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By B. H. Caudle, A. B. Dyes

In a recent publication' it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n '. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/q, = 1/(1 + y) y and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The resrilts obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce all infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of diflerent permeabilitv and thicktress or two lnyers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when wing only data over early years 01 decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index INTRODUCTION As a result of both experimental work with models and theoretical deductions, it was recently concluded' that wells having a free surface in a homogeneous reservoir producing by pure gravity drainage should have a hyperbolic decline with n = 2. The present report details efforts to extend this work on ideal homogeneous reservoirs to actual field cases. It should be remembered that both the previous work and the present extension are based on the assumption that the reservoir is at very low pressure, and hence, nearly all the potential available for driving fluid to the well is the gravity head. Attempts to apply conclusions of this study to reservoirs which have considerable pressures supplementing the gravity drive may lead to difficulty. WELLS WITH NO FREE SURFACE In a dipping gravity-drainage reservoir such as that shown in Fig. 1, some of the down-dip wells have no free surface. The previous study' showed that the up-dip wells, which have a free surface, should follow Eq. 1. The following approximate analysis, of a type which was justified experimentally for up-dip wells in the work just mentioned, leads to results for the down-dip wells.

By V. J. Driscoll

A method is given for checking pore volume reserve estimates and transient water inflzix factors utilizing early well performance. Principal applications are based on the observation that there is a convenient transient time-range in terms of well spacing in which observed pressure drop will give a good indication of fluid-in-place. Primary quantity determined is a porosity-feet value applicable in the vicinity of an observation well. Checks on porosity or net pay thickness and permeability values also are obtained. These are particularly valuable in improving quality of interpretive factors entering into pore-volume reserve determinations for larger fields. In smaller fields, direct determination of total field reserves and approximate location of boundaries may be made in some cases. Well interference and production data plus a build-up curve on the observation well are needed. The build-up curve may be taken at any time. Field applications are given. The method can be applied with the completion of the second well on a new discovery or to older reservoirs by major changes in withdrawal rates from a local area. Appropriate test length permits results to be obtained with equal accuracy on widely spaced wells. Criteria for optimizing test conditions are given. Provision is made for various boundary and well effects including incomplete observation well build-up. INTRODUCTION Due to low quality data, initial pore volume reserve and water influx estimates may often vary by a factor of two or more from results obtained at a later date. Unfortunately, by conventional methods, more reliable answers from performance usually are not available until after most significant economic decisions have been made. Furthermore, in older reservoirs, uncertainties may still exist as to original oil-in-place, recovery factors and residual oil saturations due to incomplete or inaccurate performance data. This paper outlines situations and appropriate arrangements of basic transient theory whereby well interference data can be utilized to improve the quality of estimates under certain conditions. In addition to production data on offset producers, key information required is a measured pressure drop at an observation well, corrected for any incomplete build-up due to previous production, plus a formation capacity value derived from a conventional pressure build-up plot on the observation well. The method, as outlined, is strictly applicable only to a horizontal single-layered system of uniform rock characteristics containing a homogeneous fluid of low and constant compressibility. However, under the set of test conditions devised, requirements can usually be relaxed so that it should be applicable to most low permeability gas, water and undersaturated oil reservoirs. This is an area where more reliable information is certainly needed. BASIC CONSIDERATIONS A, B, C and F as subscripts or in the text refer to producing Well A, observation Well B, a more remote producing Well C and field boundary F. Combinations such as AB refer to distances and dimensionless times in terms of distances between these points, while single letters refer to distances and dimensionless times in terms of the well-bore or field radius. Equations covering definitions of quantities and complex situations are given in the Appendix. Key equations in practical units are given in Table 2. Transient Pressure Behavior Fig. 1 illustrates pressure drop at Point B with time due to initiation of a constant rate of withdrawal from Point A. This is shown as since a quantitative under-

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By L. M. Yokum

Tremendous strides have been made in front end loaders in the last 15 years. Fifteen years ago a 21/4-cu-yd front end loader was the largest standard machine you could purchase. Today there are two commercially available 15-yd front end loaders and many 10-yd loaders. The estimated total worldwide market for all front end loaders over 1 cu yd has increased to over 30,000 units yearly. The trend for front end loaders, in general, and for the mining market, in particular, is to larger and larger loaders. Today there are 18 and 24-cu-yd front end loaders in prototype form. It is not inconceivable that within another 15 years there will be front end loaders in the 50-cu-yd class with design features quite different from today's. These larger loaders are being designed at the demand of the mining industry, and the design criteria are being directed at this market area. The costs of these larger loaders may be greater per unit of capacity, but it is the intent of the various manufacturers that they will be more reliable, be easier to service, give greater availability, live longer, and cost less to maintain, than previous loaders. It is also the intent of the manufacturers to compete directly with the large mining shovel as the front end loaders become appropriately larger and more reliable. There has been some trend in this direction in the past with smaller shovels and loaders. In Table 1 are data for U.S. production of front end loaders (5 to 6-cu-yd class and 10-cu-yd class) and U.S. production of cable-operated, crawler-mounted power shovels, draglines, and cranes (11/z to 5-cu-yd class) for the years 1965 and 1970 (Source: Bureau of Census, U.S. Department of Commerce). Many believe that the decline in shovel production, in particular, is due at least in part to the acceptance of the front end loader as a primary production tool. However, the foregoing comparison is for a smaller shovel class than for front end loaders. It has generally been a rule of thumb that a front end loader is competitive on a cost and production basis with a shovel when it is approximately twice as large as the shovel. This same relationship may not hold true with the larger 10 to 15-cu-yd electric shovels, but at some point, direct competition will probably occur. Current Trends There are many trends today that are significant. One major usage trend in large front end loaders involves load and carry operations. This application is defined as "performing the functions of loading, hauling and dumping with one machine over distances within its economical limits." Many people are using front end loaders to transport material as well as load it. It is estimated that nearly half of all 10-cu-yd front end loaders sold in 1970 went into primary load and carry work. Many times, significant savings result from using the load and carry system, instead of small truck and shovel operations, for distances in excess of 1000 ft. Strip mining in coal utilizes great numbers of front end loaders in this manner. In-pit crushing of limestone is developing on an ever-increasing level, especially in Europe, and this stimulates interest in load and carry operations. In Table 2 is a cost example for 10-cu-yd front end loader in a limestone quarry. More than likely, load and carry use will continue to increase over the next few years. While some types of mining do not lend themselves to load and carry in the pit, such areas as surge piles are applicable and should be studied. In the area of machine operating cost reduction, there

Jan 1, 1974

By A. L. Lee, M. H. Gonzalez, R. F. Bukacek

Experimental viscosity data for methane are presented for temperatures from 100 to 340F and pressures from 200 to 8,000 psia. A summary is given of the available data for methane, and a comparison is presented for that data common to the experimental range reported in this paper. Correlation of the data is presented, and predicted values are given for temperatures up to 460F and pressures up to 10,000 psia. INTRODUCTION The increasing ranges of temperature and pressure at which fluids are produced, transferred and processed in the petroleum and chemical industries stress the need for accurate information on physical properties, both for engineering calculation and for improving the methods used to estimate physical properties. A survey of the literature reveals that disagreements between published data on the viscosity of methane are common and that most investigations have been conducted over restricted temperature and pressure ranges. This situation made it desirable to undertake an investigation with a scope common to most of the literature data available. APPARATUS AND MATERIALS The apparatus used in this investigation was the capillary tube viscometer'described by Dolan,10 with modifications introduced in the general design and operation of the instrument. It has an effective pressure range from 14.7 to 10,000 psia and a temperature range from room temperature to 400F. The design of the viscometer is based on the establishment of a manometric head between two vessels containing the test fluid and a volume of mercury. The reservoirs are connected by a capillary tube through which the test fluid flows and a tube through which mercury flows. A pressure gradient is established by elevating one of the vessels above the other, the resulting flow of mercury displacing the test fluid through the capillary. The schematic diagram of the system (Fig. 1) shows the arrangement of the equipment auxiliary to the viscometer. The density cells assembly (E, Fig. 1) was not used in this investigation since reliable data are available on methane. 23 The assembly consists of a bank of eight 316 stainless steel pycnometers. Experimental values of the density of a natural gas19 and i-butane14 samples have been obtained for pressures up to 8,000 psia and temperatures up to 340F. The methane used was obtained from the Southern California Gas Co. Mass spectrometric analysis showed a composition of 99.8 percent CH4, 0.1 percent C2H6 and 0.1 percent C3H8. EXPERIMENTAL VALUES AND ACCURACY OF DATA Determinations were carried out at several temperatures. With the temperature in the cabinet controlled at a given level, a series of runs were made at various pressures. To establish pressures lower than that obtained from the methane cylinder, it was necessary to vent the gas slowly to the atmosphere until the desired pressure was reached. The consistency of the test run time for a particular condition can be used as a criterion for the accuracy of the data. A further check is obtained by comparison of the viscosity values obtained using different driving heads. To establish the instrument's reproducibility, a large number of runs were made at three completely different conditions of temperature and pressure. Data obtained were analyzed statistically to determine the most reliable value for the variance of the experimental data. It was found that the variances of the data taken at different experimental conditions were not statistically equivalent, but they were small. The largest variance was found at 8,000 psia and 100F, where the standard deviation was 0.385 micropoise. Therefore, 99.9 percent of the data can be expected to fall within 1.15 micropoises of the population mean, except for the intervention of systematic errors in operation.

By M. C. Dow

Belt conveyors generally are conceded to be the most economical method yet devised for the transportation of large quantities of bulk materials within plants. Belts are coming into greater use for transportation over long distances and are replacing other forms of long-haul conveyance. It is not the intent of the writer to comment on the design of belt conveyors, but to offer some suggestions for improvement in the operation of conveying belts, based on many years experience with belts in several stone-crushing plants. It is the contention of this writer that opportunities for improvement not fully realized by most operators exist in many plants and that a study of the individual conveyors can result in lower unit belt costs. General Reliability It is the fool-proof nature and general reliability of the belt conveyor that is responsible for its neglect. Even when abused, a belt will carry large tonnages and last a long time, often outlasting the personnel responsible for its care. Some operators look upon the purchase of a new belt as an expensive outlay every so many years, rather than a constant and steady cost amounting in belt wear alone to several dollars every operating day. This belt wear for all conveyors in one stone-crushing plant known by the writer costs 1 /12 cents per ton or $12 to $15 per hour, based on the present cost of belt replacements. The fact that these replacement costs are double those of prewar quality emphasizes the necessity of improving the conditions that make belts wear out. Some of those conditions are the responsibility of the conveyor designer, and if a serious original error has been made, this handicap cannot be overcome by the operator. If the belt is too narrow, too steep, or too fast for good loading, the operator finds that he has an inherently expensive belt. The other factors that decrease the life of a belt are more or less under his control. The two factors of most importance are the loading conditions and the alignment. Most of the cover wear and carcass cutting occurs at the loading point and if the alignment is not good under all conditions, edge wear or damage may result, Fig I. Loading the Belt It is difficult to load a belt in an ideal manner; that is, to flow the material on the moving belt at a steady rate, without impact, without turbulence, and with a velocity equal to and in the same direction as the belt. An inclined belt is especially difficult to load and particularly when its speed is over 300 or 350 fpm. Inclined conveyors require longer skirt plates to prevent spillage until the load settles. It does not seem reasonable to expect an inclined the to carry the same load as a horizontal belt of the same width and speed, because of the difficulty in loading

Jan 1, 1948

By M. C. Dow

Belt conveyors generally are conceded to be the most economical method yet devised for the transportation of large quantities of bulk materials within plants. Belts are coming into greater use for transportation over long distances and are replacing other forms of long-haul conveyance. It is not the intent of the writer to comment on the design of belt conveyors, but to offer some suggestions for improvement in the operation of conveying belts, based on many years experience with belts in several stone-crushing plants. It is the contention of this writer that opportunities for improvement not fully realized by most operators exist in many plants and that a study of the individual conveyors can result in lower unit belt costs. General Reliability It is the fool-proof nature and general reliability of the belt conveyor that is responsible for its neglect. Even when abused, a belt will carry large tonnages and last a long time, often outlasting the personnel responsible for its care. Some operators look upon the purchase of a new belt as an expensive outlay every so many years, rather than a constant and steady cost amounting in belt wear alone to several dollars every operating day. This belt wear for all conveyors in one stone-crushing plant known by the writer costs 1 /12 cents per ton or $12 to $15 per hour, based on the present cost of belt replacements. The fact that these replacement costs are double those of prewar quality emphasizes the necessity of improving the conditions that make belts wear out. Some of those conditions are the responsibility of the conveyor designer, and if a serious original error has been made, this handicap cannot be overcome by the operator. If the belt is too narrow, too steep, or too fast for good loading, the operator finds that he has an inherently expensive belt. The other factors that decrease the life of a belt are more or less under his control. The two factors of most importance are the loading conditions and the alignment. Most of the cover wear and carcass cutting occurs at the loading point and if the alignment is not good under all conditions, edge wear or damage may result, Fig I. Loading the Belt It is difficult to load a belt in an ideal manner; that is, to flow the material on the moving belt at a steady rate, without impact, without turbulence, and with a velocity equal to and in the same direction as the belt. An inclined belt is especially difficult to load and particularly when its speed is over 300 or 350 fpm. Inclined conveyors require longer skirt plates to prevent spillage until the load settles. It does not seem reasonable to expect an inclined the to carry the same load as a horizontal belt of the same width and speed, because of the difficulty in loading

Jan 1, 1948

By M. C. Dow

INTRODUCTION BELT conveyors generally are conceded to be the most economical method yet devised for the transportation of large quantities of bulk materials within plants. Belts are coming into greater use for transportation over long distances and are replacing other forms of long-haul conveyance. It is not the intent of the writer to comment on the design of belt conveyors, but to offer some suggestions for improvement in the operation of conveying belts, based on many years experience with belts in several stonecrushing plants. It is the contention of this writer that opportunities for improvement not fully realized by most operators exist in many plants and that a study of the individual conveyors can result in lower unit belt costs. GENERAL RELIABILITY It is the fool-proof nature and general reliability of the belt conveyor that is responsible for its neglect. Even when abused, a belt will carry large tonnages and last a long time, often outlasting the personnel responsible for its care. Some operators look upon the purchase of a new belt as an expensive outlay every so many years, rather than a constant and steady cost amounting in belt wear alone to several dollars every operating day. This belt wear for all conveyors in one stone-crushing plant known by the writer costs 1 1/2 cents per ton or $12 to $15 per hour, based on the present cost of belt replacements. The fact that these replacement costs are double those of prewar quality emphasizes the necessity of improving the conditions that make belts wear out. Some of those conditions are the responsibility of the conveyor designer, and if a serious original error has been made, this handicap cannot be overcome by the operator. If the belt is too narrow, too steep, or too fast for good loading, the operator finds that he has an inherently expensive belt. The other factors that decrease the life of a belt are more or less under his control. The two factors of most importance are the loading conditions and the alignment. Most of the cover wear and carcass cutting occurs at the loading point and if the alignment is not good under all conditions, edge wear or damage may result, Fig I. LOADING THE BELT It is difficult to load a belt in an ideal manner; that is, to flow the material on the moving belt at a steady rate, without impact, without turbulence, and with a velocity equal to and in the same direction as the belt. An inclined belt is especially difficult to load and particularly when its speed is over 300 or 350 fpm. Inclined conveyors require longer skirt plates to prevent spillage until the load settles. It does not seem reasonable to expect an inclined conveyor to carry the same load as a horizontal belt of the same width and speed, because of the difficulty in loading

Jan 1, 1947

By Arthur B. Yates

DIAMOND drilling has advanced and expanded during the past few years. Along with this increase there has been a marked trend to rely more and more upon drilling for the outlining of ore for reserve purposes. This is especially true underground, where men have not been available for opening up ore by crosscuts, drifts and raises. During the recent heavy call upon known ore reserves, more drilling has been done for exploration and it has become expedient to drill longer lateral holes from underground and deeper holes both from surface and from exploration headings in the mines. Furthermore, these deeper holes have to be drilled closely enough to warrant calculation of "probable" if not "proven" ore, from the results obtained therefrom. Interpretation of diamond-drill results has become more precise and reliable with the growing knowledge and understanding of the geologic structures that control the geometry of ore distribution, and this has broadened the field of usefulness of the drill. All of this has created a necessity and a demand for more accurate control of the hole as to direction, a more precise and reliable method of surveying for position, and a need for better and more complete core recovery, as well as larger cores, to provide an adequate sample. At depth the control becomes more difficult and, at the same time, more important. CONTROL A close study of drilling in various parts of the world for a period of more than 20 years has brought to light one definite rule, practically invariable; namely, that diamond-drill holes tend to deviate into a position normal to any structure existing in the rocks, such as bedding, schistosity, gneissosity, or even parting or jointing-even if the hole is started at almost any angle other than parallel with the structure. It also appears that the better developed the structure is, the more quickly will the hole get into a position perpendicular to it. It has often been said that there is a tendency for holes to "drift" in the direction of rotation. This is obviously untrue, for in a vertical hole the measure of deviation would depend upon the azimuth chosen as zero, and there is an infinite number of choices. It has been proved, however, that in homogeneous rocks there is a tendency for the hole to corkscrew, and that the direction of the spiral is the same as the direction of rotation. This may account for the belief that holes drift in that direction. Some tests have been made using right-hand and left-hand rods, and these show that no matter what the direction of rotation the hole will swing into a position perpendicular to the structure. Methods of Control The foregoing empirical rule may be used as an indirect method of control. If the prevailing structure is known, it may be advantageous to start the hole as nearly normal to it as possible, for the nearer the direction of the hole is to this ideal, the straighter it will remain. This, of course, is not always practical and in some cases is impossible. Usually such a

Jan 1, 1946

By E. S. Mardock, Robert E. Bush

The object of this paper is to report recent developments in the quantitative interpretation of radioactivity logs. The use of reference lines is described in the application of the new zero radioactivity reference line for the determination of neutron derived porosities is discussed. Illustrated examples are shown of logs from the reef limestone of the North Snyder Field and from the Lansing-Kansas City limestone of central Kansas. A method of using an interrelation factor calculated from the neutron and gamma ray curves, called the neutron Productivity number, for the estimation of productivity from sandstone formations is discussed. When used in a relative manner the neutron productivity number has aided in Predicting whether a given zone will produce gas or liquid or whether it is too shaly to produce. Examples of logs from wells in the Freites District, Venezuela, and in East Texas are shown to illustrate the application of the neutron productivitv number. INTRODUCTION The petroleum industry was introduced to some of the preliminary results of investigations into the quantitative interpretation of radioactivity logs in October, 1949." It was stated at that time that the methods presented were entirely relative because they involved the use of reference points obtained from the radioactivity log, i.e., shale reference lines, dense zone reference lines, or a combination of both shale and dense zone reference lines. These relative methods offered many advantages to the industry in interpreting radioactivity logs in terms of porosity with particular application to limestone and dolomite reservoirs. However, these relative methods did not offer the wide range of applicability desired because the esta1)lishment of reliable reference points from shale in some areas were difficult. It was recognized that a more reliable mean; of establishing reference lines was vitally needed. Such a method is now available through the introduction of an instrumeutal zero device. It is the purpose of this paper to discuss the application of this new zero reference to the quantitative interpretation of radioactivity logs. Previously all applications of quantitative interpretations of radioactivity logs have been made in limestone reservoirs with little or no emphasis placed on sandstone reservoirs. A brief resumé of investigations into the quantitative interpretation of radioactivity logs in sandstone reservoirs is presented here. This discussion deals primarily with the interrelation of the gamma ray and neutron curves and the response of the latter to the density of the fluids filling the pore space in relatively homogeneous sandstones of uniform porosity. The authors believe that the methods presented herein are only applicable locally to specific fields and reservoirs, and that they probably do not offer a wide range of applicability. However, tile authors believe that the wider use of the new instrumental zero references in sand areas will reveal more information about the specific response of the gamma ray and neutron curves to changes in lithology and saturation. Two applications of quantitative interpretation using the new instrumental zero references are presented. Examples are given which show the comparison of logs and porosity in the limestones and dolomites of West Texas and Kansas. Logs of wells in 'Venezuela and East Texas are compared with the drill stem test data, production data, etc.. to illurtrate the interrelation of the gamma ray and neutron curve: and the rise of methods involving these interrelations to determine certain saturation variables. THE QUANTITATIVE APPLICATION OF RADIOACTIVITY LOGS TO LIMESTONE AND DOLOMITE RESERVOIRS Tile theoretical basis for the gamma ray and neutron curves has been discussed elsewhere.9 he method of recording the logs and apparatus involved has also been thoroughly covered and will not be discussed here.'."".'" It has been shown that the neutron curve responds exponentially to liquid filled porosity over the 1 1/2 to 35 per cent

Jan 1, 1951

By M. Cross

INTRODUCTION The development of refining processes involving gas injection into liquid metals has seen the evolution of a variety of designs [I]. During the last few years or so the top, bottom and side blown processes have, essentially, been combined to produce a series of mixed gas blowing schemes (eg. the LBE [2,3] and LD-OB processes [4,5]). Although, a variety of mixed gas blowing processes have been carefully engineered and recorded operational experience now attests to their effectiveness, optimising their design and operational performance is another matter. Detailed process analysis of such operations is impeded by the complex nature of the physical and chemical processes involved: . fluid flow behaviour of the liquid metal and injected gases, . chemical reactions in the vessel, . mass and heat transfer within the fluid phases in the vessel, . influence of the geometry (eg. location of the tuyeres, etc.), . monitoring the operational performance. By and large, design and operating parameters evolve from a combination of laboratory scale experiments, pilot plant work and, of course, practical engineering experience. Conventionally, the gas-liquid system used to model the industrial process is air-water, for a number of valid reasons including – . visual demonstration plus geometric and (to some extent) dynamic similarity, . the fact that the system demonstrates, at least, qualitatively many of the complex features of gas injection - interaction between the gas and the liquid - the nature of the gas flow behaviour - qualitative indications of mass transfer rates Important experimental contributions to the understanding of gas liquid systems include the work of Brimacombe [6], Wraith [7], T.Robertson [8], D.Robertson [9], Guthrie [10] and Szekely [11] (these references provide starting points to identify the major published work in this area). Although air-water systems have been instrumental in providing a great deal of qualitative insight into the fluid flow behaviour of the processes, reliable quantitative predictions are more problematic. A number of workers (notably Brimacombe and colleagues [6, 12])have demonstrated that different gas-liquid systems can lead to wide variations in behaviour. Other limitations of physical modelling include the assumptions of isothermal flow, scale- up of turbulent flow behaviour and the inability to directly include the effects of chemical reactions. The above limitations in physical modelling, therefore, yield a natural role for mathematical modelling provided that it can be made comprehensive enough whilst remaining cost-effective. The major physical processes involved in gas injection systems may be summarised as . behaviour of the gas envelope structure in moving through the liquid metal . the global movement of the liquid metal . momentum interaction between the liquid metal and the injected gas . heat transfer and mass exchange via the chemical react ions. The behaviour of gas envelopes forming at a tuyere and then moving through the liquid has been investigated thoroughly by a large number of workers. Such models are generally based upon simple physic- al concepts derived from visual observation. An early model by Davidson and Schuler (DS), based upon a force balance between the liquid inertia and a combination of the bouyancy and momentum forces on the envelope, has proved to be a useful tool in predicting bubble volumes at detachment [13]. The DS model has been successfully modified in a number of ways [14-17] to cope with heat transfer and reactive transfer rates, etc. Furthermore, the basic ideas summarised above have also been confirmed on industrial converters by both Guthrie [I8] and Brimacombe [19]. Models have also been developed to predict the behaviour of the "chemical" component of some gas-liquid systems. However, one thing is clear; all gas-liquid reactive systems are governed by the degree to which effective mixing occurs. As such, the processes are dominated by the behaviour of the heat and mass exchange of the two phase fluid flow system. It is the pattern of movement of the turbulent liquid metal plus its interaction with the injected gas which must be predicted reliably, if sufficiently comprehensive comp-

Jan 1, 1984

By Robert E. Bush, E. S. Mardock

The object of this paper is to report recent developments in the quantitative interpretation of radioactivity logs. The use of reference lines is described in the application of the new zero radioactivity reference line for the determination of neutron derived porosities is discussed. Illustrated examples are shown of logs from the reef limestone of the North Snyder Field and from the Lansing-Kansas City limestone of central Kansas. A method of using an interrelation factor calculated from the neutron and gamma ray curves, called the neutron Productivity number, for the estimation of productivity from sandstone formations is discussed. When used in a relative manner the neutron productivity number has aided in Predicting whether a given zone will produce gas or liquid or whether it is too shaly to produce. Examples of logs from wells in the Freites District, Venezuela, and in East Texas are shown to illustrate the application of the neutron productivitv number. INTRODUCTION The petroleum industry was introduced to some of the preliminary results of investigations into the quantitative interpretation of radioactivity logs in October, 1949." It was stated at that time that the methods presented were entirely relative because they involved the use of reference points obtained from the radioactivity log, i.e., shale reference lines, dense zone reference lines, or a combination of both shale and dense zone reference lines. These relative methods offered many advantages to the industry in interpreting radioactivity logs in terms of porosity with particular application to limestone and dolomite reservoirs. However, these relative methods did not offer the wide range of applicability desired because the esta1)lishment of reliable reference points from shale in some areas were difficult. It was recognized that a more reliable mean; of establishing reference lines was vitally needed. Such a method is now available through the introduction of an instrumeutal zero device. It is the purpose of this paper to discuss the application of this new zero reference to the quantitative interpretation of radioactivity logs. Previously all applications of quantitative interpretations of radioactivity logs have been made in limestone reservoirs with little or no emphasis placed on sandstone reservoirs. A brief resumé of investigations into the quantitative interpretation of radioactivity logs in sandstone reservoirs is presented here. This discussion deals primarily with the interrelation of the gamma ray and neutron curves and the response of the latter to the density of the fluids filling the pore space in relatively homogeneous sandstones of uniform porosity. The authors believe that the methods presented herein are only applicable locally to specific fields and reservoirs, and that they probably do not offer a wide range of applicability. However, tile authors believe that the wider use of the new instrumental zero references in sand areas will reveal more information about the specific response of the gamma ray and neutron curves to changes in lithology and saturation. Two applications of quantitative interpretation using the new instrumental zero references are presented. Examples are given which show the comparison of logs and porosity in the limestones and dolomites of West Texas and Kansas. Logs of wells in 'Venezuela and East Texas are compared with the drill stem test data, production data, etc.. to illurtrate the interrelation of the gamma ray and neutron curve: and the rise of methods involving these interrelations to determine certain saturation variables. THE QUANTITATIVE APPLICATION OF RADIOACTIVITY LOGS TO LIMESTONE AND DOLOMITE RESERVOIRS Tile theoretical basis for the gamma ray and neutron curves has been discussed elsewhere.9 he method of recording the logs and apparatus involved has also been thoroughly covered and will not be discussed here.'."".'" It has been shown that the neutron curve responds exponentially to liquid filled porosity over the 1 1/2 to 35 per cent

Jan 1, 1951

By W. M. Rutherford

A knowledge of the limits of miscibility between reservoir oil and possible injection fluids is required for selection of the optimum miscible-injection fluid. Limits of miscibility can be estimated from the results of equilibrium phase-behavior experiments. They can also be determined by means of displacement experiments conducted in a high-pressure sandpack. This paper describes the equipment and procedure which have been developed for determining miscibility conditions by stable displacement. A systematic series of displacements of a West Texas reservoir oil was carried out. The results indicate that, at constant pressure, miscibility is a function only of the pseudocritical temperature of the injection gas. This fact, together with improved experimental methods, makes the displacement technique a rapid, reliable means for determining miscibility conditions. In conjunction with the displacement experiments, phase diagrams were constructed for the oil with dry gas and propane and with dry gas and ethane. Phase behavior of the methane-ethane-propane system was determined at 110°F. The experimental work demonstrates the feasibility of using ethane-rich gases to reduce cost and pressure requirements for miscible displacement. INTRODUCTION In recent years, interest in the miscible displacement of oil by light hydrocarbon mixtures has been high. Many pilot and a few field scale projects have been started.1 These projects have made use of various methods for achieving miscibility: (1) the LPG-slug process, (2) the enriched-gas-drive process and (3) the high-pressure gas-drive process. Some field projects have been successful; the results of others are debatable. In general, projects which have performed best have involved the injection of an appreciable fraction of a pore volume of miscible material. Economical application of miscible displacement depends strongly on the cost of the miscible-injection fluid. If an appreciable fraction of a pore volume of material is required for successful application of these methods, a precise knowledge of the minimum requirements for miscibility in terms of composition of injection fluid is essential. Therefore, reliable experimental methods for determining miscibility conditions are important, and a procedure for estimating these conditions from the composition of the reservoir fluid is highly desirable. The subject of this paper is the problem of determining conditions which result in miscible displacement of oil by light hydrocarbon mixtures. Miscibility conditions can be estimated by means of equilibrium experiments conducted in a PVT cell, or they can be determined by means of high-pressure displacement experiments. This paper describes the equipment and procedure which have been developed for the determination of miscibility by high-pressure displacement experiments. These methods have been applied to the displacement of a West Texas reservoir oil with mixtures of dry gas, ethane and propane. In conjunction with the displacement experiments, triangular phase diagrams have been constructed for mixtures of the oil with dry gas and propane and with dry gas and ethane. The effect of injection-gas composition on conditions for miscible displacement in high-pressure sandpacks and cores has been the subject of several published papers.2-5 The experimental methods used in these investigations were such that displacements were unstable, and the effects of fingering and/or gravity layover are clearly evident in the results. Miscibility conditions were probably correct in spite of the instability phenomena, but the experiments evidently were time-consuming, and limited data were reported. Systematic high-pressure flow studies which would support a correlation of miscibility conditions have not been reported; however, Wilson5 has proposed the use of pseudocritical temperature of the injection gas as a parameter and Benham, et al,6 have based a miscibility correlation on observed and calculated equilibrium data.

By C. B. Alcock, R. G. Hudson

Sulfur pressure measurements above FeS in equilibrium with iron have been carried out by the Knudsen orifice method. A comparison is made of the weight loss of the cell per unit time obtained in the above experiments, that calculated from Richardson and Alcock's measurements of the S2 pressure above FeS in equilibrium with iron, and the dissociation constant for diatomic sulfur from spectroscopic and thermal data. EXTENSIVE equilibrium measurements have been made to determine the sulfur potentials of a great many systems of metallurgical interest.' In order to confirm their reliability, to supply data which may be of use in further thermodynamic calculations, and to establish the reliability of the Knudsen orifice in obtaining accurate thermodynamic values at high temperatures, the present investigation on the pressure of the gaseous species above FeS in equilibrium with iron has been carried out. The Knudsen orifice method has been used for these pressure measurements. Experimental The apparatus and general technique for this investigation are the same as that reported for the determination of the vapor pressure of silver.' To reduce the residual gas pressure in the evacuated chamber, a titanium getter, maintained at run temperature, was introducbed. Several types of Knudsen cells were used—platinum, zircon, and fused silica. The orifice in the zircon cell was fashioned with a small diamond wheel. The same precautions were used in this investigation as were employed in the work on Mo2S2.3 The FeS-Fe mixture was prepared by heating a sample of pure FeS,, supplied by K. K. Kelley of the Bureau of Mines, with excess iron powder, cp grade, obtained from the Fisher Scientific Co. These two substances were heated in a closed Armco iron crucible at 960°C, held in a vacuum of less than 10" mm Hg for 24 hr. The mass was then removed from the cell and ground in an agate mortar. In this form it was charged to the various Knudsen cells. Heating the Knudsen cell for an additional two days was sufficient to obtain constant rates of weight loss of the cell. The data obtained in this investigation are recorded in Table I. To establish whether or not a sulfide of iron is volatile at these temperatures, 0.7646 g of the FeS-Fe mixture, described above and containing 69.2 pet Fe, was placed in the zircon Knudsen cell. Run Nos. 103 to 109 were performed on it. After the completion of these runs, the total amount of iron left in the cell was obtained by chemical analysis. It contained 0.537 g Fe, compared to 0.529 g in the original charge. Thus, there was an apparent gain in iron of 1.5 pet. This is attributed to unknown experimental error, and the conclusion is that no sulfide of iron is volatile. The vapor pressure of pure iron4 is about one thousandth that of the sulfur pressure' at these temperatures. The vapor pressure of iron inside the Knudsen cell will be almost exactly that of pure iron, since in the iron-rich phase the percentage of sulfur is of the order of 0.025 pet.At this low percentage of sulfur Henry's law is probably obeyed by the sulfur. Thus, the iron will obey Raoult's law. In any event, the vapor pressure of iron will be lower than that of pure iron and, since the vapor pressure of pure iron is negligible compared to the pressure of sulfur, the weight loss of the cell due to the vaporization of iron should be negligible. Since neither iron nor FeS is volatile to an appreciable extent, the total weight loss of the cell must be due to the vaporization of sulfur. Discussion and Calculations On the assumption that S, is the only gaseous species present in appreciable quantity, its pressure

Jan 1, 1957

By William F. List, Marvin A. Schuster

Monolithic electrooptical mosaics of 2500 photo-transistor elements with internal row and surface column interconnections have been fabricated by epitaxial-planar diffsion techniques. Unique access to any elemed of the mosaic is provided through one of the fifty X and one of the fifty Y external leads. The sensor mosaic can be used for imaging applications and has a 1:1 aspect ratio, a resolution of 100 lines per in., a dynamic range in excess of lo3, a sensitivity of 0.5 per pw, element response within a 2:l range over 75 pct of the mosaic, and a minimum detectable signal of the order of 10-' w. Design considerations which ilnpose particclar fabrication yequirements are disctussed along with some of the problems peculiar to the epitaxial and planar-dijfision techniqes by which this device is fabricated. The solid-state silicon monolith has an imaging area of 0.5 by 0.5 in. and an element center -to- center spacing of 0.010 in. J monolithic solid-state electrooptical device has been developed as the photon-sensing mosaic for use in an image-converter system.' This system is the solid-state equivalent of the vidicon and can image radiation in the visible and near-infrared regions of the spectrum. The electrooptical image converter has the desirable size, weight, reliability, and low-power characteristics inherent in solid-state devices. It is read out by direct-wire means rather than by beam-scan techniques. The packaged unit is shown in Fig. 1. A selection of material for the sensor was based on considerations of both reliable fabrication techniques and material spectral response. Silicon was selected both for its response from the lower end of :he visible to the long-wavelength cut-off above 11,000A and for its well-developed epitaxial planar-diffused technology. The electrical image is composed of M x N discrete information bits with each bit emanating from one of the individual phototransistor sensors. The interconnected mosaic concept was introduced to provide a structure which is both manageable in its number of leads and compatible with conventional viewing systems which accept XY data. Interconnections along the Y direction are provided by internally diffused strips, while interconnections along the X direction are formed by vacuum-deposited metal surface bars. Unique access to any individual element of the M x N mosaic is available through one of the M and one of the N external leads. PHOTOTRANSISTOR DESIGN A phototransistor structure2 was selected for the discrete photon detectors of which the mosaic is com- posed. Basically, the mode of phototransistor operation is such that incident quanta are absorbed in the base area of the element where they generate electron-hole pairs. If the electrons are liberated within a diffusion length of the depletion region around the collector junction, they will diffuse to this depletion region and be swept across the junction where they account for a small component of the photocurrent. Similarly, the holes which are created within a diffusion length of the emitter junction will diffuse to this region where they forward bias the emitter and so induce injection of minority carriers into the base. This accounts for the substantial transistor photocurrent. This mechanism of operation implies several design and fabrication goals for the individual sensor elements: high electrooptical conversion efficiency, sufficient carrier lifetime in the base regions, and a maximum volume in which photons can be absorbed within a diffusion length from the depletion layer about the junction. Moderately high transistor gain is desirable to permit readout at low light levels; however, very high gain has a deleterious effect on mosaic dynamic range. The mosaic must also be characterized by good uniformity of element response as well as by good isolation between elements. The above set of conditions imply that junction depths must be optimized with respect to photon ab-

Jan 1, 1967

By C. L. Pillar

INTRODUCTION The location, size, character of the ore de- posit and its adjacent formations will deter- mine the mining system best used for its ex- traction. The mining system chosen will have to be engineered to suit the ore deposit and the people that will extract it. What can be done in the Philippines cannot always be accomplished in the upper Northwest Territory of Canada. Mining operations developed under a free enterprise system are planned to achieve a satisfactory return on the capital required to place them into production. Hence, the choices made in planning and developing the mining system must be dictated by sound economics. The mining system planned must favor: 1. Maximum ore extraction of the deposit with minimal grade dilution. 2. The amount of capital expenditure used to develop and equip the mine must be in harmony with the financial policy of the group yet be sufficient to provide a reliable mining system. Excessive frills and extras that are not required for efficient, safe production should not be provided. 3. Mine production costs are determined by the amount of men, material, equipment and energy used in the production process. These must be kept to minimal limits in order to insure dependable, low cost production. Extras that later are needed in the production operation can be added as required by the operator. Basically block caving is a mining system that is normally used to extract deep seated, massive, low grade deposits of copper, molybdenum and iron where stripping ratios for open cast mining are economically prohibited. The caving system is limited in its selectivity. It is a mass production type of underground ore extraction that under favorable conditions is one of the most efficient, low cost mining systems in the world today. Usually block cave mining systems are large. They are capable of producing ore at a rate of 10,000 to 100,000 tons/day from large deposits at costs that are comparable with many open cast mining systems burdened by high waste to ore ratios. Block cave mining systems differ basically in the plan of the area layout, the method of undercutting and the method of draw. The balance of the mining system is the mechanical transportation of the drawn ore to the surface, the mine supply, drainage and ventilation systems. This paper deals mainly with the methods of draw. The method of draw to be used in a block caving system dictates the development plan of the mining area, is highly influential in the method of undercutting to be employed and the supply and ventilation system to be used. There are three basic methods of draw commonly used in today's operations. They are: Gravity draw Slusher draw LHD draw The type of draw planned will have a major affect on: Capital expenditure and time required to bring a deposit into production. Productivity, efficiency and cost of the production operation. Percent recovery of the ore deposit in both tonnage and grade. Degree of production reliability Fundamentally the type-of draw used must be compatible with the physical characteristics of the deposit to be extracted and the financial position of the mining operation. The type of draw chosen must work to advantage with the size, configuration, depth, strength and fracture pattern of the deposit and its adjacent formations. It must favor the financial protection of the planned mining operation. A Gravity Method of Draw requires a finely fragmented, easy flowing product from the caving action of the deposit. To obtain the desired economic advantage the ore deposit must also have sufficient area and height of column to permit minimal development cost on a per ton basis. The gravity system re- quires the maximum amount of development openings and uses the minimum amount of mechanized equipment of all the caving systems. It is unskilled, labor-intensive and is highly sensitive to size of ore fragmen-

Jan 1, 1981

By L. S. Kolbert, C. H. Baab

Introduction In June 1981, the Electric Power Research Institute (EPRI) issued a report titled "Control Systems in Coal Preparation Plants" to determine the status of instrumentation and automation systems in the coal preparation industry. EPRI concluded that the control systems presently being employed in the US coal preparation plants "are relatively primitive compared with those in other mineral processing industries; and analytical instrumentation is virtually non-existent." With tighter specifications on the quality of steam coal, interest is increasing in more sophisticated control systems. One type of device that is currently assisting the preparation plant operator optimize and control the coal cleaning process is nuclear based instrumentation. Nuclear instrumentation includes methods for measuring weight, level, and density as well as for performing elemental analysis on coal. Major Features and Benefits of Nuclear Measurement and Analysis Systems There are many features and benefits of nuclear instrumentation. The major benefit is that nuclear instrumentation is non-contacting. The measuring heads do not contact the process materials. This enables measurements of corrosive, abrasive, or high temperature materials with no loss of performance, reliability, or useful life. Also, there are no moving parts to wear or be fouled by dust or corrosion. Installation is simple and inexpensive. For instance, density gauges are simply clamped onto existing pipe runs. Weigh scales and level switches usually require nothing more than welding brackets to customers' equipment. Once installed, routine maintenance can be performed without interrupting the process. Thus, nuclear instrumentation is highly reliable and easily installed and maintained. The operating life of the instrumentation is virtually unlimited. Principle of Operation Nuclear belt weigh scales, point level switches and density gauges all operate on the gamma-ray transmission principle. A beam of gamma radiation from a radioisotopic source is projected through the process material either on a belt, in a vessel, or in a pipe. Opposite the source is a radiation detector whose electrical output is proportional to the intensity of the radiation it absorbs. Gamma radiation is part of the same electromagnetic spectrum that encompasses light, infrared, and x-rays. In many respects, gamma radiation behaves much like light. However, it is far more penetrating and can be transmitted through considerable thickness of materials that are opaque to visible light, e.g., several inches of steel. Types of Nuclear Instrumentation in Coal Preparation Plants There are four types of nuclear instrumentation presently being employed in coal preparation plants. They are: •Belt Weigh Scales •Point Level Switches •Density Gauges •Coal Analysis Equipment. Each type of instrumentation has a number of potential applications within the plant. What follows is a discussion of three different types of devices and their applications. Weigh Scales In coal preparation plants, weighing instruments are used for measuring material throughput, totalized weight, and batch weight on conveyor belts and other transport equipment. They are also used on drag chain conveyors, vibrating conveyors, and screw conveyors. Weighing is important for receiving the run-of-mine coal, controlling mass flow, scheduling production, and loading and shipping the washed coal to market. There are two basic types of weighing instruments: gravimetric and nongravimetric devices. Gravimetric devices are units which measure the pull of gravity on the material being weighed. Nongravimetric devices are not dependent on the force of gravity on the sample. Nuclear weigh scales are the most prevalent nongravimetric devices used. The nuclear weigh scale works on the same basic principle as other nuclear gauges. The greater the quantity of material placed in the path of a radiation beam, the more radiation will be absorbed by the material. In weigh scales, Cesium 137 source is generally placed above the moving stream of material so that the radiation is directed through the material. An ion chamber radiation detector is on the opposite side of the material. The radiation passing to the detector generates a signal which is inversely proportional to the weight of the material present. This signal is amplified and integrated with the speed of the process flow yielding the weight. The weight is indicated and can be totalized for throughput, batch control, etc. In conclusion, radiation weighing methods have become well established in the coal preparation industry throughout the world. As mentioned before, this device finds its most

