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By R. D. Carter

Methods are presented for calculating the performance of multiwell gas reservoirs. These methods account for two-dimensional, unsteady-state flow of a non-ideal gas through a heterogeneous formation. The performance can be obtained for gas reservoirs with known physical properties and configuration subjected to specified development and production schedules. These methods may prove helpful in optimizing the exploitation of gas reservoirs. The numerical solrrtion procedures given for this non-linear problem are extensions of known techniques for the linear diffusion equation. Two of these procedures are based on a new difference equation given by Saul'ev. Limitations and advantages of these procedures are discussed. An example solution is presented and is used to compare the calculation methods. INTRODUCTION Li planning the operation of a multiwell gas reservoir, it is desirable to predict its performance for each alternate development and producing schedule under consideration. This paper presents three numerical procedures that can be used to calculate such gas reservoir performance using a digital computer. These methods account for two-dimensional transient flow of a non-ideal gas within the reservoir. Extension of these methods to three-dimensional flow is possible. The paper is divided into three parts. The first describes the problem for which a solution is wanted and three numerical procedures that can be used to obtain solutions. The second discusses the information necessary to set up a problem. This part will be of greatest interest to the field engineer. The third gives data and results for an example problem. PROBLEM AND SOLUTION METHODS In the following development, a gas reservoir is regarded as a sealed, porous, permeable, heterogeneous body in which a single, non-ideal gas phase is flowing. Flow is permitted in the x- and y-horizontal directions, but is considered to be negligible in the vertical or z-direction. The reservoir can be tapped by one or more wells. Methods to be described provide a basis for calculating the complete performance of the reservoir, including rates and cumulative production from the wells, and pressure distribution and decline in the reservoir. If the isothermal flow of a non-ideal gas obeying Darcy's Law occurs in two dimensions in a region R, the governing equation in this region is:

Jan 1, 1967

By F. J. Martin, W. G. Hubler

The Beattie mine is at about the center of Duparquet township in the Province of Quebec, Canada. It is 22 miles northwest of the town of Noranda. The elevation is approximately 1200 ft. above sea level. This locality, long considered a favorable one from the geological point of view, has been prospected for over 20 years, but no discoveries of economic importance were made until the present orebody was found by John Beattie in 1930. The specific gravity of the ore is 2.77. The gold occurs in intimate association with the sulfides, pyrite and arsenopyrite, which in turn are very finely disseminated in a silicified porphyry. The bulk of the gold is associated with the pyrite, only a small proportion being with the arsenopyrite. There are small amounts of magnetite, ilmenite and chalcopyrite present in the ore. There is also some hematite in the ore that is mined from near the surface in the open pit. Metallurgical Problems and Methods or Attack 1. The ore is extremely hard and resistant to grinding. 2. The sulfide minerals are finely disseminated in the gangue. 3. The gold, in turn, is so intimately associated with the sulfides that grinding to even 5 microns will not release all of the values for cyanidation. 4. It is necessary to make a high ratio of concentration in order to obtain a product sufficiently high in gold to meet high shipping and treatment charges. Hardness of the Ore.—Owing to the extreme resistance of the ore to grinding, it was recognized that grinding costs would be high. Microscopic tests showed that grinding to 95 per cent minus 325 mesh would be necessary to liberate a sufficient amount of the values in order to obtain a tailing assaying 0.02 oz. gold per ton, which is considered to have the economical minimum gold content that can be obtained. It is not feasible to grind this hard low-grade ore (0.18 to 0.20 oz.) to 95 per cent minus 325 mesh, so it was necessary to overcome the problem in another way. The following method was decided upon: (1) Fine crushing to minus 1/4 in.; (2) relatively coarse primary grinding; flotation of low-grade concentrates in the primary and rougher circuits and discarding the

