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By L. G. Austin, R. R. Klimpel

This communication points out that serious errors exist in some current treatments of the random fracture of solids, including the prior treatments by Klimpel and Austin, Gilvarry, and Gaudin and Meloy. The problem considered in all of these papers is: what cumulative weight versus size distribution is expected for the fragments produced by fracture of a particle? The basic assumption made is that fracture surfaces propagate in random directions from weak flaws in the solid (these weak flaws being activated to fracture by applied stress), with the activated weak flaws distributed at random spatially within the solid. The previous treatments considered fracture in three dimensions, and all use similar physical models, although the mathematical techniques were somewhat different. We first noticed that these treatments were in error when we attempted to reduce the equations developed to the simple case of fracture of a one-dimensional particle, e.g. a long, thin fiber which breaks along its length. For this simple case, it is readily shown that the assumption of random fracture leads to the expression P(V) = (r/Vo) (1-V/Vo) r-1 dV (1) is the probability of occurrence of a fragment of length within the range V to V + dV; V being length dimension, from r random fractures passing through an original size of Vo to produce r + 1 fragments. This equation agreed with the one-dimensional form of an equivalent equation in the original Klimpel-Austin treatment. However, in this treatment it was then stated that, "The fractional weight below size V is [ ]

Jan 8, 1968

By Walter Renton Ingalls

The ores of zinc which are important as sources of that metal are of two classes, viz., the sulphide and the oxidized. The latter includes six varieties: zincite (the red oxide) and franklinite (the oxide of zinc, iron, and manganese), which are found abundantly only in New Jersey; and the hydrous and anhydrous carbonates, the hydrous and anhydrous silicates, which are of widespread occurrence. The hydrous carbonate is known mineralogically as hydrozincite, zinconise, or zinc-bloom; the anhydrous silicate is recognized as willemite. With respect to the anhydrous carbonate and the hydrous silicate, however, there is a confusion of name which is of old standing. Attempts to clear it away were long ago made by the mineralogists with the result that there is now a more or less national uniformity of nomenclature; but there is still an international disagreement, sometimes very perplexing and always leading to inexactness in expression, which may be considered an adequate excuse for this return to a time-worn subject. The name calamine, together with Galmei of the Germans, is commonly supposed to be derived from xadµela, which was used by the Greeks to designate the peculiar kind of ore employed with copper in their brass-making, and also the accretions which formed in the brass-founder's furnaces. Agricola, however, says that it is from calamm, a reed, in allusion to the appearance of the material, cadmia fornacum, which collected 011 the furnace-walls. But whatever the derivation of the word, it was used until within one hundred years to include all the oxidized

Jan 1, 1896

By Arthur C. Simmons

The area that produces Pennsylvania grade, which includes New York, Pennsylvania, West Virginia and a part of Ohio, increased its production in 1942 about 1,580,000 bbl. over that attained in 1941. Such an increase is substantial for this area, and measured in terms of increased output of lubricants, for which the crude is particularly suitable, it represents a needed arid worth-while addition to the lubricant resources of the United States. The year 1942 was a difficult operating period for most of the petroleum-producing areas in the United States, but the Appalachian region, owing principally to its location, type of operations, and crude value, suffered less from war influences than other areas. The state of Pennsylvania produced 17,823,870 bbl. of crude oil, which is approximately 63 per cent of the total production of Pennsylvania grade in the entire area. Production Bradford Field The Bradford field, which produces almost wholly by water-flooding methods, increased its production nearly 4000 bbl. per day over 1941 despite a very slight reduction in total number of wells completed. Well completions in the Bradford field (in both New York and Pennsylvania) includc both producing oil wells and water-intake wells. About half of the well completions are producing oil wells and the remaining half are water-intake or injection wells. About 10 per cent of the total well completions of the Bradford field were in Cattaraugus County, New York. No segregation of well completions is available, so that precise statistics cannot be given for New York and Pennsylvania.

