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By Carville E. Sparks, Rollin Farmin

TRIAL installations of rock bolts, of the slit-rod-and-wedge type, were under way at several units of Day Mines, Inc., when Korean hostilities interrupted the already slow deliveries of steel bars to the Coeur d'Alene district. Factory-made bolts had not yet been put on the local market, so the program was halted for lack of supplies. Interest was revived by a visitor's description of wooden roof bolts. These were said to have been used briefly with apparent success in a coal mine, until apprehension voiced by the U. S. Bureau of Mines caused the practice to be suspended. To make wooden bolts for trial in ground support, Day Mines acquired a second-hand doweling machine equipped with two cutting heads, one to turn out the desired round rods of 2-in. diam, the other to turn out 1-in. rods to be used as powder-tamping sticks. This machine was installed in the all-weather sawmill of the Hercules mine unit at Burke, Idaho, where fabrication of the wooden bolts commenced early in 1951. Most of the mining in the Coeur d'Alene district is along steeply dipping veins in shaly quartzite and argillite of Algonkian age. Ground support commonly is required in zones where the rocks have been sheared, brecciated, and hydrothermally altered. Pressure from the sidewalls is more troublesome than weight overhead, but both increase with the size of the mine opening. Caving may come from a progressive sloughing of irregular rock fragments or from an exfoliation and buckling of the layered wall rocks. The disintegration is thought to develop from an initial elastic expansion of the rock toward the newly-created mine opening, followed by the dilation of many tiny partings in the rock by absorption of water. As the partings widen, masses of rock develop weight and become free to fall. The function of rock bolts is to prevent or retard widening of partings in the rock supported. Wooden Bolts, Wedges and Headboards Bolt assembly used by Day Mines consists of a bolt 4 or 6 ft long, two wedges 16 in. long, and a headboard 30 in. long, Fig. 1. All four pieces are made of local red (Douglas) fir, either green or well-soaked in the mill pond before it enters the sawmill. Bolts are fabricated from cants, 2 1/4 in. sq, cut from relatively straight-grained timber with a minimum of knots and trimmed to 4- and 6-ft lengths. The bolt then is turned in the doweling machine from 21/4 in. sq to 2 in. diam round, except for a 4-in. length at one end which is left full square to provide the striking head and the shoulder that holds the headboard in position for wedging. The foot end of the bolt is slit with a thin saw for a length of about 16 in., thereby making a slot to receive the wedge against which the bolt is driven for anchorage at the bottom of the rock hole. A similar slit, 12 in. long, is made in the opposite (head) end of the bolt to receive the second wedge, which crowds the headboard against the ground at the collar of the rock hole and puts the bolt in tension. The second slot is aligned 90" from the plane of the first slot to avoid Longitudinal splitting and is notched out slightly to allow easier insertion of the collar wedge after the bolt has been driven to bottom. To prevent splitting the headboard by spreading action of the head wedge, this slot is oriented at 90" to the grain of the headboard when the pieces are assembled, Fig. 2. The wedges are similar to standard mine wedges, but more slender; they are cut 1 7/8 in. wide and 1 in. thick at the heel and taper out in 16 in. of length. The headboard, or bearing plate, is not necessary for some types of ground but generally is desirable because it helps the bolt to support an area of loose, friable rock and reduces the tendency for the rock at the collar of the hole to split away from the wedged head by distributing the pressure over a wider rock surface. The headboard may be a 24-to 30-in. length of 3-in. plank, 8 to 12 in. wide, but a similar length of rounded sawmill slab serves equally well at 20 pct of the cost. A hole of 2-in. diam is bored or punched through the center of the headboard, either at 90" or at various high angles to its surface. The bolt is inserted to its shoulder through this hole, then driven into the rock hole. Bolts, wedges, and headboards are given a full timber preservative treatment to inhibit rot. Bundles of each are immersed in a warm saturated solution of Osmose salts in water for 48 hr, removed, dripped dry, and stored in a relatively humid underground depot to cure. Most wooden rock bolts used by Day Mines are 4 ft long. Holes to receive them, about 42 in deep and 2 1/8 in. in diam, are drilled into the rock' to be supported, nearly normal to the periphery of the mine opening. The type of drill used is dictated by convenience: stoper, jackleg, or jumbo-mounted drifter. Correct depth of the hole is assured by use of a measuring stick that has been cut to the proper distance from drill chuck to the ground at the collar of the hole when a standard length drill rod is at the bottom. The bolt is seated to the shoulder through the hole in the headboard, the foot-end wedge is placed in its slot, and the assembly is inserted into the rock hole. Then the bolt is driven until it is seated solidly on the wedge against the bottom of the rock hole. Driving may be by hand with a sledge, or

