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By Eckley B. Coxe

At the first meeting of the Institute, a paper was read by Mr. Rothwell, calling attention to the importance of at once considering the great waste of anthracite coal under the present system of mining and preparing that fuel for market, and a committee was appointed to examine and report upon the method now in use. About the time the committee were selected, a general resumption of work, after the long strike, took place in the coal regions, and the members of the committee have not in consequence had as much leisure to devote to the study of the question as its importance demands. In the present preliminary report we shall merely sketch out the . plan which we propose to pursue in our investigations, so that when our fellow-members are called upon to assist us in our work by furnishing statistics, etc., they may understand more clearly for what object our inquiries will be made. As one of the most practicable methods of obtaining the information requisite for an intelligent consideration of our subject, we propose to send, from time to time, to members and others interested in the mining of anthracite coal, printed sets of questions relating to points under consideration. We would here impress upon our fellow members the importance of filling up these papers as far as they can from their own knowledge. We would, of course, wish each question to be answered as fully as possible, but we do not expect every one to answer them all. One question well answered would be of more use to us than the whole paper filled up with answers, many of

By V. M. Dobrynin

Experimental data demonstrate that physical properties of porous rocks change under pressure. In this paper an assumption is made and proved that under pressure the changes of physical properties such as porosity, density, permeability, resistivity and velocity of elastic waves are controlled to a large extent by the pore compressibility of rocks. It is also shown that the pore compressibility of rocks can be determined, within the range of pressures from 0 to 20,000 psi, by knowing the maximum pore compressibility and the magnitude of the pressure. Mathematical equations were developed which permit one to define changes in physical properties of porous rocks under pressure. These equations were verified by experimental data obtained from the study of sandstones. INTRODUCTION In studying the behavior of porous rocks under pressure in the field of petroleum technology, the most interesting aspect is the observation of those properties which characterize the rocks as possible reservoirs — for example, porosity, permeability, resistivity, density and the velocity of elastic waves. The literature dealing with this problem mainly contains data concerning the study of only one or at most two of these parameters, but not of the group as a whole. An attempt is made in this paper to find general equations involving each of these parameters, which will permit the study of the behavior of rocks under pressure. All experimental data used here were obtained from the investigation of consolidated sandstones. EXPERIMENTAL In addition to the use of published experimental data, an experiment was carried out which studied the main physical properties of sandstones under pressure. Two homogeneous quartz sandstones were chosen for this purpose: (1) the Torpedo sandstone from Kansas, and (2) the Medina sandstone from Ohio. The porosity of the Torpedo sandstone was 20.2 per cent, and that of the Medina 8.7 per cent. Permeabilities were 45 md and less than 1 md, respectively. Each sandstone contained about 5 per cent clay minerals, consisting mostly of kaolinite and chlorite, which were distributed quite evenly throughout the samples. One cylindrical sample 2 in. in diameter and 5 in. in length was cut from each sandstone and then saturated in a vacuum with a 3N solution of NaC1. This high concentration was used in order to obtain true formation factors and to decrease the swelling of the clay minerals. The methods of mounting the samples and measuring the changes in porosity and resistivity were practically the same as those described by Fatt and Mann.1,2 Changes of resistivity under pressure were studied for sandstones with 100 per cent water saturation, and for sandstones with the irreducible water saturation. The irreducible saturation was obtained by enclosing the saturated rock samples in relatively fine silicate powder so as to remove the water by capillary action. This procedure is described by Orkin and Kuchinski.3 Changes of permeability with pressure were determined at room temperature using nitrogen as the flowing medium. In studying the effects of pressure, one series of measurements was made using an internal pore pressure Pi equal to the atmospheric pressure, while the overburden pressure Pe ranged from 0 to 20,000 psi. A second series of measurements was used over the same range of overburden pressure, but with an internal pore pressure of 1,800 psi. When the results were compared on the basis of net overburden pressure (Pe — 0.85 Pi ), there was practically no difference for these two sandstones. The origin of the factor 0.85 in the expression for net overburden pressure is given by Brandt,4 Fatt5 and Geertsma.6 The relatively large bulk volumes of the sample (about 15 cu in.) made it possible to observe a

