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By J. W. Marx, R. H. Langenheim

The injection of heat-bearing fluids may offer a wider application to secondary and tertiary recovery from conventional oil reservoirs than inderground combustion since the process is more easily controlled and the reservoir requirements, in general, are less critical. In all cares, conduction heat losses to overburden and un-derburden will impose an economic limit upon the size of the area which can be swept out from any one injection point for any given set of conditions. The present report describes a method for c.rtin~ating thermal invasion rates, cumulative heated area, and theoretical economic limits for sustained hot-fluid injection at a constant rate into an idealized reservoir. Full allow-ance is made for non-productive reservoir heat losses. Required solutions can be obtained directly from the numerical tables given here, as soon as all operating conditions are specified, withou extensive mathematica1 ~nanipulation on the part of the user. The injection of a heat-bearing fluid into a reservoir is frequently proposed as a means of secondary or tertiary oil production. This form of thermal recovery may offer a wider application to conventional oil reservoirs than underground combustion since the process is more easily controlled and the reservoir requirements, in general, are less critical. Because of its large gross heat capacity, steam appears to be the most efficient heat injection medium, although mixtures of steam and other gases, hot water, hot oil and hot non-condensable gases also have been employed. Whatever the nature of the injection medium, economic evaluation of such thermal recovery processes will depend upon thermal invasion rates, or rates of productive reservoir heating, at any given time after the start of heat injection. In all cases, conduction heat losses to overburden and underburden will impose an economic limit upon the size of the area which can be swept out from any one injection point, for a given set of reservoir conditions, at any given heat injection rate. The present report describes a method for estimating thermal invasion rates, cumulative heated area and theoretical economic limits for sustained heat injection at a constant rate into an idealized reservoir, making full allowance for non-productive reservoir heat losses. Required solutions can be obtained directly from the nu- merical tables given here, as soon as all operating conditions are specified, without extensive mathematical manipulation. It should be noted that ordinary water flooding may be used to move an annular-heated zone outward, even though the economic areal limit for straight heat injection has been reached. Thus well spacing need not be confined to the areal limits as determined here. However, the present calculations do not cover such supplementary heat scavenging programs. The operating element consists of a radial flow system, concentric about the point of injection, with the idealized step function temperature profile illustrated by the dashed line in Fig. 1. The solid curve shown in Fig. 1 gives a qualitative picture of the true radial temperature distribution. It will be shown later that the expressions given below, which are derived from the simplifying step idealization (dashed line in Fig. I), also can be interpreted in terms of the more realistic temperature distribution shown in Fig. 2. For this case, the thermal invasion radius is simply redefined as the distance from injection well to the mid-point of the temperature distribution.

By J. Bulina, J. T. Brown

SINCE the inception of vacuum cold-hearth arc melting of high-temperature alloys (about 4 years ago) it has been theoretically reasoned and qualitatively found that better mechanical properties are often obtained from alloys which have been melted by this practice. Mechanical properties are emphasized in this evaluation because of their importance in design. Vacuum-arc melting has an intrinsic advantage in that it creates an ingot grain structure which is easier to forge and thus leads to greater yields for the finished product. The greater yield naturally gives the process an economic basis when the cost per pound of alloy is rather high. However, the question stressed here is, does the process create an alloy with inherently better properties? There are several theoretical reasons for suspecting that it does. One is the vacuum refining which should permit lowering the content of harmful residuals with high vapor pressures. A second is the vacuum process which should preclude the formation of harmful distribution of oxides, nitrides, or carbo-nitrides, by keeping the amount of such constituents formed to a minimum. A third is the vacuum-arc cold-hearth method which prevents the possibility of pick-up of harmful elements from a refractory crucible since none is used. Fourth, the rapid solidification rate, induced by having a cold mold and only small amounts of molten metal at any one time, minimizes the segregation of elements like titanium, aluminum, and molybdenum from the top to the bottom of the ingot. This rapid solidification rate also decreases the tendency of the above elements to form undesirable phases by segregating locally. Another less frequently considered vacuum-arc melting advantage is the inherently finer-grained ingot structure which can be produced. Finer initial grain size leads to better forgeability, and means that after relatively small reductions to billets or final forged products a finer-grained material is obtained, which, by virtue of its finer grain size, would usually have greater stress-rupture ductility.