Jan 1, 1954

By D. W. Fuerstenau

Recently R. J. Charles1 showed that comminution of brittle or semi-brittle materials in batch operations is described more appropriately by a variable energy relationship than by the specific relationships proposed by Rittinger,2 Kick,3 and Bond.' That is, the value of n in the empirical differential operation which applies to crushing and grinding (Eq. 1) is variable. Independently, Holmes' developed an identical generalized equaton for size reduction. The experimental data of Charles and Holmes show that the value of n is determined by the material and the comminuting machine and is constant for a given combination of these two conditions. The general objective of the present article is to extend the Charles-Holmes concepts to continuous ball milling. The specific objective is to analyze the operation of a vibratory ball mill dry-grinding chromite in a continuous open circuit and to develop an equation for the comminution of chromite in this mill. Basic Principles: In a batch mill the length of time during which the material is ground is a direct measure of the energy expended on the material, except possibly for exceedingly fine grinding. However, in a continuous operation, the fraction of the total expended energy which is useful for grinding will vary according to feed rate and amount of material in the mill. If the amount of material within a continuously operating vibratory mill is low enough so that only part of the expended energy is used for grinding, the extent of size reduction at constant power input must depend upon the length of time the material is retained within the mill, namely, upon retention time. The following analysis pertains to a continuous mill operating under these conditions. The empirical differential equation that applies to the comminution of brittle materials is:" dE = -Cdx/x" [1] where dE is an infinitesimal energy expenditure, C a constant, dx an infinitesimal size change, x the particle size, and n a constant. For continuous grinding in an open circuit at constant power input, P, Eq. 1 must be written as (dtr)P = -C dx/x" [la] where dt, is an infinitesimal time during which a particle of size x is in the mill, and C' is a constant. A ground product never consists of particles of single size but always comprises a distribution of sizes. In comminution, the expenditure of energy causes a lateral shift in the size distribution.', ' " The general objective of any engineering study of comminution is to correlate the magnitude of this size distribution shift with the energy expended, the ultimate aim being to cause the greatest shift with the least amount of expended energy. Although a number of criteria can be used to measure this shift, Schuhmann's size modulus has been found convenient.' Mathematically, the Schuhmann size distribution can be expressed as follows:" y = l00(x/k) [2] or in differential form: dy = [F- xa-' dx ] K, where y is percentage of material finer than size x, a is a constant that determines weight distribution among particles of various sizes, and k the size modulus that denotes the theoretically maximum-sized particle in any size distribution. By considering the energy required to reduce an element of weight of material, dy, from size x, to size x, the element of time during which the material must remain in the mill at at power will be (dt..).= J'-Cax!(dy) [3] Summing up all the elements of weight from zero to 100 for a product that conforms to the Schuhmann size distribution yields C C f Cdx,\( 100«x°-'dx\

Jan 1, 1960

By B. D. Smith, K. H. Coats

Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 50 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. INTRODUCTION Axial dispersion — the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relativeiy recent studiesl-13 and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles. In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentallv determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model. In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and johnston14 for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: The dispersion coefficient D for unconsolidated systems is correlated by u is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand.l4 Eq. 3 holds for 2 For a Do homogeneous (regular) type of packing, should be 1 or less.6 Aris and Amundson6 and Carberry and Bretton consider o to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm.15 For v /Do less than about 2, the effect of molecular diffusion must be considered and the total dispersion coeffi-

