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By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By Homer S. Frankhouser

Materials may be dredged, processed, stored and loaded for shipment at a single site in water depths ranging from 250 to 1200 ft. Solution mining may also be accomplished in deep sea situations. And, open air subsea mines with direct surface access may be developed and worked under the ocean floor. These concepts for deep sea mining are the results of extensive testing of individual components of the proposed systems by Dravo Ocean Structures, Inc., a subsidiary of Dravo Corp. A basic structure in these systems is the articulated platform. The platform consists of a gravity- type base and a buoyant cylindrical column which is constructed at an onshore location, towed to the offshore site and installed in a matter of days without use of heavy equipment. The base is also buoyant for towing purposes. This allows for gradual flooding to the point of negative buoyancy for positioning and anchoring to the ocean floor.

Jan 1, 1971

By Arthur Nomann

Recording instruments may be conveniently described under the headings of: (1) geophones, (2) amplifiers, (3) recording cameras, (4) miscellaneous parts. Geophones Geophones or seismometers are actuated by slight earth movements, and generate electrical currents, which are amplified and recorded. In all geophone desigm there is provision for differential movement between parts of the mechanism and the signal voltage is generated as a function of this differential movement. The part that conforms to the movement of the ground is called the support, and the part that remains more nearly stationary with respect to more distant unactuated parts of the earth is called the steady mass. The mechanical period of the geophone is the time required for an oscillation of the steady mass after an initial impulse is given it, and is determined by the effective stiffness of the spring joining the two parts together in relation to the weight of the suspended part. Geophones have been used with frequencies varying all the way from less than 10 cycles per sec. to several hundred cycles per second. Those with a natural frequency of less than, say, 100 cycles

Jan 1, 1940

By Arthur Nomann

Recording instruments may be conveniently described under the headings of: (1) geophones, (2) amplifiers, (3) recording cameras, (4) miscellaneous parts. Geophones Geophones or seismometers are actuated by slight earth movements, and generate electrical currents, which are amplified and recorded. In all geophone desigm there is provision for differential movement between parts of the mechanism and the signal voltage is generated as a function of this differential movement. The part that conforms to the movement of the ground is called the support, and the part that remains more nearly stationary with respect to more distant unactuated parts of the earth is called the steady mass. The mechanical period of the geophone is the time required for an oscillation of the steady mass after an initial impulse is given it, and is determined by the effective stiffness of the spring joining the two parts together in relation to the weight of the suspended part. Geophones have been used with frequencies varying all the way from less than 10 cycles per sec. to several hundred cycles per second. Those with a natural frequency of less than, say, 100 cycles

Jan 1, 1940

By Rudolph G. Wuerker

THE Krupp-Renn Process,[1] has been successfully used to treat low-grade iron ores, laterites, titaniferous sands, and other minerals, and before World War I1 25 units were built by the Krupp-Grusonwerk, Magdeburg, Germany. J. J. Howard[2] has shown theoretical advantages of the pyro-metallurgical treatment over conventional approaches; and the process was described by R. Durrer[3].

Jan 1, 1951

By E. C. van Reuth

FIFTY-three alloys have been examined in the Fe-W and Co-W alloy systems in an attempt to verify the finding of o phases in these systems as reported by Goldschmidt.' The alloys were examined metallographically and by X-ray diffraction. The 10-g specimens were made by powder metallurgy techniques. Very fine, high-purity powders were compressed in a double-acting die at 120,000 psi after hydrogen reduction. All compacts were then sintered for 200 hr at 950°C in a helium atmosphere. Metallographic investigation and X-ray diffraction proved this time to be sufficient to allow complete homogenization before the subsequent high-temperature anneal. Each specimen was then sealed into an evacuated silica capsule and annealed at 1400"or 1500 C (except two) for 25 hr. (The 60 pct Fe and 55 pct Co alloys taken to 1610"and 1680°C respectively were held at these temperatures for 1hr. However, since these structures were at equilibrium before the anneal, and in view of their resultant structures, it is assumed that they reached equilib-