By K. E. Brown, G. H. Fancher

An 8,000-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 3/8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 B/D at various gas-liquid ratios from 105 to 9,433 scf/bbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gas-liquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scf/bbl. These deviations me believed to be mainly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.l As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gas-liquid ratios and flow rates. Definite changing flow patterns do not allow any one correlation to be accurate for all ranges of flow. INTRODUCTION The ability to analytically predict the pressure at any point in a flow string is essential in determining optimum production string dimensions and in the design of gas-lift installations. This information is also invaluable in predicting bottom-hole pressures in flowing wells. Although this problem is not new to industry, it has by no means been solved completely for all types of flow conditions. Versluys,2 Uren, et al, 3 Gosline,4 May,5 and Moore, et al,6,7 were all early investigators of multiphase flow through vertical conduits. However, all of these investigations and proposed methods were very limited as to their range of application. Likewise, many are extremely complicated and therefore not very useful in the field. Only in the last decade have any significant methods been proposed which are generally applicable. The most widely accepted procedure in industry at the present time is a semi-empirical method developed from an energy balance, proposed by Poettmann and Carpenter8 in 1952. Their correlation is based on actual pressure measurements from field wells. Accurate predictions from this correlation are limited to high flow rates and low gas-liquid ratios. Although this method will be discussed in detail later, it should be pointed out that two important parameters, namely the gas-liquid ratio and the viscosity, were omitted in their correlation. The viscosity was justifiably omitted since their data was in the highly turbulent flow region for both phases, and most wells fall in this category. The gas-liquid ratio was incorporated to some extent in the gas-density term. In 1954, Gilbert9 presented numerous pressure gradient curves obtained from field data for various flow rates and gas-liquid ratios for the determination of optimum flow strings. However, no method is presented for predicting pressure gradients except by comparison to these curves. Baxendell, et al,10 proposed a method based on Poettmann and Carpenter's procedure

By William P. Blake

The occurrence of enormous masses of pure copper has given the mining district of Lake Superior worldwide reputation. The first masses brought from there excited great attention, and directed the notice of the mining world to the few particular mines from which they were taken. It may not now be generally known that nearly all the veins which are worked, and which cut across the trap ridge, contain mass copper, and that large masses are continually being raised from them. The largest continuous mass which has been taken out was probably that from the Minnesota, in 1857, which is variously stated as weighing 420 tons and 470 tons. Its length was about 45 feet, its breadth or height 22 feet, and its greatest thickness 8 feet. All such masses are very irregular and ragged in their form and thickness, thinning out generally from a foot to a few inches, and straggling through the vein until they connect with other large masses. This was the character of a mass found in the Phœnix Mine, one of the oldest on the lake, which mass altogether weighed some 600 tons. But this was really a series of masses more or less connected by strings of metal, yet no one large part of it weighed, singly, over 200 tons. A similar series of masses, weighing about 600 tons, was extracted from the Miunesota. Some of the Phœnix masses were four to five feet thick of solid copper. The Cliff Mine has yielded masses weighing from 100 to 150 tons in one piece. One of 40 tons was taken out this year, besides numerous blocks weighing from 1 to 8 tons. This mine and the Central are now yielding mass copper in abundance. It is, bf course, impossible to pick, or drill, or to break out such huge masses of solid metal when they are found, by drifting upon the course of the vein. The method of extraction is as follows: The miner picks out or excavates a narrow passage or chamber upon one side of the mass, laying it bare as far as possible over its whole surface. It is usually firmly held by its close union with the veinstuff, or by its irregular projections above, below, and at the end. If it cannot then be dislodged by levers, the excavation of a chamber is commenced behind the mass, and this excavation is made large enough to receive from 5 to 20 or more kegs of powder. In one

By A. L. Holley

The application of scientific methods to the investigation of natural laws and to the conduct of the useful arts which are founded upon them, is year by year mitigating the asperity and enlarging the outcome of human endeavor. More notably, perhaps, are these the facts in that system of productive and constructive arts of which engineering is the general name. In metallurgical engineering especially, within the period of our own recollection, how rapid has been the rate and how wide the scope of progress: the scientific discovery and mining of metalliferous veins; the economical separation and reduction of ores of every grade; the production and regulation of high temperatures; the varied improvements in the manufacture of iron, in saved heat and work, in uniformity and range of products; and, most important of all, the creation and the utilization, to be counted by the million tons a year, of the cheap constructive steels. Wonderful as this range and degree of development may appear to the public eye, the close and thoughtful observer must, nevertheless, conclude that neither the profession nor the craft of engineering may congratulate themselves too complaisantly, but that they should rather acknowledge to each other the embarrassing incompleteness of the union between engineering science and art. There is a small school of philosophers whom we may designate as original investigators, men who come close to nature, who search into first principles, and who follow that scientific and therefore fruitful method by which the relations of matter and force are discovered, classified, and brought within the reach of practice. These wonderful men do not indeed create the laws of nature, as they sometimes almost seem to, but they go up into the trembling mountain and the thick darkness and bring down the tables upon which they are written.

