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By Huey-Lin Luo, T. R. Anantharaman, William Klement

Two new metastable phases have been obtained in Au-Ge alloys by rapid cooling from the melt. One is of the hep structure with near-ideal axial ratio and may be considered a Hume-Rothery phase. The other has a complex tetragonal structure (a = 11.627Å and c = 22.191Å for the Au60Ge40 alloy) and may be looked upon as a superlattice made up of forty-four fee unit cells. Alloys with the tetragonal phase are charactevized by marked preferred orientation. The metastable constitution of the Au-Ge alloys is discussed with reference to the rate of cooling from the melt. THE Au-Ge equilibrium diagram features a rather deep eutectic near 27 at. pet Ge with a maximum solid solubility of 3.2 at. pet Ge in gold and is similar to the Ag-Ge, Ag-Si, and Au-Si diagrams.' The present study of the effects of rapid cooling from the melt on the structure of Au-Ge alloys constitutes an extension of similar investigations2-8 in this laboratory on alloys of noble metals with germanium and silicon. Nonequilibrium hep structures have so far been obtained by quenching Ag-Ge2, 3 and Ag-Si4, 5 alloys from the melt; an Au-Si alloy of approximately eutectic composition has been found6 to solidify in a noncrystalline state. EXPERIMENTAL PROCEDURES Twenty-nine alloys prepared from gold of 99.9+ pet and germaium of 99.999 + pet purity were investigated. The method of alloy preparation, the technique of rapid quenching from the melt, and the X-ray diffraction procedures were similar to those described previously.3, 4 Essentially, small sections (-20 mg) of thin alloy rods (-1 mm diam) were rapidly heated up to 1200°C in a graphite crucible under argon and the liquid alloy ejected by a helium blast onto a polished copper strip held on the inner periphery of a rotating wheel. The resulting thin foils were examined with or without the copper substrate in a G.E. X-ray Diffractometer or in a 114.6-cm-diam Debye-Scherrer camera. RESULTS Table I gives the constitution of liquid-quenched Au-Ge alloys, as estimated from intensities of X-ray reflections from the corresponding phases, viz., a (fee solid solution), ß (hep phase), ? (tetragonal phase), and diamond-cubic (dc) germanium. Despite unavoidable variations in the quenching rates, the proportions of the phases in different alloys were generally reproducible and stable at room temperature. There was no evidence of quenching strain, since the a doublets were well-resolved in high-angle Debye-Scherrer reflections in all cases except where stacking faults in the a fee and ß hep structures contributed to X-ray line broadening. The ß and ? metastable phases showed signs of decomposition to the equilibrium a phase and germanium only after a few hours annealing above 100°C. A few alloys around the eutectic composi-

Jan 1, 1965

By E. J. Pasierb, H. W. Paxton

Mavkers ill a diffusion couple in the iron-chromium system move towards the high chromium side indicating Dcr > DFe at the marker composition. By a combituztion of measurements of D& and D a: a function of composition, this is also shown independently. DFe is calculated as a function of composition. and shown to be in reasonable agreement with measured values by other workers. MEASUREMENTS of marker movements in diffusion couples have been used from time to time to demonstrate that a vacancy or interstitial mechanism may be operative. Since there is a possibility that ring diffusion1 may be operative in chromium, the present experiments are of interest in showing some non-ring mechanism in iron-chromium alloys around the equiatomic composition. EXPERIMENTAL PROCEDURE The movement of markers originally at the interface between 1-in. sq sections of pure Cr (6 mm thick) and outer slabs of 30 Cr-70 Fe alloy was followed as a function of time at temperatures from 1150" to 1425"C, in a Kanthal-wound furnace. Temperature control was +5°C over extended periods. The analyses of these alloys are given in Table I. Selection of suitable markers presented a considerable experimental problem; the eventual solution was to draw quartz rod down to 0.01 cm and seat this in V-grooves 0.01 cm deep on each side of the chromium prior to welding. A preliminary experiment in which the groove was machined in the alloy gave identical results. Welding was accomplished by passing a heavy current through specimens under moderate pressure in a helium atmosphere. This method produced good welds with a planar interface as shown by subsequent metallo-graphic investigation. Any markers which did not adequately fill their groove and showed subsequent contamination from the atmosphere during heat treatment were not considered reliable. The composite sample was ground and metal-lographically polished on the four sides perpendicular to the interface. Fiducial marks (deep milled slots) were made outside the diffusion zone to check on total volume change. All necessary measurements were made on a metallograph reading to +0.0005 cm. The samples were wrapped in tantalum foil and given diffusion anneals for times to 200 hr in carefully purified dry hydrogen in a sealed McDanel porcelain tube. Chromium-zirconium chips were introduced near the specimen as an additional getter. The specimens were cooled relatively slowly after the diffusion anneal to preserve the McDanel tube but no significant error in effective time at temperature was thereby introduced. At least 1 mm was ground off the surface before measurements were taken. It was observed that the grain size following short diffusion anneals was several mm and was appreciably larger in the 30 Cr alloy than in the pure Cr. No significant grain boundary penetration was present as indicated by the etch limit. The results are presented in the next section. Measurements of D were made by standard sectioning techniques with chemical analysis. Machining difficulties limited the

