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By K. R. Price, M. Gauna

A high seam geologic condition exists at Jim Walter Resources No. 4 mine that requires immediate rib support after a continuous miner cuts a place. High seam mining heights are typically 2.4 to 2.6 m (8 to 9 ft) and a thick rock layer is present in the upper portion of the coal rib side. The 610-m (2000 ft) mining depth at No. 4 mine induces horizontal rib line movement after excavating an entry. Horizontal rib movement greater than 305 mm (12 in.) have been noted. When lateral movement occurs in the high seam areas, the thick rock layer, and the coal above the rock layer, become fractured and tend to roll into the entry. If not adequately supported, large rib rolls develop in the place being bolted as well as in previously mined areas that endanger men and equipment. To control this, rib support must be installed in the roof bolting operation as the bolting crew works toward the face. A rib control system has been developed for this high seam mining condition using a mechanical anchor bolt placed at an angle in the rib and installed with a modified Fletcher DDM-15 bolting machine. More than 120 km (75 miles) of entry have been supported with angle rib bolts. These angle bolts constitute 43% to 60% of the total roof and rib bolt footage in the high seam portions of No. 4 mine. The angle rib bolting system has proven safer, more effective, and more efficient than the earlier support method using bolts installed horizontally into the rib. No rib roll accidents have occurred since the angle drill bolting machines were placed in service in 1981. By securing the broken rib material with an angle bolt anchored above the coal pillar, a more effective means of rib control is achieved. Angle rib bolting does not interfere with continuous miner productivity. In addition, bolting crews are now reduced from three to two people. Total drilling supply costs are about 60% the previous cost, when compared to the previous support method using horizontal rib bolts:

Jan 1, 1985

By William P. Blake

(Canal Zone Meeting, November, 1910.) A DEPOSIT of manganese-ore near Tucson, Ariz., merits notice by reason of the peculiar form in which it occurs, and as a striking. example of ore-deposition by vadose upward capillary flow of metal-bearing solutions with concentration at the surface of the country-rock. This deposit occurs at the northern end of the Coyote mountains, about 40 miles west of Tucson, upon the outcropping beds of porphyritic rock, which appear to be partly-metamorphosed strata of volcanic tufa, probably of late Secondary or of Tertiary age. The strata dip northward at a low angle, and present a series of basset-edges in parallel lines of outcrop, east and west, facing the south and extending over many acres. Successive groups of these outcrops, from 5 to 20 ft. in breadth, are coated with oxides of manganese in lustrous black films and crusts, shining in the sunlight like polished ebony, and covering the whole surface of the rock above the soil. Seen at a little distance, these croppings look like solid ledges of massive and pure ore; but closer inspection and a few blows of the hammer reveal their true nature as a superficial coating allied in origin to the blackened shining surface of rocks exposed in desert-regions, familiarly known as " desert paint" or "desert varnish,"' similar to the phenomena described by me in a former paper, but much thicker and heavier. * By reason of the death of the distinguished author, this communication, probably his last communication to technical literature, is published without revision of the proofs by him. A term first given y G. K. Gilbert. See Rocks, Rock-Weathering, and Soil; by George P. Merrill, p. 256 (New York, 1897). Superficial Blackening and Discoloration of Rocks, Especially in Desert Regions, Trans., xxxv., 371 (1905).

