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By Duk-Won Park

The PSU/MVS program, one of the computer programs for ventilation network analysis most recently developed at The Pennsylvania State University, was applied to the analysis of modifications to an existing ventilation system for a coal mine located in southern West Virginia. The program is well designed and has diversified capabilities which allow the users to make decisions on the optimum size and number of fans, the location and number of airshafts, and the optimum operational procedures. The mine had 10 working faces, from which the average production rate was about 5900 tons of clean coal per day. Two vane-axial mine fans were used in parallel at a shaft, and both of them operated simultaneously. One additional shaft was in the final construction stage and it would be used in four months to alleviate the load for the existing fans and distribute intake air more evenly. The overall ventilation surveys, including the altimeter pressure survey and the air quantity survey, were carried out in the mine entries, shafts, slopes, and gob areas. Computations were made using the above-mentioned computer program on the present condition and after one additional fan was placed in operation at the new shaft. Also, recommendations were made on the air route and fan blade settings for the most economical and efficient ventilation system. Further studies were carried out to decide the proper period when the third air shaft would be required according to the long-term mining plan. Additional branches were added for the next 4 years of the production plan, and the ventilation conditions were tested at the end of each year. Numerous combinations of blade settings and modifications of air routes were tested. It was recommended that the third air shaft be added at the end of the third year so as not to experience fan stall.

Jan 1, 1982

By Noel W. Kirshenbaum, George A. Pouska, James M. Link

Literally millions of words have been written on the subject of mineral slurry pipelining. The sheer bulk of literature on the subject should be enough to convince the interested observer that the method is both viable and widely applied. It is the intent of this paper to examine typical mineral slurry applications. This examination should reveal the reasons that the slurry system was selected over other transport modes and it should provide a framework for determining the applicability of the technique to new projects. Slurry transport involves the conveyance of solid particles by suspension in a moving liquid. Almost any combination of solids in liquids may be imagined, and the conduit may be an open channel or a closed pipe. Historically, the most numerous slurry transport applications consisted of mineral particles in water. However, current research investigations are emphasizing other liquid carriers, specifically those which have greater economic value. Among these are gaseous and liquid fuels and chemical feedstocks. Another area being investigated involves the use of the pipeline as a chemical reactor system. The long residence time and turbulent flow characteristics of the pipeline make it particularly attractive for certain chemical reactions. Because these new systems involve a valuable liquid as well as a valuable solid, there is increased attention to solid-liquid

Jan 1, 1980

By J. K. Furst

The reasons for manufacturing steel by the deplex process are, briefly…

Jan 1, 1915

By Audley H. Snow

The general drift of the discussion as to the relative merits of pressure- and exhaust-fans has resulted, if we may judge from the prevailing practice, largely in favor of the latter. The subject has been hitherto treated, however, with special reference to highly gaseous mines, the effect of the form of ventilation upon dust-explosions having been too little considered. Even in mines containing practically no gas, dust-explosions may occur; and if, as I believe, pressure-fans are to be preferred for their effect upon dust, it may be worth while to reopen the debate, and to challenge the advisability of exhaust-ventilation under certain conditions. There are several forms of colliery-ventilation, which may be described as follows: Plain or simple pressure-ventilation, in which the fan acts as a pressure-fan, and the movement of coal is unobstructed at the surface by doors or equivalent devices in drifts or shafts, the traveling and haulage. thus being in the return-current. Plain exhaust-ventilation, in which the fan acts as an exhaust-fan, the movement of coal being likewise unobstructed at the surface, and the traveling and haulage being in the intake.