By Robert H. Richards

OF the several professions-the chemist, the civil engineer, the mining engineer, the mechanical engineer-the courses of instruction, as arranged at the scientific schools, differ considerably as to the amount of practical information which the student is able to gain. The analytical chemist has facility for a very thorough review of the processes which he will be called upon to perform. The student in civil engineering by his field practical learns the use of his tools and the art of taking field-notes. The mechanical engineering student is in the vicinity of machine-shops, which he can visit, and at which . he can work. The student in mining engineering has no such advantages. The mines are at a distance, and the railroad fare to get to them is oftentimes an insuperable difficulty. The aim of these laboratories is essentially to give to the student in mining and metallurgy a chance to study on a small scale the practical parts of his profession. We cannot, in a small laboratory, build a mine to timber, to work, and to survey; we cannot make artificial quicksands and other impediments to mining. In short, we cannot study exploration; but we can study the mechanical preparation and the subsequent smelting of ores. Before presenting the plan of these laboratories it may be interesting to indicate the progress of the idea from its beginning. During the summer of 1870 President Runkle visited the mines of Colorado, and while there, conceived the idea of making an expedition with the mining students to some of the Western mining regions. He talked over the scheme with many railroad and mining men, and everywhere received encouragement. In the summer of 1871 the Institute party visited the mines of Colorado, and spent six weeks in taking notes of them. President Runkle here conceived the idea of building up a mining and metallurgical laboratory ; and by the aid of Booth & Co. of San Francisco, a stamp-mill was obtained, with the Washoe silver-working apparatus. During the year

By Eckley B. Coxe

In making surveys in the anthracite coal regions of Pennsylvania, the ordinary engineer's chain (50 or 100 feet long) is generally used, both above and below ground. Sometimes, where it is difficult to chain, as, for instance, across a chasm, a wire is stretched from one station to the other, the distance is marked on the wire and its length is then measured with the ordinary chain. Having had occasion lately to make some surveys where it was necessary to determine with great accuracy the position of the land or property line, not

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By John Henry Harden

IN 1874, with Mr. H. Y. Attrill, of Baltimore, Md., I made an examination of some property at Goderich with reference to sinking for and mining salt. With this end in view we visited all the wells in the neighborhood, but the information sought being of so unreliable a character I advised the putting down of a borehole on the property. This has since been done, the result of which has lately been published by Dr. T. Sterry Hunt in the Toronto Globe. From this there appears to have been passed through six beds of salt of an aggregate thickness of 125 feet. Rock-salt was known to exist, for, by the boring of existing wells, small crystals had been brought to the surface in the dirt, but no attempt had before been made to obtain a reliable sample or to prove the number and thickness of the beds. The question now remaining for discussion is, shall the present method of obtaining the salt be continued, or shall the beds be won by a shaft in a regular mining fashion, by which means the salt may be gotten in a condition almost ready for the market? The present mode of obtaining salt is by boreholes from 6 inches to 8 inches in diameter drilled to the beds, into which is inserted a pump. The "feeders" of fresh water intersected in drilling the well are allowed to descend on the outside of the pump-tube to the salt beds and there become saturated, when, on use of the pump, brine is obtained for evaporation. In the beginning brine can only be had in limited quantity, but by the daily application of the pump, and the gradual solution of the salt, a larger surface becomes exposed to the action of the fresh water, and a continuons supply of brine is obtained. It will then be understood that the supply of brine is dependent upon the feeders of fresh water intersected in boring the well, which, we are told, have never shown any sign of diminution, and this is the water that must be encountered in sinking a shaft. There are ten wells in operation at Goderich, the most important one to the present project being known as the Hawley Well, located at an elevation a few feet above Lake Huron at the mouth of the river Maitland, at, a much lower level and nearer to the proposed shaft than any other well in the district. At this well the feeders