Jan 1, 1935

By E. A. Holbrook

The art of ore dressing is as old as civilization itself. Jason's search for the golden fleece was perhaps only the use of sheepskins for catching gold from gold-bearing sands washed over them. From Hoover's translation of Agricola we gather that in the middle ages ore dressing had advanced through the stage of hand sorting to water concentration by jigging. German methods and apparatus continued in the lead until the closing years of the past century; indeed, it is little more than a generation ago that many ore-dressing plants in this country were designed and operated by German-trained ore-dressing specialists. Meanwhile the development of the ore deposits in this country during the nineteenth century brought forth new inventions and methods. Blake's invention of the rock breaker in 1858 and the coming of the Wilfley table about 1896 are random examples of the improvements caused by our expanding needs. Yet ore dressing remained an art developed and practiced more or less by cut and try methods. The publication of the volumes on Ore Dressing by Dr. Robert H. Richards in 1903 marks the beginning of American ore-dressing practice as a science. Previously we had as guides only a few incomplete books based on foreign practice, or scattered references and articles in our own Transactions. Dr. Richards set down all the developments that had gone before, and outlined the ways for a scientific approach to the subject. He gave us a starting point. Since then ore-dressing practice and technique in this country have set the pace for the world. Coal preparation has been called "ore dressing upside down,'' because in ore dressing we generally save a small percentage of the heavy valuable mineral and discard the lighter gangue, whereas in coal preparation we save the larger quantity of light mineral and discard the smaller percentage of heavy waste. By comparison with ore dressing the history of coal preparation is brief, extending backwards hardly 100 years, for although coal had been dug and used locally for centuries it became an important article of commerce only with the coming of the industrial revolution 150 years ago. In new mines it was to he expected that the thickest and purest seams should be worked first. So long as these lasted there was little thought of coal preparation other than hand picking of the larger impurities and simple sizing to supply the real or fancied need

Jan 1, 1934

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Apr. 10 to May 10, 1915: William W. Elmer, Tuttletown, Cal. R. R. Freeman, Jr., Wollaston, Mass. Lawrence Addicks, Douglas, Ariz. Francis R. Pyne, Elizabeth, N. J. W. F. Durand, Stanford Univ., Cal. George B. Pickett, Ophir, Colo. S. P. Cooper, New York, N. Y. R. V. Norris has been elected President of the Columbia School of Mines Alumni Association. Robert C. Sticht has been elected President of the Australian Insti¬tute of Mining Engineers.

Jan 6, 1915

By William P. Blake

THE use of diamonds upon a large scale in drilling rocks, and the substitution to a certain degree of rotary diamond drills for the ordinary steel percussion drills, marks a new era in the art of mining. Since the invention by Leschot of the diamond drill, it has steadily advanced in its utility and range of application, and in the appreciation of miners and engineers. I t must be claimed as one of the many gifts of science to the arts ; and it is, in particular, one of the fruits of the scientific education given at the Ecole Centrale, at Paris. Members are all, doubtless, more or less familiar with the construction of the drill and of the machinery by which it is applied in boring. I t is, therefore, my present purpose only to direct your attention to some recent marked improvements, made by the American Diamond Drill Company, by which the economy and efficiency of the machines have been increased. Form of Bit.-The annular or ring form of the drill-head or bit was, I believe, the earliest; and it is still in use, without essential modification, wherever it is desired to obtain a sample " core" or specimen of the rock traversed. But for mere drilling, regardless ~f the preservation of a test-core, a solid-head bit is preferred, except for very large holes. Until recently, these solid-head bits were made with a pointed cutting face shaped like an obtuse cone. This form was assumed to be the best, being most in accordance with the experience obtained with percussion drills. I t is found, however, that the exact reverse

By George S. Lockwood

Plans are moving ahead toward the July 1965 start-up date for Kaiser Steel Corp.’s new pelletizing plant at its Eagle Mountain, Calif., iron mine. Capacity will be 2 million long tons of pellets containing 65% Fe. A major portion of the output is scheduled for charging into Japanese blast furnaces as the result of a contract to supply Mitsubishi interests with 10.8 million tons of pellets over a six-year period. Kaiser's concentrating plant at Eagle Mountain plus sintering facilities at Fontana are adequate to meet the requirements of its blast furnaces, which, as a consequence, are not expected to take any substantial quantity of pellets during this period. However, some 200,000 tons of pellets per year is scheduled to be used for the production of special steels and in the open hearths as a substitute for the high-cost ores now being used.