Jan 1, 1910

AS I told you in the chapter on salts, saltpeter is a mixture composed of many substances extracted with fire- and water from arid and manurial soils, from that growth which exudes from new walls or from that loosened soil that is found in tombs or uninhabited caves where the rain cannot enter. It is my belief that it is engendered in these soils from an airy moisture that is drunk in and absorbed by the earthy dryness. Considering its effects, I do not know how to decide and say exactly what the nature of saltpeter is. The learned and very wise physicians find it salty and with a subtle sharpness both in taste and in their medical experiments. Considering its strong biting qualities, they decide to say that it is of a hot and dry nature; on the other hand when they see that it is engendered from the air and that when touched by fire it becomes inflammable and vaporous, and rises with a fearful impetus when mixed in powder for military guns, it manifestly shows itself to be of a hot and moist airy nature. And then when they see that it is shining and transparent with whiteness and is fusible in every fire in a manner corresponding to a thing of a watery nature, and since it. is heavy, it seems that it can be said to be watery in nature. To this is added the experience of touch and of the great cooling action which it has on water in summertime when wine is to be cooled, and since it crushes and breaks with but little pressure, it might be thought to be earthy in nature; especially when it is seen to change into a hard, white stone when burned with an equal amount of sulphur. Thus it seems that every one of the elemental qualities is predominant in it. Now the ancients called this, or a similar thing, nitrum. [150] Pliny, in Book XXXI of his Natural History, has said that it was a thing not much different from salt, that doctors do not seem to have yet known its nature, that it is found in various places, and that the best is found in Macedonia. But among the moderns and especially in our regions, it is not known today what it is that Pliny and other writers refer -to, since according to the aforesaid Pliny and other ancient writers it is a natural mineral. Some say that in place of, the natural kind the artificial will serve for the same medicinal purposes, since it has the same nature and is perhaps more powerful.

Jan 1, 1942

By P. Hazebroek, M. Prats, E. E. Allen

Well locations in water floods frequently do not coincide with the ideal well locations associated with the flood pattern which is used. A question of importance is. "How much oil is lost because of this?". This is the problem treated in this paper. It is assumed that each pattern in a five-spot flood has the proper number of production and injection wells but that the wells may be off-pattern. The distance by which a well is off-patern is given in terms of the pattern spacing, defined as the length of one side of a five-spot. The influence of off-pattern wells on the performance of a five-spot flood has been investigated mathematically for unit mobility ratio. All production and injection rates are assumed to remain equal. The loss in recovery resulting from pattern irregularitie: has been calculated at a cumulative water injection corresponding to a 98 per cent water-cut in a regular five-spot. Displacing a single production or injection well by about one-third the pattern distance reduces the total field recovery by 4.4/N per cent of the recovery obtainable with regular spacing, where N is the number of five-spots in the flood (assumed large). When off-pattern wells are separated by at least one regular five-spot and are displaced by less than one-third the pattern distance, the total loss in recovery in a large-scale flood is, at most, 1 per cent of the recovery obtainable from that field with a regular five-spot pattern. However, much higher losses may occur if the off-pattern wells are not separated by a regular five-spot, if the rates are imbalanced, or if the mobility of the injected water is higher than that of the crude. Although the loss in oil recovery due to pattern irregularity often may be low, the off-pattern case will always require injection of more water to reach the same final water-cut. The volume of water injected per unit volume of oil displaced has been calculated for each five-spot adjacent to a five-spot containing a single 08-pattern well. The cumulative water injection at the time of 98 per cent water-cut may be increased by as much as 37 per cent when a production well is displaced one-third the pattern distance toward an injection well. The existence of differences between actual subsurface locations and the idealized well patterns used in secondary recovery operations is well recognized. However, the methods commonly used for predicting waterflood behavior ignore such differences, even when subsurface locations are known. The reason for this is simple. The idealized well patterns are highly symmetrical and, as such, the production history of the pattern (and even of the field) can be determined from that of a few production wells—usually from only one. Consideration of the many irregular well spacings found in a specific field would entail a large amount of work, and then the results would be applicable only to that specific field. In an attempt to provide an answer to the more general problem, this paper considers a water flood having an idealized well pattern, except for one well which is not at its regular location. When several off-pattern wells are present, their contributions are assumed to be additive unless the off-pattern wells are close to each other. Only four positions of the off-center well (at x, y. of Fig. 1) are considered in this paper. These are shown

