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By AIME AIME

HOWARD H. PRESTON, professor of economics and business at the University of Washington, presented a paper before the North Pacific Section, A.I.M.E., on Jan. 23, on the "Economic Aspects of Gold and Silver." He carefully reviewed recent governmental actions that have affected those metals and gave an interpretation of their effects. A brief excerpt from his address; follows: Including the proclamation of March 6, 1933, the principal steps of the present Administration which have carried the United States off the gold standard and led up to the present program have been: (1) The Presidential proclamation of March 6 controlling gold. (2) The monetary sections of the Emergency Banking Act of March 9. (3) Mobilization of gold under Executive orders issued March 10 and April 5. (4) The gold embargo by Executive order, April 20. (5) The controlled inflation bill, May 12. (6) The joint resolution abrogating the gold clauses, June 5. (7) The Executive orders on newly mined gold, Aug. 28. (8) The President's radio address of Oct. 22 and the R.F.C. gold-buying program. (9) New anti-hoarding order calling in small holdings of gold, Dec. 28, 1933 and Jan. 15, 1934. (10) Nationalization and revaluation of gold' (Message to Congress, Jan. 15).

Jan 1, 1934

Jan 1, 1963

By F. Lowell Lawrance

JOHN SMITH, citizen of the U.S.A., has become so accustomed to reading that Congress has appropriated billions of dollars to pay war costs. that he no longer is impressed by relatively small figures, such as several hundred thousand or a few million, in connection with Government departments.

Jan 1, 1944

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By K. T. Aust

The occurrence of annealing twins in high-purity aluminum resulted in the formation of grain boundaries having orientation relationships which correspond to a high density of coincidence sites. The results provide support for the coincidence site model and indicate that large-angle coincidence boundaries have lower free energies than large-angle noncoincidence boundaries. Observations are presented concerning the coherent structure of twin interfaces in aluminum and the importance of inter-facial energy in preferred orientation. RECENT experiments1 have shown that when an annealing twin is formed during grain boundary migration in zone-refined lead, a large-angle random boundary is replaced at the growth front by a large-angle coincidence site boundary. The coincidence site orientation relationships obtained by twinning were of the type considered by Kronberg and Wilson,2 Frank,3 and Dunn.4 On the basis of the theory of annealing twins advanced by Fullman and Fisher,5 these observations indicate that the energy of a coincidence site boundary is less than the energy of a random boundary by an amount which exceeds the energy of the coherent twin boundary. This energy difference between the coincidence and random boundaries must be at least about 5 pct since the ratio of twin boundary energy to grain boundary energy in zone-refined lead is 0.05 * .014.6 Fullman7 has found that the twin boundary energy in aluminum is about 21 i 5 pct that of a large-angle grain boundary. A twin boundary energy as large as this would be expected to exclude the formation of many coincidence site grain boundaries, especially those which have a relatively low density of coin- cidence sites. Therefore, if the coincidence site model is a useful interpretation of certain large-angle boundaries, then it would be predicted that only coincidence boundaries which separate adjacent crystals with a relatively high density of coincidence sites may be obtained as a result of twinning in aluminum. The present experiments provided a means of testing this prediction since annealing twins occurred during the growth of recrystallized grains into striated, melt-grown single crystals of zone-refined aluminum. EXPERJMENTAL PROCEDURE A striated single crystal of zone-refined aluminum, about 1 cm sq and 37 cm in length, was obtained during zone melting of aluminum of 99.996 wt pct starting purity in a graphite boat under helium atmosphere.8 A molten zone of 2 to 3 cm in length, which was maintained by induction heating. was passed along the length of the bar for eleven passes at a rate of 0.9 mm per min. An additional final pass was given at a rate of 0.2 mm per min. The center portion of the zone-melted bar was characterized by an electrical resistivity ratio between room temperature and 4.2° K of 8000 to 9000. Single crystals of 1 to 2 cm in length were removed from the center section of the zone-refined bar and electrolytic ally polished in a 2:l solution of methyl alcohol and concentrated nitric acid. The specimens were then chemically polished in Alcoa R-5 solution. X-ray analysis of the single crystals indicated the presence of striations or lineage substructure having misorientations as high as 2 deg. New, recrystallized grains were introduced into each striated crystal by the technique of artificial nucleation and growth, previously described.9 During the growth of the recrystallized grains at 300' to 600°C in argon, it was sometimes found that a

