Search Documents

By G. H. Fancher

Improving economic conditions are reflected in the statistical picture of the petroleum and natural gas industry for 1933. Prices were better, demand was greater and the volume of production increased. The increase in the production of gas has been due mainly to the utilization of outlets to the new prolific gas fields of Potter and Tioga counties; of oil, to the growing demand for Pennsylvania grade lubricants. It should be emphasized that nowhere is volume of production more subject to control due to the extensive use of secondary methods of recovery and regional peculiarities than in Pennsylvania. A summary of developments in production for Pennsylvania in 1933 of necessity is brief. The data listed in Table 1 are all too few in number and not all that is desirable from the standpoint of accuracy. No state agency for the collection of data exists, no reports are compulsory. Nevertheless, because of the hearty cooperation of many individuals and public spirited corporations, it is believed that the data are as reliable as are obtainable at the present time. Furthermore, records of the past too often are lost, were never in existence or are fragmentary, to say the least. Illustrative of the condition is the fact that no thorough study of the oil and gas-producing regions has ever been made. The publications of the Pennsylvania Topographic and Geologic Survey upon the subject are noteworthy and valuable, especially the most recent one.' The Survey has been handicapped in the work by lack of time, personnel and funds in addition to the difficulties mentioned previously. It is obvious, therefore, that Table 1 cannot be completed for Pennsylvania. The data simply are not in existence. Officially there are 328 oil and gas pools or fields known by name and 58 distinct sands or horizons, one or more of which are productive of oil and gas in the various pools, but reliable data for only three general regions could be assembled.

Jan 1, 1934

By Nico Van Wingen

Experiments performed with distilled water, unconsolidated sand and dead oil for the purpose of determining the influence of oil flow on the water content of sands were described. While results found are not necessarily, therefore, identical with those that would be obtained under natural petroleum reservoir conditions, the following conclusions were drawn. 1. When oil under constant head is flowed through an unconsolidated sand, the amount of water retained in the core is inversely proportional to the specific permeability of the core. This corroborates the view that the degree to which oil displaces water out of the pore space is limited by the size of the pores. 2. For the range investigated, the displacing action of a more viscous oil of higher specific gravity was found to be the same as a less viscous oil, or lower specific gravity. 3. The amount of interstitial water retained in the sand bears an inverse relationship to the pressure head of the displacing liquid. 4. The degree of retained water saturation of the sand appears to approach 100 per cent as the specific permeability approaches zero. 5. For the higher values of specific permeability and for the pressure range investigated the remaining amount of water in the sand occupies approximately 10 per cent of the pore space. This, together with the fact that the limiting oil velocity curve approaches approximately 10 per cent water saturation as an asymptote, indicates that beyond this point removal of water is achieved only by a stripping of the grains requiring considerable pressure drops across the sands; or by a balancing of the molecular forces. 6. As the water saturation of the sand exceeds approximately 15 per cent of the pore volume, the permeability of the sand to oil decreases rapidly. 7. Sands with water saturations as high as 40 per cent were found to produce 100 per cent oil.

Jan 1, 1939

By J. Th. Erb

The total crude oil production of these islands, which in 1928 amounted to nearly 5,000,000 metric tons—about 36,500,000 bb1.—has again increased in 1929. The figures for 1929 are as follows: Metric ToNs† North Sumatra........................................ 369,930 South Sumatra........................................ 1,236,510 Java and Ceram....................................... 678,787 Dutch Borneo (including Tarakan)....................... 2,793,326 Sarawak.............................................. 759,700 Total............................................... 5,838.253 †1 metric tor1 = 7.36 bbl. on the average. This production, as far as the Dutch Islands are concerned, is owned partly by the Bataafsche Petroleum Maatschappij, the producing subsidiary of the Royal Dutch Petroleum Concern, and partly by the Kolon-isle Petroleum Maatschappij (Standard Oil Co. of N. J.), while that of the British Protectorate Sarawak belongs to the Anglo-Saxon Petroleum Co., Ltd., of London. The increase in 1929 is due partly to more intensive drilling; the rotary system, which enables drilling to be done more quickly and to greater depths than was possible with the percussion system, has come into more general use. Further, considerable extensions have been made to some of the existing fields and several new pools have been discovered, which contributed in no small degree to the increase in production. Of particular interest is the fact that the ('Niam" (Nederlandsche Indische Aardolie Maatschappij), in which the Dutch Government has a large share and which company in 1928 was producing from only two fields in South Sumatra, has discovered a pool in North Sumatra and, moreover, has struck oil on the island of Poeloe Boenjoe near Tarakan (Eastern Borneo). The deepest well still drilling is in one of the fields of the "Niam" and has reached a depth of 2269 meters (7445 feet). Notwithstanding the tropical c1imate and the dense jungle in which most of the fields are situated, the most modern scientific methods are applied in exploration, in drilling, producing and refining.

Jan 1, 1930

By Nico Van Wingen

Experiments performed with distilled water, unconsolidated sand and dead oil for the purpose of determining the influence of oil flow on the water content of sands were described. While results found are not necessarily, therefore, identical with those that would be obtained under natural petroleum reservoir conditions, the following conclusions were drawn. 1. When oil under constant head is flowed through an unconsolidated sand, the amount of water retained in the core is inversely proportional to the specific permeability of the core. This corroborates the view that the degree to which oil displaces water out of the pore space is limited by the size of the pores. 2. For the range investigated, the displacing action of a more viscous oil of higher specific gravity was found to be the same as a less viscous oil, or lower specific gravity. 3. The amount of interstitial water retained in the sand bears an inverse relationship to the pressure head of the displacing liquid. 4. The degree of retained water saturation of the sand appears to approach 100 per cent as the specific permeability approaches zero. 5. For the higher values of specific permeability and for the pressure range investigated the remaining amount of water in the sand occupies approximately 10 per cent of the pore space. This, together with the fact that the limiting oil velocity curve approaches approximately 10 per cent water saturation as an asymptote, indicates that beyond this point removal of water is achieved only by a stripping of the grains requiring considerable pressure drops across the sands; or by a balancing of the molecular forces. 6. As the water saturation of the sand exceeds approximately 15 per cent of the pore volume, the permeability of the sand to oil decreases rapidly. 7. Sands with water saturations as high as 40 per cent were found to produce 100 per cent oil.

Jan 1, 1939

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

THE award from the fund established by Mrs. John-son, in memory of her husband, J. E. Johnson, Jr., to be given to some promising engineer, not over 40 years of age, because of meritorious research, inven-tion or contribution to the professional literature of iron and steel along the lines of blast-furnace process, has been given, for, 1928, to P. H: Royster. Mr. Royster was born at Raleigh, N. C., in 1888. and graduated from the University of North Carolina, in 1907, taking his A.M. degree at, the same school in 1908. He then went to Harvard where he continued research work in physics. After engaging for a while in commercial research in the turbine department of the General Elec-tric Co. and with Cutting and Washington he joined the staff of the Bureau of. Mines in 1916 and was assigned to work on the physical chemistry of the blast-furnace process. He worked with A. L. Feild on slag viscosity and they jointly presented-to the Institute the. papers on "Temperature and Viscosity Relations in the Ter-nary System CaO-A12O3-SiO2" (TRANS. LVIII, 658) and "Slag Viscosity Tables for Blast-furnace Work" (TRANS. LVIII, 650). He also presented a paper on "Production of Ferromanganese in the Blast 'Furnace" .(TRANS. LXII, 18), and jointly with T. L. Joseph contributed a paper on "Effect of Coke Combustibility on Stock Descent in Blast Furnaces" (TRANS. LXX, 236), and another on "Pyrometry in Blast-furnace Work" which was included in the special pyrometry volume published in 1920. The titles of these works perhaps sufficiently indicate the part Mr. Royster has played in the notable research work on the blast-furnace process carried on by the Bureau of Mines, and for which the committee recommended him to the Board of Directors to receive the Johnson award.

Jan 2, 1928

By George W. Bain

SOME problems concomitant with commercial exploitation of marble are presented as examples of interesting, useful and profitable fields for application of scientific knowledge. The marble industry is only one such field and is selected because its varying new aspects are familiar to the author. However, what is true for marble is equally so in principle for many industrial minerals. The problems of any stone industry are to maintain markets, create new outlets for stone already in demand, and develop varied uses for varieties that are not so popular. Here the geologist has a different role from most of his colleagues in metal mining. The producing branch may ask about the expectable variation in thickness or size of a deposit as development proceeds. The stock department may call for the available amount of a given type of stone before accepting a large order. The sales force requires data on the use for stone from certain parts of deposits in order to divert grades to the most suitable use. The service department wants defects rectified and the cause determined to avoid recurrence. The mills want data on durability and cutting quality of abrasives. The geologist occupies no special department; he is on general call, as may be illustrated by a few types of problems that may be classified as: (1) dominantly geological in character, (2) dominantly chemical in character, (3) dominantly physical in character. GEOLOGICAL PROBLEMS The geological problems deal almost exclusively with the size of blocks. Size across the deposit is limited by thickness of individual beds, and along the strike by the space between crosscutting joints. Frequently the vertical depth of a block is reduced by exfoliation shells arising from spontaneous expansion. All these factors require consideration in developing a deposit to fill an order. Thickening of Marble Beds The limestone beds that became the marble deposits of the northern Appalachians and of the Yule locality in Colorado were seldom homo-

Jan 1, 1940

By H. R. Page, A. E. Jr Lee

A. E. LEE, JR. (author)—In addition to the paper we should like to make a few remarks. First, the seriousness of bending of the clay retort cannot be overemphasized. Not only did bending limit the length of the vessel, but it permitted corrosive fluid slags to concentrate in the belly of the retort and thus increased the possibility of boring. Bending also practically prohibited the use of cleanout machines and increased the danger of excessive fume losses by allowing furnace gases to escape around the top of the retort mouth. It will be noted that the Blackwell pottery practice places considerable emphasis on careful drying of retorts. Perhaps it is another smelter superstition, but traditionally the aging of retorts beyond a reasonable drying period has been considered important to long life. We are unable to give a good explanation of why aging should improve retorts. During the past fall in an attempt to prove a theory that the combined water in the clay decreased during aging, about 50 samples of wet retort collars were placed in a dry room when it was closed. Loss of weight, combined water and free moisture were measured each week over the 100 day drying period. The affinity of the dried retort for moisture makes difficult the accurate measurement of free water; however, there was a clearly defined free moisture change from about 12.5 pct when freshly made to about 2 pet at the end of 18 days, then a gradual loss to about 0.25 pet at 70 days and an apparent equilibrium near this figure through the 100th day. There was no appreciable change in the combined water. The change in weight of the average sample was, however, rather unusual, there being consistently a loss of weight throughout the entire 100 days. From the 63rd day on this leveled off to about 0.03 pet per week. These were small samples and certainly should have dried

Jan 1, 1950

By J. P. Hammond, C. J. Sparks, C. J. McHargue

IN a study of the effects of solid solution alloying on the deformation texture of titanium, an alloy containing 3.8 pct A1 was found to develop a (0001) [1010] texture instead of the texture characteristic of pure titanium.ls2 A short investigation has been made of the change in texture with aluminum content. Alloys containing 0.27, 0.47, 1.05, and 1.43 pct A1 were prepared by vacuum arc melting, using iodide titanium as the base material. Homogenized ingots were reduced 90 pct in thickness by cold rolling. Pole figures were obtained using the usual film techniques. Fig. 1 shows that the change from the tilted to the nontilted (0001) position is gradual. The dashed contour lines in Fig. 1 indicate the extent to which data was collected. The addition of 0.27 pct A1 resulted in a decrease in the transverse spread of basal poles. With increasing aluminum content, the amount of the tilt becomes less and the region of highest intensity takes the shape of a ring about the center of the pole figure. For aluminum contents greater than 1 pct, the (0001) [1010] texture is definitely present—the sharpness increasing as the amount of solute is increased.* It is interesting to note that Williams and Eppel-sheimer9 eported for commercial grade titanium a high intensity region 20" toward the rolling direction from the rolling plane normal in addition to. one 30" toward the transverse direction. Their basal pole figure was similar to Fig. 1, row inree. The observation that the texture changes gradually with solute concentration is similar to the results of similar studies on copper." At the present time these effects are not clearly understood. Acknowledgments This work was sponsored by the Aeronautical Research Laboratory (WCRRL), Wright Air Development Center, under Contract NO. AF' 33(038)-19574. The authors are grateful for the aid received and permission to publish these results.

Jan 1, 1958

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By John Henry Harden

It appears that in the earlier days of anthracite coal mining, 1824-25, the Lehigh region mined 76 per cent. of all the coal sent to market. During the same period Wyoming sent 12 and 5 per cent. respectively, whilst the Schuylkill sent 11 and 18 per cent., the number of tons marketed being in those days very small indeed. In the year 1828 the Schuylkill region mined over one-half of all the coal sent to market, and continued to do so for thirty years (with the exception of the year 1831), until 1858 ; since that date the production has declined very steadily in comparison with the other regions, until, in 1876, it was only 34 per cent. Wyoming, in the year 1820, was mining 40 per cent., but the production of all the regions was very small; in six years it declined to 5 per cent., increased to 34 per cent. in 1831, declined to 10 per cent. in 1838. Since which time the increase has been gradual, until 1873-75 Wyoming produced over 50 per cent. of all the anthracite coal sent to market. In 1867 the production exceeded that of Schuylkill, and has continued to do so since that time. In the year 1876, during the existence of the "coal combination," Wyoming lost 9 per cent.; during the same time Lehigh gained 7 and Schuylkill 2 per cent. over their relative production of the preceding year, the decrease of Wyoming being two and a half million tons, the increase of the Lehigh one million, the decrease of the Schuylkill nearly three-quarters of a million. The extraordinary production of the Lehigh region at a time of decreased demand and in opposition to an agreement with the other regions to limit the supply to the supposed demand mas the cause of the disagreement which ultimately broke up the combination of the great coal-producing and carrying companies. The Lehigh region produced very steadily, from 1829 to 1854, an average of about 22 per cent. of the whole production. From 1854

By R. G. Knickerbocker, A. G. Starliper, H. Kenworthy, C. H. Gorski

This report describes the progress made in the research work on the development of a new method for preparing lower-cost titanium tetrachloride and preparing titanium oxide pigment. One of the requirements for the commercial production of ductile titanium in the process used by the Bureau of Mines is a source of lower-cost titanium tetrachloride. The production of ductile titanium by a modification of the Kroll1 process, recently developed by the Bureau of Mines, requires such a source of lower-cost titanium tetrachloride to make it commercially feasible. This report describes the progress of work done at the Mississippi Valley Experiment Station at Rolla, Missouri, on the development of a new method for preparing titanium tetrachloride. During the course of this research a new method for preparing pigment-grade titanium oxide was developed. At present, the price of technical-grade titanium tetrachloride is $0.32 a pound, which makes the price of the contained titanium $1.28 a pound.2 In addition, the titanium tetrachloride must be purified further before it is suitable for processing into metal, thus making its cost still higher.3 There were 8,562 tons of rutile produced in the United States in 1947, which was 900 tons in excess of that consumed. In addition there were 13,937 tons in various stocks, exclusive of the stocks in the Government strategic stock pile. No estimates of the domestic production of rutile are given for any of the prewar years. However, in 1939, 442 tons of rutile were imported as compared to 14,307 tons in 1947. One of the reasons for the large increase in the production of rutile is the working of the Florida beach sands for ilmenite, during which a considerable amount of rutile is produced as a by-product. It would be of value to determine methods for utilizing the excess production of rutile. The Arkansas titanium deposits in Hot Spring County produced commercial-grade rutile concentrates from 1933 to 1942. These were sold mainly to England, Germany, and Russia.

Jan 1, 1950

By W. N. Logan, P. Simpson

There was less activity in the petroleum industry in Indiana in 1933 than in previous years, owing largely to adverse market conditions. The only development of any consequence was for oil in Perry and Vander-burgh counties in southwestern Indiana, a few gas wells being brought in in Jay County in northeastern Indiana. Indications are that there will be more activity in southwestern Indiana in 1934. Little change may be expected in northeastern Indiana. One hundred and sixty wells were drilled in Indiana in 1933, of which 57 were dry, 44 produced oil, 38 produced gas and 21 either were not completed or information on them was lacking. There were 153 wells abandoned and plugged in 1933, as compared to 205 in 1932. Southwestern Indiana This area centers about Gibson County and is the principal source of oil and gas production in the state. Production is from the Lower Pennsylvanian and Upper Mississippian formations. Oil production for 1932 was approximately 847,000 bbl. and for 1933 was 804,000 bbl. Gas production for 1933 was 942,000,000 cubic feet. The Siosi field, in southwestern Vigo County and northwestern Sullivan County, discovered six years ago, produced approximately 244,000 bbl. in 1932 and 223,000 bbl. in 1933. Production is from Devonian and Silurian formations. The oil is high gravity, but contains considerable sulfur. The Shelburn and other small pools in central Sullivan County produced approximately 68,000 bbl. in 1932 and 2,000 bbl. less in 1933. Production is from one or more of five horizons in the Pottsville and is obtained at 600 to 800 ft. This area also produces approximately 19,000,000 cu. ft. of gas a year, supplying the city of Sullivan. The field is over 20 years old. The Gibson-Pike County area, made up of many small pools, including several in southern Knox and southwestern Daviess counties, produced approximately 486,000 bbl. in 1932 and 450,000 bbl. in 1933. This production is from the Mansfield sandstone of Pennsylvanian and/or

Jan 1, 1934

By Roland W. Rammler

With oil consumption increasing more rapidly than known reserves in industrial countries, there has been a growing interest in the production of synthetic crude oil. The main starting materials for such production are coal, oil shale and tar sand, all of which occur in enormous quantities in North America. A process sequence suitable for all three of these starting materials incorporates a preliminary retorting step to produce oils for subsequent hydrotreating. For this retorting step, a technique known as the Lurgi-Ruhrgas process has proven highly efficient. The process has been commercially used for the flash carbonization of coal and has also been tested in pilot- plant experiments with oil shale and tar sand.

Jan 1, 1970

By Jerry G. Rose, Robert C. Howell

This paper addresses a process by which both the disposal and utilization of preparation plant coal refuse can be simultaneously accomplished with an attendant benefit of significantly increasing the percentage of extractable coal. A laboratory study is described in which coal refuse was successfully utilized as an aggregate in low cost concrete (coal-crete) mixes under simulated mine environments. Coal-crete specimens with compressive strengths of 14 000 kPa (2000 psd were consistently produced. A construction sequence and mining plans are offered for placing the low-cost coal-crete pillars in accessible areas in room and-pillar mines so that a substantial portion of the remaining coal pillars could be extracted. The method could be applicable in areas where mining procedures do not permit pillar extraction because of possible surface subsidence, roof problems, or other conditions. Possible structural difficulties with the coal-crete pillar support system are discussed. Using a discounted cash flow analysis, the economic feasibility of mining with the coal-crete pillar system is investigated. The cost of the system is compared to the cost of a mining system which would have less coal recovery. The analysis indicates that although at higher coal selling prices the coal-crete mining system may yield an acceptable rate of return, the alternative of leaving the coal pillars is more attractive at the present time.

Jan 1, 1980

By Kalanadh V. S. Sastry, D. W. Fuerstenau

A locked-cycle balling procedure has been designed to simulate continuous, closed- circuit balling drum operation in the laboratory. By this method, it is possible to simulate the surging in green-ball production rate and circulating load that is experienced in industrial balling circuits. Through an investigation of the effect of feed rate on the stability of the locked-cycle, balling process, it was found that higher feed rates lead to increasing instability in the process. An analysis of the experimental ,results is presented and the utility of the locked-cycle experimental technique for evaluating the stability of an industrial balling drum operation is discussed.

Jan 1, 1976

OBSERVERS in more than negligible number appear to believe that the achievements of engineers during the last generation have been an affliction rather than a blessing to society. Quite accurately they perceive that scientific progress and technologic advance have reduced to a fraction-often a small fraction-the amount of manual effort required to accomplish a given unit of useful work. They have seen men, as a consequence, deprived of employment in a particular industry; and this so-called technological unemployment they have denounced as inimical to the workers and consequently to the whole social order in progressive nations. To those who subscribe to this thesis the story of the Porphyry Coppers may not make palatable reading, for it is an amazing record of engineering and technologic achievement. But to those others who take the longer and broader view that economic and social progress cannot enduringly lag far behind advance in the realm of science and engineering; and that any improvement in the means and method of doing essential things eventually must make the world a better place in which to live; to these the record of the development of these great mines can- not but be a source of delight. It is an outstanding example of the advantages of mass production coupled with the fruits of scientific research and inventive genius. More, it reflects the pioneer spirit, the initiative, the self-reliance, the independence of thought and action that are traditional with the mining engineer. The word porphyry is a geologic term, the significance of which will be elaborated in later chapters. The essential characteristics of the deposits that are universally, if not quite

Jan 1, 1933

By Adrian E. Ross

DRILLING through caving formations in diamond drill holes at depths greater than 2000 ft has long been a serious problem. These caving formations are normally passed only by casing the hole or by cementing the hole. Casing the hole is possible only when a resulting smaller hole is acceptable. In as much as only a limited number of reductions are economically practical, cementing is frequently considered the only method suitable for solving these problems. Cementing either by pumping a slurry into the hole or by dropping cylinders containing cement has proved satisfactory on holes under 2000 ft. In holes substantially deeper than 2000 ft these methods are not satisfactory, since during the pumping process cement separates out, whereas cylinders usually break before the bottom of the hole is reached. A new procedure, the injector method, apparently solves these problems.* With this method, cement is lowered in the hole in a cylinder, the cement being

Jan 1, 1952

By Alvin W. Schillinger

During the past ten years, the Calumet Div. of Calumet & Hecla, Inc. has conducted extensive exploration and mining in the footwall of the Osceola amygdaloid lode in the native copper district in Michigan's Upper Peninsula. In an attempt to delineate more clearly the extent and nature of high-grade footwall copper mineralization, 876 diamond drill and long steel holes aggregating slightly more than 47,000 ft have thus far been drilled from the accessible hanging-wall workings. Early in this program it became obvious, through inspection of footwall workings in progress, that due to the erratic and bunchy occurrence of the native copper in the footwall zone, the exploration drilling was failing to outline completely the extent of the oreshoots. Early drilling results indicated isolated pockets of ore whereas in actual practice the footwall was found to be fairly thoroughly mineralized in shoots within the ore zone. Based on drill results only, the "success factor" (discovery ratio) was only 34%.

Jan 11, 1964

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958