Sep 1, 1910

By T. V. Philip, Paul A. Beck

IN a previous note1 it was pointed out that the available information suggests a distinct correlation between the occurrence of the CsCl-type ordered structures formed in equi-atomic binary alloys of transition elements and the location of the components in the periodic table. A definite increase in the bond strength between unlike atoms, as compared with that between like atoms, is indicated when, in binary alloys of iron group elements, the other component is changed from chromium to vanadium or tantalum, to titanium. Laves and Wallbaum,2 eported a CsCl-type ordered structure for the stable intermediate phase at the equi-atomic composition in the Ti-Fe system (and also in the Ti-Ru and Ti-Os systems). On the other hand, Tagaya, Nenno, and Nishiyama8 found no ordering of this kind in the body-centered-cubic solid solutions in the Cr-Fe system. It was concluded' that the occurrence of a CsC1-type ordered phase of intermediate stability may be expected in the V-Fe system. Preliminary results were described: suggesting that at least some degree of order does exist in the equi-atomic alloy VFe, annealed at 1200° C and quenched in cold water. Using CrK radiation, at least one weak superlattice line was found in the X-ray diffraction pattern which could be indexed as (100). and which disappeared, as expected, when FeK radiation was used. It was found more recently that the impurity phase (presumably VN), previously giving rise to additional X-ray diffraction lines and thus preventing definite indentification of the (111) superlattice line,' can be eliminated by preparing the alloy by arc melting in a helium atmosphere. The alloy specimen melted in this manner had clean surfaces and showed very littte, if any, nitride phase in the microstructure after annealing in vacuum at 1250°C and quenching. The relative intensity of the (100). superlattice line with CrK radiation was greatly increased and, in addition, a fairly strong (Ill) , superlattice line and even a detectable (210) , super- lattice line was obtained, when the powder produced by filing from the 1250°C annealed and quenched specimen was reannealed in vacuum at 625°C for 1 hr. By using a cellulose acetate film as a filter in front of the photographic film in order to absorb the soft radiation resulting from air fluorescence, the background intensity could be reduced considerably in relation to the intensity of the diffraction lines. All three superlattice lines, (100),, (111)., and (210)a, disappeared, as expected, when a radiation other than CrK, was used.1 For the powder reannealed at 625ºC, the strongest lines of the s pattern also appeared weakly, indicating that during an: nealing at 625°C a small amount of transformation took place from the body-centered-cubic to the u phase. However, since all superlattice lines to be expected in the 0 angle range used were actually very clearly present, it was evident that the high temperature body-centered-cubic phase had transformed into a CsCl-type ordered structure before much s phase could form. Reannealing filings for 1 hr at 700°C resulted in complete transformation into the u phase. After 1 hr at 650°C the transformation into IT was not quite complete, the strongest body-centered-cubic diffraction lines were still present, although fairly weak, and only the (100), super-lattice line was detectable (extremely weak). These findings not only confirm the previous conclusionsL as to the existence of a CsCl-type ordered structure in the Fe-V system, but they also indicate that this metastable ordered structure forms at about 600°C preceding the formation of the stable s phase, while at 1250°C the disordered body-centered-cubic phase is stable. The faint (loo) , super-lattice line previously observed in specimens quenched from 1200°C was probably due to the fact that the quenching of the powder in an evacuated fuse:! quartz capsule was not fast enough to prevent completely the ordering reaction on cooling. The present results conform with the suggestion that the A-B bond, in relation to the A-A and B-B bonds, increases in strength from CrFe to VFe to TiFc. It is, therefore, of interest to compare the measured values of the average atomic diameter for these three alloys with the corresponding average atomic diameters calculated from the atomic radii of the elements concerned. ASSUming A-B contacts

Jan 1, 1958

By F. T. Davis

Many contributors have added to the fund of knowledge in the basic sciences related to mineral dressing during the past year. During 1964, the French edition of the Proceedings of the VIth International Mineral Processing Congress together with discussions was printed. Also, complete Preprints of papers delivered at the VIIth IMPC were published in September1. Over a third of the papers presented at VIIth IMPC dealt with fundamentals. COMMINUTION It has been postulated by Ponceleta that flaws need not exist before a stress is applied but rather the flaws are created at the tip of a propagating crack at a stress well below the theoretical breaking stress.

Jan 2, 1965

The accompanying sketch shows the interesting position of Salt Lake City with reference to Western mining areas and justifies its title "The Center of Western Mining." In the last twenty years, the area embraced within a circle of 600 miles radius with Salt Lake City as its center has produced 79.87% of the gold, 91.9% of the Silver, 77.47% of the copper, 53.61% of the lead and 26.55% of the zinc produced in the United States, including Alaska. This area also contains the greatest coal deposits of the continent, some of the greatest oil deposits, great iron deposits and many other important mineral resources. The 600-mile circle contained 69% of the active operators of other than coal mines and 40% of the men employed in mines other than coal mines of the United States, including Alaska, for the four-year period ended with 1923.