Jan 8, 1964

By R. V. Whetsel, V. R. Garfias

For some time the writers have been compiling and analyzing statistics of consumption and production of petroleum, its products and related fuels, in order to arrive at a fairly accurate picture of the world-wide situation of the petroleum industry. In production, crude oil, natural gasoline, benzol and alcohol blended with motor fuel have been considered. In consumption not only refined products, but crude consumed as fuel, refinery losses, ships' bunkers and blended fuels have been taken into account to obtain a true balance between supply and demand. Statistics from practically every country and territory have been studied, and where actual figures were not available the estimates have been based on all the data available. The figures in Table 1 indicate that during the last five years the world's production has exceeded demand every year and that the aggregate difference is some 207,150,000 bbl. The supply in the United States exceeded consumption by 111,401,000 bbl. over the same five-year period and in 1931 and 1932 the demand exceeded supply, while outside the United States the excess of output over demand was 95,749,000 bbl. Table 2 combines the excess production in the United States with its favorable balance of exports over imports, showing that the United States has reduced its storage over the five years by about 136,-595,000 bbl., while in Table 3 it is shown that, including its excess of imports from the United States, the rest of the world has added 343,-745,000 bbl. to storage during the period in question, the greatest accumulation coming in 1934. Table 4 shows the world's consumption classified by countries according to the principal products. These tables also indicate that at the end of 1934 the statistical position of the petroleum industry outside the United States was decidedly unstable, a situation that probably will become more acute as a result of the added Iraq production; and that the present favorable statistical position of the industry in the United States, which is partly due to the excess of exports over imports, may be to some extent jeopardized by the unstable situation in the foreign market.

Jan 1, 1935

By Robert H. Aborn, J. J. B. Rutherford

It is now well known that troublesome intercrystalline corrosion may occur in austenitic stainless steels following exposure of the metal to a temperature within the range 1000° to 1500° F. (540° to 815° C.). The present paper describes a satisfactory method of estimating the extent of such corrosion, based on the measurement of the electrical resistance of a specimen before and after attack. This new method enabled us to study quantitatively the effect of several factors upon intergranular corrosion in the 18 Cr, 8 Ni type of alloy. The results show that susceptibility to this attack increases with increasing carbon content and grain size and appears to pass through a maximum for certain combinations of temperature of sensitization and period during which the alloy was maintained at that temperature; and are in complete accord with our interpretation of the mechanism of this phenomenon. The method is probably applicable to other metals or alloys subject to intercrystalline attack, such as the aluminum alloys of the duralumin type. The methods hitherto in use for estimating the degree of intergranular attack fall into three types: (1) microscopic examinationll (2) macroscopic examination of fractures, and (3) determination of the time required for complete failure or disintegration.2 None of these lends itself very well to a measurement of the extent of corrosion. The first two are qualitative in nature and the third provides an arbitrary value largely dependent on individual judgment, since failure is a progressive phenomenon and not a sudden event. Our experience is that weight-loss determinations, although valuable in some types of corrosion investigations, bear no simple relation to intercrystalline corrosion in this type of alloy, as is to be expected since the phenomenon probably involves only the thinnest films between adjacent metallic grains. Measurement of electrical resistance has been used recently in the study of some types of corrosion,3 but seems not to have been applied to

