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By A. C. Freeze

The first use of electric punched card accounting machines as an aid in calculating reserves at the Sullivan mine in Kimberly, B.C., was made in January, 1948. At that time their use was limited to totalling individual reserve blocks for the various reserve classes and for calculating total metal content. The immediate objective was to increase speed, improve accuracy, and to effect some savings in labor that could be employed more usefully elsewhere. It was recognized also that the potential for achieving even greater advantages was excellent. The initial experiment proved so successful that it was inevitable that the use of the method would expand. Thus, for the past nine years assay data from core hole and development headings have been processed by these machines and the results integrated with the program of calculating reserves. It was also learned that the machines could store and classify a large amount of other information concerning the mining characteristics of each reserve block in addition to tonnage and metal content. This has proven very useful for the preparation of monthly production reports as well as in long term planning, in forecasting production schedules, and in analysing the results achieved.

Jan 4, 1961

By A. Eilers

(Butte Meeting, August, 1913.) A NUMBER of the copper refineries in this country have lately separated some of the rarer metals from the slimes in the refinery tanks One of these has furnished me the following table of recoveries from given amounts of blister. I publish . this to show the proportions, to gold and silver and to each other, in which these rarer metals may be expected to occur in copper from certain localities.

Jan 6, 1913

By Albert G. Zima

According to recently puhlished statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet. Drill Tools Modern rotary drilling tools are the product of ingenious design and careful selection and adaptation of materials used in their construction. They must withstand terrific abrasion and, because of their compactness, must be designed to resist exceedingly high unit stresses. In bits, core drills and reamers, the bodies are made of either forged or cast alloy steels, heat-treated to develop a combination of high strength and toughness. To provide sufficient strength to the threaded portions and to protect the threads from distortion or damage, the box or pin sections of the tools are hardened to approximately 310 to 330 Brine11 hardness number. Drill and reamer cutters are generally of the movable type; i.e., serrated cones, cylinders or disks, which can readily be replaced when

Jan 1, 1935

By H. A. Bedworth

ALLOYS of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry1 proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche3 and Corson.4 The constitution of the system has also been recently investigated by Matuyama,5 and in the laboratories of the American Brass Co. by Smith.6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of, the constitution of copper-silicon alloys, the solubility reaches its maximum value, 6.7 per cent. silicon, between 721° and 782° C. At 852° C. the solubility is 5.25 per cent., while at 400° C. it is only 4.1 percent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent. silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By Albert G. Zima

According to recently puhlished statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet. Drill Tools Modern rotary drilling tools are the product of ingenious design and careful selection and adaptation of materials used in their construction. They must withstand terrific abrasion and, because of their compactness, must be designed to resist exceedingly high unit stresses. In bits, core drills and reamers, the bodies are made of either forged or cast alloy steels, heat-treated to develop a combination of high strength and toughness. To provide sufficient strength to the threaded portions and to protect the threads from distortion or damage, the box or pin sections of the tools are hardened to approximately 310 to 330 Brine11 hardness number. Drill and reamer cutters are generally of the movable type; i.e., serrated cones, cylinders or disks, which can readily be replaced when

Jan 1, 1935

By Paul M. Tyler

NOW that the dust of World War II has settled and we and our allies are faced with extravagant losses of men, money, and materials, virtually the only hope that the United States and Britain have in the way of reparations lies in the capture of industrial, technical, and scientific secrets. Even during the war American and British scientists and technicians gained access to German factories, questioned German personnel, studied German documents, and endeavored generally to keep pace with new discoveries in science, industrial technology, and process development. Under various agencies this work continued for two years after the war. Altogether at least 600 American scientists and industrialists have gone to Germany and brought back reports and several times as many British, Canadian, and. Australian investigators have been similarly engaged under co-operative arrangements designed to assure the maximum of coverage with a minimum duplication of effort. As a result of these investigations and document studies, about 500 or 600 reports have been prepared on metallurgical and allied subjects. Those by American authors or joint teams have been listed in the annotated Bibliography of Scientific and Industrial Reports, issued by the Office of Technical Services in the U. S. Department of Commerce. Many of the British reports are also available in this country through the same office or through a British representative in New York. Since it was my duty to read most of these reports for

