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By M. H. Cullender

The performance characteristics 01 gas wells producing from formations which fail to stabilize within a relatively short period of time are obscured by the interrelation of the coefficient (C) and the slope "n" of the conventional back-pressure curve q = C(P2 f- p2s)n An empirical method is presented whereby the characteristic or true slope (11) of the back-pressure curve may be determined for a particular gas well. For those gas wells which do not stabilize within a relatively short period of time, the coefficient (C) is considered as a variable with respect to time and as a constant only with respect to a specific time. Thus, the back-presrure performance of such a well is presented as a series of parallel curve5, each curve representing the performance of the well at the end of a given time interval. Through use of the method presented, a simple presture gradient is developed and maintained within the drainage area around a producing gas well during the test period in order that the variation of the coefficient (C) with respect to time does not obscure the true value of the lope. INTRODUCTION The back-pressure method of testing gas wells as set forth by Schellhardt and Rawlins1 is dependent upon the requirement that a series of flow rates and corresponding pressure data be obtained under stabilized conditions. These data arc then plotted on logarithmic coordinates of flow rate (Q) vs difference in squared pressures (P2f — P2s) in order to determine the constants (C) and (n) for Equation 1. With respect to this method of presenting the performance characteristics of a gas well, it should be pointed out that although Equation 1 is an empirical relationship, the form of the equation was justified to a considerable extent by an independent development by Muskat and Botset.2 This development was theoretical in nature; however, certain assumptions with respect to the type of flow existing (viscous vs non-viscous) were madc which may or may not be correct. As the use of the method presented by Schellhardt and Rawlins spread through the industry, it became evident that the method of testing was applicable for those wells which approached stabilized prbducing conditions within a relatively short period of time. Performance characteristics could not be determined by this method, however, for wells which approached stabilized protlucing conditions slowly over a considerable period of time. This characteristic of "slow stabilization" has generally been associated with gas wells producing frorn reservoirs of low permeability. As the demand for natural gas continued to grow through the years, a great number of wells were completed in reservoirs of low permeability which exhibited "slow stabiliz:~tion" characteristics. Consequently, the problem of determining the true performancc characteristics of these wells became more apparent. It is with this problem in mind that the isochronal performance method of determining the flow characteristics of gas wells is presented.

Jan 1, 1956

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)

Jan 1, 1942

W. O. OWEN,* Washington, D. C. (written discussion?). Few people appear to realize that the time to reach the crippled soldier is when he is first hurt. In my own judgment, the best time to reach him is before he is hurt, by showing him what other cripples have themselves clone of their own initiative, without Government-support, rendering themselves self-supporting, able to bear a little bit more than their own weight, so that they may lay aside a little bit for a rainy clay and some for a little fun in

Jan 5, 1918

By C. W. Baxter

Eveleth Taconite Co. was formed in 1963 to mine and beneficiate taconite on the Mesabi Range. Its Thunderbird mine is located mid-way between the cities of Eveleth and Virginia, Minn. The program for blasting restraints here is unique not only on the Mesabi Range but possibly in the world. The ore is a hard siliceous taconite. Its structure varies from bedded to massive with prominent vertical jointing. The jointing of the top or outcrop of the orebody is a challenge for the blasting practices as it is the source of an estimated 75% of the secondary breakage.

Jan 11, 1972

Important chemical and other technical engineering work necessary, for the prosecution of this war is being carried on by the Bureau of Mines Experiment Station, at Washington, D. C. The services of trained men of the following classifications are urgently needed Bacteriologists Instrument makers Biologists Laboratory Assistants Chemists, Inorganic Laborers Chemists, Organic Machinists Chemists, Physical Physiologists Chemists, Electro- Plumbers Chemical Engineers Steamfitters Draftsmen Stenographers. Electrical Engineers Skilled labor of various kinds If your training fits you for any of these occupations, send to the Bureau of Mines, American University Experiment Station, . Washington, D. C. for blank forms. When properly executed and returned by you, these forms will be placed on file, and when a vacancy occurs you will be considered for it and will be notified if your services are desired. If you are a registrant in the draft, and have not yet been- ordered to camp, it may be possible to have you immediately inducted into the service for work here. If you are not in the draft, but feel that you wish to serve your country in the present crisis, you can enlist, or serve as a civilian. Serve your country where you can serve it best. VAN H. MANNING, Director.