Jan 1, 1932

By Charles A. Ashburner

A very limited development has been made of the coal-fields of this Territory. This is to be accounted for by the fact that a number of the coal-fields lack railroad transportation, by the distance of other fields from the consumers (due to restricted settlements), and finally by the poorer quality of a number of coals which have been mined as compared to others which can be economically imported into the Territory. The consumption of coal in Utah during 1886, outside of that used by the railway companies, was: Tons. Utah coal,..........110,000 Wyoming coal,. .....19,000 Colorado coal,........* 4,945 Total,........... 133,945 It is estimated that there are 1100 miles of railroads in the Territory which use coal for fuel. The consumption of these roads for the year is estimated at 100,000 tons, making an aggregate consumption in the Territory of 223,945 tons. The consumption of coal in Salt Lake City duriug the year was as follows: Tone. From Grass Creek mines,.......21,000 " Pleasant Valley Company's mines,.. 12,700 " Utah Central Company's mines,.9,000 " Bock Spring mines,.6,500 " Almy mines .. ., .. .. . 6,000 " Miscellaneous sources,..5,800 Total ,.........60,000

Jan 1, 1888

By E. B. Ekren, F. C. Frischknecht

Recently released results of surveys employing the slingram and turam methods show the applicability of electrornagnetics in mapping new areas containing both oxidized and unoxidized iron in the Lake Superior region.

Jan 10, 1961

SECTION I Page Page Report of Nominating Committee. v Employment li Proceedings of St. Louis meeting. , vi Local Section News.: liv Engineering Foundation, Report Affiliated Student Societies lvi of Secretary xxxviii Forthcoming Meetings lvii Engineering Council xlii. Library lviii Suggested College Course on the Membership lxiii Human Side of Engineering... xlii Biographical Notices: Engineering Societies Club of Alexander Bryden. By C. L. Hawaii xlv Bryden lxxxiii Members in Military Service .... xlv E. F. R o e b e r . B y J. W. Meeting of Board of Directors...' xlvii Richards lxxxv 1918 Dues xlviii Institute Committees lxxxvi Transactions for 1917 xlviii Officers and Directors xciv Personal xlix

Jan 12, 1917

ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) A member of the Institute who has had many years' experience in office management for prominent mining engineering and metallurgical companies, and who is now located in the West, would like to secure an executive position with a firm or company engaged in mining or metallurgy, located in the East, and preferably in New York. No. 139. Member, aged 36, married, graduate mining engineer, 14 years' active experience as engineer, superintendent, and manager of large coal-mining operations. Wide experience in development and operation of

Jan 10, 1914

By John V. Beall

Ten years ago, upon coming home to New York, we had money in the bank, a portfolio of stocks, a rent- controlled apartment overlooking the Hudson and we didn't own an automobile. This was bliss! The just reward of industry and careful management of the fruits of our labor in the mines overseas. Although we kept up a delaying action, the family was pushing hard for a house in the suburbs. We were able to find something wrong with every house that came up but, finally, in a weak moment made the unlikely compromise of putting ten dollars down on a piece of property in Westchester County.

Jan 1, 1971

By Robert C. Munro, Kenneth M. Reim

NEW IDRIA INTRUSIVE For the most part this ultrabasic mass is a highly sheared serpentine, the exposed rock being made up of small serpentine chips and plates, the faces of which have been slickensided. Throughout this sheared material there are residual blocks of serpentine and highly to moderately serpentinized peridotite. The faces of these resistant blocks show rounding and slickensiding and their size varies from pebble size to diameters of over 5 ft. Certain areas have seemingly resisted the shearing stresses and remain as moderately fractured serpentine. Throughout the ultrabasic mass are bodies of silica-carbonate rock, silicified serpentine and minor concentrations of magnesite and chromite.

Jan 9, 1962

By Toyohiko Hirota, Fukuo Itoh

Oil and natural gas aside, sea floor mineral resources currently being exploited in Japan are offshore sand and gravel and deep-sea manganese nodules. The mining of sand and gravel has already started. With regard to manganese nodules, the geophysical investigation and the study of the mining method are also underway. This report outlines the activity of a few Japanese firms, the Deep Ocean Minerals Association formed by some 30 private firms, Government agencies, a public corporation and two government research institutes. Researches on new exploration instruments, properties of deep-sea sediments and the mining method currently conducted by the National Research Institute for Pollution and Resources are described in detail.