Jan 1, 1962

By Walter O. Snelling

Discussion of the paper of WALTER 0. SNELLING, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 100, April, 1915, pp. 695 to 704. A. C. McLAUGHLIN, San Francisco, Cal.-It seems to me that Mr. Snelling's work, if it is what it appears to be, is one of the most important contributions to petroleum technology that has been brought out iii the last 25 years. If his end products are what they seem to be, he has made a discovery, which, in my judgment, will revolutionize the petroleum industry. As to industrially carrying out these processes I do not think there is the slightest difficulty, for I have had some work recently where crude oils were handled successfully at a temperature of 750°F. and pressure of 750 lb. per square inch. WILLIAM A. WILLIAMS, San Francisco, Cal.-What metal did you use, Mr. McLaughlin? - A. C. McLAUGHLIN.-Ordinary seamless tubing, extra strong. WILLIAM A. WILLIAMS.-Tests were made in Dr. Rittman's experimental plant at Pittsburgh, upon samples of residuum furnished by Mr. Bell, the residuum being the remainder of the crude oil after the lighter fractions had been removed. After the material had been run through Dr. Rittman's plant, yields of from 43 to 58 per cent. of material, boiling under 150°C. were obtained. The distillate had a peculiar odor, due to the presence of benzene, toluene, and other unsaturated hydrocarbons. W. N. BEST, New York, N. Y.-What is the difference between the Rittman and the Snelling process or system? WILLIAM A. WILLIAMs.-The fundamental difference is that reactions take place under relatively higher temperatures and pressures and with none of the oil present in its original or liquid state, while the reactions secured by Mr. Snelling and other investigators have been from the liquids in the presence of some vapors. Under such conditions as Mr. Snelling operates, the temperatures and pressures used are limited and the flexibility in the control of these variables is extremely limited when compared with the Rittman process.

Jan 1, 1916

Jan 1, 1967

Jan 1, 1967

At the meeting of the Board of Directors of the Institute on Jan. 26, 1917, the following actions were taken: Messrs. A. C. Clark, Lawrence Addicks and G. D. Van Arsdale were appointed Tellers to count ballots for Officers and Directors. Messrs. T. T. Read, V. S. Harper, and. E. J. Hall were appointed Tellers to count ballots on revised spelling. The Finance Committee's audit for the year 1916 was approved and ordered filed. The Report of the Finance Committee upon the method of raising this Institute's share of the deficit on the additions to the building was approved and accepted. Upon the recommendation of the Secretary, increases in the salaries of some of the employees were approved. The St. Louis Section received an appropriation of $200 for the year 1917. The Columbia Section received an appropriation of $150 for the year 1917. The Montana Section received an appropriation of $100 for the year 1917. The Colorado Section received an appropriation of $175 for the year 1917. The Utah Section received an appropriation of $125 for the year 1917. The Puget Sound Section received a set of Transactions in standard binding. The International Engineering Congress received a loan of $300 until the Congress can realize upon some of its assets.

Jan 3, 1917

By A. R. Denison

The area discussed in this report comprises a group of 38 counties lying in the northeast corner of Texas. It covers all, and extends beyond, the borders of what is commonly described as the East Texas Basin. It includes two major oil fields, Van and East Texas; two major gas fields, Bethany and Waskom; and a number of fields, both oil and gas, of lesser importance. All commercial oil production comes from beds of Upper Cretaceous age and almost exclusively from the basal member, the Woodbine sand. Gas is produced from both Upper and Lower Cretaceous beds with the newer production from the older beds. East Texas Field This field continued as in 1932 and 1933 to dominate the drilling and production situation throughout the oil business. A total of 3681 producing wells was completed in this field during 1934. This is an increase of 1215 over the 2466 producers completed during 1933. Total wells

Jan 1, 1935

By F. Weinberg, L. MacAulay

DAVIS,' in an investigation of solute redistribution along molten rods of dilute silver in tin, concluded that at horizontal temperature gradients below approximately 5°C per cm very little convective mixing takes place. Cole and winegard2 observed temperature oscillations in horizontal melts of tin, with temperature gradients of several deg per cm. They associated the temperature oscillations with the presence of convective flow in the melt. At temperature gradients less than 1°C per cm they did not detect convective flow. In the present work, direct measurements of con-vective flow in liquid tin have been made using a radioactive tracer technique. The results indicate that extensive convective flow occurs at temperature gradients below those previously reported. The apparatus used to determine the extent of con-vective flow is shown in Fig. 1. The graphite boat Fig. l(a), has two rectangular channels both of which contain molten tin. Radioactive Ag110 in the form of Sn-0.2 pct Ag alloy was introduced at the end of one channel, by rotating the cylinder shown. A series of fixed thermocouples were positioned along the center of the second channel to determine the temperature gradient. It was assumed that the two channels had identical temperature distributions. The graphite boat was inserted into a vycor tube which was surrounded by a multiple winding tube furnace as shown in Fig. l(b). The tin was melted in an argon atmosphere. The distribution of Ag110, as a function of position along the boat at a given time after introduction of the ~g"', was determined with the

Jan 1, 1970

By Donald H. McLaughlin, John H. Moses

IN the latitude of Lima, the broad uplifted block that forms the Andes is made up of a complex sequence of folded and faulted sediments and volcanics, broken by large and small bodies of granitic rocks and porphyries with which the principal mineral deposits are closely associated in both time and space. The intrusives are a final episode in the geologic history as revealed by the consolidated rocks, for after their emplacement and after the formation of the primary ore deposits in and about them the record is simply one of long continued erosion and uplift.