Jan 1, 1960

By R. D. Satterley

The Sherwood mine is an iron-ore mine owned and operated by the Inland Steel CO. in the Iron River district of the Menominee Range in Michigan. The property consists of an 80-acre tract in the village of Mineral Hills, about a mile north of the city of Iron River. The Ore mined is a reddish brown, nonbessemer hematite and limonite. The ore bodies lie in a large syncline having an east-west strike and are associated with a rock structure that is folded in a complex manner. The two 40-acre tracts run north and south and the shaft is at about the center of the north forty. The shaft is 1286 ft. deep, with the principal operating level at a depth of 1000 ft. from surface. A new level at a depth of 1200 ft. is in process of development. The ore body at the 1000 ft. level is east and west at approximately the line between the north and south forties and at this elevation is from 50 to 250 ft. wide and extends above the level at varying heights of from 50 to 250 feet. The 1000-ft. haulage drift extends south from the shaft, through the east-west ore body to the slates on the south side of the body. The ore body was intercepted in the drifting at about goo ft. from the shaft and was about 200 ft. wide at that point. A crosscut was extended to the east and west property lines along the south boundary of the ore body. This east-west ore body is laid out in areas go ft. wide for stoping with pillars 40 ft. wide. With this plan a stope is approximately 80 by 200 ft. and has a pillar on both sides that is approximately 40 by 200 ft. The ore has a height of from 50 to 250 ft. above the elevation of the level, therefore the height of the stopes varies in accordance with the height of the ore body at each location. From the crosscut, two main raises, each 6 by 7 ft., are put up into each 80 ft. stope area (Fig. 1). One of the main raises serves as a manway and the other as an ore raise, through which the ore is transferred from the stope to the tramming equipment. The original layout as for scraping of the ore from under the stopes into the ore raises. The ore raise is put halfway (east and west) along the 80-ft. stope area and usually is in iron formation. The manway and ore raise are on approximately 15-ft. centers. These main raises are Put up to a height of from 22 to 30 ft. above the level floor, then from the toll of the ore raise a scraper drift (8 X 8 ft.) is driven across the width of the ore body, which is in the neighborhood of 200 ft. From the scraper drift, mill raises are put up at 12½-ft. centers, staggered on opposite sides of the drift, and these are extended 23 ft. above the elevation of the scraper-drift floor. The sublevel connecting the top of these mill raises is called a mill "sub." Other sublevels are developed parallel to the scraper and mill subs at 25-ft. vertical intervals above the mill sub. The mill sub and the other subs above the mill sub are known as sublevels or dog drifts, and are 4 ft. wide and 6 ft. high. These dog drifts

Jan 1, 1946

By Hsun Hu, R. S. Cline

In an earlier publication1 it was shown that a single crystal of Cu-4 wt pct Al cold-rolled in the (110)[112] orientation was stable up to 95 pct reduction, although the orientation spread was considerable larger than in a similarly oriented and cold-rolled copper single crystal. When rolled to 99 pct reduction, the copper crystal retained its initial orientation and a high degree of sharpness of texture, whereas the Cu-4 pct

Jan 1, 1969

By John W. Cloud

The delivery of blows upon roadway structures by the locomotive engine at high speed, althongh long recognized, has, perhaps, not been as generally understood in severity, relation to speed, and cause as is desirable in matters of such importance. Some points of explanation, with illustrative disgrams, are, therefore, submitted to your attention, preparatory to a note 011 " Steel for Bridges," also submitted. In order that a locomotive may run at high rates of speed with-

Jan 1, 1881

IRON AND STEEL COMMITTEE. ALBERT SAUVEUR, Chairman. A. A. STEVENSON, Vice-Chairman. HERBERT M. BOYLSTON, Secretary, Abbot Bldg., Cambridge, Mass. John Birkinbine, William Kelly, J. S. Unger, William H. Blauvelt, Charles Kirchhoff, Felix A. Vogel,. James Gayley, Richard Moldenke, Leonard Waldo, Henry D. Hibbard, Joseph W. Richards, William R. Walker, Henry M. Howe, C. F. W. Rys, William R. Webster, Robert W. Hunt, E. Gybbon Spilsbury, Frederick W. Wood: J. E. Johnson, Jr.,