Jan 1, 1961

By J. B. Wagstaff, R. A. Buchanan, J. F. Elliott

High speed photography through blast-furnace tuyeres showed coke particles moving rapidly. Model studies showed a raceway was formed and gave quantitative results which were correlated with actual blast furnaces. Another study showed the similarity between hanging and the flooding of a packed column. This was explored by models. THE combustion zone before the tuyere in an iron blast furnace is a vital region because here are generated: 1—most of the gases on which the furnace depends to carry out its basic operation of reducing iron ore to the metallic state, and 2—the major fraction of the heat required in the nearby regions of the furnace for the various reduction reactions, the fusion of the slag, and the melting of the iron. Since the greater part of the coke is consumed in this region, the descent of the burden must be greatly affected by the characteristics of the tuyere zone. This region then would seem to be a profitable field for study. Fortunately, a view into this important zone is available to the operator through the tuyere peep sight. Here he sees relatively dark pieces of coke "dancing" in the blast. What he sees is of considerable help in interpreting the behavior of the furnace at a given time but the very rapidly moving particles and the intense radiation obscures what is happening very deep in the zone. This investigation was initiated in the hope that a better understanding of the combustion region could be obtained by using a high speed camera with a maximum speed of 3000 frames per sec. It seemed the best practical method of "slowing down" this characteristically violent action within the highly luminous field. Model studies and tuyere probing also have been used to aid in explaining the observed phenomena. Above the combustion zone, but below the fusion zone, there is probably a region in which the coke is comparatively stationary. Here are zones in which the gases must flow up through the granular bed counter to descending liquid slag and metal. There is no easy way to observe this zone in a blast furnace, but model studies have been of some help in explaining the nature of the zone and the laws governing the flow of the fluids involved. The whole problem is difficult and involved and any approach to a complete solution may require long investigation. This preliminary report has been written, therefore, because it is believed that appreciable progress has already been made that would be of interest to others. Tuyere Studies, Chemistry and Kinetics It is well known from the early work of Kinney and coworkers1,2 that combustion of carbon before the tuyeres appears to occur in two zones: Zone A: C + O, = CO2; AH77°F. = — 14,108 Btu per lb of carbon [I] Zone B: CO2 + C = 2CO; H77°F = + 6,183 Btu per lb of carbon [2] Zone A (Fig. 1) is close to the tip of the tuyere and zone B is somewhat farther back; there being a transition region in which both reactions occur. It is interesting to estimate the rate at which coke is burned before a tuyere with a wind rate of 90,000 cfm in a modern furnace having 18 tuyeres. Approximately 0.55 lb of carbon is consumed by eq 1 per tuyere per sec. A like amount disappears by eq 2 for a total consumption of 1.11 Ib per sec per tuyere. Assuming the coke is 85 pct C and has a bulk density of 30 lb per cu ft, this figure can be converted to a total of 1.30 lb of coke with a bulk volume of 0.043 cu ft disappearing per sec per tuyere. At the temperatures prevailing in the combustion zone (according to Kozlovich,³ he maximum is about 3400°F), the rate at which carbon is con-