Jan 7, 1950

By W. Tovote

THIS paper is based upon 12 years' experience in the Southwest, including three years that were spent in constant traveling as examining engineer for the Phelps-Dodge Corporation. The material was gathered during rather extensive work in Bisbee, Clifton-Morenci, Globe, and Tombstone, and also on short and rapid trips into most of the mining camps and prospect fields of New Mexico, Arizona, the desert country of California, and as much of Sonora as was safe at the time. My methods of observation and my deductions are not put forward as new or scientific; they are simply rough field methods, based upon short notes, rough sketches, and largely upon memory, which I have found useful for coordinating geological data for the purpose of passing quick judgment on mining possibilities in certain districts exhibiting uniform characteristics. The opportunities for observation have been better these last few years than ever before, clue to the unprecedented activity in mining, which has caused the reopening of hundreds of old mines and the starting of even more numerous prospects all over the mining States. POSSIBLE SYSTEMS OF CLASSIFICATION By Geological Provinces There are a number of well defined geological provinces in the territory under discussion, and a study of their individual features is of interest. The following are a few of those that axe most striking in their uniformity. 1. The "Desert province," extending roughly from. Wickenburg, Ariz., to and beyond Barstow, Cal. In its north-south extent it reaches up to the Colorado River and clown into Sonora, but overlaps other provinces. It is characterized by a worn-down basement of schistose and granitic rocks, on which rest remnants of Paleozoic and pre-Paleozoic sediments, including very old limestones. The sediments are disrupted and contorted. Alteration in the mineralized areas is very prominent, especially in the schists and limestones. Cenozoic volcanic rocks, principally of semi-basic composition, have been intruded into this complex and sometimes cover it as lava flows.

Jan 10, 1918

By C. A. Pierce

STUDIES of roof and floor movement are of interest to those actively engaged in mining. This is especially true in the case of an entirely new area where there is no precedent for guidance. The potash deposit being mined is in the southeast corner of New Mexico, about 20 miles east of Carlsbad. The deposit was formed by the land-locked, shallow, Permian Sea that extended through parts of western Texas, Oklahoma, Kansas, southeastern Colorado, and eastern New Mexico. The saline deposits vary from 500 to 4000 ft. thick. Neither of the companies operating in this area has delimited its com-mercial ore bodies. As all production so far has been from Federal and State leases, the Department of the Interior and the State of New Mexico have a direct interest in the development and extraction of these ore horizons. The ore is composed of an intimate mechanical mixture of sylvite (potassium chloride) and halite (sodium chloride). It lies generally in a horizontal bed varying from 5 to 12 ft. in thickness, and has a cover of approximately 1000 ft., consisting of about 500 ft. of salt beds and 500 ft, of sediments. The immediate mine roof for several feet is principally salt with some potash and clayey material. The next 500 ft. above, from the standpoint of structure, may be considered rock salt with a few inter-bedded potash members. The upper 500 ft. is of sedimentary (Permian and Triassic) origin and contains several water-bearing formations with flows varying from 10 to 500 gal. per minute. This water intensifies the interest in convergence problems as the ore and surrounding for-mations are water soluble. Potash salt (sylvite) and rock salt (halite) are plastic minerals. Plasticity is defined as a "property of solids by virtue of which they hold their shape permanently under the action of small shearing stresses but are readily deformed, worked, or molded under larger stresses."1

Jan 1, 1938

By S. C. Lindsay, D. J. I. Evans

With each year that passes hydrometallurgical processes are being more widely used to recover base metals from ores and concentrates. Generally these processes involve liquid-solid separation of metal-bearing liquors from barren residues. This may be done by countercurrent decantation, thickening and filtration, or filtration or centrifuging only. Choice of method is governed by chemical and physical characteristics of the pulps; cost of labor, power, materials, and waste disposal; and even by the amount of capital available when building plans are under way. Since all these controlling factors change with time and location and with technological advances, the separation method must be re-evaluated when new plants or expansion programs are contemplated. At the Sherritt Gordon refinery in Fort Saskatchewan, Alberta, an ammonia pressure leaching process recovers nickel, copper, and cobalt from the nickel concentrate produced at Lynn Lake, Manitoba.' Pregnant liquors are separated from the barren leach residues in a thickener-filter liquid-solids circuit. The decision to use this type of separation was based on a summation of economic factors during the pilot plant and design stages. Although countercurrent decantation was not incorporated in the refinery flowsheet, the problems solved in thickening the leach residues and the experience gained in operating the commercial plant are pertinent to countercurrent decantation, particularly where it is applied to slow-settling leach slurries or slurries having a relatively high vapor pressure of a valuable, obnoxious, or poisonous vapor.

Jan 1, 1960

By Gregory Comstock

THERE is a growing interest in the possibilities presented by the manipulation of metal powders, which justifies an attempt to summarize their character and potential value. A summary of this kind presents an opportunity for making a classification of metal powder products into several general types. Our present knowledge of the finer and more abstract aspects of many of the principles involved in metal powder technique is extremely limited. Any conclusions as to the ultimate value of the process will, therefore, for the present at least, be of doubtful value unless they are substantiated by its products. The number of such products is increas-ing. A study of their diverse and unusual characteristics; an examination of the methods by which they ale made, and a consideration of the reactions that take place during their fabrication, in so far as we can define them, should afford as good an evaluation of this interesting development as it is possible to make at this time. A critical study of this kind results in a formidable list of special attributes, which apparently are characteristic of applied powder metal-lurgy. A comparison of these special effects with the end products and well defined limitations of the melting and casting process indicate that often they may very well be considered as being special advantages. They are subject, of course, to certain not as yet so well defined limita-tions of their own. Based on current products only, a necessarily con-densed summary of the more striking special attributes of the metal powder process follows.

Jan 1, 1938

By Charles Sanford, William B. Schmidt, Eugene Moroni, John Murphy, Richard Bullock

An industry/government team sponsored by the Dept. of the Interior completed a study tour of the underground coal mining industries in Great Britain and Germany to review new and emerging coal mining technology. The group found that differences in tradition, mining conditions, and industry capabilities have led to different approaches in technological developments, many of which have the potential for application in U. S. mining. Both countries are working to improve materials and procedures for roadside pack wall. The British are developing a pump-packing system in which bentonite, water, stone, and a special cement are pipelined to the pack area to form a low strength compressible pack wall. The German industry is using anhydrite or blotzdammer to form a high strength pack wall. Both countries are using full-face tunnel-boring machines. The German industry has had considerable success with shield-type longwall supports.

Jan 1, 1977

By George Watkin Evans

During the past ten or twelve years, the average reader of newspaper and magazine articles has been led to believe that enormous deposits of high-grade coal exist in the northland and that these can be mined for practically nothing. But much of the reputed glitter and attractiveness of Alaskan coals disappears when viewed at close range. Many areas of coal-bearing rocks are widely distributed geographically from Cape Lisburne, on Bering Sea, to Admiralty Island, south of Juneau. Bituminous coal is found at Cape Lisburne, on the Bering Sea, at Five Finger Rapids on the upper Yukon, and at Herendeen Bay and Chignik Bay; lignite is found on the Kobuck River, along the Yukon River from points near the mouth to Tonakat, near Rampart, at Dawson, on the east shore of Cook Inlet, and in the Tanana Valley, 50 mi. south of Nenana. The Susitna and Matanuska Valleys contain coal ranging from lignite to anthracite, and in the Bering Lake district, there are coals ranging from semi-bituminous to anthracite. No effort will be made to describe all of these fields, but the writer will confine himself to the four principal fields, namely, the Nenana field! in the interior of Alaska, tributary to the Fairbanks district; the Matanuska field, in the Matanuska Valley; the Kachemak Bay field on the east shore of Cook Inlet; and the Bering River field, east of the mouth of Copper River. Nenana Coal Field The Nenana field occupies an area east of the Nenana River 70 mi. (112 km.) southwest of Fairbanks and approximately 50 mi, from the town of Nenana, which is located at the junction of the Alaskan Railway and the Tanana River. It is on the northern flank of the Alaskan Range and occurs within the foothills of that district. The elevations range from 1000 to 4000 ft. (304 to 1219 m.). Future developments may prove the field to extend from a considerable distance west of the Nenana River to the headwaters of the Tanana River. The coal measures are of Tertiary age and are probably Eocene. They are not badly deformed by folding, but portions of the field show

Jan 1, 1922

By W. G. Matteson

In 1915, the State of California passed a law of great scope and importance. This law has been in successful operation for a year and may be briefly described as an act " establishing and creating a department of the State Mining Bureau for the protection of the natural resources of petroleum and gas from waste and destrucbion through improper operations in production; providing for the inspection of petroleum and gas wells; requiring all persons operating petroleum and gas wells to make certain reports" and providing the necessary officers and assessments to carry out the provisions of the act. The statute provides for a separate department of the State Mining Bureau, under the general supervision of the State mineralogist, with a staff composed of a "state oil and gas supervisor" and four deputies. It rules that all petroleum and natural gas wells shall be drilled, operated or abandoned under the supervision of the State supervisor, who shall order such tests or remedial work as seems to him necessary to protect the interests of property owners and the general public. It also provides for a board of arbitration to consider orders given by the supervisor which are not acceptable to the well owner. Section 18 of the act, which is the provision that is directly related to this paper, requires ('the owner of any well referred to in this act to keep a careful and accurate log of the drilling of such well," and further requires that this log shall show the character and depth of the formations passed through or encountered in the drilling, particularly the location and depth of the water-bearing strata; the character of the water encountered (so far as ascertained); whether the water was shut off, and, if solat what point; that it shall show completely the amounts, kinds and size of casing used; the depth at which oil-bearing strata are encountered; the depth and character of the strata, and whether all water was successfully and permanently shut off so as to prevent percolation or penetration into the oil-bearing strata. This log is to be kept in the local office of the owner or operator, subject to the inspection of the supervisor or any of his deputies at any