Jan 1, 1965

By F. F. Craig

A series of both welter and gas puttern Hoods was made in the laboratory to study the oil recovery performances of .such operations. These tests were contlrrctt~tl on consolidated sandstone models, using oil. water, and gas. The model floods were scaled to reprotlrrce field performance under gas arid water five-spot injection. X-ray shadowgraphs permitted observation of the gross fluid movement within the models. A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The area1 sweep efficiency. tit breakthrough for dispersed gas drives is much higher than previorsly expected, Iying in the range of 50 to 100 per cent. A method is presented for predictitig the water-oil ratio performance of five-spot pattern water flood., in uniform sands. This method is verified experimentally for the cotidition of 120 free gas initially present and for va1ues of gas saturation normally encountered in fields following depletion operations. Prodrrction perfort?zut~cc for pattern gas injection is also predictable by this method. INTRODUCTION In field pattern hater flooding or dispersed gas injection operations, the displacing fluid (water or gas) is injected and oil is produced through wells which are, area-wise. small openings in a large container or rescrwir of oil. As a result, not all of the area between the injection and producing wells is necessarily contacted by the injected fluid by the time it first reaches the producing wells. The question arises in predicting oil recovery. as to what traction of the pattern area involved is contacted by either the injected water or gas due to the relative position of the injection and producing wells. This is the areal sweep efficiency. It is also desirable to know how well arrangement affects the oil production performance. A solution to this problem has been attempted by many means. Mathematical analysis¹,²,³, and electrolytic models', have been used to establish a breakthrough areal sweep efficiency of 73 per cent for a five-spot pattern in which the ability of the oil to flow ahead of the invading fluid is equal to the ability of the invading fluid to flow in the invaded zone. All of these studies simulate only one of many field conditions. Improved studies of areal sweep efficiency at breakthrough were made using the fluid mapper5, poten-tiometric models" and X-ray shadowgraph techniques. In these it was possible to study the effect of variations in mobility of the injected and displaced fluids, and so to cover a wide range of field conditions. The limitation of these studies is that, with these models, it was not possible to simulate the saturation gradient behind the flood front when oil is displaced by gas or water. In the most recent published technical paperS on the subject, a method was presented for predicting the oil recovery performance after breakthrough in a five-spot pattern water flood. The method involved correlations which were obtained experimentally using miscible fluids. One limitation of this work was that a saturation gradient, usually found in immiscible fluid displacement, was absent in these studies. Also the laboratory studies did not cover the situation of a water flood following oil recovery by depletion drive. as is the situation in most field water floods. The tests reported in this paper were made using oil. water, and gas, thus eliminating the simplifications of former studies. Also reported are laboratory studies on

Jan 1, 1956

By K. E. Brown, F. W. Jessen

It is deemed feasible to store atomic reactor fuel wastes in salt dome cavities when the differential pressure acting on the cavity does not exceed 3,000 psi and the temperature is less than 400°F. Tests at pressure increments of 1,000 psi were conducted on a 2-in, cylindrical cavity contained in a 6-in. long X 6-in. diameter salt core. The cavity exhibited stability under pressures up to 3,000 psi and temperatures to 300°F. At temperature ranges of 100 to 400°F and with pressures of 5,000 psi and above continuous deformation of the cavity resulted. Initial movement of the salt was observed at all pressares. This was evidenced by vertical deformation and cavity size reduction. INTRODUCTION The development of storage techniques for safe disposal of atomic reactor fuel wastes is a goal of the Atomic Energy Commission. Salt domes have been used successfully for storage of liquefied petroleum gases and hence should prove to be suitable for liquid waste products of atomic reactors. The purpose of the following work is to evaluate the practicability of utilizing salt dome cavities for such wastes and to de-termine particularly the effect of pressure and temperature on a salt cavity. This work represents a part of a comprehensive study covering the over-all problem of storing re- actor fuel wastes in salt domes and/ or salt beds. The problem of accurately determining the stresses which exist in rocks in the earth's crust is indeed a complex one. Theoretical studies have differed widely in many of the basic assumptions about the physical properties of the rock itself. Some solutions of problems in underground stress analysis assume that rock is elastic, homogeneous and isotropic in character; others assume that rock possesses plastic, viscous, elasticovis-cous properties, or a combination thereof. Experimental evidence has shown that salt possesses plastic, viscous and elasticoviscous properties.' Recent work has shown that salt becomes more plastic with temperature.' APPARATUS AND PROCEDURE For experimental study a cylindrical cavity was chosen for analysis since it provided maximum volume per unit of depth with constant diameter. This particular cavity shape, allowing for irregularities, can be easily leached out of salt domes in field operations. For the purpose of approaching underground storage conditions as nearly as possible, the following factors were considered: (1) control of pressure and temperatures, (2) measurements of temperature gradients throughout salt mass, and (3) measurement of structural stability of salt cavities. In order to obtain triaxial pressure on the salt cavity without resorting to the application of fluid pressure directly on the salt mass, a system was designed whereby the same effect could be produced through axial loading only. By cutting a core to close dimensions to fit a steel test cylinder and applying axial pressure, a lateral pressure was obtained. This equipment is shown in Figs 1 and 2. A steel cylinder was made from