Jan 6, 1918

By J. Jr. Hudy

The objective of this investigation of the Cendrex was to determine the applicability of the X-ray instrument for the measurement of the ash content of coal. Developed by the Dutch State Mines, this instrument is designed to provide ash analysis of any desired coal product with only a 5-minute lag between sample collection and analytical result. The unit could, with limit controls, be used to feed back signals to preset the separating gravity of coal washers, control the ratio of various coals needed to produce an acceptable blend, and permit the sorting of a washed product into two qualities, one which is below and the other which is above a prescribed ash content. This unit can also be used discontinuously for rapid determination of samples of coals taken in the usual manner.

Jan 7, 1968

By E. D. Leavitt

I desire to state briefly my views respecting the great practical value of the Watertown testing-machine, and the necessity that exists, for an able permanent commission to supervise its operations, in order that the results of all tests made thereon may be properly worked out and rendered available for public use. It is doubtless known to the Institute that this machine has, for the past two years, been placed at the service of the public upon payment of a per diem charge. It was my privilege to be among the first to use the testing-machine, and the results of my first experiments were of such importance, owing to the great capacity and extreme accuracy of the machine, that it has since become my practice to have tests of all materials used in constructions that came under my charge, made at Watertown. As a conseqnence, nearly one hundred tests have been made on my account directly, and some two hundred and forty additional for work built from my designs. It may be confidently affirmed, that the factor of anxiety on all these structures is exceedingly small .m far as the quality of material is concerned, and it is undoubtedly a very great advantage for parties interested in construction to have

Jan 1, 1882

By William Glenn

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

Jan 1, 1889

By AIME AIME

THE joint symposium on gases in metals on Tuesday: Feb. 16, between the Iron and Steel and the Institute of Metals divisions opened the technical sessions for both of these bodies. After a few words of introduction by P. D. Merica, R. S. Dean presented a paper by V. H: Gottshalk and himself on the solubility of gases in metals.

Jan 1, 1932

By Charles Macdonald

WROUGHT-IRON eye-bars for bridges and roofs, designed upon what is known as the pin connection system, have been successfully manufactured in this country for some years. The most approved methods employed have been the hydraulic upsetting process, and by die-forging under a hammer. In upset eyes the fibre of the iron is necessarily much distorted ; and in bars of considerable size, this disturbance seriously impairs the strength of the connection. Mr. Collingwood, in discussing my paper on "Proportions of the Heads of Eye-bars," read before the American Society of Civil Engineers, Jan. 21st, 1874, submitted sketches of certain bars intended for the anchorage of the East River bridge, which had been exposed to the action of sulphuric acid a sufficient length of time to thoroughly cleanse the surfaces, and expose the condition of the fibre. These sketches are here reproduced for the purpose of illustrating the effect of this methpd of manufacture. In Figs. 1, 2, and 3, it will be observed that the fibres at A, and E, have been folded back upon themselves and otherwise twisted and disturbed, in a manner not calculated to inspire confidence in the integrity of the connection. To compensate for this defect, a large excess of metal is thrown into the eye; but a method of manufacture which involves such a necessity, even although it be the one giving the best results thus far, all things being considered, is far from being perfect.

Jan 1, 1879

By Samuel G. Bonasso

The article by Benavides and Schuster provides an in-depth study of this transportation alternatives for a four-mine complex in western Kentucky. The examination of aerial tramways was not undertaken as an alternative solution. We feel this is an oversight since industrial ropeways are competitive with both belt conveyance and overland truck hauling. In fact, there are aerial tramway system, operational today, which are 100 years old and operating with some original components. Maybe unfortunately, there are no fixed rules or guidelines whereby the most cost-effective means of transporting and handling material for a given situation may be selected. Each situation must be evaluated m the variables that influence the selection of the desired alternative can be clearly defined. However, there are in-place industrial ropeway system that have proven economically feasible over a range of 1.6-50 km (1-31 miles). The more difficult the terrain, the greater the cost efficiency.

Jan 1, 1984

By R. M. (Mike) Robb

Introduction The requirements to investigate a wide range of alternatives and analyze a variety of ‘what if’ questions make the automation of pit design a requirement in today’s rapidly changing mining industry. The wide-spread application of computers has relieved the engineer of much of the tedious and error-prone work related to mine design. He is thus free to do the creative and innovative thinking for which he is trained. It is now possible to investigate a large number of alternative pit designs in a reasonably short time period. In the past it was very easy for a team of engineers to consume 12 to 14 man-months in the detailed hand design of a large open pit. The pressure of today's mining industry, the desire to investigate a variety of alternative designs, and the shortage of qualified engineers make the slowness of hand design less preferred.