Jan 1, 1953

By Phillip E. La Moreaux

Fluoride, generally less than 0.5 ppm, is present in ground water from rocks of Paleozoic age and older, in northern and eastern Alabama. Some of the water-bearing formations in the Coastal Plain area of the State yield water with as much as 6.8 ppm fluoride. IN June 1940, the U. S. Geological Survey, in cooperation with the Geological Survey of Alabama, began a study of the ground-water resources of the part of Alabama where water is obtained from Cretaceous rocks. The purpose of the study was to determine the quality, quantity, occurrence, and availability of ground water in that area. These studies have been expanded to include ground-water investigations in the area of Tertiary rocks, or southern quarter of the State, and certain areas in northern Alabama. The first report issued on these studies was by C. W. Carlston,1 of the Alabama Geological Survey. In the present paper all references to ground-water data for the Cretaceous area are taken from this earlier publication. In 1945, the Dentistry Division of the Alabama Department of Public Health became interested in the correlation of tooth decay and mottled enamel with the chemical quality of ground water used for public supplies in the State. Through a cooperative arrangement between the State Department of Public Health and the Ground Water Division (now Branch) of the U. S. Geological Survey, a report by the author2 was published in 1948. These two reports give accurate information on the occurrence of fluoride in the Coastal Plain of Alabama. At present, only scattered information is available on fluoride in ground water of the crystalline-rock or Piedmont area and for the Paleozoic area of Alabama, but it is hoped that in the future more complete information on the presence of fluoride in ground water in these areas can be collected. Outline of Geology and Ground Water: As described by Adams,3 the State of Alabama includes parts of two major geologic divisions, the Appalachian region and the Coastal Plain. The boundary between these divisions is irregular and is known as the Fall Line of the Atlantic and Gulf Coast States. The Fall Line enters Alabama near Phoenix City, extends westward to Wetumpka, Clanton, and Tuscaloosa, and then swings northwestward to the northwest corner of the State. The Appalachian region in Alabama includes three major provinces, the Piedmont province, the Appalachian Ridge and Valley province, and the Appalachian Plateau province (fig. 1). The rock formations in the Piedmont province in east-central Alabama are mainly of pre-Cambrian age, chiefly crystalline schists and gneisses injected by younger igneous rocks (fig. 1, I). They are faulted and folded and have a complicated structure. These rocks are the oldest and among the most complex rocks in the State. Generally, only small yields of ground water are obtained from rocks in this area. Even though ground water is of great importance for the development of domestic and farm supplies in rural areas and a few small industrial and municipal wells, yields in the area from individual wells generally range from 5 to 25 gpm and rarely exceed 50 gpm. The geologic formations of the Appalachian Ridge and Valley province and the Appalachian Plateau province (see fig. 1, II, and III) are separated on the basis of their structure. These rocks are of Paleozoic age, ranging from Cambrian to Carboniferous, and comprise a succession of formations consisting chiefly of shale, sandstone, limestone, and dolomite, aggregating many thousands of feet in

Jan 1, 1951

By Phillip E. La Moreaux

Fluoride, generally less than 0.5 ppm, is present in ground water from rocks of Paleozoic age and older, in northern and eastern Alabama. Some of the water-bearing formations in the Coastal Plain area of the State yield water with as much as 6.8 ppm fluoride. IN June 1940, the U. S. Geological Survey, in cooperation with the Geological Survey of Alabama, began a study of the ground-water resources of the part of Alabama where water is obtained from Cretaceous rocks. The purpose of the study was to determine the quality, quantity, occurrence, and availability of ground water in that area. These studies have been expanded to include ground-water investigations in the area of Tertiary rocks, or southern quarter of the State, and certain areas in northern Alabama. The first report issued on these studies was by C. W. Carlston,1 of the Alabama Geological Survey. In the present paper all references to ground-water data for the Cretaceous area are taken from this earlier publication. In 1945, the Dentistry Division of the Alabama Department of Public Health became interested in the correlation of tooth decay and mottled enamel with the chemical quality of ground water used for public supplies in the State. Through a cooperative arrangement between the State Department of Public Health and the Ground Water Division (now Branch) of the U. S. Geological Survey, a report by the author2 was published in 1948. These two reports give accurate information on the occurrence of fluoride in the Coastal Plain of Alabama. At present, only scattered information is available on fluoride in ground water of the crystalline-rock or Piedmont area and for the Paleozoic area of Alabama, but it is hoped that in the future more complete information on the presence of fluoride in ground water in these areas can be collected. Outline of Geology and Ground Water: As described by Adams,3 the State of Alabama includes parts of two major geologic divisions, the Appalachian region and the Coastal Plain. The boundary between these divisions is irregular and is known as the Fall Line of the Atlantic and Gulf Coast States. The Fall Line enters Alabama near Phoenix City, extends westward to Wetumpka, Clanton, and Tuscaloosa, and then swings northwestward to the northwest corner of the State. The Appalachian region in Alabama includes three major provinces, the Piedmont province, the Appalachian Ridge and Valley province, and the Appalachian Plateau province (fig. 1). The rock formations in the Piedmont province in east-central Alabama are mainly of pre-Cambrian age, chiefly crystalline schists and gneisses injected by younger igneous rocks (fig. 1, I). They are faulted and folded and have a complicated structure. These rocks are the oldest and among the most complex rocks in the State. Generally, only small yields of ground water are obtained from rocks in this area. Even though ground water is of great importance for the development of domestic and farm supplies in rural areas and a few small industrial and municipal wells, yields in the area from individual wells generally range from 5 to 25 gpm and rarely exceed 50 gpm. The geologic formations of the Appalachian Ridge and Valley province and the Appalachian Plateau province (see fig. 1, II, and III) are separated on the basis of their structure. These rocks are of Paleozoic age, ranging from Cambrian to Carboniferous, and comprise a succession of formations consisting chiefly of shale, sandstone, limestone, and dolomite, aggregating many thousands of feet in