Jan 12, 1913

Elected Died 1882 *ABBOTT, ARTHUR V 1906 1903 * ADAMS, CHARLES C. 1905 1884 *ADDY, MATTHEW 1896 1894 *ALLFN R B 1896 1874 *AMIOT, H 1892 1886 *AMSLER, CARL 1894 1895 *ÅNGSTROM, CARL 1901 1895 *ARMSTRONG, JOHN F 1898 1882 *ARNOLDS, HUGO 1886 1875 *ASHBURNER, CHARLES A 1889 1872 *ASIIBURNER, WILLIAM 1887 1883 *ATKINS, C M , JR 1885 1897 *AYERS, WILLIAM 1898 1885 *BABCOCK, GEO H 1893 1884 *BAILEY, EDWARD 1889 1880 *BAILEY, JACKSON 1887 1900 *BALLOU, FRANKLIN 1903 1886 *BARNES, F W 1892

Jan 1, 1910

By Edgar Kidwell

To any one acquainted with the practical conditions surrounding the mining engineer and mine-manager, especially in this country, the presentation to the American Institute of Mining Engineers of a paper on the above subject will need no explanation. The members of this profession are continually called upon to design and erect, both above and underground, structures which involve the use of beams. Not to mention the various buildings connected with large mining operations, I need only refer, in support of this statement, to trestles, derricks, headworks, etc., on the surface, and to timbered stations and other spaces of large span in the mine-workings. Notwithstanding the rapidity with which iron and steel are replacing wood in the construction of large buildings, there will always be cases in which the use of metal will be unadvisable. Especially will this be true in districts remote from large cities. Works of temporary character will continue to use timber. High freight-charges, the liability of delays in delivering iron, and the temporary character of many of the structures, will for many years to come make it advantageous for the mines west of the Mississippi and on Lake Superior to construct their buildings almost exclusively of wood. The timber-resources of the country are decreasing so rapidly that already the engineer finds difficulty at times in obtaining beams of large size. This difficulty will steadily increase, and will force the constructor to resort more frequently to built-up beams, such as have long been used in Europe, owing to the difficulty of obtaining there such large sizes of timber as have

Jan 1, 1898

By M. Baeyertr

Since 1915 many papers and books have covered industrial applications of X-rays from various angles. Two of the more recent are a paper by Fink and Archer, which describes in detail the technique of radiography, and a paper by Clark2, which embraces the whole field of X-ray metallogmphy. This paper, therefore, is confined to work of the X-ray Laboratory of the Western Electric Co., which naturally divides into two categories: radiography and diffraction patterns of various types. Radiography Radiography is the field in which the application of X-rays has had most general appeal among the industries which produce or use metals and alloys. Equipment permitting the examination of heavy sections of metals less permeable than aluminum or other light alloys requires apparatus capable of generating hard X-rays over a considerable period of time. The equipment used in the work presented in this paper is practically identical with that described by Fink and Archer in their paper on radiography in industry and is easily capable of penetrating 1/8 in. of lead. Radiography is used in two major groups of problems: (1) in the development of cquipment and tools and (2) in studies of materials. So far there has been no instance in which the use of radiography for routine inspection is justified. This is partly due to the fact that the manufacture of telephone apparatus involves the production of many identical parts by standardized procedures and equipment that has had development and trial before being put on a regular production basis. It is during this stage of development of equipment and tools that radiography has been used to particular advantage.

Jan 1, 1931

By Charles S. Barrett, Robert F. Mehl

It is generally understood by workers in the field of the crystal structure of metallic alloys that terminal solid solutions are of two types, the substitutional and the interstitial. In reviewing the literature, the work of Weissl on the crystal structure of the alpha copper-tin alloys was encountered, in which a new type of terminal solid solution was proposed. In brief, Weiss' findings showed that the density of the alloys calculated from the side of the unit face-centered cube on the assumption of simple substitution—that is, with four atoms to the unit face-centered cell—was much higher than the density measured directly. It was suggested that the assumption of four atoms to the unit cube is not valid for these alloys, and that each unit cube contained less than four atoms; in other words, that one tin atom replaces more than one copper atom, leaving some atomic positions unoccupied. Such a structure, if verified, would have far-reaching significance in the study of the crystal structure of metallic alloys. It would indicate a complexity in terminal solid solutions not hitherto suspected and might encourage work leading to the discovery of other alloys of the same type, and perhaps to types intermediate between it and the two recognized types. It is of importance, therefore, to reinvestigate these alloys with respect to the type of solid-solution structure obtaining therein. Materials and Experimental Method The alloys were prepared from electrolytic copper cut directly from the cathode and the high-purity tin furnished by the U. S. Bureau of Standards for the calibration of thermocouples. No analyses for impurities of these materials or of the finished alloys were made, since such impurities as might be present could have only a wholly inappreciable effect upon the data obtained and the conclusions drawn. The alloys were made by melting the weighed copper charge in a graphite crucible under a KCl-LiC1 flux with later additions of NaC1, using induction heating. When the copper was melted the weighed portions of tin were