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 de¬mands. 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 fur¬nishing 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 informa¬tion requisite for an intelligent consideration of our subject, we pro¬pose 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 ques¬tion 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

Jan 1, 1873

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 H. F. Haller

COLUMBIA-SOUTHERN'S Barberton limestone mine, 8 miles southwest of Akron, Ohio, is a million-ton-per-year producer from a depth of over 2200 ft in a district where other underground mining at this depth is unknown. Mining extracts 46 of the top 51 ft from a formation of Devonian limestone discovered by drilling in the 1890's. The same drilling revealed extensive salt deposits below the lime- stone, which led to the location of the chemical plant at Barberton as a division of the Pittsburgh Plate Glass Co. in 1899. Soda ash was the principal product of the plant, and as production increased the demand for limestone increased. Columbia's first attempt to secure a reliable all-weather source of stone was the development of a quarry at Zanesville, Ohio, in 1919. Zanesville production eliminated some of the stock- piling required by the use of Michigan stone, avail- able only during the lake shipping season. Stone from some Zanesville horizons, however, was found to be more suitable for cement production than for soda ash, and rail transportation remained an important factor. As demand continued to increase, plans were made to develop the Barberton deposit.

Jan 12, 1954

By B. D. Cullity

AS methods for measuring fiber textures become more exact, it becomes justifiable to scrutinize an observed pole-density curve for evidence of minor texture components. These are disclosed by minor maxima or abnormally broad major maxima. One possible source of these minor components is twinning of the main component. In cubic metals and alloys, there are two kinds of twins: 1) Annealing twins in face-centered cubic metals. These are reflection twins on {Ill), and they can be expected to be present in recrystallization textures. 2) Deformation twins in body-centered cubic metals. These are shear twins on (112). Although usually formed only by impact, they might conceivably be present in the deformation texture of severely cold-drawn wire. Fortunately, both kinds of twinning lead to the same orientation relationships. It thus becomes possible to prepare a single list of angles between various planes in parent crystal and twin, which is helpful in examining pole-density curves for evidence of twinning in any cubic metal or alloy. Such a list of interplanar angles is given in Table I. This table consists of three parts, corresponding to the three major texture components—<100>, <110>, and <111>-most commonly found in the fiber textures of cubic metals. The table lists the angle between the pole of {hkl}, in either the parent crystal P or the twin T, and the fiber axis <uvu>. The crystals with <uvw> parallel to the wire axis are here

Jan 1, 1959

By Takahide Wakamatsu, Shigeru Mukai

Fundamental investigations were made on the treatment of slime and the chrysocolla flotation, both of which are urgent problems to be solved in copper oxide mineral flotation. Unfavourable effects of slime on flotation are caused by the slime adsorption at the air/liquid Interface as well as the slime coating on the mineral surface. The adsorption of slime at the air/liquid interface was measured by using various kinds of slime particles. As a consequence, goethite, bentonite and talc tended to adsorb markedly at the interface. As a desliming method, slime flotation with a polymer flocculant such as polyethylene-oxide prior to the ordinary copper oxide flotation was found to be effective. The use of both a copper-avid organic reagent and an alkyl xanthate was examined for a selective collection of chrysocolla through xanthate adsorption tests, chrysocolla float- abllity tests and flotation tests for synthetic and natural ore. The copper-avid reagents used were salicylaldoxime, 8- hydroxyquinollne and benzoin-a-oxime. As a result, the ad- sorption of higher xanthate such as amyl xanthate on chrysocolla as well as the chrysocolla-to-air bubble attachment was increased by the presence of a copper-avid reagent under suitable reagent addition and pH of pulp. Flotation tests for synthetic and natural ores confirmed that chrysocolla could be floated sufficiently and selectively with a copper- avid reagent like 8-hydroxyquinoline or salicylaldoxime with its subsequent collection by amyl xanthate.