Jan 1, 1951

By E. H. Kelton, R. D. Grissinger

In designing structural members of steel and some other materials the design engineer has available recognized values of elastic modulus and safe working stress that may be substituted in well-known engineering formulas to give him desired cross-sectional areas and deflections for a particular part. Zinc, on the other hand, has no generally recognized modulus. It flows under continuously applied loads. Therefore, the designer of structural members must use a range of working stresses depending on the continuous load and the amount of permissible distortion. The only method of obtaining these values is by creep testing. Creep testing of zinc has been carried on for some 20 years by this laboratory, covering a wide range of zinc and zinc alloys. Types of test included tension, compression, and simple and cantilever beams at temperatures ranging from o to I50°C. Specimen conditions ranged from as-cast or as-rolled to accelerated aged in steam or dry air. Effects of plating were investigated also. It is not the intention of this paper to expound all these factors but rather to present the final data on well-known zinc die-casting alloys and to suggest means of applying these data to engineering design. Early Work In the early work on creep testing of zinc, the direct-loading tension method was used. However, direct loading of die castings was unsatisfactory because of the high loads required. For instance, a standard die-cast tension bar having a cross-sectional area of about 0.049 sq. in. would require a direct load of about 1000 lb. for a unit stress of 20,000 lb. per sq. in. Also, tests were made at nominal room temperature, but normal variations caused fluctuations greater than those due to experimental error or other causes, so that control of this variable within ±1/2°C. seemed essential. These two factors led to the development of an apparatus described by J. Ruzicka,' in which the specimens were loaded by means of a lever and were held at constant temperature by means of an oil bath. While Ruzicka's apparatus yielded excellent check results, it seemed desirable to have some setup by which literally hundreds of die-cast specimens could be tested at the same time. This would permit the conducting of a number of low-load tests designed to run 10 years or longer and still leave capacity for current high-load work. Beam testing in a constant-temperature room was the answer. Test Method Preliminary work indicated that die-cast beams of various lengths and cross scctions yielded the same result within reasonable limits regardless of whether they were tested as simple beams, uniformly loaded beams, or cantilevers. Accordingly, the simplest type was adopted. This was a,

Jan 1, 1945

By R. M. Scafe

Although hydrogen has been intensively studied in its relation to steel quality, the methods of sampling and determinations are still open to question. It is true that various procedures have been proposed but actually there has not been sufficient agreement to establish a common base from which to work. As a result, it is difficult, to say the least, to correlate the reported results of some of the investigators in this field. The present symposium, premised on methods rather than effects, should prove of considerable value. For the purpose of this discussion two methods of sampling and analysis will be considered. First, sampling of molten steel in the ingot mold by use of an evacuated tube and cylinder using conventional methods of analysis for the gases collected; second, analysis by vacuum extraction involving the use of heating equipment and the determination of the amount of hydrogen evolved from solid steel samples by measurement at reduced pressures. Both methods have been used at Duquesne Steel Works and it is believed that either may be used with considerable benefit if the limitations of each method are recognized. Evacuated Tube and Cylinder Sampling devices for gases in molten steel suggested by various investigators range from very cumbersome and complicated devices to the relatively simple evacuated tube and cylinder used by Soler for deter- mining the CO content of the bath. This latter device was adopted (Fig. I) and modified to meet conditions at Duquesne Works. The principal modifications were in placing the cylinder at the side of the tube and the use of a sleeve on the immersion end of the tube. The first modification was made so that the cylinder could be readily detached and taken to the laboratory; the second, because of the difficulty encountered in obtaining an airtight seal after sampling and because of our practice of re-using the tube. Rigid control of the method of sampling and of the handling of the sample according to plan are of primary importance in hydrogen determinations. This applies to both the sampling of molten steel and the determination of the hydrogen content of cold steel samples. Except for a few preliminary samples taken from spoons, all work on molten steels using the evacuated tube was confined to the sampling and analysis of molten steel during the pour. As mentioned, uniformity of sampling was a basic consideration. As a result, every effort was made to follow definite sampling techniques and procedures. These included control of the depth below the surface from which the sample was taken, the timing between the shutoff and taking of the sample, as well as maintenance and care of the equipment. The distance below the surface at which the sample was taken was readily controlled bv means of a crosspiece and centering device attached to the tube. The steel was poured into the mold to the hot-top junction, the tube was then lowered into the 75

