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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

Lieut. Louis J. Brunel, now in France, was commissioned on July 27, 1917, as Second Lieutenant in the Engineers Reserve Corps, assigned to the 7th U. S. Engineers, Dec. 10, 1917, and has been with the American E. F. since Mar. 26, 1918. He was assigned to the staff of the General commanding the 5th Field Artillery Brigade, as Engineer Officer, on Aug. 6, 1918. E. Ross Housholder writes that "the record for pontoon bridge building was broken Sept. 25, 1918, by Section A, Co. 4, 5th Engineer Officers' Training School, at Camp Humphreys, Va., of which I am a member. The time was 15 min. 11 3/5 seconds. We then proceeded to break the record for dismantling in 9 min. 57 1/5 seconds. The length of the bridge section was 200 ft. The post band was sent out to meet us, and we feel proud of this record. I have met quite a few A. I. M. E.

Jan 11, 1918

By AIME AIME

A THOROUGHLY satisfactory crowd turned out at the fall meeting of the Industrial Minerals Division and took an active part in the entire program. On Thursday afternoon, Sept. 24, a limestone plant was inspected, technical sessions occupying the attention of the visitors all day Friday and Saturday morning. Headquarters were at the Nittany Lion Inn, an attractive hostel on the Penn State campus, at State College, right in the center of Pennsylvania. We are still in the dark, despite inquiries, as to just what breed of lions Nittany lions are. As nearly as we could find out, Nittany is not a Biblical name, as it sounded to us, but a corruption of the name of an Indian princess, or maiden, or maybe just girl that haunted those parts in bygone times and after whom a near-by mountain was named. Penn State athletes are "lions" and there you are. The meeting was supposed to be a joint one with the American Ceramic Society's Materials and Equipment Division; but it was quite evident that the Institute had a much better publicity agent than the Society, which bothered Ross. Purdy, the aggressive secretary of the ceramic people, no end. However, Secretary Purdy saw to it that everyone present fully understood that the Ceramic Society was present, so that that contingent all but stole the show, its representatives presiding at every meeting. The Pittsburgh Section of the American Ceramic Society was also supposed to be holding its fall meeting there at the same time, but made no trouble at all for anybody, as one of the speakers remarked.

Jan 1, 1936

By Walter G. Perkins

T SEEMS almost sheer presumption to attempt' to discuss Russia in its present chaotic political and economic condition, and were it not that at least two certain absolute factors are continuously at work, it would be impossible to' even approach the subject with any degree of intelligence. These are the inborn love of peace of the people and the national character of the cooperative movement. The love of peace inborn in the soul of every Russian, the desire to be left alone and to- live his life among his home village surroundings, is probably one of the two greatest factors that will make the continuance of the present conditions of civil war impossible. One army or the other may sweep up and down the country. but the Russian peasant will: remain in his own village if not literally darken out. This love of peace is evidenced by the fact that there is no country where personal safety is greater than in Russia in normal times. I have traveled in many isolated parts, carrying considerable sums of money and persolial equipment that; in itself, would be a fortune to any peasant, and have never even encountered a condition in which the most wildly imaginative person looking for adventure, 01: trouble, could muster up even a suspicion of fear. This statement applies also to Southern Siberia and Northern Turkestan, which are inhabitated by the nomadic tribes of Khirghese origin.

Jan 1, 1920

By AIME AIME

Change of Meeting from Birmingham to Chattanooga. In consequence of the disturbed conditions attending a long¬continued labor strike in Alabama, the meeting of the Institute was changed from Birmingham, Ala., to Chattanooga, Tenn., where it will. begin on Thursday evening, Oct. 1, 1908. Information. of this change bad been sent to the newspapers through the Associated Press, and by circular to all members, when news was received of the sudden and unexpected termination of the strike referred to. It was, unfortunately, too late to change once more the arrangements for the meeting. But it is hoped that the cordial invitation of the citizens of ,Birmingham may be renewed and accepted at a future time, not too remote. Office Facilities for Visiting Members. A separate room in the suite occupied by the American Institute of Mining Engineers on the ninth floor of the United Engineering Society Building, has been equipped with furniture and telephone extension for the temporary use of members of the Institute or of sister societies, or visitors suitably accredited. Members of the Institute visiting New York for a short time, who need office facilities during their stay, or members residing in the city. who need temporary office accommodation, can arrange to have set apart for their exclusive use a room, equipped with office furniture, telephone, etc.,. in the suite of the Institute. It is not the intention to give possession of the room to any individual for an indefinite time, but to offer to members of the Institute an opportunity to acquire a well-located, well-equipped business headquarters to carry on transactions which