Jan 1, 1925

By ROBERT. RICHARDS

I. INTRODUCTION The object of this paper is to enlarge the field of settling velocities treated by me in my former papers, Close Sizing Before Jigging, and Sorting Before Sizing.' There seemed need of work both on coarser and on finer sizes. Messrs. A. Sidney Warren and M. L. Nagel undertook the investigation for the coarser sizes, from 12.85 mm. down to 2.05 mm. diameter. Their work, because of the closer spacing and because of the increased number of observations and consequent stronger averages, called for a revision of the former work. Messrs. G., A. Barnaby and Ralph Hayden undertook this part of the work, from 2.49 mm. down to 0.28 mm., which is near the limit of sifting. Their work covers the ground much more minutely and comprehensively than the former papers. There remained to be covered the portion of the field too fine for investigation with the sieves. This part, covering the range of grains from 0.48 to 0.03 mm., was undertaken by Mr. E. S. Bardwell. For it he used the elutriation method. II. THE FIRST, OR COARSEST, SECTION OF THE FIELD. The first desideratum in this investigation was a series of sieves for sizing the sands preparatory to making the tests. It became necessary, therefore, to decide on a sieve-scale for this purpose. A sieve-scale is a series of sieves in which the dimensions of the holes of the successive members form a series increasing by a. definite ratio. There are three natural sieve-scales : 1, progressing by doubling the width of the hole for each suc-

May 1, 1907

By B. C. Allen

Liquid surface tensions of copper and 18 Group IV-A to VIII transition metals (Ti, Zr, Hf, V, Cb, Ta, Mo, W, Re, Ru, Rh, Pd, Os, Ir, Pt, Fe, Ni. Co) have been measured by the static pendant-drop and dynamic drop-weight methods on the same rod sample. The drops were formed by electron-bombardment heating in high vacuum. Application of necessary corrections enabled determination of surface tensions to k2 pct and agreement between methods to * 1 to 4 pct for all the metals studied. Evidence is presented that the liquid surface was well screened by metal vapor, suggesting negligible adsorption of gaseous impurities and that the surface tensions measured are characteristic of the metals involved. Correlations between liquid surface tension and melting point, molar volume, heat of vaporization, and atomic number are presented and discussed. Temperature coefficients of surface tension were calculated using Eötvös' law. SURFACE tension and interface energies of metals are the result of incomplete atomic coordination resulting in a force perpendicular to the boundary, tending to minimize its area. These energies are important in many phases of metallurgy, including microstructure, sintering, joining, electronic emission, and lubrication, which in turn affect many physical and mechanical properties of metals. Liquid surface tension refers to the interface between the liquid and its own vapor or nonreactive atmosphere, and is considered a physical property of the liquid. Since equilibrium shapes can be readily obtained with liquids, the units of surface tension (force per length) and interface energy (energy per area) are interchangeable. Thermo-dynamically, the surface tension ?LV is given by the change in free energy F with surface area A at constant pressure P, temperature T, and composition N: for commercially important refractory metals, vanadium, columbium, tantalum,13,14 molybdenum,14 and tungsten,l5 and none for the rare platinum-group metals and rhenium. Measuring the surface tensions of transition metals is difficult because of their high reactivity and melting points. Of the many techniques available,16-18 the pendant-drop 19-21 and drop-weight methods17,22 are considered superior because they can be modified to eliminate persistent sources of contamination such as supports and capillaries necessary in the popular sessile drop, capillary rise, and maximum-bubble-pressure techniques. The necessary modification is to melt a drop on the tip of a vertical rod, which provides support through a solid of the same composition.13,15 The object of the work was to study the surface-tension behavior of copper and transition metals, having reasonably low vapor pressures. Liquid surface tension of each pure metal was systematically determined by using a combination of the static pendant-drop and dynamic drop-weight methods on the same rod. Liquid drops were formed by electron-bombardment heating in high vacuum. EXPERIMENTAL WORK As indicated in Table I, the metals studied were high purity and generally were obtained in rod form. The exceptions were titanium and zirconium, which were machined from crystal bars, and molybdenum (tot 11, osmium, and ruthenium, which were sintered and arc cast into rods. All the metals were ground or swaged to desired sizes between 1- and 7-mm diam, and centerless ground round and smooth to a finish better than 50 µ in., rms. Each rod was thoroughly cleaned with steel wool, degreased, acid etched, and dried. In a typical run, the rod was vertically clamped in a modified floating-zone electron-bombardment furnace designed after Calverley23 and Carlson.24 The specimen was outgassed and maintained positive at several kilovolts in a dynamic vacuum of 10-5 to 10-7 mm. The bottom end was enclosed by a tantalum pillbox and heated by electrons emitted from a hot concentric tungsten filament mounted on a movable bracket. The bombardment power was slowly raised until melting was observed. Power requirements ranged from 30 w for copper to 1300 w for 4-mm tungsten. The stabilized and out-gassed drop of near-maximum size was photographed at 4. 1X on panchromatic film at desired time inter-