Jan 1, 1917

By S. J. Hardison

IN the fall of 1912, the appearance of water in the oil of the Nevada Petroleum Co., Coalinga, Cal., made necessary the installation of a dehydrating plant to reduce the water below the 3 per cent. limit prescribed by the agency. Unlike the mining industry, technical literature of the oil industry is limited and extremely unsatisfactory. Until the recent efforts of the Petroleum and Gas Committee of the American Institute of Mining Engineers, no concerted movement has been instituted to secure publication of papers dealing with the problems of the oil business, and because of the additional fact that dehydrating of oil has not been practiced in California to any extent up to comparatively recent time, it was found necessary to experiment in order to determine the most satisfactory plan for this purpose. It is easy to write regarding successful enterprises, but, while not so pleasant, it is equally desirable to write of failures so that others may be saved the loss incident to such investments. The water in this oil occurs both free and as an emulsion. Free water easily settles out, but the emulsion requires treatment. So far as can be determined, the emulsion consists of globules of water surrounded and enveloped by a film of, oil. Starting with this hypothesis, the theory has been evolved that in order to break up this emulsion the water must be heated at least to boiling point, when an explosion takes place destroying the globule. Unfortunately, this condition was not recognized in the installation of the first plant, which was planned on the following lines: A heater was arranged so that all the oil from the wells could be heated before reaching the shipping tanks, these being already fitted with coils for steam heating. Tanks were filled with about 4 ft. of water, live steam was turned into the coils and the water brought nearly to the boiling point, when the heated oil was run in. This for a time was partly successful, but the length of time necessary to apply this heat was too great for practical operating.

Jan 3, 1915

By Leroy Gardner

EVERY reader of this paper is well aware of the fact that the prolonged inhalation of large amounts of free silica dust results in fibrosis of the lungs, and that other inorganic dusts, except those of asbestos and the mineral poisons, are thought to be relatively harmless. But probably few have had opportunity to visualize the effects of silica, asbestos and other minerals upon living tissues. The ideal demonstration would be based upon sections of lungs from human beings that had inhaled com-parable concentrations of different dusts for a unit period of time. Such material is generally difficult to obtain and in some instances is of ques-tionable value because the subject has been exposed to more than one kind of dust. A demonstration could be prepared from the lungs of animals. However, so many months or even years are required to com-plete the exposure to each kind of dust that enough material has not been accumulated. For a general survey of the action of different types of dust, I am therefore compelled to use the tissues of animals that have been injected with suspensions of dust particles. The injection method offers certain advantages. The quantity, the particle size and the state of dispersion can be controlled with sufficient accuracy so that the tissue responses to different minerals can be accu-rately compared. The method insures contact between the tissues and the mineral particles; protective mechanisms, which may prevent the inhalation of certain types of foreign body, never come into play. If the pathway of injection be one that minimizes nonspecific injury, the tissue responses may simulate those produced by inhalation but they develop somewhat more rapidly. It should always be remembered that injection methods merely demonstrate the capacity of various kinds of minerals to provoke reaction in the tissues; whether the same substances are inhaled from atmospheric suspension and accumulate in the lungs in dangerous quantities can be demonstrated only by inhalation.

Jan 1, 1938

By Emery C. Olsen

Most coal mining areas of the Western United States are characterized either by thick beds, steep pitches or heavy cover. Individually, each of these may present inherent safety hazards that influence mining. When all are met at one location, the combined effect is to make the safe operation of the mining property a challenge to management. These combined conditions are met in the coal mines of the Columbia-Geneva Steel Div. of the United States Steel Corp., in southeastern Utah. This coal bed measures up to 16 ft in thickness, the pitch is as much as 25 % and mining is under a cover approaching 3000 ft. The Sunnyside coal bed is found in the Book Cliff Mountains, a great escarpment extending from west of Castle Gate, Utah, some 180 miles to Grand Junction, Colo. West of Green River, Utah, the Book Cliffs swing sharply to the north because of the domelike uplift of the San Rafael Swell to the south- west. It is in this northerly extension of the Book Cliffs that the Sunnyside coal in the Blackhawk Formation of the Mesa Verde Group, Upper Cretaceous Age is found. The strata are transected by numerous faults with from a few inches to as much as a hundred feet of displacement. All of these faults have had some effect on the mining operation, either in roof control or, in the case of major faulting, the pattern of mine development.

Jan 10, 1963

By Michel Daghert, Michel David

In the exploitation of large porphyry type deposits where a cut-off has to be applied and where "internal waste" exists, planning people ask the geologist for the estimated grade of small blocks. Comparison with actual production figures and blast hole assays shows that any kind of weighted average of neighboring DDH (diamond drill hole) samples provides an excessingly smooth picture of reality, resulting most of the time in overevaluation of tons of ore. Solutions based on examination of Past production data exist14 but it would be necessary to have a solution which can be applied before production starts as the preceeding problem also results in an overestimation of the total reserves, often by as much as 20%, thus changing the mine life accordingly and destroying any "optimum planning" which could have been done. The proposed alternative is to forecast the grade distribution of small blocks in a larger block, sufficiently well documented. Several Possible ways to estimate these distributions are reviewed and emphasis is placed on recently developed methods (source G. Matheron) where the coefficients of the orthogonal polynomial series expansion of the distribution of any size of block are directly estimated by kriging. The efficiency of the technique is tested on a level of the Cyprus Pima open pit where the predicted recovery is compared to actual production figures.

Jan 1, 1980

By G. L. Chierici

Starting from Muskat's theory of water and gas coning, maximum permissible oil production rates without water and/or free-gas production have been determined, in a broad range of reservoir and well parameters, using the potentiometric model technique. The main assumptions made are as follows: (1) the reservoir rock is homogeneeous (either isotropic or anisotropic); (2) the volume of the aquifer underlying the oil zone is very small, so that it does not contribute to reservoir energy; and (3) the gas cap expands at a very low rate, so that it can be assumed to be in quasi-static conditions. The results obtained are presented in the form of diagrams which can be used for solving two types of problems: (1) given the reservoir and fluids characteristics, as well as the position and length of the perforated interval, determine the maximum oil production rate without water and/or free-gas production; and (2) given the reservoir and fluids characteristics only, determine the position and length of the perforated interval which optimize the maximum permissible oil production rate, without water and/or free-gas production. INTRODUCTION In oil reservoirs where the oil-bearing formation is underlain by an aquifer which does not participate in the production mechanism, water-coning is a limiting factor to the flow rates of producing wells. Production rates are usually kept to a value that will prevent the water from entering the wells. The entry of water into a well lowers its productivity by increasing the weigbt of the fluid column; moreover, the separation of water from the effluent, at the surface, may constitute a very difficult problem in cases of heavy viscous oils. A similar situation is encountered in oil reservoirs with a gas cap overlying the oil-saturated zone; here a downward gas cone is induced by the flow of oil towards the producing wells. Production rates must be low enough to prevent the gas from being produced; producing gas from the gas cap would be a waste of energy. Of course, water-coning and gas-coning phenomena can occur at the same time in the same reservoir if the oil-producing formation is both overlain by a gas zone and underlain by a water zone. Due to its relevant practical importance, the mechanism of coning was studied by many people.2,3,5-8 Defining the conditions for getting the maximum water-free and/or gas-free oil production rate is a difficult problem, often encountered under one of the following aspects: 1. Predict the maximum flow rate that can be assigned to a completed well without the simultaneous production of water and/or free-gas. 2. Define the optimum length and position of the interval to be perforated in a well, in order to obtain the maximum water and gas-free production rate. A systematic study of these problems was made by means of the electrical analog technique. The results of this study are presented here, under the form of a set of curves providing solutions for the above stated problems. These curves are valid only for homogeneous forrnations, either isotropic or anisotropic. Should the formation be non-homogeneous (by horizontal or vertical variation of permeability, shale diaphragms, fractures, etc.), a specific potentiometric study would be required for each specific case. Especially when shale diaphragms of some radial extension are present, the critical rates observed are much larger than would be expected from the diagrams. STATEMENT OF THE PROBLEM In the present study the aquifer is supposed to be of such limited volume that it does not contribute to the energy of the reservoir. Moreover, the gas cap is supposed to expand at such a low rate that the potential gradient in the gas cap is negligible. Under static conditions water-oil and gas-oil interfaces (T1 and T2) are both horizontal. When the reservoir production starts, below each well these interfaces take a cone-like shape (Fig. 1) having as an axis the axis of the well. This shape results from the equilibrium between potential gradients in the oil zone and gravitational forces due to density differences between oil and water and between oil and gas. Assuming the oil-bearing formation to be homogeneous and the oil to be incompressible, the analysis of the problem (see Appendix) shows that the oil-water and gas-oil interfaces are stable only if the oil production rate of the well is not higher than the following values.

Jan 1, 1965

By L. A. Rapoport, W. J. Leas

The original Burkley-Leverett theory has been extended and a more detailed formulation of the waterflood behavior in linear horizontal systems is presented. Particular consideration has been given to the evaluation of capillary pressure effects and differential equations permitting an explicit evaluation of these effects have been derived. On the basis of the developed theory it is recognized that the flooding behavior is dependent upon the length of the system and the rate of injection. At the same time it has been determined that systems of different lengths yield the same flooding behavior if the injection rates and or the fluid viscosities are properly adjrrsted or "scaled." It has also been found that the sensitivity of the flooding behavior with respect to rate and length decreases as any one of these {actors increases in value and that for sufficiently long systems and high rate.; of water injection the flooding behavior becomes independent of rate and length. or "stabilized." To such stabilized conditions the theory formulated by Buckley and Leverett is applicable. A number of laboratory flooding tests have been made and good agreement Iraq been found between theory and experimental observations. The experimental results are discussed and it is shown that under field conditions the flooding behavior is usually stabilized. As a result of these finding; a procedure is indicated for evaluating field performances either on the basis of tests performed with commonly available core samples or by means of calculations using relative permeability data INTRODUCTION In recent years the development of methods for evaluating oil recovery by waterflooding has been the object of considerable research. A theoretical analysis of the mechanisms involved in the displacement of immiscible fluids was originally established by Buckle!- and Leverettl and experimental investipatio~~s have been made by numerons workers." Many of the experimental results are in mutual agreement and bear out several significant features of the flooding mechanism as predicted by theory. Thus it lias been generally recognized that a flood corresponds to the movement of a steep saturation hank or "front" (primary phase), followed by additional gradual oil displacement (subordinate phase). It has also been found that for any porous medium the flooding behavior is largely dependent upon the oil-water viscosity ratio and that for increasing values of this ratio the relative importance of the primary displacement phase decreases while that of the subordinate phase becomes more pronounced. Although the studies to date have clarified certain aspects of the flooding process. they have given rise to observations of a somewhat contradictory nature that cannot he explained in terms of the original theory. These observations pertain mainly to the effect of injection rate or pressure gradient upon recovery. Some investigators report laboratory tests that indicate incresing oil recoverieq with increasing rates of water injectill, others find the flooding behavior to be independent of and other. mention lower oil recoveries with increased injection rates.3 The conflicting evidence indicated above creates considerable uncertainty with respect to laboratory testing procedures and the utilization of the resulting data for field evaluations. The principal purpose of this paper, then, is to resolve these Uncertainties by means of a comprehensive theoretical and experimental investigation of the flooding meanism. THEORETICAL DEVELOPMENT Derivation of Flooding Equations The mathematical description of transient flow phenomena is based upon the consideration of the various processes occurring during an infinitesimal time interval in an infinitesimal volume element and upon the correlation of these processes with those occurring in the adjacent elements. The volume elements are defined as being infinitesimal in comparison to the overall dimensions of the porous system, yet each sufficiently large so aS to encompass the full range of pore openings encountered throughout the system. If a porous system can arbitrarily be subdivided into an infinite number of volume elements all possessing the same distribution of pore openings and if this distribution is unformly continuous. the system may be said to be homogeneous. Such a homogeneous porous medium is considered in the present studivs. It is furthermore postulatecl that only oil and water are present in the pornu wediu. that they act a- totally incompressible and immiscible fluids. and that gravity effects are negligible. In n linear flow system of unit cross sertional area. as treated here. the infinitesimal volume element.; to he considered are cylindrical ".slices" of thickness dx. oriented perpendicularly to the direction of flow. The equations applicable to any such volume element. at my time. describe the movement. of oil and water across the element:

Jan 1, 1953