Jan 1, 1945

By Walter R. Hibbard, Harold Margolin

DURING preliminary tests on the aging of a Cu-plus 5 pct Ag alloy,' a specimen which had been overaged 24 hr at 550°C was annealed in a nitrogen-hydrogen atmosphere first for 2 hr and then for an additional 28 hr at 600°C. After each anneal the specimen was cooled to room temperature in about ½ hr and X-ray photograms were made. The first film, Fig. la, revealed two sets of copper-base lines, one intense and corresponding to the parameter at 550°C, the other fainter and shifted away from the beam, corresponding to the larger parameter at 600°C (see arrows). The 30-hr film, Fig. lb, revealed the same two sets of copper-base lines with a reversal of intensity. In neither case do the copper lines form a broad band which would be indicative of a range of compositions. This phenomenon is thus a "discontinuous" type of solution. A similar phenomenon was observed in a Ag-rich Cu-Ag alloy.' Finlay and Hibbard9 have suggested that directional rather than random solution of precipitate occurs in some alloys. Conceivably, for Cu-Ag alloys, the matrix-transition-precipitate precipitation sequence is reversible for the re-solution of the precipitate caused by rapidly raising the annealing temperature of an overaged specimen. A copper-base transition structure supersaturated with solute might be formed around the precipitate as it dissolves, thus obviating the necessity for a gradually changing solute composition of the matrix. The solute atoms then might be transferred rapidly and locally from the transition to the matrix phase in the proper amount and at the proper location to obtain directly the new ex- panded solid solution. The theory implies a minimum of diEusion of solute in the matrix (i.e., no significant range of matrix composition) and possibly suggests that the composition of the transition structure will vary with the conditions of re-solution. A transition copper phase found in aged Cu-Ag alloys1 might fulfill this function. Evidence regarding this suggestion could be obtained in Cu-Ag alloys by overaging a specimen until no trace of the expanded copper lattice is present and then subjecting the specimen to a retrogression treatment. Re-appearance of the transition copper phase would confirm the theory. Additional details could be secured by varying both aging and retrogression temperatures. References 'H. Margolin and W. R. Hibbard, Jr.: Effect of Ternary Additions on the Age Hardening of a Copper-Silver Alloy. Trans. AIME (1951) 191, p. 174; Journal of Metals (Feb. 1951) TP 3002E. 2 W. Ageew, M. Hansen, and G. Sachs: Decomposition and Changes in Properties of Super-saturated Silver-Copper Alloys. Ztsch. Physik (1930) 66, p. 350. 3W. L. Finlay and W. R. Hibbard, Jr.: Some Effects of Applied Stresses on Precipitation Phenomena. Trans. AIME (1949) 180, p. 255; Metals Technology (Sept.