Jan 1, 1963

On Sept. 22 to 26, the Institute will hold its 120th meeting in Chicago. The program arranged provides for technical sessions on: Mine Taxation, Non-ferrous Metallography, Coal and Gas, Milling, Oil, Industrial Organization, Geology, Non-ferrous Metallurgy, Mining and Local Resources, Iron and Steel, Symposium on Sulfur Coals, Symposium on Pyrometry. Inspection trips have been arranged to: Gary Steel Plant. La Salle District: Zinc smelters, coal mines, cement works, America's first permanganate plant, many varied industries, scenic trips. North Chicago and Milwaukee: Mining-machinery manufacturing plants, tungsten and molybdenum reduction plants. East Chicago and Whiting: Lead refinery, oil refinery. Franklin and McCoupin: Coal fields. Chicago: Nearly every kind of metallurgical and manufacturing industry. MONDAY, SEPT. 22d Morning Registration, Non-ferrous Metallurgy, Coal and Gas. Afternoon Coal and Gas Milling Industrial Geology, etc. Evening Smoker. TUESDAY Morning Gary. Afternoon Gary. Iron and Steel. Evening Oil, Iron and Steel.

Jan 9, 1919

The Industrial Minerals Division met jointly with the Materials and Equipment Division of the American Ceramic Society at State College, Pa, Sept 24-26 Headquarters were at the Nittany Lion Inn Thurs- day afternoon was devoted to a tour of inspection of the Bell Mine, American Lime and Stone Co , Bellefonte, Pa The party returned to State College for dinner and in the evening the Division's executive committee held a brief session There were four technical sessions Friday morning, Mining, afternoon, Beneficiation, Saturday morning, Industrial Minerals and Beneficiation There was an informal banquet at the Nittany Lion Inn Friday night with 93 present Edward Steidle was toastmaster Brief talks were made by President F C Flint and Secretary Ross Purdy, of the American Ceramic Society, Oliver Bowles, Chairman, Industrial Minerals Division, Adrian Morse, assistant to the president, Pennsylvania State College, and George Otis Smith, past president A I R'I E

Jan 1, 1937

By Randall L. Neal

This paper discusses the impact of taxes at the state and federal level on typical on-shore oil and gas exploration economics in the USA. Taxes considered are the windfall profits excise tax, state production (or severance) taxes, state income tax, and federal income tax. Also considered will be market prices for oil and gas in the USA. The effect of government take as a percent of revenue, on rate of return, discounted Payout, and discounted cumulative cash flow is shown on the attached tables. The conclusion drawn is that tax laws, while rarely the most important factor to be considered when drilling a well, can have significant impact on the profitability of oil and gas ventures, and should be considered when determining where to drill. Hypothetical exploration wells were analyzed for the impact of tax laws on project profitability. The results of this study show that when factors other than taxes are postulated to be the same (such as producing rate, capital, operating costs, and prices), cash flow can vary by as much as 68% due to the differences in the tax laws. Other significant findings for the cases studied include: (a) that discounted payout varied by as much as 1.8 years, (b) that rate of return differed by up to 67% and (c) the total tax rate as a percentage of revenue had a maximum variance of 33%.