Jan 1, 1979

By Robert A. Cummings, Francis S. Kendorski

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

Jan 1, 1983

The following resolution was prepared, by the War Minerals Committee and was submitted by it to the Board of Directors of the American Institute of Mining Engineers, asking that it be passed by the Board and used to the best advantage to secure the end desired. WHEREAS, the steel industry of the United States is almost entirely dependent on the importation of foreign manganese ores, the consumption of which for the year 1918, it is estimated, will exceed 850,000 tons; and WHEREAS, the ships now engaged in transportation, especially from Brazil, are needed with ever increasing urgency for supplying our Army and Navy forces abroad; and WHEREAS, much shipping may be spared from manganese transportation and the domestic sources of manganese may be utilized, provided the steel manufacturers of the United States will cooperate to this end by taking advantage of the possibility, in open-hearth and Bessemer practice, of so called "residual" manganese, and by using spiegeleisen instead of ferromanganese, thereby following the example already set by three large and prominent steel producers; BE IT RESOLVED, that the Board of Directors of the American Institute of Mining Engineers urges the steel manufacturers of America, for patriotic reasons, to give immediate consideration to the development and utilization of domestic manganese ores; to use no ferromanganese, except for the manufacture of grades of steel below 0.15 per cent. carbon, to use domestic ores whenever possible in place of the high-grade imported ores; and to urge their associates and colleagues in this and other possible ways, to vie with one another in releasing ships for importation of any materials that cannot be secured or produced in this country.

Jan 1, 1918

Equilibrium in Lead Smelting. By S FREDERICK RAVITZ AND KENNETH E FISHER (Tech Pub 681, also Trans , vol 121 2300 words) Four liquids are ordinarily produced in lead smelting, namely, bullion, speiss, matte and slag To determine whether these exist together in equilibrium, the distribution of gold and silver among them was measured To crucibles containing similar mixtures of all four products, varying amounts of silver were added, and the crucibles were heated together under the same conditions for 3 hr, during which the charges melted and separated into four layers After cooling, these layers were assayed for silver, and the distribution coefficients, 1 e , the ratios of the concentration of silver in any particular layer to that in the bullion, were calculated In each experiment, each distribution coefficient was found to be constant, regardless of the amount of silver used Similar results were obtained using gold instead of silver The constancy of the distribution coefficients indicates that the bullion, speiss, matte, and slag exist together in equilibrium

Jan 1, 1937

My bets are on you, every time! But who is right? In the "cobalt issue" of our favorite magazine, January 1951, you stated: "By far the best immediate United States prospect for, large amounts of cobalt is the Blackbird mine of the Calera Mining Co., which is operating for Howe Sound Co., in Leinhi County, Idaho." In the March 1 issue of Saturday Evening Post, Ernest F. Mechlin, Jr., chief cobalt section, National Production Authority, states: "The Bethlehem Steel Co.'s Cornwall, Pa. ore bed is the principal domestic source." Maybe he should have said: "was the principal domestic source", or perhaps Howe Sound's Idaho cobalt is still in the prospect stage in Mr. Mechlin's opinion, perhaps in yours too. KATHARINE W. CARMAN GEOLOGIST 933 MICHIGAN AVE. EVANSTON, ILLINOIS Mr. Mechlin is correct in his statement that Cornwall is the principal domestic source of cobalt, but within the year, Blackbird production should greatly exceed that from Cornwall. Calera is expected to ultimately produce 3 million lb per year, whereas Cornwall averages 520,000 lb per year. -Editor.