Jan 1, 1976

By T. S. Lovering

The Moffat tunnel passes through the continental divide about 50 miles west of Denver, Colo., on the Denver & Salt Lake R. R.: It is 16 ft. wide, 24 ft. high, and 32,383 ft. long, a distance of a little more than 6 miles. The advantages accruing from its construction may be briefly summarized as follows: The tunnel eliminates 27 miles of grade averaging more than 3.5 per cent. and actually running well over 4 per cent. in many places, and changes the steepest grade from 4.5 to 2 per cent. It reduced the peak of the railroad from 11,660 to 9249 ft. which enables one engine to pull four times as much freight as it could before the tunnel was built. If the Denver & Salt Lake R. R. completes its line, this road will shorten the distance between Denver and Salt Lake City by 200 miles and will have no steeper grades than the lines now connecting the two cities. The proposal to drive the tunnel through the divide dates back about 25 years and D. H. Moffat, who was the leading spirit in the organization of the Denver & Salt Lake R. R. spent much of his time and energy in efforts to raise money for the tunnel that bears his name. He was unsuccessful and died before the work was started. In 1920 an effort was made to obtain state legislation favoring a bond issue to finance three important railroad tunnels in Colorado but the measure was defeated, largely through the efforts of the citizens of the region near Pueblo. A few years later devastating floods caused the Pueblo voters to seek relief from the state and at this time they withdrew their objection to the tunnel bond issue. As a result, a $6,720,000 bond was issued to finance the Moffat tunnel. Construction bids were so high that the work was finally allotted on a scheme analogous to a cost-plus basis. The contract was awarded to Hitchcock and Tinckler, who are paid a fee of $140,000 for driving the tunnel. All bills are paid by the Moffat Tunnel Commission. The contract was let Sept. 19, 1923, and Hitchcock and Tinckler agreed to complete the work by July 19, 1927. In the event of finishing before this date they were to be given a bonus of $1000 a day and

Jan 1, 1928

The following is a 'partial list of members and guests who called at Institute headquarters during the period Oct. 10, 1917, to Nov. 10, 1917. Edwin T. Blake, Berkeley, Cal. Alfred C. Lane, Tufts College, Mass. H. M. Boylston, Cambridge, Mass. W. G. Matteson, Houston, Texas. W. B. Cogswell, Syracuse, N. Y. E. Francis M'Crossin, Birmingham, Ala. Paul R. Cook, Zaruma, Ecuador. R. E. Murray, Butte, Mont. F. W. DeWolf, Washington, D. C. Edmund Newton, Minneapolis, Minn. A. Faison Dixon, Venezuela. J. J. Ormsbee, El Paso, Texas. W. H. Dufur,, Oil City, Pa. Pablo Ortega, Havana, Cuba. Maxwell E. Erdofy, Lieut. Engr. Officers'. W. E. Pomeroy, El Paso, Texas Reserve Corps, New York. J. C. Ralston, Spokane, Wash. Evan Fraser-Campbell, Scotland. W. L. Remick, Chrome, N. J. David B. Gemmill, Crown King, Ariz. Howard D. Smith, San Francisco, Cal. F. Lynwood Garrison, Philadelphia, Pa. Harold C. E. Spence, Steeple Rock, N. M. C. J. Hall, Spassky, Siberia. R. K. Stockwell, Salt Lake City, Utah. H. Hamada, Tokyo, Japan. Maurice W. Summerhayes, Timmins, Rush M. Hess, Bouse, Ariz. Ont., Canada. A. Howard Higgin, London, England Malcolm M. Thompson, Morsemere; N. J. A. O. Ihlseng, Joplin, Mo. Nicholas Truschkoff, Petrograd, Russia. T. Ishikawa, Japan. H. J. Wendler, Los Angeles, Cal. C. H. James, Tucson, Ariz. Ira T. Wright, Hurley, N. M. R. R. Landon, Philippine Islands. C. Yabe, Japan. Robert W. Bissell has now become associated with Gunn, Richards & Co., of New York, N. Y. Major Reginald W. Brock is giving a course in a school for commanding officers in England.