Jan 1, 1982

By William Campbell

(Cleveland Meeting, October, 1912.) THE structure of iron and steel, though the object of so much study and research for the past 25 years, is by no means thoroughly understood. In the first place, we have three or more distinct iron-carbon thermal diagrams, each with its own supporters, and each representing a theory of the structure and constitution of cast-iron. In the second place, by reason of the fact that austenite, the solid solution of carbon in iron, decomposes in the solid state into ferrite, or pure iron, and cementite (Fe3C), and that quenching from above this transition-range, no matter how rapid, cannot entirely prevent the change and thus preserve the austenite by itself at ordinary temperatures, it happens that under the microscope we find, in addition to the ferrite, Fe3C, and austenite, which the thermal diagram of steel requires, it series of transition-products with distinctive structures, to which have ,been given the names martensite, troostite, sorbite, etc. Now these transition-products, in addition to the solid solution, austenite, have been the source of much controversy, at times very bitter. One side would insist that, say, troostite was an entity, which the other side would deny, pointing out that it must be a transition-mixture, with a particular structure. That austenite was a solid solution of carbon in iron has been denied by one school ; we have been told that Fe24C dissolved both Fe3C and Fe, and thus gave rise to a whole series of quenching-products-all this in spite of the fact that no matter how the thermal diagrams differ in regard to cast-iron, they all agree in regard to the solid solution, austenite, for Fe24C finds no place on the diagram. Thus it happens that while the authorities fight both in regard to the iron-carbon diagram and the structures met with in hard- * Associate Professor of Metallurgy, Columbia University in the City of New York.

Dec 1, 1912

By W. R. Shimer

IN his valuable report on Finishing Temperatures and Properties of Rails, I Dr. G. K. Burgess, Chief of the Division of Metallurgy, U. S. Bureau of Standards, has begun a line of investigation which should be continued by those interested in the subject, and who have proper facilities for carrying put the work. For the past year or more the Bethlehem Steel Co. has been conducting experiments to learn the effect of rail finishing temperatures on their physical properties and microstructure and the results are here given for the consideration of those interested in the rail situation. . Considerable differences of opinion have been expressed by various authorities, in the past, as to the effect of large or small grain size and high or low finishing temperatures of steel rails on their physical properties and wearing qualities. Low finishing temperatures and, therefore, low shrinkage, have been advocated on the theory that the wearing qualities would be improved. Others have recommended high finishing temperatures. The generally accepted cause for rail failures, due to the development ,of transverse fissures, is excessive wheel pressure on hard rails. One of the causes advanced for hard rails has been that they contain too high per centages of carbon and manganese; another that the rails were finished at too low a temperature, i.e., at or near the critical point. In the experiments herein described the rails were rolled from reheated blooms. All the rail blooms were charged hot in a reheating furnace and brought up to about the original ingot-rolling temperature before rolling into rails. These rails gave better results in deflection, withstood a greater number of drops before breaking, and showed greater ductility, than. rails of identically the same composition and section which were rolled, direct from the ingot. Rails rolled from reheated blooms, finished at somewhat higher temperatures than when rolled direct from the ingot, have a different microstructure, which the writer does not believe is due so much to the difference in finishing temperatures, as to the difference in

Jan 3, 1915

By GEO M. FOWLER

AN appraisal of the activities of the mining geologists during 1936 clearly indicates the ever in- creasing utilization of geology in the search for ore. Few men with geo- logic training are idle at present; this is particularly true regarding recent graduates. Many have accepted employment in distant fields, such as the Philippines and South America, and greatly increased mineral production from these places reflects their activities. In North America, regions of intense mineralization formerly important are being restudied in greater de- tail and with better understanding; as a result, new mineral wealth is being found in many such districts. Much is being done by private companies and individuals, and it is to be hoped that mining companies will increasingly make available the purely scientific results of such studies by permitting their geologists to publish. On such generosity to a large extent will future advances in ore finding depend.

Jan 1, 1937

By Donald H. McLaughlin

THE activity and enthusiasm of pioneers still prevail among workers in applied geophysics1.- Within the year, new devices have .been tried out, instruments and technique have been improved and the methods of application to commercial problems have been increased in many ingenious ways. There is still great need for more skillful interpretation of results in terms of geology, but oil the whole geophysical prospecting is making encouraging progress toward finding its proper place and function in engineering and geological practice. Spectacular successes continue to be reported, particularly .from the Gulf Coast, where the race for salt domes has not slackened, and encouraging results have been giined elsewhere in the mapping of structures in the search for oil. In the mining field, however, it can hardly be claimed that the same measure of success has been obtained, for brilliant efforts worthy of wide recognition have been overshadowed to some eatent by the unfortunate outcome of surveys undertaken unwisely without recognition of the limitations of the work. Consequently, hopes were aroused that could not be fulfilled, and it must be admitted in an impartial survey that there are a few regions, chiefly in the far north, where the standing of geophysical prospecting is somewhat doubtful and where the course of public opinion regarding it shows a certain similarity to the history of the market during the past few months. Reliable work, however, is steadily going 011 and it can confidently be expected that the methods will eventually be regarded in many regions as an essential part of the technique of securing geologic data needed for intelligent exploration.