Jan 1, 1952

By A. M. Gaudin, D. W. Fuerstenau

IN concentration of certain ores by soap flotation, prevention of quartz flotation is desired; the contrary is true in treatment of some oxide iron ores. Experimental study of the flotation of quartz goes back at least a quarter of a century.' Clean quartz does not float with fatty acids or soaps but does float when activated by one of many metallic salts. Control of pH is important. Broadly speaking the problem of quartz flotation has been approached from the empirical side, as was the related topic of flocculation or dispersion of quartz suspensions? Empirical studies indicated the existence of critical relationships between the additions of collector and activator. These additions were not stoichiometric for the formation of soaps of the activator cation. For example, Gaudin and Rizo-Patrona found optimum quartz flotation at pH 10.6 using barium activation and oleate collection when the molar ratio of oleate to barium was 1 to 1 instead of 2 to 1, as would be called for formation of Ba(OL),. Cooke and Digre" ' found that if calcium is the activator, a minimum quantity of that agent is required for effective flotation when the pH is 11.5. In other words, if the concentration of Na' exceeds 10 -2.5 mols per liter or if the concentration of H exceeds 10-11 mols per liter, the concentration of Ca++ in solution required for quartz activation is increased. This suggests that H+ is much more effective than Na+ on 10-2.5 quartz, perhaps in the ratio ofp or 108. Schuh- mann and Prakash6 studied anew the activation of quartz by barium, calcium, aluminum, and ferric iron. Salts of these metals are activators provided they are in stoichiometric excess over the collector used with them. Alkaline-earth salts are effective only in alkaline circuits. Important as they are in giving data on the effect of various agents on quartz, all these studies fail to give information on the detailed structure of the quartz-solution interface. A beginning in this direction was made by Gaudin and Chang,? who measured the adsorption of radioactively marked barium and laurate ions at quartz surfaces, and by Gaudin. Spedden, and Laxen,8 ho measured the adsorption of radioactively marked sodium at quartz surfaces. Work has also been done by Bell0 n measurement of the adsorption of sodium ion and chloride ion at quartz-solution interfaces. In all these experimental measurements of adsorption, the solid was centrifuged or filtered from the bulk of the liquor with which it had been associated; and the composition of the solid surface was ascertained by analysis, after allowance was made for the ionic composition of the liquor included with the centrifuged solids on the assumption that it is identical to the bulk liquid. Adsorption measurements give only the total amount of collector adsorbed at the quartz-solution interface; they give no indication of the distribution of these adsorbed ions at the interfacial layer. It is the ionic structure of the solid-solution interface and its importance to flotation that is the subject of this paper. The structure of this interfacial layer can be investigated by means of electrokinetic methods so that by combining electrokinetic studies with adsorption measurements, a more complete picture of the quartz surface may be obtained. The following studies were made to ascertain how electrolytes used in the soap flotation

Jan 1, 1956

By James C. M. Li

The Petch relation between the flow stress and the gain size is derived from a consideration of gain boundary sources of dislocations without the need of dislocation Pile-ups. Three mechanisms for inierpreting the yield stress: the gain boundary strength, the unpinning of Frank-Read source near a grain boundary, and the generation of dislocations from the grain boundary are compared and the condition of their equivalence is shown. The effect of the average angle of misfit of pain boundaries is found to be sma11 and so is that of the average angle of misfit of subboundaries having impurities. The effect of impurities on the ledge density in the grain boundary is treated thermodynamically and a relatwn is proposed for the variation of Petch slope with impurity activity. The effect of temperature on the Petch slope is interpreted as due to the change of ledge structure in the grain boundary. It is indicated that the effect of annealing temperature may be more important than that of the test temperature and therefore should be studied. The effect of plastic strain on the Petch analysis is deduced from a work-hardening equation in which the generation of dislocations has first-order kinetics and the annihilation of dislocations has second-order kinetics. It is concluded that the Petch slope will decrease with plustic strain if the rate of annihilation of dislocations is sufficiently large. Critical experiments which may shed light on the mechanism for the Petch relation are suggested. THE relation between the yield or flow stress, 0, and the grain size, l, was first proposed by all' and later studied more extensively by Petch and co-workers, who also proposed a similar relation for the fracture stress and deduced from these a grain-size effect of the ductile-brittle transition temperature. The microscopic mechanism used by all' and petch2 involves a pile-up of dislocations of like sign generated from a Frank-Read source. The yielding or flow takes place when the pile-up exerts sufficient stress at the grain boundary so that the plastic deformation can propagate from one grain to another. If the average strength of the grain boundary is ai and the average length of the pileup is lp, the Petch slope, k, is given by" where p is the shear modulus, b the Burgers vector, and v the Poisson ratio. This slope will be independent of the grain size if l/lp is a constant. This is possible, since, if the Frank-Reed source is situated near the grain boundary, lp = 1, and if it is situated in the middle of the grain, Ip = 1/2. cottrell,12 also using the pile-up mechanism, proposed that the stress concentration at the grain boundary will initiate Frank-Read sources near the grain boundary and in this manner a Lüders band can propagate from one grain to another. Assuming that the average distance between the Frank-Read sources and the grain boundary is 1, and the unpinning stress of the Frank-Read sources is op, Cottrell obtained the following Petch slope: This slope will be independent of the grain size if ls is independent of the same, which is not as obvious as the condition, Ip = I for Eq. [2]. In addition to this assumption, the direct relation between the Petch slope k and the unpinning stress, up, was recently questioned by Johnsonon grounds that it is inconsistent with the following observations: the independence of k with temperature and strain rate, and the small k in columbium, which, like iron, has a sharp yield point. As pointed out by ohnson," the most important objection both to the Hall-Petch mechanism, in which the strength of the grain boundary plays the role in yielding, and to the Cottrell mechanism, in which the unpinning of Frank-Read sources plays the role in yielding, is the lack of direct observation of the pile-ups. The dislocation structure in deformed iron has been examined recently in the electron microsope.'-' Dislocations appear to be generated from grain boundaries or other interfaces; they form clusters and tangles within the grain at very early stages of deformation, even in the Lüders band, if the deformation is slow or at normal and elevated temperatures. Although it is still too early to interpret bulk properties from thin-film observations, it does seem worthwhile to look for a mechanism for the Petch relation which does not require dislocation pileup. SUBBOUNDARY SOURCES In order to show that a consideration of grain boundary sources can lead to the same Petch relation as does the consideration of the strength of the grain boundary, we shall first discuss the case of a simple tilt boundary whose elastic properties have been studied in detail.17 The strength of a partially