Jan 12, 1917

Discussion of the paper of J. K. FURST, presented at the Pittsburgh meeting, October, 1914, and printed in" Bulletin No. 94, October, 1914, pp. 2493 to 2514. W..McA. JOHNSON, New York, N. Y.-On discussing this paper I am open to the criticism of "bringing coals to Newcastle," as I, a zinc man, am bringing new ideas on steel to Pittsburgh. But still the view of an outsider can be valuable to the insider. Any multistage process, where each apparatus operates on its particular part of the work at a high efficiency, constitutes an advance in the state of art. But in multiplicity there can be complication and ensuing loss and inefficiency. The duplex steel process is not the pronounced success which was predicted for it by its adherents, for several of such plants have reverted to plain open-hearth methods. If we regard broadly refining processes, such as the Bessemer, open-hearth, puddling, copper refining, lead cupelling, nickel refining, we find that in general refining processes are intermittent and 'concentration processes are continuous. (This generalization I believe to be original with me; it was communicated to Dr. E. F. Roeber, editor, and appeared as an editorial in Metallurgical and Chemical Engineering, March, 1905.) Where we desire primarily quality in a metallurgical operation we must put a batch of metal in the furnace, work on it until we get it to the required purity, test it, and take it out; whereas, if we desire primarily quantity we shove ore into a furnace and smelt it as fast as possible, allowing conditions to make a non-uniform product provided only we get tonnage. From general commercial principles, I believe that the weak point of the duplex process is that the operation is not a money maker unless the plant is kept at. 90 to 95 per cent. of its rated capacity, or unless the Bessemerizing is done so often that it is practically continuous. For in some manner the operation should be made continuous and the control on the tonnage should be commercially flexible. The commercial rigidity of having to control purity exactly increases operating costs without a corresponding gain. Conversely, the chief reason for failure of "steel from ore direct" is that it makes a final operation continuous, which should be naturally intermittent.

Jan 4, 1915

By T. A. Wright

THE SAMPLING of waste materials containing copper, lead and tin has taken on a new significance within recent years, and is of increasing importance, on account of the entry of some of the copper refineries into this field and the tendency towards consolidations among the smelters. In the past, such material was sold on the basis either of a rough or grab sample or of casual inspection of the lot. The two principal sources of this waste are the processes of fabrication and the scrapping of automobile, electrical, plumbing, railroad and other equipment. In both cases much material can be sorted, salvaged and sold by classification and grade to be melted "as is" or with the addition of new or virgin metal. The increasing care in classifying exercised in the large manufacturing plants tends to increase the proportion of this usable scrap; on the contrary, the increasing use of more complex and special non-ferrous alloys tends to make sorting and grading more difficult in turnings, borings, clippings, etc., and consequently is making sampling of more moment. In tin, lead, aluminum, and zinc furnace by-products such as ashes, drosses, skimmings, etc., the trade practice of evaluation has not varied much. For instance, tin drosses, battery lead, and aluminum skimmings are ordinarily sold on what is called "metallic button" or "metallic recovery" or "metallic yield." Copper and lead waste, however, is being sold more and more on actual copper and lead contents based on sample and chemical analyses. This paper will be devoted chiefly to the sampling of materials suitable only for refining and recovery of one or more of the metals present. The methods described are often based on the fact that but one metal, such as copper, is to be paid for. The loss of volatile constituents in melting does not appreciably affect the final copper result, as the "after-melting" assay can be readily calculated to the "before-melting" basis, but if smelter efficiency continues to increase, so that in time zinc, for instance, may be recovered on a paying basis, the method of sampling dirty brass, for example, will have to be changed also.

Jan 1, 1928

By H. J. Morel-Seytoux

The influence of patten, geometry on assisted oil recovery for a particular dispIacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presents (1) very brieily, the methods and mathematical derivations required to obtain the results of engineering concern, and (2) typical results in the dorm of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston- like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. ,These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M = 1 and the numerical results for non-piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed farm solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-fIood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Jan 1, 1967