Jan 1, 1960

Jan 1, 1967

By Herman Poole

WHEN finely divided ferrous sulphide, FeS, is roasted at a moderate, carefully regulated temperature, the iron and sulphur are oxidized, the first products being probably ferrous oxide and sulphurous acid. In the presence of oxygen of the air the ferrous oxide soon becomes ferric oxide and in the presence of oxygen and the ferric oxide the sulphurous acid oxidizes to sulphuric acid. These facts are well known, having been established by Plattner many years ago. As a further reaction, some of the sulphuric acid parts with a portion of its oxygen to oxidize more ferrous oxide to ferric oxide, and a portion of it escapes uncombined or else unites with the iron oxides to form sulphates. Ferrous sulphate is usually soon oxidized to ferric sulphate and if the heat becomes sufficient this is then decomposed into sulphuric acid and ferric oxide. As a result of these reactions a mass of more or less pure ferric oxide is formed which is generally made porous by the escaping gases and, if rabbled properly, practically all the sulphur is expelled. If ferric sulphide or ordinary pyrites, FeS2, is roasted, a portion of the sulphur sublimes and usually burns to form sulphurous or sulphuric acid, although at times and under favorable conditions some of the sulphur is driven off uncombined and can be collected as such. Under ordinary methods of roasting, however, only a small portion escapes combustion. By the combustion of the sulphur an increase of heat is de¬veloped and, as a consequence, the reactions mentioned take place more rapidly and actively-more sulphuric acid is formed and the oxidation is more complete-nearly all the iron being left as ferric oxide with practically no sulphate or ferrous oxide. When the iron sulphide is in lumps the roasting proceeds generally as with fines, but with some changes due to mass. The

Sep 1, 1905

Jan 1, 1967

By Walter C, Smith

Metallic bismuth was known in the Middle Ages and the name is supposed to come from the German Wismut. The origin of the German name is uncertain. References to bismuth are found in the writings of Valentine, Paracelsus, and Agricola between 1450 and 1550. Early specimens of bismuth were very impure and often were confused with antimony, tin, and zinc. About the middle of the eighteenth century, J. H. Pott, C. J. Geoffroy, and Torbern Bergman succeeded in producing fairly pure bismuth and showed it to be an elementary metal similar in many respects to lead.

Jan 1, 1953

By Helmut Thielsch

In recent years an ever increasing amount of interest has been directed toward research studying the principles and various applications of sonic and supersonic waves. Though still in their early stages of practical development, sonic vibrations are already used in the emulsifi-cation and degasification of liquids. Metals exposed to sonic or ultrasonic vibrations while solidifying show a considerable amount of grain refinement. Often sound waves are applied instead of radiography to test engineering materials for internal cracks and flaws.' In the field of pure research these waves are used in dispersion and also in coagulation of particles or liquids in gaseous or, under certain conditions, in other liquid systems. In the settling and thickening of slurries considerable time is necessary to compress the solid particles and to squeeze out the liquid to obtain as low a dilution (liquid to solid ratio) as possible. Various methods have been developed to increase the amount of coagulation of the very fine solids (colloidal or semicolloidal) and to shorten the over-all time. The addition of small amounts of electrolytes and the warming of the suspension represent merely the more important techniques. Some of the effects of supersonic vibrations have been reported previously. From preliminary studies, therefore, it was hoped that by application of sonic vibrations it would be possible to reduce the time required to thicken such materials to a specific dilution, as well as to thicken to lower ultimate dilutions than could be obtained by quiescent settling alone. By increasing the volume thickened per unit time—i.e., improving the plant efficiency— great savings in equipment and time would be obtained for industrial processes. Also, faster settling rates should result if coagulation of particles could be increased. Experiments have been conducted for a period of several months in the Allis-Chalmers laboratory to study the effect of sonic vibrations on settling of particles of different sizes and concentrations. Apparatus The sedimentation apparatus used in these experiments is illustrated in Figs. I and 2. The essential features are the stationary field coil and the movable voice coil. Both windings are placed around a solid iron core. A leather diaphragm connected to the steel frame holds the voice coil in place. A brass rod is fastened to the voice coil with a metal disk connected to the other end. This disk is sealed to the lucite cylinder with a flexible rubber diaphragm. The lucite tube is 17 in. long; its inner diameter is 2½ in. and the wall thickness is ¼ in. The tube is calibrated on the outside in 10 c.c. divisions for a total of 1000 cubic centimeters.