Jan 1, 1930

By Mark E. Emerson

INTRODUCTION A long time has passed since geologists encountered encouraging mineralization in their regional exploration program for base metals deposits. Detailed drilling during the following two field seasons served to delineate the configuration of the deposit. Various statistical techniques were employed to provide confidence levels regarding the extent of the reserves and to categorize them according to whether proved, indicated or inferred. At this juncture, it appears that the company has an orebody. Time elapsed? - three years; money spent? - $2.5 million. Much remains to be done before the orebody becomes a mine. The company urgently needs to develop new orebodies to replace its existing mines which are being depleted. It therefore has expended sizable amounts in exploration, the life blood of the company. A staff of specialists is maintained to evaluate new projects and to conduct feasibility studies. The scale of new mining projects today is beyond the resources of most mining companies. Bank financing, therefore, is often vital if the company is to survive. The following scenario describes how a company goes about evaluating mine projects and what is needed to meet lender's criteria in securing the needed financing. MINE PLANNING Now that the company engineers have taken over the project, their concern is no longer with finding ore but in developing it. An exploration shaft has been put down and a tunnel driven into the orebody to verify, on a large scale, what has been seen so far only in pencil- like drill cores. A large tonnage bulk sample is mined and shipped off to an independent metallurgical process laboratory for beneficiation testing. The budget is expended to cover engineering studies. Preliminary capical and operating costs are developed in- house and profitability studies are made based or1 assumptions concerning the markets for the main product and the indicated gold, silver, and other by-products. Time elapsed? - four years; cost to date? - $3.5-$4.5 million. The staff prepares its own pre-feasibility study. After review, the Executive Committee authorizes management to proceed with full-scale studies. The task is to make preliminary designs and to develop definitive capital and operating cost estimates. Specialized consultants will be engaged to study slope stability for the open pit and rock strength if underground recovery proves more feasible. If it is near the sea, an oceanographic report might be commissioned to see if the tailings can be disposed of off shore. Environmental impact studies are commissioned from a firm familiar with government requirements and regulations in this important area. The company subscribes for an expensive multi-client study of the supply- demand-price outlook for the product to support its own long-range price forecast. Now all the numbers are available to make a definitive appraisal of the value of the project. Cash flow analyses and sensitivity studies follow. Reams of computer printouts are generated. Time elapsed: five years. Amount spent? - up to $9 million, depending on the size, complexity and attractiveness of the project. Marginal projects always take longer. Finally, an engineering and construction (E&C) company is given the task of integrating and compiling all the data into a feasibility study. The results of dozens of reports, memoranda, computer printouts, and charts are boiled down to one final summary report of a few hundred pages together with conclusions and recommendations. After thoughtful review at a board meeting, the directors authorize management to proceed with detailed engineering work - provided that