By Persifor Frazer

I DESIRE to say that, owing to the number of papers which have been more or less crowded at this session of the Institute, and the fact that, as one of the Local Committee, I have the distinguished honor to feel somewhat like one of the hosts, I should not tax the patience of members at this late hour, but would have my paper read by title were it in any way possible to do this. But the task I have set myself this evening is to present to the eyes of the members of the Institute certain objects which have occupied more or less of my time during the last eighteen months or two years. The objects I allude to are some of the igneous rocks of this country, which, until quite recently, have been less understood than any others. It will be well known to some of the members that some of the cooled lavas of a previous age of our planet, when not directly coarsely crystalline and granular, were considered and spoken of as " natural glasses," or perfectly uncrystalline, vitreous, or hyaline masses of matter. Among the first results of the use of the microscope was the dispersion of this fallacy. Sir David Brewster, Mr. H. C. Sorby, and William Nichol (the discoverer of the celebrated calcite prism, which bears his name), had, with greater or less success, examined sections of various rocks and minerals, both by transmitted and reflected light, and also in the form of powder. But, until the genius of Vogelsang undertook the subject, these investigations had no permanent value, nor did they constitute an independent line of mineralogical and geological research. Since the close of his labors, by Vogelsang's premature and much-lamented death, the subject has been made one of renewed interest by his brother-in-law, Ferdinand Zirkel, as well as by Rosenbusch, Tschermak, and many others abroad, and at home by the commencement of a systematic study of the traps of Connecticut by Messrs. E. D. Dana and G. W. Hawes, of New Haven, and by the splendid set of described sections of the traps of the West which have been furnished by Zirkel to illustrate Clarence King's report. I had the honor of presenting a large number of thin sections of our traps at the Washington meeting, for the inspection of the members, with the aid of a table microscope belonging to the Smithsonian Institution. Here I propose to project these sections upon the

By B. W. Frazer

In the numbers of the Engineering and Mining Journal of June 27th and July llth, 1874, there appeared some very complete statistics of the working of some anthracite blast-furnaces belonging to a large establishment in this country, followed by calculations of the heat requirements of the furnaces, similar to those which have been made for European furnaces by Mr. I. Lowthian Bell, Prof. Gruner, Prof. Akerman and others. To the author of these valuable papers, Mr. John A. Church, of New York, the thanks of American iron metallurgists are due for this attempt (the first, to my knowledge at least), to attack systematically and scientifically the problem of economy of fuel in our anthracite blast-furnaces, by applying the formulas obtained from European practice and from the experiments of European metallurgists, to the determination of the amounts and the modes of distribution of the heat production and absorption in our furnaces. In order to facilitate a comparison of the results thus obtained for the anthracite furnaces in question with those obtained for the best types of European coke furnaces, I have reduced 60 the same standad of heat units (the product of the ton and the degree Centigrade), and placed side by side, the calculations of the heat requirements of one of the furnaces of the Clarence works, as given by Mr. Bell, of a furnace at Pouzin, on the banks of the Rhone, given by Prof. Gruner, and of the anthracite furnaces for 1869-73, as given by Mr. Church. Table I shows the different conditions of working of the three furnaces, of which Table II gives the respective heat requirements. I have made this latter table in such a manner as to give for each furnace its heat requirements, both according to the views of Mr. Bell and those of Prof. Gruner. Mr. Bell assumes that all the carbonic acid produced by the decomposition of the carbonate of lime of the charge, is reduced to carbonic oxide by contact with solid carbon ; also, that the carbon of t,he pig iron is a portion of that deposited in the ore in the upper part of the furnace, by the dissociation of carbonic oxide. Prof. Gruner, on the other hand, assumes that all the carbonic acid of the carbonates of the charge escapes unreduced, and that the carbon deposited in the upper part. of the furnace, by the dissociation of carbonic oxide, is again converted into carbonic oxide or

By T. B. Brooks

THE iron ores of the Marquette region are mostly extracted in open excavations; hence the process is more properly quarrying. Several attempts at underground work have been made, which have not, on the whole, been successful. The Edwards mine has been almost entirely wrought by candle-light. The slate ore pit, NO. 1, of the New England mine, is now worked in the same way, as is also the Pioneer furnace pit of the Jackson mine. The Champion mine was opened systematically for underground work, with two levels, 60 feet apart, and three shafts at distances apart along the bed of 200 feet; but this idea has been practically abandoned, the greater part of the ore in that mine being now taken out in open pits. Several other mines have occasionally worked underground stopes, but only temporarily; if such stopes could not be opened out to daylight, they have usually been abandoned. In brief, it may be said that no considerable amount of ore has as yet (1870) .been extracted underground in the region, and of that so mined very little has been taken out at a profit; and I may add that it seems to be the belief of the most experienced mining men that this state of things will hold for some time to come for reasons which will appear. Nearly the same remarks may be applied to the mines of the Iron Mountain region, Missouri, the ores of which are very similar in character to those of Marquette. Some of the New York and New Jersey magnetic deposits are wrought open, but this is the exception, underground mining there being the rule. The following brief sketch of the geological structure of the Marquette deposits will indicate some advantages of the method of mining employed. The iron-bearing (Huronian) series of rocks, are stratified beds, the principal ore formation being overlaid by a quartzite, and underlaid by a diorite, or greenstone. This ore formation is made up, first, of pure ore; second, of "mixed ore" (i. e., banded