Jan 1, 1943

By W. A. Oates, J. S. Blakemore, E. O. Hall

AS part of an investigation into the effect of hydrogen on the serrated yielding of Ni-Cu alloys,' it was necessary to determine the solubility of hydrogen in the alloys of interest. With the exception of the work by Fukusima and Mitui2 who investigated the solubility of hydrogen in solid Ni-Cu alloys at 20 wt pct intervals at 1050°, 700°, and 350°C, the information in the literature is limited.3-10 Alloys were prepared from deoxidized Analar Copper and Mond Nickel pellets.' Wire samples were hydrogenated at 7.8 atm in an autoclave consisting of 5 ft of thick-walled Inconel 600 tube with a resistance furnace around the middle portion. The top end, at room temperature, was fitted with a safety valve, a calibrated pressure gage, and a sample inlet, while the bottom end, again at room temperature, was filled with water. After reaching equilibrium samples were quenched by dropping from the high-temperature region of the autoclave into water. They were then quickly transferred to liquid nitrogen where they were stored until analyzed for hydrogen using an Exhalograph.11 The results, which are shown in Fig. 1, represent the mean of two separate determinations on each sample. Because of the lower level of hydrogen at the high copper end of the series, the results here are of poor precision using this method. Fortunately, the results of Himmler9 using the Sieverts technique are available for these copper-rich alloys (>80 at. pct Cu)

Jan 1, 1969

By Ziebell, Howard A.

THE Washington magnesite deposits, located in the hilly and mountainous northeastern part of Washington, occur as massive lenses in a sedimentary series made up of dolomite, shale, and quartzite, into which basic dikes have intruded. The ore pattern resembles a series of disconnected chain links extending approximately 25 miles in a south-west direction. Magnesite in this district is all crystalline and closely associated with dolomite, talc, serpentine, and basic dike rock. All deposits which have been developed are near the surface so that quarry-bench mining has been possible. For over twenty years hand sorting magnesite ore at the quarry face was standard practice. Ore cars were hand trammed on 30-lb rail systems which led from the face to ore passes or raises for the magnesite ore and to the waste dumps for disposal of the rejected waste material. This system was somewhat modified by the use of Dempster Dumpster trucks. The ore was, however, still sorted by hand from the calcium and silica bearing waste rock. Power equipment. consisting of one 3/4-yd electric shovel, was

Jan 1, 1949

By Francis T. Havard

A Reply to the Discussion by Mr. Francis T. Havard of the Paper by Mr. Henry W. Edwards, which was read at the Atlantic City Meeting, February, 1.904. (Annual Meeting, February, 1905.) MR. HENRY W. EDWARDS, Grand Junction, Colo. (communication to the Secretary) :* Effect of Heat. It should be remembered that the coefficient of expansion of concrete is nearly that of iron; therefore in constructing flues the design must take account of this important detail. The cracking of flues, mentioned by Mr. Havard as having occurred at a temperature of 100° C. and above, . were possibly caused by neglecting to appreciate the extent of the expansion and contraction of the concrete. Effect of Atmospheric Moisture.-The moisture present in the atmosphere is exceedingly injurious to flues of any material, and those made of concrete are no more susceptible than of brick. My experience with flues of the Monier construction, having walls from 1.5 to 2.5 in. thick plastered upon a net-work of iron rods, was unsatisfactory from the standpoint of dura¬bility.

Mar 1, 1905

Safety and health are no longer secondary responsibilities but must be of paramount concern to every mining operation, according to Anthony J. Thompson, an attorney with Hamel, Park, McCabe & Saunders of Washington D.C. The Mine Safety and Health Administration (MSHA) forecasts an estimated 19,000 inspections during 1979, and the economic and psychological impact of these inspections may he significant. To illustrate his point Thompson reviewed the experiences of a relatively large operation during a recent MSHA visit. The inspector was on the premises for two months, issuing between 250 to 300 "significant and substantial" (s&s) citations. During the most intensive period, about one month in duration, the operation experienced a production loss estimated between 2500 to 3000 tons; an accident rate up 30% over the previous month and 20% over the same month in the preceding year; 100% of the safety director's and safety engi¬neer's time was devoted to the inspection; 50% of top level management's time; and 90% of the mid-level or front line supervisory's time.