Jan 1, 1985

By Paul A. Taylor

MUCH information concerning pegmatites which was thought to be true a few years ago has been proved false, and what is now actually known about some pegmatites is not true of many others. The erratic and seemingly unpredictable structure and variable composition of this class of mineral deposits has been widely emphasized. Even parts of the same pegmatite body exhibit marked differences in texture, mineral composition, width, and attitude. Constructive geological thinking in respect to pegmatites now aims to establish general laws rather than to stress the confusing diversity of features having no special economic significance. Substantial progress has been made in classifying different types of these deposits according to general features, internal structure, mineralogy, and origin. In some cases it has even been possible to block out tonnage reserves in advance of mining. It is still easy, however, to make highly erroneous predictions after a preliminary examination of a pegmatite prospect. Pegmatites are important to the economic well being of the country and to its military security. They furnish virtually all the feldspar, strategic mica, beryl, columbium, tantalum, and caesium utilized in the United States, as well as sundry other minerals and significant amounts of lithium and rare earth minerals and gems. With the exception of vermiculite, occasional ilmenite-rutile, and perhaps soda-lime feldspar and garnet deposits, basic pegmatites are of little economic importance. Consequently in this paper, as in common parlance, the term pegmatite generally relates to coarsegrained acidic rocks or what is aptly called giant granite. Available data indicating the size and importance of the production and trade in specified pegmatite minerals are summarized in Table I. Geological Features Much of the latest thinking on the economic geology of pegmatites is now available in a 115-page monograph' by a group of experts who participated with geologists of the Federal Geological Survey in the widespread wartime investigations. Doubtless the most significant feature of the monograph is indicated by the title, The Internal Structure of Pegmatites, but it also contains a vast amount of other new information and includes the assimilated concepts of many earlier writers, whose works are given in a comprehensive list of references. The shape, size, attitude, and continuity of many pegmatite bodies is controlled by the structure of the older rocks in which they occur. If the older rocks are easily penetrated, e.g., biotite schist, most of the pegmatites in a given district will be found outside the parent granite mass as exterior pegmatites. Marginal pegmatites are more prevalent if the older rocks are massive, unsheared, and sparingly jointed. Networks of pegmatites are abundant in highly-jointed rocks. In strongly foliated schists the bodies are usually lenticular, whereas in highly-folded areas they assume tear drop, pipe or pod-like, bow-shaped, or sinuous forms. Jahns2 recognizes five major shape classes: l—dikes, sills, pipes, and elongate pods; 2— dikes, sills, pipes, and pods with bends, protuberances, or other irregularities; 3-—trough-or scoop-shaped bodies with or without complicating branches; 4—bodies with the form of an inverted trough or scoop; and 5—other bodies, including combinations of the above and miscellaneous shapes. Many pegmatite deposits are scarcely big enough to be recognizable as such. Most of them, in fact, are small tabular deposits less than 4 in. wide and usually without economic concentrations of minerals. On the other hand, some pegmatites are more than a mile long and over 500 ft wide. The ratios of length to breadth range from 1 : 1 to 1 : 100. Although the vertical dimension bears no invariable relationship to strike length, tabular deposits or large lenses are often symmetrical enough to show nearly as much continuity down dip as in their horizontal extension, and some pipes or pods are amazingly persistent in the vertical plane. Small pegmatites often string along a fairly definite trend line; in a given district major bodies may lie roughly parallel, and where only a few of them do not, the erratically disposed bodies generally differ in composition from those conforming to the regular pattern. This does not apply, however, in all districts. Characteristically, pegmatite veins pinch and swell or split into branches. When they pinch out entirely it is often possible to find a new body by prospecting the extension of the strike or dip, but the chances of finding a hidden deposit are ordinarily too uncertain to justify much subsurface prospecting. Diamond drilling may yield valuable information as to the continuity of known deposits whose upper portions are well-exposed. Some deposits, in fact, can be proved up for hundreds of feet by surface trenching and then intersected by drill holes at various depths like any other vein-like deposit. Others twist and branch, apparently defying all efforts to explore them short of actual mining.

Jan 1, 1954

By D. M. Thayer, P. B. Linkson

High intensity wet magnetic separation methods have received much attention in the search for alternative and effective methods to treat weakly magnetic minerals. This paper examines the incorporation of such techniques in the beneficiation of a non-sliming specular Michigan Hematite. The dependence of separation efficiency and beneficiation of specular hematite on various parameters controlling the operation of such a device is investigated experimentally. Particular attention is focused on particle size limitations imposed in these separations. In light of these data, metallurgical balances are presented and an attempt made to rationalize the various models suggested in the literature.

Jan 1, 1982

By J. C. Smock

The magnetic and polaric properties of magnetite, or magnetic iron ore: are fundamental facts in magnetism. The disturbing erect of this mineral upon the magnettic needle in land surveying must have been very early observed. The difficulties arising from this source are still almost insurmountable in making accurate surveys in districts where this ore occurs to any extent, either as a rock

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation [ ] in which y = cumulative percent finer, x = particle size, = distribution modulus, and k = size modulus. Charles found that the energy consumption in comminution is usefully expressed by another empirical relation, [ ] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; ( 1-n) is the slope of a plot of log E vs log k. Holmes has presented energy equations similar to Eq. 2.