Jan 1, 1952

By Ronald C. Koo

SMALL additions of potassium, aluminum, and silicon as oxides (referred to as dope) to tungsten have been known for several decades to have a very large effect in raising the recrystallization temperature and altering the recrystallized grain morphology of heavily drawn wire. Previous investigations of this doping effect1 6 have led to various speculations but all failed to deduce unequivocally the physical state or the mechanistic influence of the dopant. Recently, walter7 has observed, by transmission electron microscopy, strings of "fine particles" in heavily rolled and annealed doped tungsten sheet and concluded that they were particles of mullite (Al6Si2013). His conclusion was inferred from the electron diffraction patterns of large particles ex-trated by carbon replication of fractured surfaces of slabs rolled from sintered ingots. That the strings of "fine particles" in heavily rolled and annealed sheet were also mullite was an assumption for which no evidence was presented. A similar investigation has been carried out in this laboratory over the past 2 years on a variety of tungsten wire: doped tungsten, and undoped tungsten, as well as 218 doped tungsten purchased from the Lamp Metals and Components Department of the G.E. Lamp Division. Although the electron microscope observations are similar to those reported by Walter, the writer has reached a different conclusion concerning the physical state of the dopant in annealed tungsten. The purpose of this communication is to present evidence that the strings of "fine particles" observed in transmission specimens are not mullite, but are voids. In the present investigation, tungsten wire, 0.88 mm in diam, was rolled into ribbon 0.2 mm by 125 µ thick. The ribbons were annealed in vacuo at a pressure of -1 x 10-5 Torr and then thinned electrolytically in a 2 pct KOH solution. Fig. 1 shows a typical transmissicjn electron micrograph of a sample annealed at 1700°C for 30 min which reveals rows of closely spaced voids having a light contrast (referred to as "fine particles" by Walter) aligned parallel to the working direction. Stereo micrographs (by D. Moon, Westinghouse Research and Development Center) have shown that these voids do not exist on the surfaces of the specimens as a result of thinning but are within the thin-foil specimens. The following experiments have been performed to verify that these are indeed voids. I) Effect of Annealing. Voids are absent in unannealed specimens and appear only after annealing. This behavior cannot be explained if they were solid particles such as mullite. Precipitation (in an unquenched specimen) upon annealing requires solute elements having decreasing solubilities with increasing temperature. Although the solubility of aluminum in tungsten does decrease with increasing temperature, precipitation requires a concentration in excess of 1.4 wt pct,8 which is at least two orders of magnitude higher than the aluminum content in doped tungsten. It is also unreasonable to assume that particles aligned in rows initially present in unannealed specimens were too

Jan 1, 1968

By Walter Miller

Crude oil stocks were some 10,000,000 bbl higher on June I, 1947, than at any time during 1946 but the extremely heavy refinery runs the last half of 1947 cut crude inventories to approximately the 1946 closing level of 225,000,000 bbl. Many refiners were seriously short of crude oil during the year. This shortage was reflected in numerous advances in the posted price of crude, justified in part as an incentive for more production but more generally due to competitive bidding. Some purchasers of crude, endeavoring to keep their plants running, resorted to the payment, either directly or indirectly, of premiums above the posted price. Another common practice employed by some suppliers of crude oil was to demand refined products in exchange or trade for their raw material. The refined products picture has darkened in spite of record throughputs. Stocks of gasoline and light and heavy fuel oils were uncomfortably low at the beginning of the year and were in general still lower at the close. The rationing of some products, principally gasoline, to dealers and stations? initiated during the year, gained momentum as stocks continued to diminish. The emphasis placed by the manufacturers of oil-burning equipment on the convenience and economy of heating with oil, together with the tight situation in coal, has developed a tremendous demand for burning oils. Consumption of liquefied petroleum gas for domestic and household fuel had more than doubled in 1946 over 1943, and the demand seems to be limited only by the ability of the equipment builders to furnish necessary storage. transportation, and burning equipment. The supply situation is likely to become more acute in 1948. Demand for petroleum products is being pushed to new heights not only by the unprecedented domestic market but by a sudden and drastic upswing in estimates of military and governmental requirements. Additionally, oil exports are running far below the volume requested, amounting to less than forty percent in a recent quarter, and export licenses are reportedly being approved on the basis of urgent need *only. AX recent White House release sees little likelihood that estimated requirements of the sixteen nations participating in the proposed Marshall Plan can be met in full over its projected life—1948 to 1951. Present demand dictates maintenance of refinery operations at the highest possible level and the Bureau of Mines has forecast daily average crude runs in 1948 of 5,265,000 bbl. The Economics Advisory Committee of the Interstate Oil Compact Commission recently estimated the 1948 demand for petroleum products at nearly 6 pct above 1947. They further estimate daily average crude runs of 5,375,000 bbl in 1948, some 2 pct higher than forecast by the Bureau of Mines. Projected demand exceeds supply to the extent that Capitol Hill is reportedly investigating ways of enabling oil companies to act in concert without danger of antitrust prosecution, such as elimination of crosshauls, pooling of products, and lowering of octane.