Jan 11, 1979

By Thomas M. Drown

THE method usually employed in accurate determinations of sulhur in pig-iron and steel is to treat a weighed sample of borings in a flask with muriatic acid, and to pass the gaseous products through an alkaline solution of lead or silver, which precipitates all the sulphur of the sulphuretted hydrogen in the form of sulphide of lead or silver. The sulphide thus formed is subsequently oxidized by aqua regia, bromine, or other oxidizing agent, and the sulphuric acid formed precipitated in the usual way by chloride of barium. I have substituted for the alkaline metallic solution, a solution of permanganate of potash in the strength of one gramme of permanganate to 200 cubic centimetres of water, and find that it gives results quite as accurate as those obtained by using an ammoniacal solution of silver. By the employment of the permanganate it will be readily seen that there is considerable saving of time and work. In order to test the accuracy of the method, six samples of pig-iron borings were weighed out (about six grammes each) and treated identically

Jan 1, 1874

By Linn Bradley

R. J. WYSOR, So. Bethlehem, Pa. (communication to the Secretary*). At our plant (Bethlehem Steel Co.), we have had several Bradshaw burners under course of construction and erection for some time, but up to the present we have not had opportunity to put them in service. I regret that I can not take part in the discussion with some actual results from these, burners. Mr. Huessener properly emphasizes the importance of obtaining the highest combustion temperature practicable in boiler practice, which demands a near approach to perfect combustion conditions. The ideal burner is the one which, while meeting the various mechanical, requirements, fulfills the above condition under a wide range of gas pressure. The question as to the relative value of hot raw gas and cold washed gas for boiler use is a very interesting one. I think that in the past the importance of low temperature of washed gas sometimes has been over-emphasized. Mr. Huessener has pointed out that so far as temperature is concerned, no advantage accrues in washing gas below 100° F. In

Jan 3, 1917

The following delegates were appointed to the National Conservation Congress on May 2, 3, and 4, 1916, in Washington, D. C. HENRY S.. DRINKER, a GEORGE OTIS SMITH, A. F. Lucas, - W. L. SAUNDERS, VAN H. MANNING. President Ricketts was appointed delegate to the dedication ceremonies of the new buildings of the Massachusetts Institute of Technology in June. W. L. Saunders was appointed delegate to the ceremonies in celebration of the 150th Anniversary of the founding of Rutgers College to be held in October. George C. Stone was appointed delegate to the meeting on Standard Screen Scale of the U. S. Bureau of Standards. George D. Barron and Thomas T. Read were appointed delegates to the Second National Exposition of Chemical Industries to be held in New York in September. It was resolved, that the Institute shall pay the transportation of the Secretaries of the Local Sections to and from the Arizona Meeting. It was resolved that certain general topics' should be selected for discussion at the next meeting of the Institute and a session devoted to each.

Jan 6, 1916

By Thomas M. Brown

The method usually employed in accurate determinations of sulphur in pig-iron and steel is to treat a weighed sample of borings in a flask with muriatic acid, and to pass the gaseous products through an alkaline solution of lead or silver, which precipitates all the solphur of the sulphuretted hydrogen in the form of sulphide of lead or silver. The sulphide thus formed is subsequently oxidized by aqua regia, bromine, or other oxidizing agent, and the sulphuric acid formed precipitated in the usual way by chloride of barium. I have substituted for the alkaline metallic solution, a solution of permanganate of potash in the strength of one gramme of permanganate to 200 cubic centimetres of water, and find that it gives results quite as accurate as those obtained by using an ammoniacal solution of silver. By the employment of the permanganate it will be readily seen that there is considerable saving of time and work. In order to test the accuracy of the method, six samples of pig-iron borings were weighed out (about six grammes each) and treated identically

By J. K. Brooke, R. M. Dreyer

For mining engineers and geologists accustomed evaluating metallic mineral deposits, the problems inherent in determining the worth of non- metallic industrial minerals deposits for the chemical processing industry often comes as a rude shock. These difficulties lead to different, and often much greater, problems in financing the development of such deposits than would normally be anticipated for economic sources of copper, molybdenum, iron, nickel and other metallic minerals. The chemical processing industry is one of the two principal consumers of non-metallic mineral production, the other being the construction industry. In the last decade, the volume of industrial minerals consumed by chemical processers has in- creased by 30%, and further increases are forecasted. To satisfy this growing demand, many new sources of these minerals must be found and developed. For those of us who will become involved in such work, the following brief analysis of the major problems to be expected may be of help in developing a realistic approach to evaluating and financing such a deposit and selling the product to consumers.