Jan 1, 1948

By G. M. BUTLER

TWENTY-ONE of the states in the Union, the Territory of Hawaii, and seven provinces of Canada now have in operation laws requiring that professional engineers be registered or licensed. In addition, two states require that civil engineers be registered, and one other state demands registration of structural engineers. Moreover, nearly every year sees additions made to the list. The registration movement, fostered by the American Association of Engineers, now has the powerful, energetic backing of the An1,erican Society of Civil Engineers, which is itself now fostering registration legislation, and there is a strong sentiment in favor of registration in the American Institute of Electrical Engineers and the American Society of Mechanical Engineers. Only in the American Institute of Mining and Metallurgical Engineers is anti-registration sentiment, strongly dominant, but many members of this organization are enthusiastic advocates of registration.

Jan 1, 1930

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 C. W. Hall

MINE executives, as a rule, have always been willing to adopt new ideas of operation, or to listen to proposals which might increase the effectiveness of their enterprise, more especially so if they could be shown how definite results might be attained by introducing any conception suggested. In these days of high wages, high cost of supplies, and high taxes, operators are even more inclined to accord consideration to innovations or improvements, and many go so far as to employ men to conduct special investigations and make studies for the purpose of advancing production. Where a man is brought into an organization to do work of an efficiency nature, it often creates resentment among the operative heads because of having their work directly scrutinized, or investigated, and there is a tendency, if not actually to obstruct, to fa.il to cooperate; in which case the investigator is handi-

Jan 1, 1925

By W. S. Ayres

I. INTRODUCTION. THIS cavern was discovered Oct. 22, 1904, by Mr. Charles H. Deutschman, in company with whom I made, May 29 to June 3, 1905, at the request of Mr. Howard Douglas, Superintendent of the Canadian National Parks, the first exploration of it for the Canadian government. The results were stated in a paper, orally presented, with lantern-views from my photographs, at the British Columbia Meeting of the Institute, Victoria,, B. C., July 5, 1905.* The present paper embodies also the results of a second examination, made Oct. 25 to 29, 1905. The accompanying map, Fig. 1, will serve as a guide to the following description. II. LOCATION. The cavern is situated at snow-line, at the head-waters of Cougar creek, on the west slopes of the Selkirks, about 2 miles north from Ross Peak water-tank, and 5.5 miles west from Glacier House, on the main line of the Canadian Pacific Railway. It was then reached by an arduous climb from the water-tank, up the ravine of Cougar creek, for 8,000 ft. (2,000 ft. of altitude) over rock- and snow-slides, and through a thick tangle of alders. But an easy and very picturesque trail has, during the past summer, been opened by the government from Glacier House. Figs. 2, 3 and 4 represent views, not heretofore published, of the grand scenery of this region, so rapidly becoming the-object of attraction to thousands of tourists from all parts of the world. These views, as well as those shown in. Figs. 5, 6, 7, 8

Jan 1, 1907

By Yu A. Chernegov

Building up the USSR's economic strength was the result of all the achievements and successes of our economy. The Soviet Union was the first to begin planned guidance of the economy. The mining industry of the USSR, which holds the first place in the world output of mining production, has always been considered as the main raw materials basis of the country's economy. High and stable development rates are a feature of planned economic management, based on the social ownership of the means of production. During the past ten years from 1965 to 1875 the national income used for consumption and accumulation increased practically by 1.9 times. There has been no inflation, no unemployment in the Soviet Union for about forty years already. High and stable growth rates of the production of mining industries and that of the branches, which are their direct consumers are characterized by the data in table I. The achievements and successes of the economy's development are to a great extent determined by the three planning components, which are as follows:

Jan 1, 1977

By Lucius W. Mayer

WHILE the mind of the financier does not normally run along channels similar to those of his technical adviser, engineers, because of their exactness, are ever more called upon to manage affairs where financial matters are involved. It is, true, not a relatively large number have thus far functioned in this capacity. It is also true that the essentially financial mind could not serve in a responsible engineering position; for to be a successful engineer one requires precise thinking, making due allowance for factors of safety. To be a financier seems to require less aptitude for exact thinking than of enthusiasm and confidence in capitalizing prospective possibilities. Both require imagination, the engineer being, more conscious of the limitations of natural conditions. It is to be regretted that the engineer' stands so far aloof from financial matters. Many consider them- selves successful, as did Steinmetz, as long as their reward is the consciousness that they are giving supreme service to mankind. They are 'generally happy in their work and, like our honored brothers who are teachers, gain their greatest satisfaction, not in the amount of their remuneration so much as in the service rendered society and in the excellence of results achieved. Indeed, these sentiments bespeak character and command respect.

Jan 1, 1924

By A. Lubinski, J. E. Hansford

Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through Such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs. INTRODUCTION Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to unde-sired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated.' However, in wells where the maximum permissible dogleg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll.' The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in doglegs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures. FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffce to read only through the section Abrupt Dog-Legs. 1. Concept of the two extreme kinds of idealized doglegs: gradual and long dog-legs and abrupt dog-legs,' 2. Concept of why the bending moment in drill pipe un- der tension is the largest in the vicinity of the tool joint,' 3. Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension,' and 4. Definition of the rate of change of over-all hole angle (dog-leg severity)." Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.

Jan 1, 1967

By D. R. Uhlmann, T. P. Seward, O. Chalmers

A magnetic field has been used to damp out liquid convection during the solidification of castings. Ingots of Al-2 pct Cu were poured from various sperheats (10" to 65°C) into a room-temperature graphite mold located between the poles of an electromagnet. The effect on ingot structure of varying the strength and time of application of the magnetic field was investigated, and the results are interpreted in light 01- current theories of ingot structure. In the solidification of alloy systems, thermal gradients in the melt and differences in density of the constituents are expected to produce convective motion in the liquid. The thermal convection caused by temperature gradients should be present during the freezing of both alloys and pure materials, while the solute convection caused by density differences should be of concern only for alloys. The possible influence of this natural convection on the structure of castings has been discussed by Ruddle,' Chalmers, and Tiller. More recently, an experimental investigation of such effects was carried out by Cole and Bolling. These workers took stationary molds containing lead- and tin-based alloys and. using a brine solution. quenched them from various superheats above their respective liquidus temperatures. When grids were placed across the mold diameter to suppress convection, the grid region was later observed to contain a larger percentage of columnar grains than other parts of the casting or than similar castings poured without the grids present. From thermocouple measurements, they found the temperature in the grid region to be higher than that in the region outside the grids throughout the freezing process, and concluded that convection should be an important mode of heat transfer in normal castings. In addition to such convection arising from thermal gradients or differences in density of the constituents, a further source of convective motion, which we shall call "momentum convection", may be particularly important in small (laboratory-size) castings. By this term we refer to the convective motion produced in the initial pouring process, a motion which is damped out as the linear momentum and angular momentum of the liquid are dissipated. Besides these sources of convection, which are present to some extent in all castings. external influences may also be effective in producing convective motion. Examples of such "forced" convection which have been discussed in the literature include stirring the melt, shaking the mold, rotating the mold, and so forth The purpose of the present study was to examine the effect of convection on the structure of castings poured into a cold mold. In this work, a magnetic field was employed to damp out the convective motions within the liquid, and hence control the extent of con- The effect of a magnetic field on convective currents in a conducting liquid is to induce eddy currents which oppose and damp out the convective motion. vection. The technique of magnetic damping was previously used by Utech and F1emings" in their study of convective effects on impurity banding and other substructure in alloy crystals grown unidirectionally from the melt. In their investigation, fields as small as 200 gauss were found to be effective in damping the convection currents which influence the banding. I) EXPERIMENTAL TECHNIQUE In the present study, alloys of A1-2 wt pct Cu were poured into a room-temperature graphite mold. The mold, in the shape of a circular cylinder, 2 in. ID, 2-3/4 in. OD, 5 in. inside height, and 5-1/2 in. outside

Jan 1, 1967

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with 'References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler' of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler's work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950

By R. S. Sinha

A properly designed pre- and post-grouting program aided with coherent construction sequence and adoption of flexible design approach provide a practical combination to solve excavation problems in a hostile rock environment: intensely fractured and sheared. The Pacheco Pumping Plant demonstrates the utility of an engineered grouting program.