Jan 1, 1948

By Walter Miller

Crude oil stocks were some 10,000,000 bbl higher on June I, 1947, than at any time during 1946 but the extremely heavy refinery runs the last half of 1947 cut crude inventories to approximately the 1946 closing level of 225,000,000 bbl. Many refiners were seriously short of crude oil during the year. This shortage was reflected in numerous advances in the posted price of crude, justified in part as an incentive for more production but more generally due to competitive bidding. Some purchasers of crude, endeavoring to keep their plants running, resorted to the payment, either directly or indirectly, of premiums above the posted price. Another common practice employed by some suppliers of crude oil was to demand refined products in exchange or trade for their raw material. The refined products picture has darkened in spite of record throughputs. Stocks of gasoline and light and heavy fuel oils were uncomfortably low at the beginning of the year and were in general still lower at the close. The rationing of some products, principally gasoline, to dealers and stations? initiated during the year, gained momentum as stocks continued to diminish. The emphasis placed by the manufacturers of oil-burning equipment on the convenience and economy of heating with oil, together with the tight situation in coal, has developed a tremendous demand for burning oils. Consumption of liquefied petroleum gas for domestic and household fuel had more than doubled in 1946 over 1943, and the demand seems to be limited only by the ability of the equipment builders to furnish necessary storage. transportation, and burning equipment. The supply situation is likely to become more acute in 1948. Demand for petroleum products is being pushed to new heights not only by the unprecedented domestic market but by a sudden and drastic upswing in estimates of military and governmental requirements. Additionally, oil exports are running far below the volume requested, amounting to less than forty percent in a recent quarter, and export licenses are reportedly being approved on the basis of urgent need *only. AX recent White House release sees little likelihood that estimated requirements of the sixteen nations participating in the proposed Marshall Plan can be met in full over its projected life—1948 to 1951. Present demand dictates maintenance of refinery operations at the highest possible level and the Bureau of Mines has forecast daily average crude runs in 1948 of 5,265,000 bbl. The Economics Advisory Committee of the Interstate Oil Compact Commission recently estimated the 1948 demand for petroleum products at nearly 6 pct above 1947. They further estimate daily average crude runs of 5,375,000 bbl in 1948, some 2 pct higher than forecast by the Bureau of Mines. Projected demand exceeds supply to the extent that Capitol Hill is reportedly investigating ways of enabling oil companies to act in concert without danger of antitrust prosecution, such as elimination of crosshauls, pooling of products, and lowering of octane.

Jan 1, 1948

By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann's hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. 'Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author's Reply) Dr. Fuerstenau's interesting comparison of rod milling and ball milling

Jan 1, 1961

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951

INTRODUCTION The meaning of cash flow has already been defined as after-tax earnings available for use by the corporation or business. It is therefore apparent that a significant part of mineral economic evaluation is concerned with correct and accurate computation of taxable income under existing tax laws, and the proper treatment of tax allowances and deductions. The various methods of depreciation, depletion, and amortization are all means whereby the investor can earn back or recover, before taxes are imposed, the investments made for purposes of doing business or for the production of income. Each of these three types of tax deduction are applied to different investment items such as property, equipment, buildings, research, etc. The cost of buildings, equipment, machinery, and transportation equipment are representative of capitalized business costs that must be recovered by depreciation over the life of the asset. The property investment costs of acquiring natural resources such as minerals, oil and gas, and standing timber are examples of investment costs that may be recovered by depletion. Several other capitalized business costs, such as research expenses and trademark expenses, may be recovered by amortization. The term "capitalized" means that the in- vestment cost is not deducted as an operating expense in the year that it is incurred, but is spread out over a period of years through depreciation, depletion, or amortization deductions according to lawful schedules. Of course, any capitalized cost can only be deducted once. The other costs of doing business which are not capitalized, such as labor and operating costs, are said to be "expensed," i.e., they are written off for tax purposes in the year they occur. DEPRECIATION Depreciation, according to US tax law, is a deduction from taxable income permitted as a "reasonable allowance for the exhaustion, wear and tear of property out of its use or employment in a business." The original cost of the property is the usual basis for determining depreciation. Since depreciation write-off is applied over the useful life of the asset, the first step is to determine the estimated useful life or its allowable depreciable life. These two lives may or may not be the same. No average life is applicable to all types of depreciable assets under different conditions or in different types of business. It is the taxpayer's responsibility to determine the useful life of the asset according to his own operating conditions and experience, within the guidelines set by the US Internal Revenue Service (IRS). The Class Life Depreciation Range (ADR) System permits the taxpayer to choose from a range of depreciable lives at 20% below or above the present guideline life. The second step required in calculating depreciation is to determine an estimated salvage value for the asset. The salvage value is an estimate, made at the time of acquisition, of the amount of money which can be realized by the sale of the asset at the end of its useful life. The four depreciation methods most widely used in the US are: (1) the straight-line method, (2) the declining balance method (double declining balance), (3) sum of the years - digits method, and (4) units of production method. Straight-Line Depreciation Method The straight-line depreciation method is the simplest for calculating depreciation. The depreciation for each year is determined by subtracting the estimated salvage value from the first cost of the asset and dividing the result by the years of life. The method gives equal annual deduction over the depreciable life. Salvage value equal to or less than 10% of the first cost may be ignored. [first cost - salvage Straight line = years of life ] Declining Balance Depreciation Method Declining balance depreciation, or double declining balance (DDB) as most frequently applied, is used for accelerating depreciation in the early years of the asset and is the fastest depreciation method allowed by the US Internal Revenue Service. The declining balance