Jan 1, 1976

By F. L. Holderreed

A choosy in what they would smelt. The furnace charge had to be coarse, and it had to be rich. They discarded fines in excess of about 1/10 the total weight. They wanted 10% copper content and fussed about anything with as low as 5%. They concentrated the copper content of the charge as much as they could by prior selection. They roasted off enough sulfur to further enrich the copper content of the succeeding fall of matte (a melt of cuprous and ferrous sulfides or Cu2S.FeS). Then they desulfurized the iron and fluxed it by carefully adding silica (quartz, not silicates) for a slag of lower density than the cuprous sulfide (Cu2S or white metal). After skimming off the slag, they further desulfurized the white metal by blowing the molten bath with compressed air. The result was blister copper. Yesterday Their techniques and furnaces? Some experimented with mechanically rabbled roasters, but their standard roasting practice was burning coarse sulfide ore in 250-ton heaps. These heaps, approximately 24 x 24 x 6 ft, were burned for about 75 days down to 6-10% sulfur. The turnaround time for a given roasting position was 100 days. Assuming the base was a hearth, the calculated rate of treatment was on the order of 0.004 tpd per sq ft.

Jan 1, 1971

By H. M. Chance

THE present value of most coal properties resides largely in the coal remaining to be mined, which thus constitutes the most important asset. The object of this paper is to discuss methods commonly used in computing the value of mineable coal. To distinguish clearly between such coal values and the values of other property, the several kinds of property values may be divided into classes; this is necessary to avoid unintentional omissions of items of importance. VALUE OF COAL RESERVES Judicial decisions prescribe, and appraisers commonly accept, current sales value as the preferred means for determining the value of transferable property. With few exceptions a property is worth the sum that can be realized from its sale by a willing seller to a willing buyer, a sale in which compulsion urges neither party, and between whom there is no community of interest to fix a value; or it is worth at least as much as a responsible buyer will offer for it. Actual sales of like property or bids from responsible buyers for the property, or for substantially like property, are the best established methods for determining values. Only in the absence of such sales or bids can valuations by other methods be entertained, and only for reasons of weight can sales values be set aside. Sales of coal in the ground, as customarily carried out through lease, under royalty agreements, are therefore the most trustworthy means available for determining the value of coal reserves.

Jan 6, 1926

By D. Turnbull, J. H. Hollomon

IN the most general sense, solidification refers to the formation of crystalline material from either a gas or a liquid. However, in this symposium, only the formation of crystals from liquids will be considered. Thus, in our present study the problem of solidification becomes that of determining the mechanism of the transition from a liquid to a crystalline solid, and our particular interest is in the transformation of metals from the liquid to the crystalline state. Metal liquids are seldom composed of only one kind of atom. Often solute atoms are added intentionally to make an alloy, or they may be present accidently because of incomplete purification. Furthermore, there may be small solid particles of various other crystals present in the liquid. Such small crystals may persist if their melting points are higher than any temperature to which the liquid is heated. Prior to solidification, the liquid metal usually is poured from one container to another. The second container, called the mold, usually is at a lower temperature than the container, or the crucible, in which the metal is liquified. The first solid that forms upon contact with the mold generally is of a different composition than the liquid, usually containing fewer foreign atoms or dissolved impurities. Heat is evolved upon solidification and is dissipated through the surroundings. Tree-like crystals, or dendrites, grow from the container walls and branch into the melt, enriching the remaining liquid in impurity atoms. In some alloys the remaining, relatively impure liquid continues to solidify until no liquid remains and the branches of the original crystal are cemented together. In other alloys, particles with a second type of crystal structure appear before solidification is complete. First the nature of the liquid and the solid states will be considered and then the mechanism of the initial formation of crystals from pure and alloy liquids. Later the problem of the growth of these crystals and the complexities of solidification in a mold, where the temperatures are not uniform and the composition of the melt changes continuously, will be discussed. LIQUID AND CRYSTALLINE STATES A liquid is an aggregate of atoms arranged with no apparent regularity (over distances of more than a few atom diameters). Nevertheless, any given atom generally has a definite number of nearest neighbors at definite distances, and thus order may be said to exist over a short range. In a crystal, on the other hand, a regular array of atoms continues for many hundreds or thousands of atom diameters, and a long-range order is apparent. Thus, a crystal having long-range order can be reproduced by linear translations for 10-5 cm or more of some fundamental unit possessing short-range order. A crude illustration of the difference between liquid and crystalline structures can be obtained by comparing the possible arrangements of oranges in a crate. If the oranges are simply dumped into the crate haphazardly until it is filled, the oranges will represent a static model of a liquid.