Jan 1, 1963

By C. B. Scotty, E. F. Egan

INTRODUCTION The neutron-garnma log has been used for stratigraphic correlation by the oil industry for a number of years. In the past few years, the quantitative application of the log to provide information with respect to porosity has received considerable attention. The basic concept of quantitative interpretation has been pointed out in the literature.1 It shall be the purpose of this paper to develop by empirical means a method whereby the relationship of porosity to neu. tron-gamma deflection may be predicted for various bore hole diameters. This relationship is applicable to the present commercially available neutron-gamma log run in open hole. Data available at present are insufficient to establish similar correlations for cased holes. Through the development of such a correlation, the importance of the various factors which influence the log become evident. NEUTRON-GAMMA CURVE The logging tool conisists of a source of neutrons and a means of detecting and measuring gamma rays, the detector being shielded from the direct emission from the source. The gamma rays reaching the detector have three sources of origin: (1) the natural gamma radiation emitted by the formations, (211 induced gamma radiation resulting from neutron bombardment. (3) gamma rays emitted by the source and scattered by the formation. It has been found that a neutron derived porosity correlation is best for shale-free formations. Under this condition the natural gamma ray radiation is quite low, and therefore, will be neglected in this work. The induced gamma ray radiation resulting from neutron bombardment is predominantly a function of the hydrogen atom concentration of the substance penetrated. Due to the geometry of the presently used system, the neutron-gamma curve indicates low radioactivity opposite high hydrogen concentration and high radioactivity opposite low hydrogen concentration (Figs. 1 and 2). Having a curve which measures hydrogen atom concentration, it follows that if the matrix of the formation penetrated consists only of atoms other than hydrogen, and if the fluid filling the pores is either oil or water, the curve should be an indication of porosity (both oil and water have practically the same number of hydrogen atoms per unit volume'). The above criteria for a porosity (Correlation are fulfilled in clean sandztones and limestones in which the pore volume is completely filled with liquids (oil or water), but not in formations containing either free gas or shale or both. Free gas. even under pressure, contains considerably less hydrogen per unit volume than oil and water; therefore, a variation in response on the curve would be expected. Camp- bell and Winter,' indicate that this difference in hydrogen concentration is sufficient to distinguish between sands containing water or oil and those containing dry gas. Shale is a mineral that contains hydrogen in its molecular structure in addition to the hydrogen which is present in the water of hydration. Thus, in formations containing variable amounts of shale, the hydrogen concentration indicated by the curve is not a direct indication of porosity. Bush and Mardock' have indicated that a correction may be made by use of the gamma ray curve to provide a porosity correlation. Since the induced gamma rays are predominaiitly a function of hydrogen concentration, it would be anticipated that the fluid filled bore hole would materially influence the logs. It has been pointed out that the neutron-gamma curve response decreases with increase in hydrogen concentration, therefore, the response due to the induced gamma ray component decreases with increase in fluid filled hore hole diameter. The scattered gamma ray component of the log increases with increase in bore hole diameter. Although there is an

Jan 1, 1952