Jan 8, 1962

By E. H. Jr. Crabtree

THE productive area of asphalt-bearing sandstone in Missouri is near the Missouri-Kansas state line near Nevada, the county seat of Vernon County about 100 miles south of Kansas City. While produc-tion thus far has been confined to Vernon and Barton counties, there are known deposits in adjacent counties. The area is served by four rail-roads: the Missouri Pacific, the Kansas City Southern, the Missouri-Kansas & Texas, and the St. Louis & San Francisco. The plant of the Reliance Rock Asphalt Corporation is in Vernon County, about 5 miles west of Nevada, at Ellis, a flag station on the Missouri, Kansas & Texas Railroad. A siding has been built to the plant so that the finished product can be loaded directly into railroad cars. The property consists of a lease of 240 acres in one block. All portions of the property not required for quarrying or processing the asphalt-bearing sandstone are used for farming by the fee owner. The entire tract is very flat so that there are no transportation difficulties from quarry to plant.

Jan 1, 1935

By E. M. Cox, A. S. Skapski, N. H. Nachtrieb, M. C. Bachelder

D. T. ROGERS*—The conclusions drawn in this paper have important practical significance to the steelmaker and the metallurgist if, in practice, it is demonstrated that metallic copper in the charge will pick up sulphur from the furnace atmosphere and thus increase the sulphur content of the bath. The problem of residual copper arising out of increasing copper in the scrap available to the industry is, in itself, a matter of concern to the steel maker. If, in addition to the often detrimental effects of high residual copper upon the physical properties of some important steel grades, there is to be a complication of the sulphur problem, then we have a set of conditions that bodes no good for the open hearth melter and the open hearth metallurgist. M. B. BEVER*— Investigations of gas-metal equilibria continue to be of interest, especially as new possibilities for improving experimental techniques emerge. Higher purity of reacting substances, better refractories, improved methods of temperature control and an increased awareness of the pitfalls of high-temperature equilibrium work are

Jan 1, 1950

By John H. Bassarear, Harold W. Sorstokke

The fourth expansion within 10 years was completed at Pima Mining Co. during late 1971. The first three expansions increased capacity from 3000 to over 40,000 tpd. Conventional crushing and grinding practices were used in the original 10-section mill. Total capacity is now approximately 54,000 tpd. Expansion IV includes a new primary crusher and a radial stacker conveyor that feeds stockpiles for both concentrators. The -8-in. primary product is fed from the reclaim stockpile to the new mill by two pairs of pan feeders, each pair feeding a separate conveyor. The reclaim conveyors each feed 28 X 12-ft semiautogenous mills operating with an 8% charge of 4-in. balls. Autogenous discharge is screened, oversize recycling by conveyors, with -%-in. undersize feeding two conventional 161/2 X 19-ft ball mills in closed circuit with cyclones. Cyclone overflow is pumped to three parallel rows of 300-400 cu ft flotation cells. Rougher and scavenger concentrates produced are sent to the original mill for regrind, cleaning, and filtering.