Jan 2, 1960

By Allan M. Hale

The paper discusses past trends in phosphate reclamation, indicating advantages and disadvantages of land and lakes, sand tailings capped with overburden, phosphate slimes capped with overburden, and overburden fill reclamation. In addition, new techniques of reclamation such a clay settling-pond disposal and wetland restoration are discussed.

Jan 1, 1983

By James T. Wood

STRATIGRAPHY structure and closure of the Paloma field are discussed, with some details regarding the present state of development. The Paloma anticline, a large dome modified by faults, is the largest single closed dome in the southern San Joaquin Valley without surface outcrop or topographic expression. It owes its discovery to geophysics. Of nine wells drilled to the Stevens sand, seven are productive. The ultimate productive area may approximate 3000 acres when the limits of the field are determined.

Jan 1, 1942

By Pradeep K. Rohatgi, Clyde M. Adams

An analysis of heal conduction in the freezing of a solution has been performed. The case considered is the semi-infinite mass of solution, bounded by a con-stant-temperature plane with one-dimensional heat flow, Numerical cooling rate and freezing rate distributions hare been calcutated for the particular case of unidirectional freezing of aqueous solutions against. a cold copper chill. The solution at each level parallel to the chill surface is subjected to a spectra of frcezing rates; the freezing rate is inilially lour., passes through a maximum, and then decreases until solidification is camplete. Arange and maximum freeeing rates are inversely proportional to the square of distance from the chill surface. The temperature of the chill surface in contact with the solution remains constant during solidification. Experimentally, it is observed that deudrite sparing increases linearly with distance from the chill surface; in the light of heat -flow analysis this means that the dendrile spacing is imersely proportional to the square root of the maximum freezing rate. SOLIDIFICATION of liquids is accompanied by rejection of latent heat at the solid-liquid interface. The over-all rate of liquid to solid transformation is governed by the rate of heat extraction. Analysis of the heat transfer in the liquid during freezing is important since it determines the freezing rate and resulting structure. A considerable amount of work has been done on metallic systems since solidification is frequently a major step in processing metals. Unidirectional freezing from heat sinks has been treated by several investigators.1-4 Much of the work has been limited to the simpler case of substances such as pure metals which freeze isothermally at a unique transformation temperature. In this case the thickness of the solid zone y, next to a chill surface. is a parabolic function of the time. 8. where a and b are constants. Eq. |1| is a close approximation giving the progress of solidification for the case in which there is a small but finite thermal contact resistance at the interface between the freezing liquid and the chill.' It has been used with some success in connection with large steel ingots4 when the therma1 contact resistance is negligibly small (as is the case when water is brought into contact with the metal chill). The constant, b. becomes zero and Eq. [l] is then exact. even when the thermal properties of the chill and the freezing liquid depend on temperature. Analysis of unidirectional solidification of solutions is more complicated since the latent heat is evolved over a range of temperatures. Next to the all-solid zone in contact with the chill surface there is a solid plus liquid zone in which solidification takes place. Although the equations presented are considered quite general the numerical and experimental results are for freezing of aqueous solutions from a copper chill. I) EXPERIMENTAL PROCEDURE Solutions of potassium chloride, sodium chloride. and lithium chloride have been used. These solutions form a eutectic: a typical phase diagram is shown in Fig. 1. A solution at its liquid us temperature is poured into a tygon tube mounted on a relatively large copper chill. The chill is immersed in a freezing mixture of dry ice and acetone at -70°C. A thermocouple connected to a high-speed recorder was mounted near the top of the chill to measure the fluctuation in the temperature of chill surface in contact with the solution. In this system the progress of solidification can be visually observed through the tygon tube. After the specimens freeze to a desired height they are removed from the copper chill and stripped from the tygon tube. Longitudinal and transverse sections are cut from the specimen for micrographic examination. Specimens in the form of a thin slice are mounted on a transparent glass slide by freezing small drops of water around the periphery. They are then polished on a series of emery papers; the final finishing is done on a soft tissue paper. A Leitz Biological microscope was used for structural observations; photography was

Jan 1, 1968

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979