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By G. C. Wallick, W. R. Foster, J. G. Savins

The theory of the differentiation method for the Couette flow experiment is reviewed. Particular attention is given to the requirements on data analyses in the case of the class of non-Newtonian materials described as viscoplastics, i.e., materials characterized by a yield point or yield stress. Here changes in boundary conditions arise when the shearing stress attains a critical value with the result that the form of the basic integral equation for Couette flow is determined by the flow conditions existing during the measurement. INTRODUCTION In the preceding papers in this series,l,2 the salient features of the differentiation method of rheological analysis in Poiseuille-type flow were discussed. It was shown that a dual differentiation-integration method analysis of the Poiseuille flow of idealized generalized Newtonian and visco-plastic models could be used to develop a spectrum of highly sensitive response patterns in terms of certain characteristic derivative functions. These functions were shown to optimize the selection of the most appropriate functional relationship between f(p) and p from the Poiseuille flow experiment. The present paper reviews the theory of the differentiation method as applied to the equally important Couette flow experiment. We will also discuss the range of variables over which the basic integral equation for Couette flow is applicable when the non-Newtonian material is of the viscoplastic type, i.e., characterized by a yield point or yield stress. THEORY Having described the application of the differentiation method to Poiseuille-type flow in the preceding papers, we now proceed to the case where the test liquid is confined to the annular space between coaxial cylinders of length L, one of which is in motion, i.e., Couette flow, formulating the basic integral equation after the method of Mooney.3 The observed kinematical and dynamical quantities are the angular velocity O and the torque T. Here, the one nonvanishing component of the shear-rate tensor is

By J. S. Rinehart, W. C. Maurer

The mechanics of impact crater formation in rock, particularly sandstone, has been sutdied, the velocity range being approximately that normally associated with oilwell gun perforators. The bullets were small steel spheres having diameters of 3/16, 9/32 and 7/16 in; impact velocities ranged from 300 to 7,000 ft/sec. The craters have two distinct parts — a cylindrical hole (or burrow) with a diameter the same as that of the impacting sphere, and a wide-angle cup comprising most of the volume of the crater. The burrow is fornred as material in front of the projectile is crushed and pushed aside, forming a cylindrical hole surrounded by a high-density zone. The clip forms as fractures are initiated in front of the projectile and propagate along logarithmic spirals, approximaling maximum shear trajectories, to the free surface of the rock. A most significant observation (made for the first time) was that, below the base of the cup in one type of sandstone, there are a group of similar fractures, not extending to the surface, which are spaced uniformly a few millimeters apart. Each fracture follows roughly the contour of the base of the cup and appears to require a certain threshold impulse to initiate it. These fractures comprise a relatively high fraction of the total, newly exposed surface area. The volume of the material removed by crushing varies as the first power of the impact velocity and the volume removed by fracturing, as the second power of the impact velocity. Penetration varies linearly with the impact velocity and is inversely proportional to the specific acoustic resistance of the target material, the proportionality constant being dependent upon the shape of the projectile. INTRODUCTION Yield of oil from a producing well is frequently enhanced by firing bullets and shaped charges through the well casing into the oil-bearing rock, forming craters and fractures from which oil can flow more readily. The purpose of this investigation has been to develop a better understanding of the mechanics of impact crater formation in rock, particularly sandstone, the velocity range being approximately that normally associated with oilwell gun perforators. FORCES OPERATIVE DURING IMPACT When a projectile moving at considerable velocity strikes a- massive target such as oil-bearing sandstone, intense and complex transient stress situations develop within both the projectile and the rock or sandstone against which it is striking. Usually the struck rock fails, the missile or projectile penetrating into the rock to some depth where it comes to rest or is forcibly ejected from its burrow by expansion of a plug of target material compressed in front of it. When the impact velocity is very high, the projectile itself may fail, breaking apart or becoming distorted; this situation is not considered here, the discussion being limited to nondeforming projectiles. Many experimental studies'.' have been carried out to determine the nature of the mechanics of crater formation and the salient features of the forces coming into play, some of the earliest studies being the French Army experiments performed at Metz between 1835 and 1845.' The stratagem in most instances has been to make a post-mortem examination of the crater, measuring volume and depth of penetration and deducing force relationships from these observations rather than performing the more difficult (usually almost impossible) feat of measuring stresses during penetration. In many materials, the force acting during penetration of the projectile is found to be the sum of two components—(1) a constant force, independent of the velocity, representing some inherent strength of the target material; and (2) a component, proportional to the square of the velocity, representing inertial forces. For such materials, the average force per unit area acting on the projectile at any instant while it is in motion and being decelerated may be written F/A = a + bv2 . . . (1) where v is the velocity of the projectile at that instant, A is the cross-sectional area of the penetrating projectile taken normal to its trajectory, and a and b are constants which are dependent upon the target material and the shape of the projectile. It follows that the total penetration s is given by .........(2) where v, is the velocity of the projectile when it just strikes the target. Values of a and b for spherical projectiles impacting in a loose sand-gravel mixture and compacted earth were obtained in the Metz experiments. For sand-gravel, a and b are 620 psi and 0.0115 (psi) (ft/sec)', respectively; and for compacted earthworks, a and b are 432 psi and 0.0008 (psi) (ft/sec)'. Figs 1 and 2

