydrogen, the copper becomes ruptured along the grain boundaries to a depth sharply limited by the previous penetration of oxygen as delineated by the inner boundary of the subscale. Obviously the sensitivity to this kind of hydrogen embrittlement is engendered by the introduction of oxygen during the oxidizing anneal, but beyond this the mechanism of the process, and hence the controlling factors, remain obscure. There are several possibilities: (I) oxygen dissolved in the copper matrix of the subscale may, upon cooling prior to the hydrogen anneal, precipitate as cuprous oxide which is subsequently reduced by hydrogen as in the familiar case of hydrogen embrittlement; (2) oxygen in solid solution in copper may itself confer susceptibility to embrittlement by hydrogen; (3) the normally refractory oxides such as those of aluminum, silicon and titanium may themselves be reduced by hydrogen when in contact with copper; or (4) the precipitated oxides of the subscale may be complex compounds such, perhaps, as SiO2.Cu2O, which are partially reduced by hydrogen. These possibilities have been examined, and it has been concluded that the first three and possibly the fourth are operative collectively or individually under more or less predictable conditions. Effect OF Precipitated Cuprous Oxide and Dissolved Oxygen The literature provides no definite proof that oxygen in solid solution in copper can confer susceptibility to hydrogen embrittlement; indeed, the research of Leiter2 seemed to indicate the opposite—that to produce the effect, cuprous oxide must be present in massive form and in a more or less continuous network along the grain boundaries. To test this point, pure copper has been annealed in hydrogen under conditions designed to ensure the presence in various samples of: (I) precipitated cuprous oxide, (2) dissolved oxygen only, and (3) no oxygen in any form. Very pure copper" said to contain no oxygen and no spectro-scopically detectable traces of any other element (that is, no individual detectable impurity in quantity greater than 0.0001 per cent) was used. Strips of this material cold.-rolled 75 per cent to 1/8 in. in thickness were subjected to the following treatments, the results of which are noted:

Jan 1, 1941

By Frederick N. Rhines, William A. Anderson

The investigations of Wymanl have demonstrated that copper deoxidized with several of the commonly used agents that confer immunily to ordinary hydrogen em-brittlement can still be embrittled if it is annealed alternately under oxidizing and reducing conditions. During the oxidizing cycle, oxygen diffuses into the copper and frequently deposits a subscale composed of the oxide of the residual deoxidizing agent. Upon subsequent reduction with hot hydrogen, the copper becomes ruptured along the grain boundaries to a depth sharply limited by the previous penetration of oxygen as delineated by the inner boundary of the subscale. Obviously the sensitivity to this kind of hydrogen embrittlement is engendered by the introduction of oxygen during the oxidizing anneal, but beyond this the mechanism of the process, and hence the controlling factors, remain obscure. There are several possibilities: (I) oxygen dissolved in the copper matrix of the subscale may, upon cooling prior to the hydrogen anneal, precipitate as cuprous oxide which is subsequently reduced by hydrogen as in the familiar case of hydrogen embrittlement; (2) oxygen in solid solution in copper may itself confer susceptibility to embrittlement by hydrogen; (3) the normally refractory oxides such as those of aluminum, silicon and titanium may themselves be reduced by hydrogen when in contact with copper; or (4) the precipitated oxides of the subscale may be complex compounds such, perhaps, as SiO2.Cu2O, which are partially reduced by hydrogen. These possibilities have been examined, and it has been concluded that the first three and possibly the fourth are operative collectively or individually under more or less predictable conditions. Effect OF Precipitated Cuprous Oxide and Dissolved Oxygen The literature provides no definite proof that oxygen in solid solution in copper can confer susceptibility to hydrogen embrittlement; indeed, the research of Leiter2 seemed to indicate the opposite—that to produce the effect, cuprous oxide must be present in massive form and in a more or less continuous network along the grain boundaries. To test this point, pure copper has been annealed in hydrogen under conditions designed to ensure the presence in various samples of: (I) precipitated cuprous oxide, (2) dissolved oxygen only, and (3) no oxygen in any form. Very pure copper" said to contain no oxygen and no spectro-scopically detectable traces of any other element (that is, no individual detectable impurity in quantity greater than 0.0001 per cent) was used. Strips of this material cold.-rolled 75 per cent to 1/8 in. in thickness were subjected to the following treatments, the results of which are noted:

Jan 1, 1941

By U. F. Kocks

SINGLE slip and a single parallel array of edge dislocations have been obtained in silicon single crystals by homogeneously bending them in a four-point dead-loading device at 1000°C around the [211] axis with [253.] as the tensile axis which encloses an angle of 40° with the glide plane. Other orientations or lower temperatures proved unsuitable. The homogeneity of the bending was checked by the method shown in Fig. 1. The chemically polished specimen was exposed to parallel light from a microscope-stage lamp. The sharpness of the focus of the reflected light is an approximate measure of the circularity of the sample. This method permitted the determination of the actual radius of bent specimens within 10 pct accuracy. The etching solution developed to show up dislocations consisted of the following volume parts: 2 HF, 1 HNO,, 2 CH,COOH, 1 a solution of 5 wt pct of CuNO, in water (Rosi'). The acetic-acid content was adjusted to produce fine well-defined etch-pits in about 2 min at room temperature. The effectiveness of the etch did not depend on the crystal-lographic orientation of the face etched. The number of etch pits produced after a given deformation was checked in the usual way against the Cahn formula' and showed good agreement. As it is to be expected from the orientation of the primary system there are slip steps on the top and bottom faces but not on the side faces (perpendicular to the bending axis), whereas etch pits appear on the side faces but not on the top and bottom faces. This is different only for occasional dislocations of a secondary glide system. All the micrographs included have been taken in places where the most of secondary glide could be seen. From this it is evident that in the homegeneously deformed region the number of secondary dislocations was less than 1 in 1000 of the primary type. Dislocation Distribution—A series of tests with varying amounts of deformation is shown in Figs. 2(a-c). An observation that can readily be made from these pictures is that the linear density of dislocations within slip lines is relatively constant and independent of the amount of deformation. "Slip line" in this context is understood to mean a line that is a straight connection of individual etch pits. The heavily pitted bands which can be seen in each of these three pictures may be resolved fairly definitely, at higher magnifications, into many "slip lines" the distance between them being of the order of 0.5p The distance between dislocations in slip lines is of the order of 2p and it is also fairly constant in going from the neutral zone outward. The higher over-all dislocation density in the outer regions of any sample and the higher total number in a more heavily deformed sample, are effected by a larger number of "slip lines." The relative constancy of the dislocation distance within an individual slip line is surprising. The absence of pile-ups" may imply, if there is no rear- rangement on unloading," that there are no substantial obstacles to slip in this case. It seems that the equilibrium distribution of the dislocations in each active slip plane under the higher external stress on

Jan 1, 1959

By J. O. Scott

Transient pressure behavior of wells intersected by a single vertical fracture has been examined by means of a heat pow analogy. Results are correlated in terms of dimensionless pressure change and dimensionless transient time. The resulting curves are found to lie between the dimensionless curves for a cylindrical well and a line source when effective well radius is expressed as one-fourth of the total fracture length. Results are also shown for various degrees of afterflow. Use of the curves provides a means of determining reservoir permeability, wellbore radius, and thereby fracture length, even when the final slope of the transient curve is not obtained. Superposition of curves may be used to confirm existence of vertical fractures in the reservoir adjacent to the well or to indicate a damaged zone on the fracture face. INTRODUCTION Hydraulic fracturing has become a standard well completion practice for the purpose of increasing flow. Results are normally gauged in terms of some sort of "stabilized" flow rate established before and after the treatment. This procedure may be misleading because pressures in or around the well do not become "stabilized" during the test period. Transient pressure tests on fractured wells can overcome the objections to stabilized flow tests by indicating when a stable pressure gradient is reached. In addition, the transient pressure tests can be used to determine formation flow capacity and effective wellbore radius. The effective wellbore radius may be used as a measure of the success of the fracturing operation. The slope and position of the transient pressure-log time curve may be used to determine the flow capacity and wellbore size after sufficient lapse of time so that the pressure gradient in the vicinity of the fractures becomes constant. However, in tight reservoirs or in short tests this condition may not be reached. Presence of the fractures in tight reservoirs may cause a constantly increasing slope to the transient pressure curve. If this slope is picked too soon, formation flow capacity will appear high and the fracture size will appear too small. This paper is intended to clarify the early transient behavior of vertically fractured wells. It shows how formation flow capacity and wellbore size can be determined even though the maximum slope of the transient pressure curve is not obtained during the test. Development of the techniques of transient pressure analysis for wells has been summarized by Perrine.' He reviews the various definitions of wellbore effects such as skin effect, productivity ratio, damage factor and condition ratio. In the present paper, use of these terms is avoided by defining an effective wellbore size. For the fractured well this effective wellbore size is larger than the actual wellbore. Assumptions made are constant flow rate at the well, constant fluid compressibility, constant fluid mobility and uniform porosity and formation thickness. From the basic differential equations of flow, two different solutions may be obtained. The first, the line source solution, is commonly used in transient pressure analysis.' It expresses the change in pressure at any radius due to withdrawal or injection of fluid at the line source from an infinite reservoir at uniform initial pressure. This equation, in oil field units: is