Jan 9, 1908

By G. Reinberg, C. D. Clarke

Most underground mining operations are dependent on pumping installations to keep the mine unwatered. The reliability of such installations is obviously of paramount importance. The volume of water to be handled is often considerable, and the total head is relatively high. In these cases, both capital cost and operating expense of the pumping installations will become significant factors in overall mining costs. To insure reliability and to keep efficiencies, and hence operating costs, within acceptable limits it goes without saying that mechanical maintenance of a mine pumping installation must receive scrupulous attention at all times. Large mine pumping installations today almost invariably use multistage centrifugal pumps, since positive-displacement units would not be economically competitive except under very unusual conditions of small volume combined with extremely high heads. Centrifugal pump maintenance, under ideal circumstances, would be confined to parts subject to normal running water, i.e., bearing surfaces, stuffing box packing, and shaft sleeves. Under adverse conditions, however, metal may be lost from the wetted surfaces of a pump by erosive or corrosive action of the pumped fluid, and maintenance costs can easily attain enormous proportions.

Aug 1, 1956

Jan 1, 1966

By B. F. Zwick

The entire production of oil in Ecuador so far has come from the Santa Elens Peninsula, Province of Guayas. Both the shallow fields of the northern and the deeper fields of the southern part of the peninsula have been in constant exploitation, though the former are of doubtful economic value. In Table I herewith, which commences with the total amounts produced by the various companies up to 1940, annual company totals are given for the succeeding years. The figures for 1944 have been partly estimated. Table 2 gives figures on casinghead gasoline. Shell Company of Ecuador (formerly known as Anglo-Saxon) has continued active exploration in the Oriente region east of the Andes, and during 1944 the Company's first wildcat well was spudded in. International Ecuadorean Petroleum Co. (formerly International Petroleum Co., Limited) has pursued an active exploration campaign since the latter part of 1939, and a drilling string was placed in operation about a year later. A second string of tools was added during 1943 and a third a few months ago. Ten wildcats, all dry, have been completed in this period, two wells are drilling at the present time and other locations are on the program. Seven of the wells thus far drilled are in the area between Guayaquil and the Santa Elena Peninsula, one up the Daule River beyond Balzar, one on Puna Island in the Guayas Estuary and one in the northern province of Esmeraldas. Both the present drilling wells are in the Guayaquil-Santa Elena zone. The situation in regard to concessions has changed during the past four years because I.E.P.C. has made its selections from the extensive Daule-Guayas Study Concession, as a result of which large tracts were returned to the Government; because of the expropriation of the holdings of the "Ecuapetrol," a German concern whose acreage has passed into other hands; the Peruvian-Ecuadorean boundary settlement, which has reduced Shell's holdings somewhat; and the transfer of most of the holdings of the Cia. Minero-Petrolera del Pacifico to I.E.P,C. The greater part

Jan 1, 1945

By Edward H. Robie

Jan 1, 1971

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization and at a minimum of expense. J. V. W. Reynders is chairman of the Endowment Committee.

Jan 1, 1923

Jan 1, 1957

Jan 1, 1967

By R. Kossowsky

Structural changes in Be-Cu, Be-Ni. Be - Ag, and Be-Fc alloys pressurized in a solid medium were invesligated by resistivity measurements , X-ray diffrac lion in situ and metallogvaphic examination. Some limited tests in liquid medium were also conducted. Good correlation was oblained between diauges of slope of relative resistance us pressure and changes in diffraction pattern. Metallographic examination rez:ealed that the copper, silver, and nickel alloys lwiu heauily due to the applicalion of pressure at room temperature. Using polarized light technique {1012}, {1011}, and possible {1010} twinning planes were identified. At eleuated temperature twinning was moslly confined to the {1012} planes. Although twin-ning could be promoted by application of hydroslutic pvessure (liquid medium), it was strongly enhanced by the pvesence of a nonhydvostatic shear component due to pressurizalion in a solid medium. It was further obserced that a decrease in grain size inlnibiled twinnitzg activily. A great deal of effort has been expended in recent years to render beryllium useful for structural applications. Efforts were concentrated towards a possible phase change and to promoting other than basal deformation modes. Quenching experiments to obtain the high-temperature bcc phase have failed,' nor were alloying additions successful in improving ductility of the brittle hcp phase.2 Herman et a1.3 have reported a new {1011} twinning mode in a Be-4.4 wt pct Cu alloy oriented for a C axis compression sustaining loads to 440,000 psi. A new approach using high-pressure techniques was undertaken at Curtiss-Wright, Wright Aeronautical Division Laboratories. Marder4 reported a 25 pct decrease in relative resistance of commercially pure beryllium at 92 kbar. He proposed that this discontinuity corresponded to the bcc phase found at high temperature; however, X-ray diffraction in silu did not confirm a phase transition.5 contre6 has recently shown that the bcc transition in pure beryllium is lowered to 800°C at 80 kbar accompanied by a 50 pct increase in relative resistance. The purpose of this paper is to report on one phase of an investigation of the effects of high pressures and temperatures in beryllium alloys, namely, twinning behavior in Be-Ni, Be-Cu, Be-Fe, and Be-Ag alloys pressurized to nearly 100 kbar and temperatures up to 200°C. EXPERIMENTAL METHODS Material was obtained from Nuclear Metals, Inc., in the form of a 1.5-mm-diam wire extruded in stainless-steel cladding at 1600° F. Nominal composition of the alloys is listed in Table I, and the major impurities are are given in Table 11. Pressures to 100 kbar* were ob- tained using a National Bureau of Standards type 100/400 ton tetrahedral unit supplied by Barogenics, Inc. This type of apparatus contains a retaining sleeve with a conically tapered internal surface and four pressure-intensifying anvil assemblies with tungsten carbide tips. The 10-mm-long specimen fits into a pyro-