Jan 1, 1930

By Lyon F. Terry

SPEED-UP of production of crude oil and its products, accompanied by rising prices and the organization of the industry on a war basis, featured the economic aspects of petroleum in 1941. Early in the year American tankers were urgently requested by the British to replace losses and offset slower transit under convoy. Some forty American owned tankers were first assigned to Britain and an additional forty-odd ships were transferred during the summer. This threatened to reduce our transportation facilities from Gulf ports to the Eastern seaboard below requirements, especially should sinkings have increased and the British needed more ships. Co-ordinator Ickes began preparations for restricting gasoline consumption in the Eastern district and plans were formulated for the construction of an emergency trunk pipe line from Texas to New York and Philadelphia refining centers, and for a gigantic tanker-building program. Sales of new oil-heating units in the East practically ceased. The companies were urged to transport as much oil as possible by tank car and by October 140,000 barrels of oil per day were reaching the East Coast district by rail, sufficient to meet 8 per cent of total requirements. But British sinkings from July through October decreased 63 per cent compared with the four months ended June 30, Britain began the return of tankers, the construction plans were dropped, and the threatened shortage was thus averted.

Jan 1, 1942

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By V. F. Swanson

At the AIME meeting in Tampa in Oct. 1966, an empirically developed equation was presented which allowed the calculation of free settling velocity for any sized particle: 1 [ ] This equation requires the use of two parameters a and p which are coefficients derived from boundary layer theory.2 It was possible to develop values of a and p for several minerals by back calculation of published data. The original equation had one major flaw. When the fluid density exceeds the density of the solids, the solution to the equation becomes imaginary. A flaw was indicated also by the fact that galena and sylvite both having cubic cleavage, did not have similar values for a and b. Galena gave calculated values of a = 1.082 and g = 3.11, while sylvite gave values of a = 1.870 and p = 2.56. These flaws prompted further study of the equation, resulting in the following empirical modification: [ ] It is obvious a real solution of the equation is possible for all values of ps and p. When PL > PS, V is negative, indicating that the particles will rise against the attraction of gravity. The validity of the modification is borne out by the fact that when values of a and p were back calculated for galena and sylvite using the modified equation, both minerals gave values of a = 1.038 and p = 3.01. With the modification shown in Eq. 2, Newton's friction factor becomes [ ]

Jan 1, 1976

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz's model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965

By Wallace E. Pratt

TO SERVE their primary function of balancing supply with demand. crude-oil prices must not only return full cost plus a reasonable earning to the efficient producer but they must also offer an additional reward to stimulate exploration sufficiently to maintain adequate reserves. High prices increase the volume and efficiency of exploration; low prig e- -Idle exploration. Over the last decade average prices for crude oil have been much lower than for the proceeding ten years, and lower even than the average over the life of industry. Under these circumstances no one should be surprised to learn that over this same recent period of discovery of new oil fields has also lagged and fallen below its average level for the previous decade. Crude oil prices have been too ion to support the required activity in wildcatting.

Jan 1, 1941

By Schumacher, Earle E.

THE solidus line above the solid solution field in the lead-antimony system was originally determined by Dean and his associates1 from heating curves. They did not regard this line as having been accurately fixed and in their more recent publications2 the curves drawn do not follow closely the original data. The precise location of the solidus line is of importance in the extrusion of lead-antimony cable sheath, as the temperature of the metal in this process must be less than the lowest temperature at which any part of the alloy in the lead-press charge becomes liquid. It is very desirable, however, to operate at as high a temperature as possible, as the rate of extrusion for a given pressure is approximately doubled for an increase of 10" C. in temperature. The precise location of this line is also important in the investigation of ternary systems of lead, antimony and a third metal. For these reasons, and because of the differences reported in the literature, data were secured on the lead-antimony solidus line by the classical quenching-test procedure.

Jan 1, 1927