By Don C. Blackmar

The production of non-ferrous secondary metals has become a large and important industry in the United States, and deals with practically cvery type of manufacturing concern. Its business is unique in that it generally buys frorn its customers as well as sells to them, whether they are individuals, cities, corporations, or the United States government. Its operations are of vital importance to the success and prosperity of nlany of the nation's most important manufacturers; yet there are few industries about which less is generally known by those outside it, whether concerning the rliagnitude of its operations or the details of its actual technique. The industry itself is to blame for this meager publicity, because its technical men have made few attempts to openly exchange ideas, in spite of the excellent examples set by the iron and steel or the copper and brass industries. Whether this is due to the ancient shroud of secrecy generally supposed to cover smelting operations, or because its technical men actually felt that the industry was too puny to be interesting, is hard to say. This paper will consider its subject in a general way, attenlpting to show something of the size and importance of the industry, as well as its fitness to do its work well. Attention will be called to the sound economic reasons for the handling of non-ferrous wastes by specialists, and to the often unseen losses of metals and labor which occur when manufacturc~rs rcclairn thrir own metallic wastes. Magnitude of the Modern Industry No particular thought is given to the kitchen accident whereby a ruined saucepan is sorrowfully tossed into the ash can, yet it is a fairly safe guess that within a month this saucepan, together with hundreds of its follows, will again be in service, perhaps in an autonlobile crankcase, or in an electric vacuum sweeper. It is by this conversion of the useless into the useful, whether from home or large manufacturer, that the secondary tonnage is built up.

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Robert F. Mehi

The mechanical behavior of metals and alloys is presumably conditioned by two factors; namely, the crystallinc symmetry and the interatomic forces. Considerable attention has been given to the first of these factors through the recent advances in X-ray technique. It is the purpose of the present paper to call attention to the importance of the second of these factors, to point out promising methods of investigation, and to present some pertinent data. Plastic deformation takes place by slip along atomic planes.' This slip may be inhibited in a number of ways: by the interatomic forces of, cohesion which bind the atoms rigidly in a lattice structure, which in pure metals is usually of high symmetry; by latticc distortion caused by solid solution formation or by mechanical strain; by the intercrystalline boundaries whcrc slip is restrained, probably by the non-registration of the atom planes in adjacent crystal1ites;2 and by the presence of small hard particles which serve to "key" the slip along the atom planes.5 In pure metals, and perhaps also in solid solutions, the atom planes of easiest slip are those exhibhing the greatest density of atomic population and the greatest interplanar distance4 and apparently can now be pre-dict,ed from the analysis of the lattices. Concerning the interatomic forccs, which resist this slip by holding the atoms firmly together, little is known. Most textbooks on physical metallurgy, following the work of Bot-tone,5 correlate the hardness of the pure metals with the atomic volume,