Jan 1, 1951

By H. K. Shearer

The principal events in the oil history of south Arkansas, north Louisiana and Mississippi in 1930 have been: In Arkansas, very little activity, except for discovery of deep oil production at Urbana, and completion of the first oil well in Miller County. In Louisiana, continued development of the Zwolle area, bringing production up to about 10,000 bbl. per day; practically complete development of the Carterville oil-producing area; discovery and drilling of the rather disappointing Holly area, and discovery of Trinity gas production at Sugar Creek, Claiborne Parish and Rodessa, Caddo Parish. In Mississippi, discovery of the Jackson gas field, in Hinds and Rankin counties. Proration of oil runs was not put in effect in these areas during 1930, because the natural decline of the older fields brought production below the demands of local markets. The only effect of the oversupply and low price of oil was the curtailment of some drilling which might otherwise have been done. Drilling in Arkansas reached the lowest stage since the discovery of oil, with less than 100 completions. Louisiana showed some increase in drilling over 1928 and 1929, but almost half of the wells were drilled primarily for gas rather than oil. As no review on north Louisiana production has been prepared since 1927, and there was none on south Arkansas for 1928, the developments of the three years, 1928, 1929 and 1930 are here briefly discussed.

Jan 1, 1931

By R. W. Raymond

In a paper on the Divining-Rod (Transactions, xi., 411), presented at the Boston meting, in February, 1883,I suggested, among other signs of which the skilled prospector might consciously or unconsciously avail himself in the search for springs of water or mineral deposits, the presence of particular grasses or shrubs, and the general appearance of the flora. There are not wanting, in the literature of our art, indications that greater attention was paid to such signs in ancient days than at present. It is the tendency of a scientific age to ignore, or regard as superstitious, what cannot be classified or explained. But the acute though unscientific observation of earlier times often, doubtless, accumulated facts which it would be worth our while to re-examine. It is highly probable that the mining prospectors of the sixteenth and seventeenth centuries, to go no further back, were close students of nature, and knew, though they could not explain, and, for reasons of private gain, would not communicate, many curious and significant facts. We can generalize better than they could; but for that very reason we are, perhaps, their inferiors in observation. They let nothing pass, because all things were equally significant to them. We take wider views, and miss more. And, no doubt, there still exists among practical millers, prospectors,, hunters, Indians, etc., an unwritten.

Jan 1, 1887

By Edwin F. Brush, John Chipman

Published data on the activity of carbon in binary and ternary austenite at 1000°C are reviewed. The composition variables are . The coefficient, Vj, has the value for substitutional elements but may be assigned a ualue -1 for silicon to effect a simplification on the mathematical treatment. The activity coefficient PC = is obtained from gas equilibrium data. For the ternary systems studied the Henrian activity coefficient is given by the expression: The principle advantage in cornparison with the analogous expression in terms of atom fractions is found in the fact that for most systems the final term and in many the last two terms are zero. Values of the interaction parameters are tabulated and the graphical comparison of the equation with experirt~ental data is sho,wn in several figures. The thermodynamic properties of the solid solution, austenite, are of considerable importance in the heat-treatment of alloy steels and in other aspects of ferrous metallurgy. Early studies embodied in the Fe-C diagram have been extended to include other binary and some ternary diagrams. Our best hope of obtaining a useful thermodynamic treatment of reactions in complex alloy steels will not be found in quaternary and quinternary phase diagrams but in determinations of activities and interaction relations among the several solute elements. The foundation for such a development was laid by smith&apos; in his early studies of the activity of carbon in Fe-C alloys and his subsequent work on Fe-C-Si, Fe-C-Mn, Fe-C-Ni, and Fe-C-Co solid solutions.2"4 Other observers have also made noteworthy contributions and these will be discussed and correlated here in the light of a somewhat simplified mathematical treatment of solute interactions. Fe-C AT 1000°C In a recent review of the thermodynamic properties of binary Fe-C austenite it was shown that the simple mathematical treatment employed by smith&apos; was capable of describing all the published results on this solution. The treatment utilizes the atom ratio, yc = nC/nF,, rather than the atom fraction. The activity of carbon is proportional to the equilibrium gas ratio, either measured on a scalk in which the activity of graphite is taken as unity or, alternatively, aC may be set equal to yc at infinite dilution. In either case the ratio aC/y = (PC, the activity coefficient. It was found that the experimental data of smith1 and those of Diin-wald and wagner; Bungardt, Preisendanz, and Lehn-ert,&apos; and Scheil, Schmidt, and Wiinnings at temperatures of 800" to 1200° C as well as reliable data on the solubilities of graphite and cementite could be represented by the equation for which graphite is the standard state: The data on alloyed austenite have been obtained at 1000°C. For this temperature, the "Henrian" activity coefficient (which is unity at infinite dilution) is: FOr an interstitial solute such as carbon in austenite it has been shown by statistical mechanicsg that the activity in the infinitely dilute solution is proportional to the ratio of the number of lattice sites occupied by carbon to the number of yet unfilled lattice sites. A variable zz proportional to this ratio serves as a useful measure of concentration:" in which b is the number of lattice sites provided by each atom of solvent; in austenite b = 1. The Henrian activity approaches zz at infinite dilution and the ratio a is the activity coefficient. The effect of a change in concentration is then given by: It has been shown further that in some systems the derivative in Eq. [4] remains constant over a wide range of concentrations. In such a case second-order terms become negligible and the Henrian activity coefficients is:

Jan 1, 1969

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By S. Weinig, E. S. Machlin

IN a previous study of the grain boundary stress relaxation phenomenon,&apos; the authors had arrived at the conclusion that two successive steps were involved in the complete relaxation of stress at a grain boundary. These two steps were grain boundary migration and grain boundary slip. It was further suggested that the slower of these two processes is rate controlling. In an attempt to ascertain the validity of the above, a study of grain growth kinetics on the same alloys used for the previous study was undertaken. Separate wire specimens, 0.030 in. diam, in the same as-deformed state (99 pct reduction in area) as in the previous investigation were heated to the various temperatures for a sequence of times. The compositions used and the temperatures of testing are summarized in Table I. A statistical determination of grain size was then made on each specimen, using the average length of traverse between boundaries as a measure of the grain size. Examples of typical results obtained are shown in Figs. &apos;1 and 2. The grain growth law D = ktn was found to fit most of the data. Using this relation, values of the grain growth exponent n were calculated and the inter -esting dependence of n on solute content shown in Figs. 3 and 4 was then obtained. Also, it was found that the constant K which was obtained from extrapolation is roughly independent of solute content. (K is uncertain to within ±25 pct.) An estimate of the activation energy for grain growth was made using the technique of Burke? This method utilizes the plot of the reciprocal of time necessary for the grain size to increase from a definite starting size Do, to a final size D, for each isothermal heat treatment. The slope of this curve corresponds to the heat of activation for the process. In Fig. 5 the rate of grain growth is plotted against the reciprocal of absolute temperature. The activation energies were obtained from these curves and are summarized in Fig. 6. Discussion It is interesting to note that the same saturation in the variability with concentration has been found for the grain growth exponent n in this research as was found in the previous researches on both grain boundary stress relaxationa and internal friction of dislocation origin." The significant feature is that saturation in the variation of these properties has been found to occur at about the same level of solute concentration, namely, between 0.1 and 0.5 atomic pct. The only characteristic common to these different quantities is that solute adsorption at grain boundaries and dislocation can take place and affect these values in a similar fashion. Thus, it is concluded that the grain growth exponent n depends upon solute adsorption at the grain boundaries. It appears, therefore, that theoretical considerations leading to the contrary conclusions5,6 have not treated the real process by which solute atoms exert their effect on grain growth. Prior to the analysis of the observed activation energies, certain of the aspects of the aforementioned grain boundary stress relaxation investigation will be briefly reviewed. It was found that with the addition of solute atoms the grain boundary stress relaxation peak (internal friction vs temperature) decreased in intensity. Simultaneously a second peak was observed which increased with increasing solute atoms. Both of these peaks were shown to be the result of grain boundary stress relaxation. They have been termed, respectively, poire peak and solute peak. It was suggested that the solute peak was dependent upon grain boundary migration, whereas the pure peak was a manifestation of grain boundry slip. Activation energies for both peaks were obtained as a function of Solute content. The value of the activation energy in the temperature range corresponding to the solute peak was

Jan 1, 1958

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-