By N. H. MacMillan, W. M. Mularie, R. E. Jackson, A. R. C. Westwood

The initial results of a study of the environment-sensitive microhardness and diamond rotary drilling behavior of granite and its constituent minerals quartz and feldspar (microcline)1 have established that many similarities exist between the environment-sensitive mechanical (chemomechanical) behavior of these materials and that of the simpler solids such as periclase, soda-lime glass, and alumina4 studied previously, at least as far as n-alcohol (straight-chain alcohol) environments are concerned. The results of this study (hereafter designated study I) also suggested that the rate of drilling of granite in these environments is controlled by the chemomechanical behavior of its quartz constituent, and is greatest in those environments which impart a zero l-potential to this phase, thereby maximizing its hardness. Now, cationic surface-active species strongly influence the l-potentials of silicate minerals. For this reason they are widely used in mineral separation operations. In particular, dodecyl trimethyl ammonium bromide (DTAB) was found in study I to produce f 0 for quartz at a concentration in water of 107 to 10-4 moles per 1. Accordingly, the influence of dilute aqueous solutions of this surfactant on the drilling behavior of granite also was examined in study I. This revealed that granite could be drilled three to four times faster in 10-° molar aqueous DTAB than in water, and confirmed by experiment the suggestion that granite is most effectively drilled with a diamond core bit in environments which impart a zero l-potential to quartz. According to O'Connor and Buchanan' however, the isoelectric point for quartz in aqueous DTAB solutions occurs at a concentration of .•.•2 x 10-° moles per 1, rather than [101 to 10-1] moles per 1. To confirm the results of study I, therefore, a more comprehensive investigation of the [ ]-potentials of quartz, microcline, and Westerly granite in aqueous DTAB environments has now been undertaken. At the same time an examination has been made of one of the basic assumptions of the current conceptual understanding of chemomechanical effects. In this view, although hardness changes occur essentially instantaneously following wetting of the solid, they are confined to a surface layer at most a few micrometers (µm) deep. Hence, to maximize the influence of chemomechanical effects on bit penetration rate only shallow cuts should be taken. Practical penetration rates are then obtained by increasing bit rotation speed. Experimental l-potentials were determined by the streaming potential technique using an automated rapid-cycling apparatus recently developed by Martin Marietta Laboratory from a design by Somasundaran and Kulkarni. The drilling studies employed 3.2-mm-OD 120-grit diamond-loaded core bits with a wall thickness of ~0.7 mm, and bit rotation speeds of 2200 and 25,000 rpm. The load applied to the bit was independent of the depth drilled in both cases. The 2200 rpm measurements employed the same drill press and puddle drilling technique as used in study I. The higher rotation speed was obtained using a water-driven dental turbine drill. In the case, the surface active fluid was pumped down the axis of the bit to ensure efficient wetting and flushing of the drilling debris from the hole. In both cases drilling rate was measured by the parameter D(200), defined as the average rate of bit penetration during the interval from 150 to 250 sec after drilling commenced.

Jan 1, 1976

By Donald M. Liddell

From a commercial standpoint, the only beryllium mineral warranting attention is beryl, 3Be.Al2O3.6SiO2, which is of fairly widespread occurrence. The chief deposits are in Brazil, Argentina, India, Canada and Portugal. When pure this contains about 14 per cent of beryllium oxide. The mineral richest in beryllium is phenacite, (BeO)2SiO2, or beryllium orth-osilicate, which contains 45.55 per cent beryllium oxide when pure, and if anyone is ever fortunate enough to discover a large deposit of it, it will revolutionize beryllium metallurgy. Gadoljnite, zBe0.Fe0.2Yz0~.zSi0~, is also often referred to as a beryllium mineral, though the occurrences are comparatively scant and it is of more interest as a source of yttrium than it is of beryllium. There has been a good deal of talk recently regarding some occurrences of helvite in the United States. Helvite is a complex manganese-iron beryllium silicate and, apart from difficulties that would arise in its treatment because of its compo-sition, the beryllium content of the known deposits is not high. Early Metallurgy The elemcnt beryllium was first isolated by L. N. Vauquelin in 1797.~ He crushed and heated beryl, having the idea that this heating made it more readily amenable to attack by chemicals, and then mixed the mineral with three times its weight of caustic potash and fused the mixture. The melt after cooling was dissolved in hydrochloric acid: dehydrated, and again taken up with hydrochloric acid and filtered to separate the silica. The filtrate was treated with an excess of potassium carbonate and the precipitate after draining was leached with a solution of caustic potash, which dissolved the alumina. The undissolved material was, in Vauquelin's own words, "une terre nouvelle." He dissolved the precipitate with nitric acid and evaporated it to dryness, took up with hydrochloric acid and threw the iron out with potassium hydrosulphide, though he found that to make a complete separation of the iron involved a second treatment. The solution, after throwing out of the iron, had a pronounced sweet taste, and though Vauquelin always speaks of working on "terre du beril" he suggests that the new element should be known as "glucine" (glucinum) from the Greek word for sweet, because of this outstanding property. Vauquelin did considerable work on the comparison of aluminum and beryllium, working out a separation of most of the aluminum based on its precipitation as alum. His work is reviewed at some length, since ordinarily his procedure is incorrectly stated. It will also be recognized by those who have studied beryllium metallurgy that a good many technicians have followed his ideas since, including preheating the beryl before treatment. The fusion with

Jan 1, 1944

By Sheldon P. Wimpfen

EVERYWHERE in mining circles the talk is of this new development of hard faced or insert bits which hints of many changes to come in mining practice and rock drill equipment. In the past fifteen years new equipment has appeared in rapid succession which brought one change after another in rock breaking practice. Detachable bits were an innovation which met with wide success. Blasthole diamond drilling has proven itself. Only recently, fusion piercing was announced as a possible solution to the problem of breaking taconite ores. For several years this interest in new methods has been growing and various experimental usages of tungsten carbides in rotary type rock drilling bits have been partially successful. American experts in rock drilling have been concerned with the subject for ten years but actual commercial practice was begun by European manufacturers and mining companies. At this time nearly every manufacturer of rock drilling bits is working on some type of an insert bit. On the Rand, European manufacturers are testing out various types of insert bits. The problems relating to rock drilling in South Africa vary greatly from ours. The bulk of the drilling there is limited to the 31/2-ft holes that are drilled for breaking the gold bearing reef ore. Rock drilling in most mines is far more diversified. Both drifting and ore breaking call for holes varying in length from 4 ft up to as much as 50 ft and more.