Jan 1, 1968

Jan 1, 1963

Jan 1, 1955

By Robert Pack

INTRODUCTION SOONER or later in the development of any natural resource it becomes highly desirable to know the quantity of this resource in the country as a whole, as well as of the part that is being developed, for the general course and. conduct of the development work must be governed to some extent by the total supply available. An accurate estimate of the quantity of any natural resource is difficult to make; yet if one is diligent enough one can obtain a pretty accurate idea of the quantity of marketable timber, the acreage of tillable land, or the horsepower that may be developed from the streams, for these are things that may be measured. But any attempt to estimate the quantity of some mineral in the ground appears to enter the realm of imagination and it seems that the estimate can be nothing more than a blind guess. It may appear to be especially futile to attempt to determine the quantity of oil and gas that is available in the ground, for these minerals are so vagrant that even if the quantity now available should be known quite exactly, the quantity that will eventually be obtained may be much less, for certain losses in the extraction of both oil and gas are unavoidable, and just what these losses will be cannot be predicted. Though necessarily inaccurate, estimates of such mineral reserves are, however, of distinct value, for they summarize the existing knowledge of the deposits of the mineral and thus enable those who are interested in some industry that depends in one way or another on this mineral to formulate a rational commercial policy. Some time ago, when the price of gasoline suddenly rose in a rather spectacular manner, the writer was one of the U. S. Geological Survey geologists called upon to help to estimate the quantity of oil that could be obtained in the United States, for the fear had become widespread that perhaps the rate of increase in the price of gasoline was a measure of the rate of depletion of the supply of petroleum. It thus became his

Jan 8, 1917

Jan 1, 1971

Discussion of "The Ordering Transformation in Titanium-Aluminum Alloys Containing up to 25 at. pct Aluminum" by F. A. Crossley, Trans, TMS-AIME, 1968, vol. 242, pp. 726-30. Dr. Blackburn, in his response, pointed out that the c/a ratio of the Ti-26 at. pct A1 alloy quenched from 900°C is 1.6006 and not 1.5965 as plotted in Fig. 19. An error in transcription was made in preparing Table V of Ref. 1 (F. A. Crossley, Trans. TMS-AIME, 1966, vol. 236, p. 1174). The corrected Fig. 19 strengthens rather than weakens the argument that a martensitic transformation occurs in alloys containing from 15 to 18 at. pct Al. A Study of the Factors Which Influence the Rate Minimum Phenomenon During Magnetite Reduction, by P. K. Strangway and H. U. Ross, Trans. TMS-AIME, 1968, vol. 242, pp. 1981-88. Page 1883 Reverse Figs. 5 and 6. Sigma—Its Occurrence, Effect, and Control in Nickel-Base Superalloys, by J. R. Mihalisin, C. G. Bieber, and R. T. Grant, Trans. TMS-AIME, 1968, vol. 242, pp. 2399-2414. Pages 2403, 2407, and 2414 Arrows should appear on Figs. 4 and 9; a sigma is missing from Table IV; line 2, page 2414, change "case" to "cast". These are published correctly in the bound volume. Index, December Issue There were a few omissions in the Author Index. These have been corrected and published properly in the bound volume.

Jan 1, 1970