Jan 1, 1974

By J. L. Bray, S. T. Ross

The paper provides electrometallurgical data on the problem of germanium removal from zinc sulphate solutions. Germanium traces have caused much concern to the zinc refiner. Confirmatory evidence of interaction between germanium and cadmium is presented. Statistical analysis of data expands its significance and enhances its value. Further research is outlined. THE literature contains many references to the effects of trace amounts of germanium in the production of electrolytic zinc. One of the authors had experience with this troublesome element as early as 1917 at Trail, B. C. In 1929, Tainton and Clayton' reported that concentrations of as little as one part per million of germanium were sufficient to cause serious losses in current efficiency. Liddell2 reported that trace amounts of germanium cause marked lowering of the hydrogen overvoltage of electrolytic zinc cells, so that commercial production was impaired. Bray3 recorded the history of germanium in relation to electrolytic zinc production, noting that concentrations below 10 ppm have been found to yield low current efficiencies and copious hydrogen evolution. Koehler' stated that germanium "when present to the extent of a small fraction of one part per million per liter, causes serious evolution of hydrogen with a corresponding reduction in current efficiency." Recently, however, S. W. Ross" reported, from Risdon, Tasmania, that "in the course of leaching . .. dissolved traces of germanium... if not removed almost completely ... increase the reversion of cadmium during the filtration of the copper-cadmium precipitate and reduce the current efficiency during subsequent analysis." The copper-cadmium precipitate referred to is the residue from the zinc-dusting purification of zinc sulphate leach solutions. In the face of such conflicting testimony and with the increasing industrial importance of pure germanium and zinc it was decided to investigate the relationship between cadmium and germanium. Furthermore, other work by the authors showed certain discrepancies to exist in the theories of Tainton, et al. In the laboratory, without marked efficiency decreases, the authors have deposited zinc successfully from solutions containing as high as 1 g per liter of germanium. This could be done only when there was no cadmium present. Preliminary investigations of the suspected rela- tionships were carried out by means of emission spectrographic analysis using a beryllium internal standard. Several solutions containing 100 g per liter of zinc, as zinc sulphate, and 1 g per liter of cadmium, as cadmium chloride, were prepared. These concentrations were on the order of those obtained during a commercial low-acid leaching process. Varying concentrations of germanium were added to these solutions so that the range of 0.0000 to 0.5000 g per liter of germanium was covered. A 250 ml sample of each solution was agitated with 2.5 g of zinc dust for 30 min, filtered, and the filtrates were examined spectroscopically. Qualitative evidences of cadmium traces were found in those filtrates which originally contained above 10 ppm of germanium. Reliability of the analytical method did not permit quantitative investigations since cad-Table I. Current Efficiencies Obtained at 0.0000 and 1.5000 G per Liter Cadmium Concentrations Ge Concentrastion,* Cd Concentration,* EtBclenoy, G per Liter G per Llter Pot 0.0000 0.0000 84.270 0.0010 0.0000 94.849 0.0050 0.0000 92.649 0.0075 0.0000 94.039 0.0100 0.0000 96.084 0.0000 1.5000 93.460 0.0010 1.5000 95.158 0.0050 1.5000 92.148 0.0075 1.5000 91.260 0.0100 1.5000 84.546 • Cd and Ge concentrations shown are those existing before zinc-dust purification. mium determination in the concentrations present in zinc-dusted solutions lacks sufficient sensitivity for reproducible results. As a consequence of the inability of the investigators to obtain acceptable results through direct quantitative analysis, an indirect approach was devised. This indirect method involved a study of the current efficiency, in a model zinc cell, as a function of the concentrations of cadmium and germanium. Variables such as cell temperature, voltage, current density, anode spacing, relative electrode area, degree of agitation, cathode preparation technique, time, acid concentration, and solution volume were held constant. Fig. 1 shows the cell used. The current was fur-

Jan 1, 1952

By Walter Rose

It is the purpose of this note to call attention to the circumstance complicating the attainment of uniform gas-liquid distributions in multi-phase flow systems, and especially in those of the so-called Hassler type.' Although the complication arises directly as a consequence of gas compressibility and the dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature.' In fact, it is only the paper of Geffen et al.3 which gives any experimental evidence that a problem exists. On the other hand, previous authorsl,4,5 have made the tacit, albeit fallaceous assumption that uniform gas-liquid distributions automatically are established in linear flow systems by the expedient of maintaining the pressure gradients equal in the flowing gas and liquid phases. Such a device, it can be shown, will succeed only if the immiscible fluids are both equally compressible or both essentially non-compressible. Another necessary condition required before uniform fluid-fluid distributions can be achieved is that the porous matrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic media only when the curvature of each interface of contact between wetting and non-wetting fluids is everywhere the same throughout the interspaces. This is a necessary condition which follows from the consideration that variation in interfacial curvature gives rise to finite capillary pressure gradients and therefore to variation in the saturation distribution. That this is not a sufficient condition follows from the consideration that hysteric possibilities allow for different saturations even though the capillary pressure gradient is zero. In any event, it will- be recalled that it is the intent in the Hassler scheme of relative permeability determination' to obtain initially (by the capillary pressure drainage or imhibition process) uniform conditions of fluid distribution in the core sample, and then to maintain this uniformity during mixture flow so that the resultant fluid mobilities which are calculated will refer to steady-state transfer under fixed conditions of uniform saturation. If the flowing fluids are incompressible, it is recognized that employment of the same value of the pressure gradient in each fluid will result in maintenance of the initially obtained condition of zero capillary pressure gradient. On the other hand, the consequence of gas compressibility is that the gradient in the gas pressure varies from point to point in the flowing stream. and since the pressure gradient in an incompressible liquid is constant it is thus impossible to maintain zero capillary pressure gradient during the simultaneous flow of gas-liquid mixtures. Therefore, one would expect to observe a variation in the gas-liquid saturation in the directions of the capillary pressure gradients, depending in magnitude on the particular way saturation changed with capillary pressure. In order to formulate the manner gas compressibility effects prevent the attainment of uniform gas-liquid distributions during mixture flow, consider a linear flow system of unit length. As noted, it is necessary to assume an isotropic medium (viz. one where permeability is independent of position and direction). One then can arbitrarily set the pressure