Jan 1, 1947

THE strike and dip of bedded formations is readily determined by trigonometry if some marker horizon is intercepted by three holes. If no marker can be identified and if orientation of the cores is unknown, as is the usual case in diamond drilling, the determination still can be made readily by the use of a stereonet if the bearing, inclination, and angle the bedding makes with the core axis is known for each of the three holes. Such determination, valid only if the bedding orientation is fairly uniform within the area drilled, is considered simpler, faster, and more effective than any solution previously published. Method: The steps of this procedure are as follows: 1) Mark north and south poles on tracing paper placed over stereonet.* 2) Plot the three diamond drillholes by drawing a line from the center of the net in the direction of the bearings of the holes. Then rotate the paper until each line, in turn, lies along the equatorial diameter of the net; the end of each line is determined by the inclination of the hole measured in degrees from the periphery toward the center of the net along the equatorial diameter. Fig. 1 illustrates a vertical hole and a hole inclined at —23" due east. 3) With the projection of one diamond drillhole along the equatorial diameter, measure from the end of the hole, to the east and then to the west, a dis- tance in degrees equal to the core axis-bedding plane angle. Find two more points by measuring the same number of degrees north then south along the great circle from the end of the drillhole. Draw a circle, the center somewhere along the direction of the projection of the drillhole, to connect these four points. Draw circles for the other two diamond drillholes in the same manner. See Fig. 1 for two circles representing core axis-bedding plane angles of 35" and 23" and Fig. 2 for these plus a third circle representing a core axis-bedding angle of 42" in a hole bearing S 50 W inclined at —52". 4) Rotate the tracing paper until one great circle on the stereonet is found which is tangent to all three of the circles or parts of circles derived in the previous step. Trace this great circle on the paper and join its ends with a straight line passing through the center of the net. The bearing of this line is the strike of the bedding. In Fig. 2 the bedding strikes N 77 E. 5) Rotate the paper until the strike is along the polar diameter of the net. The dip of the bedding is determined by measuring along the equatorial diameter the distance in degrees from the periphery of the net to the great circle derived in step 4. The dip of plane illustrated in Fig. 2 is 55" to the N 13 W. Fig. 3 indicates the solution for three holes whose bearings and inclinations are N 20 W and —43o, due E and —30°, S 30 W and 23" with core axis-bedding angles of 30°, 50°, and 43" respectively. The bedding (stippled area) strikes N 44 W and dips 70" to the southwest.

Jan 1, 1956

By R. W. Gurry

When a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, yet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. Experimental Procedure Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;' it suffices to state here that the carburization lasted about I40 hr. at 760°C. (1760°F.) and 44 hr. at iiio°C. (2030°F.), these periods being long enough-—on the basis of the calculations presented later—to ensure that the specimen was about 99.9 per cent saturated at each temperature. The specimen was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully carburized specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

By R. W. Gurry

When a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, yet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. Experimental Procedure Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;' it suffices to state here that the carburization lasted about I40 hr. at 760°C. (1760°F.) and 44 hr. at iiio°C. (2030°F.), these periods being long enough-—on the basis of the calculations presented later—to ensure that the specimen was about 99.9 per cent saturated at each temperature. The specimen was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully carburized specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

By C. Scala, F. Bernstein

General expressions are derived relating the streaming potential to the electrochemical potential of a permeable junction separating two electrolytic solutions. By the methods of irreversible thermodynamics, these potentials are related to the flux of mobile species arising from differences in pressure and chemical composition. The flux is conveniently expressed as a transference number, the equivalents of a mobile species transferred through the junction per faraday of electricity. At constant pressure, the flux equation gives the electrochemical potential across the permeable junction. The streaming potential across the junction is obtained by imposing the condition of constant chemical composition. The familiar expression for the borehole SP is shown to be a particular solution of the general flux equation. The derived exprersions were verified in experiments with seven shale samples. Both the theory and experimental data provide additional proof of the presence and magniturle of the streaming potential in shales. INTRODUCTION In the interpretation of electric logs, there has been much concern over the correction to be made to the recorded SP for an electrokinetic or streaming potential originating from the difference in pressure between the mud column and the formation. It was long recognized by M. R. J. Wyllie that such an electrokinetic potential source mas in the mud cake opposite permeable sands.' More recently, M. Gondouin and C. Scala2 showed an additional but opposing electrokinetic source of potential to be in shale beds. Their work was supported by the very extensive and excellent work of Hill and Anderson.3 n the present contribution, the general relationships between the electrochemical potential and the corresponding streaming or electrokinetic potential are examined and clarified. A notable advance towards understanding the relation between the various sources of electrical potential in a borehole has been the application of the now common methods of irreversible thermodynamics to describe the passage of ions and water through charged electrolyte junctions such as in shales.' The advantages of these methods are twofold. Unlike classical thermodynamics, they can be applied to non-equilibrium sys- tems, i.e., systems in which flow takes place, provided the flow processes have reached a steady state. They also permit conventional thermodynamic properties to be related to the steady-state dynamic properties. These methods arc used here specifically to derive expressions relating the potential behavior of shales in terms of ion and water transport. Experimental verification of the expression for the shale streaming potential is given which in turn offers theoretical support to the existence of a streaming potential in shales.' Importantly, the relative contribution of transport parameters to the SP is clarified. The theoretical treatment is essentially that of Lori-mer, Boterenbrood and Hermans3 ut has been extended to derive the general expression for the SP.