Jan 1, 1984

[University of Alaska College, Alaska Mining Society MAURICE BUTLER, President EARL FOSSE, Secretary RAYMOND J. BARBER, Faculty Sponsor R. H. OGBURN, Counselor University of California Berkeley, California Mining Association THEODORE OLSEN, President ARTHUR K BOURRET, Secretary FRANK H. PROBERT, Faculty Sponsor GRANVILLE S. BORDEN, Counselor D. C. JACKLING, Associate Counselor Carnegie Institute of Technology Pittsburgh, Pennsylvania The Metals Society EDWARD J. BOYLE, President W. T. LANKFORD, JR., Secretary M. GENSAMER, Faculty Sponsor EDGAR C. BAIN, Counselor]

Jan 1, 1940

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By N. Mungan, J. L. Thompson

Laboratory displacement tests were performed to study oil recovery elficiency by gravity drainage in fractured systems under miscible conditions. The porous media used were cylindrical Berea and Blue Jacket sandstone cores containing a number of well-defined, artificially formed, vertical and subvertical fractures. Butane and Soltrol 130 were the two miscible fluids used. The purpose of the study was to examine the influences of the displacement rate, fracture density, fracture orientation, fracture permeability, matrix permeability, crossflow, core length and connate water on the oil recovery. It was found that displacement rate, matrix permeability and the subvertical fractures affected oil recovery most. The critical flow rate, based on the matrix permeability, was found to be a significant factor in the process. For displacement rates below the critical flow rate, the oil recovery efficiency appeared to be unaffected by the density of the subvertical fractures. At the high displacement rates, the fracture density becomes important, with the recovery being the most efficient in the core having the greatest number of the subvertical fractures. The magnitude of the fracture permeability, the fracture orientation, the core length and the connate water have little effect on the oil recovery efficiency. INTRODUCTION Gravity drainage under miscible conditions from relatively thick reservoirs can be a very efficient recovery process, especially at low flow rates where the gravity forces are dominant and, consequently, the adverse viscous fingers associated with the unfavorable viscosity ratio are minimized or eliminated. Such a process might involve injection of an LPG or some solvent bank at the crest and then driving the bank with dry gas. For some favorable combination of reservoir temperature, pressure and oil composition, there may be no need to inject any solvent bank, since enrichment of the dry gas by the light ends of the crude creates an in-situ solvent bank. Slobod and Howlett2 have studied the effects of gravity segregation in vertical unconsolidated porous media under miscible conditions in the laboratory. The main variables in their study were the viscosity ratio, the density differences and the rate of flow. In this study, the objective was to find the influence of fractures on gravity drainage under miscible conditions. A greater number of related variables were also studied. LABORATORY STUDY CORE DESCRIPTION Displacement tests were performed mostly in cylindrical Berea sandstone cores. In a few cases in which a much lower matrix permeability was desired, Blue Jacket sandstone cores were used. The vertical fractures were formed by cutting the cores with a thin circular blade or by parting them along a bedding plane. The vertical fracture plane always contained the axis of the cylindrical core. The subvertical fractures, cut with a saw, were inclined 45' from the horizontal. The line of intersection between the planes of the vertical and subvertical fractures was parallel to the circular faces of the cores in all cases except one, as depicted by VF3HF-2 in Fig. 1. Fracture geometry of the other cores is also given in Fig. 1. Tables 1 and 2 give the physical properties of the solid and fractured cores, respectively. The suffixes and prefixes shown for each core have been used throughout the paper so that the reader may discern the fracture geometry from the core numbers.

Jan 1, 1970