Jan 1, 1985

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By M. G. Benz, J. F. Elliott

The austenite solidus of the iron-carbon system has been determined using a series of diffusion couples, each of which consisted of a specimen of austenite held in contact with a melt saturated with austenite. After the equilibrium distribution of carbon had been established by diffusion at a specified temperature, i.e. the austenite specimen had become austenite of the solidus conzposition, the diffusion couple was cooled, sectioned and anazlyzed for carbon. The solidus was found to be a straight line: A revised iron-carbon temperature-composition diagram is presented, COMPOSITION has a marked effect on the temperature at which austenite begins to melt and the austenite solidus of the iron-carbon system describing this effect has been the subject of many investigations.1-10 The significant results of these investigations are presented in Fig. 1. The experimental methods and purity of the materials used in them are summarized in Table I. In plotting the data in Fig. 1 no attempt has been made to convert these results to the International Temperature Scale of 1948," except for the data of Adcock,5 as this conversion would do little to reduce the uncertainty that exists as to the position and shape of the solidus. A point of major concern in evaluating these data is that the alloys studied, except those used by Adcock, were not binary alloys of iron and carbon, Table I. Also, it would appear that several of the methods did not permit equilibrium to be established through the system being studied. All that can be said for the results of these investigations is that they indicate only approximately the location of the solidus with the uncertainty as to its location at 1 pct C being approximately 100°C. The current investigation was undertaken to provide reliable data by which the austenite solidus could be established. It was hoped that information on the liquidus also could be developed at the same time, but experimental limitations prevented this as austenite segregated from the liquid on cooling. After a careful study of possible experimental methods and extensive laboratory tests, it was decided that the use of a series of austenite-liquid diffusion couples would provide the most reliable results. This paper describes the method and its results and also includes a complete iron-carbon temperature-composition diagram based on what are considered to be the best available data. EXPERTMENTAL METHOD The diffusion couple used for this investigation consisted of a small cylindrical pellet of austenite held in contact, at a specified temperature, with a melt saturated with austenite. The composition of the cylindrical austenite pellet was chosen to be approximately 0.1 wt pct C less than the estimated

Jan 1, 1962

By W. D. Kruger

Methods for analyzing flooding or cycling projects by means of two-dimensional flow calculations are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The accuracy of such analyses depends on the basic reservoir data employed, especially the absolute permeability distribution in the reservoir; however, absolute permeability data normally are determined from well flow tests and/or core measurements and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. A calculation procedure is presented for determining the areal permeability distribution in the reservoir. Use of the procedure allows verification of the basic reservoir data through the matching of past reservoir conditions, thereby providing proper data for reliable predictions of future operations. The calculation procedure is a numerical technique based on a mathematical model of the reservoir and is designed for solution by means of an electronic digital computer. Results from field application of this procedure are presented. Permeability distributions from measured data are compared to those calculated to indicate the need for the analysis. Comparisons of field-measured and calculated pressure distributions are given to establish the validity of the calculation procedure. The conclusions of this paper are (I) use of the calculation provides data that allow a match of past reservoir conditions and thus reliable prediction of future operations; and (2) the procedure should, where applicable, be used to provide adequate reservoir data for use in two-dimensional flow calculations and related reservoir analyses. INTRODUCTION One means of providing more precise engineering control over reservoir operations during all stages of depletion is to develop some type of model to simulate the reservoir, using information developed from the behavior of the prototype to predict the performance of the actual reservoir. The use of mathematical rather than physical models for this purpose has been gaining in importance recently because of the application and availability of electronic computers. Mathematical models avoid instrumentation difficulties and allow easier handling of large-scale problems. At present, analyses employing two-dimensional models are common, and thought is being given to the use of models in three dimensions. The use of multi-dimensional models is necessary to show not only what is occurring in the reservoir, but also where in the reservoir the phenomena of interest are taking place. Methods for analyzing flooding or cycling projects by means of two-dimensional numerical models are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The applicability of numerical models and the results of using such analyses have been presented through field examples. The references indicated here discuss fully the data necessary to build the mathematical reservoir model and the way the model is used to study or predict the future performance of the reservoir. The accuracy of the analysis of such projects depends on the basic reservoir data employed in the construction of. the model. In order to be sure the model represents the reservoir, it must be used to match some known set of reservoir conditions, i.e., to match past reservoir performance. The accuracy of the model is directly dependent upon the absolute permeability distribution in the reservoir; however, absolute permeability data are normally determined from well flow tests and/or core measurements, and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. There is always the need for better data and for verification of existing data. The purpose of this paper is to show the use of the mathematical model to match past performance in flooding or cycling projects, the use of numerical techniques to adjust the basic absolute permeability data if necessary so that a match is obtained, and in this way to generate the effective areal permeability distribution of the reservoir. A review of the basic concepts of the numerical model will be given, followed by a discussion of the data-adjusting technique for matching past performance. TWO field examples will be cited to show