Jan 1, 1947

By Helmut Thielsch

In recent years an ever increasing amount of interest has been directed toward research studying the principles and various applications of sonic and supersonic waves. Though still in their early stages of practical development, sonic vibrations are already used in the emulsifi-cation and degasification of liquids. Metals exposed to sonic or ultrasonic vibrations while solidifying show a considerable amount of grain refinement. Often sound waves are applied instead of radiography to test engineering materials for internal cracks and flaws.' In the field of pure research these waves are used in dispersion and also in coagulation of particles or liquids in gaseous or, under certain conditions, in other liquid systems. In the settling and thickening of slurries considerable time is necessary to compress the solid particles and to squeeze out the liquid to obtain as low a dilution (liquid to solid ratio) as possible. Various methods have been developed to increase the amount of coagulation of the very fine solids (colloidal or semicolloidal) and to shorten the over-all time. The addition of small amounts of electrolytes and the warming of the suspension represent merely the more important techniques. Some of the effects of supersonic vibrations have been reported previously. From preliminary studies, therefore, it was hoped that by application of sonic vibrations it would be possible to reduce the time required to thicken such materials to a specific dilution, as well as to thicken to lower ultimate dilutions than could be obtained by quiescent settling alone. By increasing the volume thickened per unit time—i.e., improving the plant efficiency— great savings in equipment and time would be obtained for industrial processes. Also, faster settling rates should result if coagulation of particles could be increased. Experiments have been conducted for a period of several months in the Allis-Chalmers laboratory to study the effect of sonic vibrations on settling of particles of different sizes and concentrations. Apparatus The sedimentation apparatus used in these experiments is illustrated in Figs. I and 2. The essential features are the stationary field coil and the movable voice coil. Both windings are placed around a solid iron core. A leather diaphragm connected to the steel frame holds the voice coil in place. A brass rod is fastened to the voice coil with a metal disk connected to the other end. This disk is sealed to the lucite cylinder with a flexible rubber diaphragm. The lucite tube is 17 in. long; its inner diameter is 2½ in. and the wall thickness is ¼ in. The tube is calibrated on the outside in 10 c.c. divisions for a total of 1000 cubic centimeters.

Jan 1, 1947

By Kenneth Cotingham

Many factors joined in reducing drilling activity in Ohio in 1942. Conservation Order M-68 was important, but other things, such as operators and members of drilling crews joining the armed services and going into war plants, had an important part. The reduction in number of completions was considerable. In 1941, the total of wells drilled was 1561 but in 1942 the total was 1008. The total initial daily open flow discovered by the 701 gas wells drilled in 1941 was 492,000 M cu. ft., whereas the open flow of the 471 gas wells completed in 1942 was 314,488 M cu. ft. The total initial daily production of the 333 oil wells drilled in 1941 was 10,300 bbl., and in 1942 the 181 oil wells had a total daily initial of 7570 bbl. The average daily initial per gas well therefore was somewhat less in 1942 when compared with the preceding year, but the initial per ail well increased about 36 per cent over 1941. General Activity The total depth of the 652 oil and gas wells drilled in 1942 was 1,597,000 ft. The most active county was Perry, where 63 oil wells were drilled, most of them in Clayton township. In Morgan County. where 43 gas wells were drilled, the greatest activity was in York and Marion townships. Medina County was third in number of wells drilled, although of the total of 33 gas wells in the county, 26 were in the new Hinckley township pool. The total initial open flow of these 26 wells was 39,202 M CU. ft., and was considerably larger than from any other single area. Muskingum was an active county, particularly Washington and Wayne townships, in each of which seven gas wells were drilled, and Blue Rock and Harrison townships, in each of which five gas wells were drilled.