Jan 1, 1951

By Walter Rose

It is the purpose of this note to call attention to the circumstance complicating the attainment of uniform gas-liquid distributions in multi-phase flow systems, and especially in those of the so-called Hassler type.' Although the complication arises directly as a consequence of gas compressibility and the dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature.' In fact, it is only the paper of Geffen et al.3 which gives any experimental evidence that a problem exists. On the other hand, previous authorsl,4,5 have made the tacit, albeit fallaceous assumption that uniform gas-liquid distributions automatically are established in linear flow systems by the expedient of maintaining the pressure gradients equal in the flowing gas and liquid phases. Such a device, it can be shown, will succeed only if the immiscible fluids are both equally compressible or both essentially non-compressible. Another necessary condition required before uniform fluid-fluid distributions can be achieved is that the porous matrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic media only when the curvature of each interface of contact between wetting and non-wetting fluids is everywhere the same throughout the interspaces. This is a necessary condition which follows from the consideration that variation in interfacial curvature gives rise to finite capillary pressure gradients and therefore to variation in the saturation distribution. That this is not a sufficient condition follows from the consideration that hysteric possibilities allow for different saturations even though the capillary pressure gradient is zero. In any event, it will- be recalled that it is the intent in the Hassler scheme of relative permeability determination' to obtain initially (by the capillary pressure drainage or imhibition process) uniform conditions of fluid distribution in the core sample, and then to maintain this uniformity during mixture flow so that the resultant fluid mobilities which are calculated will refer to steady-state transfer under fixed conditions of uniform saturation. If the flowing fluids are incompressible, it is recognized that employment of the same value of the pressure gradient in each fluid will result in maintenance of the initially obtained condition of zero capillary pressure gradient. On the other hand, the consequence of gas compressibility is that the gradient in the gas pressure varies from point to point in the flowing stream. and since the pressure gradient in an incompressible liquid is constant it is thus impossible to maintain zero capillary pressure gradient during the simultaneous flow of gas-liquid mixtures. Therefore, one would expect to observe a variation in the gas-liquid saturation in the directions of the capillary pressure gradients, depending in magnitude on the particular way saturation changed with capillary pressure. In order to formulate the manner gas compressibility effects prevent the attainment of uniform gas-liquid distributions during mixture flow, consider a linear flow system of unit length. As noted, it is necessary to assume an isotropic medium (viz. one where permeability is independent of position and direction). One then can arbitrarily set the pressure