Jan 1, 1945

By John D. Morgan, Sylvain J. Pirson

An instantaneous and continuous analysis of a mineral suspension should be of great value in controlling various mineral preparation processes. Described herein is a method of analysis based on the use of high-frequency alternating current, which, under certain restrictive conditions, could be of use. Theoretical Considerations In a suspension of conductive minerals, the electrical effect primarily responsible for the variations in electric conductivity is the capacitance. In Fig Ia, let an alternating voltage E be applied across two electrodes F and F', between which are two rows (S and T) of mineral particles, all of approximately the same size, immersed in a fluid. Let the number of rows of particles between the electrodes be R and the number of particles in each row be N. If A is the area of a particle, D is the distance separating two particles, and k is a constant depending on the fluid, the capacity, CO, of the particle system will be given by: KRA C°= ND Referring now to Fig Ib, let R, the number of rows, be held constant, but let N, the number of particles in each row (S and T), be increased X-fold. The capacity, C1, of

Jan 1, 1949

By E. Hornbogen

The deformation mechanisms of a iron-phosphorus alloys were compared at 20oand —196°C. Alloying with phosphorus increases the resistance to slip, but has little effect on the resistance to twinning. The stress for onset of twinning is nearly independent of temperature, but there is an increasing tendency for cleavage along (112) twin boundaries with decreasing temperature and increasing phosphorus content. FIVE iron-phosphorus alloys and one high-purity iron (0.004 pct C, 0.004 pct N, 0.05 pct O) were vacuum melted and cast, then homogenized for 6 hr at 1100oC and water-quenched. Single crystals were cleaved from the coarse grains produced in this manner. The hardness was measured* on polished (100) surfaces of the crystals at 20" and -196°C. Laue back-reflection patterns indicated a deviation of not more than 3 deg from coincidence of the {100} plane with the surface. The deformation mechanisms were studied by relief effects on the polished surfaces. Yield points in compression (0.5 pct offset) were measured with polycrystalline material. At 20°C the addition of phosphorus to a iron leads to a change from slip to twinning as the main deformation mechanism, Figs. 1(a), (b). Between 2 and 4 at. pct P slip and twinning occur simultaneously. In alloys with more than 4 at. pct P twinning is the main deformation mechanism and slip was observed only in the neighborhood of twin intersections. All cracks at 20oC were on (100) planes, some initiated by twins.' From measurements made at-196oC, hardness and yield points of all the alloys were nearly constant and the same as the hardness of high phosphorus alloys that deformed by twinning at 20°C, Figs. 2 and 3. In the high-purity iron, plastic deformation at -196°C occurred by both slip and twinning, but deformation in the iron-phosphorus alloys appeared to be entirely by twinning. In the high phosphorus alloys a large number of cracks formed along the (112) twin boundaries and at intersections of twins, in addition to the (100) cleavage, Fig. 1(c). DISCUSSION In , iron, plastic deformation can occur either by slip or by twinning, depending upon composition,

Jan 1, 1961

By J. Gordon Parr, D. H. Polonis

IN a previous study of hypereutectoid Ti-Ni alloys' a substructure was observed in quenched powder specimens when the constitution was 100 pet retained ß body-centered-cubic phase. The alloy powders were quenched from 1000°C by a blast of helium gas and precautions already described were observed throughout the work, to minimize contamination. Ogden et al.2 have previously observed subboundaries in the ß phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-rich a precipitation. The nitrogen content of the Ti-Ni alloys does not exceed 0.02 pet and the quenching rate was sufficiently rapid to suppress precipitation reactions. Since X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon, it seems unlikely that this substructure is explicable in terms of nitrogen content. Fig. 1 shows the substructure in adjacent grains of 100 pet ß phase in a quenched 6 atomic pet Ni alloy. Fig. 2 shows adjacent ß grains in a similarly treated alloy; one grain contains marked intracrys-talline boundaries and the other is completely free from any substructure. The suberystals appear to have fairly regular shapes, suggesting a regular orientation relationship among them. Tempering the retained ß structure at temperatures below the eutectoid eliminates the substructure at an early stage of ß decomposition. At the present time it is possible only to guess at an explanation for this subboundary phenomenon, since very little work has been reported on substructures resulting from phase changes. It is believed that the present phenomenon is due to poly-gonization resulting from unrelieved stresses set up

Jan 1, 1957

Jan 1, 1966

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