Jan 1, 1943

By Kenneth Cotingham

Many factors joined in reducing drilling activity in Ohio in 1942. Conservation Order M-68 was important, but other things, such as operators and members of drilling crews joining the armed services and going into war plants, had an important part. The reduction in number of completions was considerable. In 1941, the total of wells drilled was 1561 but in 1942 the total was 1008. The total initial daily open flow discovered by the 701 gas wells drilled in 1941 was 492,000 M cu. ft., whereas the open flow of the 471 gas wells completed in 1942 was 314,488 M cu. ft. The total initial daily production of the 333 oil wells drilled in 1941 was 10,300 bbl., and in 1942 the 181 oil wells had a total daily initial of 7570 bbl. The average daily initial per gas well therefore was somewhat less in 1942 when compared with the preceding year, but the initial per ail well increased about 36 per cent over 1941. General Activity The total depth of the 652 oil and gas wells drilled in 1942 was 1,597,000 ft. The most active county was Perry, where 63 oil wells were drilled, most of them in Clayton township. In Morgan County. where 43 gas wells were drilled, the greatest activity was in York and Marion townships. Medina County was third in number of wells drilled, although of the total of 33 gas wells in the county, 26 were in the new Hinckley township pool. The total initial open flow of these 26 wells was 39,202 M CU. ft., and was considerably larger than from any other single area. Muskingum was an active county, particularly Washington and Wayne townships, in each of which seven gas wells were drilled, and Blue Rock and Harrison townships, in each of which five gas wells were drilled.

Jan 1, 1943

By H. OSBORG

THE patent literature of alloys for the last two decades or so indicates that the number of liatents referring to smaller and smaller percentages of essential alloying constituents is on the increase, whereas the number of patents relating to considerable percentages of alloying additions becomes smaller. The claims regarding physical properties indicate consistently higher and more rigid values and show the possibility of modifying the physical properties by only slight changes in the percentage of minor constituents or by applying different methods - of treatment. Alloys of the same base have been made suitable for a number of different applications by intelligently and rigid- ly controlling their composition, melting, casting, working, and heat-treatments. Other trends indicated in the development of modern alloys are higher corrosion resistance, higher fatigue limits, and "stability" in volume.

Jan 1, 1937

By L. P. Durham

DuRing the early mine development period, 1929 and the first part of 1930, a 300-ton pilot-plant concentrator was built at Nkana mine of the Rhokana Corporation, Northern Rhodesia. This plant operated from May 26, 1930 until Oct. 26, 1931, treating 101,080 tons of Nkana ores and producing 4372 tons of concentrate. The plant was built, primarily, as a test unit to determine the grinding characteristics, floatability, etc. of the Nkana ores and other ores of the Rhodesian copper belt and to supply sufficient data on which to base the design of a 5000-ton concentrating plant at Nkana mine. The test unit operated wholly on development ores and no attempt was made to grade or select the ores from any section of the mine. The average assays for the 17 months of operation are given in Table 1. The first ground was broken for the 5000-ton concentrator during June, 1930, and the construction of the plant was completed in November, 1931. The plant started on Dec. 10 and has operated continuously since that date: The whole of the concentrating plant is compact and closely connected, yet with sufficient space for expansion of all sections up to 20,000 to 25,000 tons per day capacity. Mining operations are carried on along a length of about four miles on the easterly limb of the Nkana syncline. This length includes the North orebody, from which all production has thus far originated, and the Mindola orebody, now being developed for production. The ore-bearing measures in the North orebody are leached for some 75 ft. below the surface; the oxidized zone varies in vertical extent from 100 to 150 ft. Practically all the ore below the 200-ft. level is sufficiently

Jan 1, 1935

By F. H. McDowell

The increasing interest in the subject of electrical separation warrants the addition to what has already been written of a few lines covering the practical workings of the Tilly Foster mill under the direction of Mr. E. S. Moffat, General Manager. Since my last paper was presented to the Institute, Mr. S. P. Tomkins, the superintendent, has had thrust upon him for solution several problems complicated by the introduction of new conditions. 1. The richer portion of the lean ore dump, and that nearest the railroad track, having been worked up in 1890, the handling of the balance, including a largely increased amount of rock, could only be accomplished at an increased cost. 2. The tailings had accumulated close about the mill to such an extent that arrangements had to be perfected to move them further away.

Jan 1, 1893

Organization Place Date 1919 American Railway Engineering Association Chicago, 111. Mar. 18-20 Society of Industrial Engineers New York, N. Y. Mar. 18-21 American Electrochemical Society New York, N. Y. Apr. 3-5 National Foreign Trade Council Chicago, Ill. Apr. 24-26 American Iron and Steel Institute New York, N. Y. May American Institute of Electrical Engineers Lake Placid, N. Y. June

Jan 3, 1919