Jan 1, 1951

By G. D. Hobson, I. Mrosovsky

Material balance relationships for expansion-type reservoirs above the bubble point have been discussed in recent years by H. N. Hall and M. F. Hawkins, Jr. The former drew attention to the effects of rock compressibility, and the latter to the effects of the compressibility of any interstitial water. Hawkins derived a general relationship which took note of oil, water and rock compressibilities, and then by assuming first, the absence of interstitial water and secondly, no effects due to interstitial water or rock compressibility, obtained relationships symbolically of the same form as those previously derived directly by Hall. Hawkins defined his terms clearly, and noted an approximation, due to the omission of a term involving the product of two compressibilities, made in reaching his final equation. There is, however, possible ambiguity with regard to Hall's written definition of the oil production term. One interpretation would mean that the produced oil and initial oil-in-place, if both required as stock tank barrels, would be obtained by using different formation volume factors in the conversion in order to satisfy the conditions implicit in Hall's formulae. The other would involve an approximation which, if used, was not stated. In both Hall's and Hawkins' studies the effect of the approximation or inconsistency is very slight. Nevertheless, it may be justifiable to give a somewhat more consistent derivation, since the complexity of the final relationships is not thereby greatly increased. Let the initial pore volume be Vi and the volume after a pressure drop of Ap, V. Then V = V, (1 - ?p . cr), where c, is the rock compressibility expressed as change in pore volume/unit pore volume/unit pressure change, and is defined with the initial pressure as base. Suppose that the interstitial water saturation under the initial conditions is Sw. The total volume of interstitial water under those conditions will be ViSw. If the volume of the water after dropping the pressure by ?p is V., this will be given by Vw = ViSw (1 + ?p.c,w), the compressibility of the water being c, which is ex- pressed using the volume at the initial pressure as base. If Boi is the reservoir volume factor of the crude oil for the initial reservoir conditions, and B. the equivalent factor when the pressure has dropped by ?p, with N the initial amount of oil expressed as stock tank barrels. N.Boi = Vi - V,Sw If n is the amount of oil produced (in terms of stock tank barrels) as a result of the pressure drop ?p, the remaining subsurface volume of oil at the lower pressure will be Bw, and Bc can be related to the compressibi:ity of oil and the pressure drop, and if c, is the compressibility factor based on the initial conditions, The relationship derived by Hawkins was case to a standard at the lower pressure, while a term (Ap) had been dropped, because of its smallness arising from its dependence on the products of two compressibility factors. When there is no interstitial water and rock compressibility can be ignored, Eq. 1 reduces to:

Jan 1, 1957

By N. L. Muench, J. S. Osba

Research conducted previously has demonstrated that spectral analysis of gamma radiation from the naturally radioactive elements present in earth materials permits detervination of the relative concentrations of these elements. This research suggested that spectral analysis of gamma radiation resulting from neutron bombardment of elements not nor-mally radioactive might serve to identify these non-radioactive elements, and might permit their quantitative determination. To investigate this possibility, laboratory experiments were conducted in which various earth materials were subjected to bombardment by neutrons from a polonium-beryllium source, and in which the spectra of the resultant gamma radiation were analyzed. The geometry of the lab-ortory system was designed to simulate wellbore conditions. The laboratory work demonstrated that some elements not only can be identified with relative ease, but also can be determined quantitatively. This finding indicates that the use of an intense source of more energetic neutrons may lead to the identification and measurement of additional elements of interest by means of induced nuclear reactions. INTRODUCTION In recent years the applications of nuclear physics to the producing branch of the petroleum industry have become increasingly numerous. One significant development, an outgrowth of nuclear science which is of potential importance in well logging, has been the analysis of gamma-ray spectra of naturally radioactive elements in earth strata. The work of Brannon and Osoba1 has demonstrated that presently available equipment and techniques may be used to determine the relative concentration of thorium, potassium, and uranium in underground strata by means of gamma-ray spectral analysis. Success of the research on spectral analysis of naturally radioactive elements suggested that spectral analysis of induced radioactivity might serve to identify, and perhaps measure quantitatively, those elements which normally are not radioactive, but which become radioactive on neutron bombardment. It was to investigate this possibility that the research described in the following sections was undertaken. THEORY OF INDUCED NUCLEAR REACTIONS Of fundamental importance is the fact that an element, when bom- barded with neutrons, emits gamma rays of energies characteristic of that element. Therefore, in theory, an element may be identified by analysis of the energy spectrum of the neutron-induced gamma radiation. If a neutron impinges upon the nucleus of an atom, any one of several reactions may occur. For identification of elements in earth formations the more important are listed below: 1. The neutron may be elastically scattered, as in a collision between two billiard balls. In this case the total kinetic energy is conserved, and no nuclear radiation is emitted. 2. The neutron may be inelast-ically scattered, as in a collision between two automobiles in which case the total kinetic energy is not conserved. The lost kinetic energy reappears in the form of gamma radiation. 3. The neutron may be captured, in which case the neutron becomes a part of the target nucleus, and a gamma ray is emitted. For example, if the target nucleus is H1, the pro-duced nucleus will be H3, and gamma radiation of a particular energy will be emitted. 4. The neutron may produce nuclear fission, or may enter into miscellaneous reactions which result in the emission of

Jan 1, 1958