Jan 1, 1980

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By J. Orkiszewski

A method i.s presented which can accurately predict, with a precision of about 10 percent, two-phase pressure drops in flowing and gas-lift production wells over a wide range of well conditions. The method is an extension of the work done by Grifith and Wallis and was found to be superior to five other published methods. The precision of the method was verified when its predicted values were compared against 148 measured pressure drops. The unique features of this method over most others are that liquid holdup is derived from observed physical phenomena, the pressure gradient is related to the geometrical distribution of the liquid and gas phase (flow regimes), and the method provides a good analogy of what happens inside the pipe. It takes less than a second to obtain a prediction on the IBM 7044 computer. INTRODUCTION The problem of accurately predicting pressure drops in flowing or gas-lift wells has given rise to many specialized solutions for limited conditions, but not to any generally accepted one for broad conditions. The reason for these many solutions is that the two-phase flow is complex and difficult to analyze even for the limited conditions studied. Under some conditions, the gas moves at a much higher velocity than the liquid. As a result, the down-hole flowing density of the gas-liquid mixture is greater than the corresponding density, corrected for down-hole temperature and pressure, that would be calculated from the produced gas-liquid ratio. Also, the liquid's velocity along the pipe wall can vary appreciably over a short distance and result in a variable friction loss. Under other conditions, the liquid is almost completely entrained in the gas and has very little effect on the wall friction loss. The difference in velocity and the geometry of the two phases strongly influence pressure drop. These factors provide the basis for categorizing two-phase flow. The generally accepted categories (flow regimes) of two-phase flow are bubble, slug, (slug-annular) transition and annular-mist They are ideally depicted in Fig. 1 and briefly described as follows. RUBBLE FLOW (FIG. 1A) The pipe is almost completely filled with the liquid and the free-gas phase is small. The gas is present as small bubbles, randomly distributed, whose diameters also vary randomly. The bubbles move at different velocities depending upon their respective diameters. The liquid moves up the pipe at a fairly uniform velocity and, except for its density, the gas phase has little effect on the pressure gradient. SLUG FLOW (FIG. 1R) In this regime, the gas phase is more pronounced. Although the liquid phase is still continuous, the gas bubbler coalesce and form stable bubbles of approximately the rame size and shape which are nearly the diameter of the pipe. They are separated by slugs of liquid. The bubble velocity is greater than that of the liquid and can be predicted in relation to the velocity of the liquid slug." There is a film of liquid around the gas bubble. The liquid velocity is not constant—whereas the liquid slug always moves upward (in the direction of bulk flow); the liquid in the film may move upward but possibly at a lower velocity, or it may move downward. These varying liquid velocities will result not only in varying wall friction losses, but also in a "liquid holdup" which will influence flowing density. At higher flow velocities, liquid can even be entrained in the gas bubbles. Both the gas and liquid phases have significant effects on the pressure gradient. TRANSITION FLOW (FIG. 1C) The change from a continuous liquid phase to a continuous gas phase occurs in this region. The liquid slug between the bubbles virtually disappears, and a significant amount of liquid becomes entrained in the gas phase. Although the effects of the liquid are significant, the gas phase is more predominant.

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations