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By Norbert R. Morgenstern

INTRODUCTION An understanding of the role of water in controlling the stability of rock masses is central for a rational approach to the subject. The presence of water can hinder mining opera- tions in two ways: 1. excessive discharge 2. excessive pressure It should be noted that if the rock mass is very tight, excessive pressures can exist without large discharges. Alternatively, if abundant water is available and the rock mass is open, then substantial discharges can occur under quite small pressures. The problems associated with excessive discharge are usually well understood by the mining engineer. Vehicle mobility is inhibited, some areas are flooded and hence become inaccessible; at best, a costly nuisance exists. The methods of solving these problems are also well-known to mining engineers. They generally involve tapping the source of the excessive discharge and channeling it away in such a manner that any hindrance to the mining operation is minimized. The effects of water pressure on the stability of rock masses are less obvious and the following will be devoted solely to this aspect of the problem. The manner in which water pressures enter into the consideration of stability is made clear by an understanding of the concept of effective stress. THE CONCEPT OF EFFECTIVE STRESS The simplest mechanical model for the problem of rock slope stability consists of a rough, rigid block sliding down an inclined plane under the influence of gravity. This is illustrated in [Fig. 1]. The down-slope component of the weight of the block tends to produce movement which is resisted by the shearing force generated by friction along the base of the block. The shear stress per unit area inducing movement is

Jan 1, 1971

By H. V. W. Donohoo

Exploration in 1955 was marked by a trend toward large-scale programs using a number of geophysical techniques. These programs were initiated both to locate new mineral districts and to bring individual prospects into production. All 14 companies replying to the author's questionnaire include geophysics in the general exploration routine whenever it is applicable, and five companies carry on extensive geophysical programs. Nearly all report that company personnel perform the surveys. In addition to these firms there are the many smaller operators who contract much of their geophysical work. There are indications that the volume of such contracting is sizable.

Feb 1, 1956

WHEN Georgius Agricola, in 155o, dedicated his now famous De re Metallica to the rulers of Saxony, Thuringia, Meissen, and other, smaller principalities, he included in his review of previous works on similar subjects reference to two books written in German: one, an "anonymous, rather disorganized account of assaying for metallic content and of metals," which must be the Probierbüchlein, the other, "dealing - with veins, written by Calbus of Freiberg, a well-known physician."* Calbus is mentioned a second time-and cited-at the end of the Third Book of De re Metallica. Comparison of the citation with the Bergbüchlein leaves no doubt that Agricola considered Calbus of Freiberg the author of the latter work, although all the editions of the Bergbüchlein known now were published anonymously. It is generally accepted by those who have dealt with the bibliography of the Bergbüchleint that Calbus was Ulrich Rülein von Kalbe, who served the City of Freiberg, in Meissen, as health officer in 1497, as member of the City Council in 1509, and as mayor in 1514 and 1519. He died at Leipzig in 1523. In connection with the very garbled description of the mining compass toward the end of Chapter 3 of the Bergbüchlein it is of interest that von Kalbe is supposed to have been not only a physician of repute but a mathematician, astronomer, mine sur-

Jan 1, 1949

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By V. Annamalai, J. B. Hiskey

Abstract-The kinetics of copper cementation on a rotating disc of pure aluminum were studied as a function of chloride ion concentration, rotational speed of the aluminum disc, hydrogen ion concentration, copper ion concentration, and temperature. The optimum experimental conditions for all the parameters were determined. Chloride ion was found to destroy the naturally existing aluminum oxide film, and enabled the cementation reaction to proceed. A two-step rate, observed in most of the experiments, was attributed to the attainment of a roughened surface. An Evans diagram for the copper-pure aluminum system was constructed and utilized in predicting the controlling mechanism of the system. At low temperatures (<33°C), the rate with an experimental activation energy of 20.36 kcal mol-1 was controlled by the presence of an oxide layer. While at higher temperatures presence of an oxide layer. While at higher temperatures (>33° mol-1 was controlled by ionic diffusion. The deposits obtained were pure copper and not a copper-aluminum alloy. The amount of aluminum dissolved was determined for each experiment, and the maximum excess consumption was found to be only 40%. The structural characteristics of the copper deposits were studied using a scanning electron microscope. These observations indicated that the deposits were either bulbous, massive crystalline, or dendrites of different degrees of fineness depending on the experimental variables. The reaction rates seemed to depend on the deposit structures in a predictable way when a particular experimental parameter was varied.

Jan 6, 1978

By C. W. Drury, E. J. Hall

The iron-nail method of assaying has been used for a number of years, but has not met with the approval of all assayers. The method possesses advantages which may be given as follows: (1) no preliminary treatment is required; (2) a lead button of proper size can be obtained; (3) it is economical. On the other hand, it has its disadvantages, which may be summed up as follows: (1) it is not applicable to ores containing large amounts of impurities other than sulphur, as practically all the base metals will contaminate the lead button ; (2) the slag is unsatisfactory in the larger number of fusions; (3) the method was known to give low silver results under certain conditions and the gold results were questionable. It was with the idea of determining the extent of this latter disadvantage that the following investigation was undertaken. It is well known that the fusion obtained in the lead assay is far more satisfactory than that in the " nails method" for gold and silver. The principal difference in the charges as a class is the presence of considerable reducing agent in the lead charge, and a limited oxidizing action in the nails charge, dud to PbO. The possibility of improving the nails fusion by simulating the lead charge was the reason for using argol in some tests, even though there were reasons for expecting this would have an objectionable effect on the results. Preparation of the Gold-Bearing Material. The materials containing gold and silver used in the following experiments were prepared rather than selected, in order to have a definite working product excluding undesirable elements. A high-

Jan 1, 1914

By F. H. Newell

Measurements of the amount of water flowing in many of the larger rivers of the west have been made by the United States Geological Survey, and by this means the daily discharges of these rivers have been computed for a period of over two years. These measurements have been confined mainly to that part of the country commonly known as the arid region, where the rainfall is insufficient for the needs of plants most useful to man, and the supply of water, not only for agriculture, but also for mining and all other purposes, falls below the demands made upon it. In such localities flowing water has a great value, for without it many industries are impossible. Experience has shown that in the western part of the United States, over an area a little less than two-fifths of the whole extent of the country, there are great bodies of fertile land enjoying a genial climate, and in every way adapted to the support of a large population, except in the one particular of water-supply. By utilizing the water available, portions of this rich land can be rendered valnable. In other words, the laud-values rest directly upon the prospects of a continuous artificial water-supply. The same is true of many mineral lands, which require for hydraulic mining, or for the supply of concentrating-works, stanip-mills, etc., a certain water-supply, and are impaired in value if this supply is inadequate or irregular. The pressure of this need upon the mining industry is not so widespread, or in the first instance so severe as upon agriculture; but as different regions become more thickly settled, and the two industries compete for a water-supply not sufficient for both, it, is probable that the miner will suffer. But he can snspend operations with less inconvenience than the farmer. Agricuitural land, if the watersupply is not continuous, becomes a desert; on the other hand, the profit of mining is greatly enhanced by the presence of agricultural

Jan 1, 1892

By J. T. Eash, E. M. Wise

Platinum and palladium are the most generally useful, most ductile and least rare members of the platinum family. They have many important applications in the pure state but for other applications it is frequently desirable to harden them and otherwise modify their properties by alloying small amounts of the other platinum group metals with them. These alloys are frequently required to withstand very drastic forming operations and to possess certain mechanical properties to fulfill specific requirements. For these reasons a knowledge of the tensile properties and annealing characteristics of pure platinum and palladium as well as their more useful commercial alloys is important to the user and the fabricator. The present work was undertaken to fill this need. Rather brief (5 min.) annealing treatments were employed to render the data of maximum practical value and all tests were conducted upon 0.050-in. dia. wire, initially reduced 50 per cent in area by cold drawing, for the same reason. Conclusions 1. Pure (thermocouple grade) platinum reduced 50 per. cent by cold drawing exhibits the following tensile properties: ultimate tensile strength, 36,000 lb. per sq. in.; proportional limit, 27,000 lb. per sq. in.; elongation, 2.5 per cent in 2 in.; reduction in area, 95 per cent. When fully annealed by treatment at 1100°C. its properties are: ultimate tensile strength, 20,700 lb. per sq. in.; elongation, 30 per cent in 2 in.; reduction in area, 93 per cent. 2. The addition of alloying elements in moderate amounts markedly increases the strength and annealing temperature without much detriment to the ductility. The behavior and properties of variously hardened platinum alloys are considered in some detail. The behavior of a 20 per cent iridium

Jan 1, 1935

By J. T. Eash, E. M. Wise

Platinum and palladium are the most generally useful, most ductile and least rare members of the platinum family. They have many important applications in the pure state but for other applications it is frequently desirable to harden them and otherwise modify their properties by alloying small amounts of the other platinum group metals with them. These alloys are frequently required to withstand very drastic forming operations and to possess certain mechanical properties to fulfill specific requirements. For these reasons a knowledge of the tensile properties and annealing characteristics of pure platinum and palladium as well as their more useful commercial alloys is important to the user and the fabricator. The present work was undertaken to fill this need. Rather brief (5 min.) annealing treatments were employed to render the data of maximum practical value and all tests were conducted upon 0.050-in. dia. wire, initially reduced 50 per cent in area by cold drawing, for the same reason. Conclusions 1. Pure (thermocouple grade) platinum reduced 50 per. cent by cold drawing exhibits the following tensile properties: ultimate tensile strength, 36,000 lb. per sq. in.; proportional limit, 27,000 lb. per sq. in.; elongation, 2.5 per cent in 2 in.; reduction in area, 95 per cent. When fully annealed by treatment at 1100°C. its properties are: ultimate tensile strength, 20,700 lb. per sq. in.; elongation, 30 per cent in 2 in.; reduction in area, 93 per cent. 2. The addition of alloying elements in moderate amounts markedly increases the strength and annealing temperature without much detriment to the ductility. The behavior and properties of variously hardened platinum alloys are considered in some detail. The behavior of a 20 per cent iridium

Jan 1, 1935

By C. F. Cornell, Henderson, A. F. Dunyon, D. A. Dahlstrom

IN processing magnetic taconites several steps of crushing, grinding, classification, and magnetic separation are required to produce a 60+ pct Fe concentrate. Usually the final concentrate is in a slurry form of 55 to 70 pct solids by weight and is further characterized by a particle size of 60+ pct -325 mesh. In taconite plants already completed or under construction the conventional method used to obtain pellets suitable for blast furnaces is to filter the concentrate slurry, ball the filter cake, and then harden the green pellets in a traveling grate or in a vertical shaft furnace. Large tonnages must be handled in minimum floor space, with reduced maintenance and lowest possible operating cost. Filtration must therefore achieve two objectives: 1) high filtration rate-in terms of pounds of dry solids per hour per square foot of filtration area-at a low filtrate solids concentration, and 2) a filter cake moisture that will always permit efficient balling within the normal fluctuations of plant operating conditions. If moisture contents are too high, balling may be impossible or result in a mushy ball without enough green strength for the firing operation.

Jan 3, 1957

By L. B. McConville

The general term "tar sand" refers to sand that contains varying amounts of dense, viscous petroleum. Tar sand deposits have been found throughout the world, often in the same geographical area as conventional petroleum. The largest one by far is known as the Athabasca Tar Sands, in the province of Alberta, Canada. Actually a group of three deposits, these particular sands underlie an aggregate area of more than 12,000 sq miles. Current estimates place the contained raw petroleum at about 700 billion bbl; and via currently available technology, the amount of recoverable synthetic oil may be as much as 300 billion bbl-which is roughly equivalent to five times the combined US and Canadian total crude oil reserves. With the ever-widening gap between energy supply and demand, mining and petroleum companies are now evaluating all possible energy resources-both developed and underdeveloped-and, certainly, the Athabasca Tar Sand deposit is one of the more important ones to merit such attention. The first section in ME deals with the geology and historical developments; the other four sections, with mining methods, extraction technology, economics, and outlook.

Jan 1, 1975

By Ralph E. Davis, Lyon F. Terry

The rapid expansion of the natural gas industry in this country during the past three or four years has necessitated the construction of a number of long and comparatively large diameter high-pressure pipe lines This period of expansion and construction is still at high tide, and the current year will doubtless surpass all prior years in mileage and capacity of gas line installation. The fundamental economics of the business of long-distsrier transportation of natural gas may be briefly and simply stated, although most careful consideration must be given the actual determination and integration of the several more important factors which determine the ultimate success or failure of such a project. Reduced to its simplest form, a sound natural gas transportation project requires: 1. A competent source of gas, where the combination of quantity of gas available, cost of production, and longevity meet the given requirements. 2. A market, reasonably certain to endure in the face of any probable competition, of satisfactory size and price, and having a sufficiently favorable load factor. 3. A cost of installation of pipe line systen and an operating cost such as will, with honest and reasonably efficient management, afford a net operating return sufficient to attract the necessary capital required. In a11 new projects of this kind it is necessary that thehe three cssentials to ultimate success be assured. Hence the necessity of competent surveys of gas supply, and of market, both industrial and domestic. The prudent engineer will allow for "factors of safety" in reaching his conclusions just as he would in the design of a bridge. This paper deals primarily with but one of the major considerations enumerated above, I. e, the economic design of the pipe line system. The "pipe line system" will be considered to include (1) the pipe Iine, and (2) a series of compressor plants along the pipe line for maintaining

Jan 1, 1929

By Strathmore R. B. Cooke, Iwao Iwasaki, C. S. Chang

PYRRHOTITE has long been considered a gangue mineral to be eliminated as tailing in the treatment of various sulphide ores. However, in recent years the world-wide lack of sulphur resources has called attention to this mineral as a potential source of both sulphur and iron. Its importance as an economic mineral, however, has not been particularly emphasized. For this reason very little is known about its response to flotation, except that it can be depressed easily in alkaline circuit, by long aeration,1,2 addition of oxidizing agents3 or by starch.4 The object of this work was to study the floatability of pyrrhotite. This includes the effect of oxidation by aeration, of copper activation, and of change in pH.

Jan 2, 1954

By L. M. Barker

THE New Cornelia Branch of the Phelps Dodge Corporation is at Ajo, Pima County, Ariz. It is at the southern terminus of the Tucson, Cornelia and Gila Bend Railroad, which connects with the Southern Pacific Railroad at Gila Bend, Ariz., approximately 43 miles to the north. HISTORY Early history of the Ajo district has been related by A. W. Allen1 and by T. A. Rickard.2 Briefly, steps looking to the large-scale development of the ore body were instituted as early as 1912. This work culminated in the equipment of the property for open-pit mining by steam shovels. Ores initially mined carried economic amounts of copper carbonates as the principal copper-bearing mineral. Treatment methods developed for the extraction of the copper content involved leaching and a 5000-ton leaching plant was constructed and placed in operation in early 1917. Description of methods and equipment employed in this plant has been given by A. A. Tobelmann and James A. Potter.3 As exhaustion of the carbonate ore body neared, and mining oper-ations exposed an adequate tonnage of sulphide ores, a 5000-ton con-centrator was constructed for their treatment. That plant has been described by H. Kenyon Burch.4 Construction was completed and the plant was placed in operation in early 1924. Changes made in the original plant to improve practices and increase production will be the subject of subsequent paragraphs of this paper.

Jan 1, 1939

By D. L. Wood

This investigation was concerned with the aluminum-oxide particle dispersions, the mechanical properties, and the re-c,uystallization characteristics of some internally oxidized copper-aluminum alloys. Obserued hardness vaviations are in agreement with variations in oxide particle size revealed by electron metallographic studies. The increase in yield strength caused by internal oxidation is quite sensitive to matrix grain size and is accompanied by a loss of ductility, particularly at higher temperatures. Elevated temperature ductility is con-side,vably improved if major grain reorientation is accomplished by ve recrystallization prior to testing. The oxide particles offer a considerable restraint to softening during annealing after cold deformation. THE diffusion of oxygen under appropriate conditions into a suitable alloy causes solute oxide particles to be precipitated at an inward moving interface.1,2 Previous work has shown that the hardness

Jan 1, 1960

By Richard Miller

WORK was undertaken two years ago at the Hammond Laboratory for the purpose of determining the magnitude of the elastic range in single crystals of pure metals by means of creep tests, the assumption being made that if a true elastic range exists, the elastic limit represents the maximum stress for no creep. A sensitive extensometer was constructed, and creep tests were made on zinc single crystals at a variety of loads and temperatures1. It was soon discovered that there is tip measurable elastic limit in ductile zinc single crystals at, or above, room temperature. The inference that pure metallic single crystals may not possess a definite elastic range was not justified, however, since zinc had been tested in creep only above its recrystallization temperature, and several investiga-tors2,3,4 had already shown that above the recrystallization temperature polycrystalline metals will flow under very small stresses, while below that temperature stresses of a much larger magnitude are required. For that reason, it was decided to extend the study of the elastic limit to other metals having a higher recrystallization temperature than zinc. Aluminum and silver were selected, because of the ease of obtaining pure materials and of preparing large single crystals, and because the crystallo-graphic glide system of these metals is well known. Owing to the limited time available, the elastic range was investigated by slow tensile tests rather than by creep tests.

Jan 1, 1937

By E. S. Machlin

The kinetics of vacuum distillation, vacuum-melt surface reactions, crucible-melt surface reactions and boiling are analytically investigated. No disagreement with experiment is obtained upon applying a rigid flow model to describe the behavior of the melt in the vicinity of reaction surfaces. The theory focuses attention upon measureable parameters rather than upon the adjustable parameter, stagnant layer thickness, associated with other theories. The rigid flow theory is thus capable of quantitative evaluation and experiments to achieve this evaluation are suggested. KINETICS, rather than thermodynamics, often determine the degree of refinement achieved in vacuum melting. There is little understanding, however, of the kinetic principles involved in vacuum refining. This paper represents an attempt to achieve this understanding. There are two reactions which need to be con- sidered. The first is the refining reaction. The second shall be called the polluting reaction. It is the reaction associated with the introduction of components of the crucible into the melt. The mechanisms of both reactions are unknown. Many models can be constructed to describe either the refining or polluting reactions. For example, consider the refining reaction C + Q = CO(g). One model that can be imagined is that the carbon and oxygen combine in the melt to form CO which then diffuses to a melt-

Jan 1, 1961

By W. M. Courtis

In compliance with the suggestion in Mr. Emmons&apos;s paper on the Genesis of Certain Ore-Deposits (Trans. xv., 125), that facts should be accumulated for study and future compilation, I wish to put on record, before the data are lost, a section of the Animikie series of rocks and the vein-phenomena exposed by the explorations at the Duncan mine, Port Arthur, Thunder Bay, Lake Superior. This may serve as a supplement to my paper on this district (Trans. v., 473). I trust this information will not be without interest at. the present time. The recent discoveries of very rich silver-ores at Rabbit and Silver Mountains, on the same belt, have brought the district once more before the public; and a study of the facts here set forth may assist some fellow-engineer in the determination of the value of property offered for sale in this neighborhood. The vein at the Duncan mine was tested to a depth of over eight hundred feet by shaft and drifts, and to nearly a thousand feet with

Jan 1, 1887

By W. B. Hall, Joy D. Lewis

Mine-run ore is received at Vitro in gondola cars and fed directly to a Cedar Rapids impact crusher. Following screening, the undersize travels through a recently installed three-stage sampling plant where successive cuts are executed by conventional Geary-Jennings type cutters to produce a final sample of 1 lb per ton of raw ore fed. Crushed ore is transported to one of three storage silos or to stockpile, depending upon grade and type of amen- ability. This permits the blending of a mill feed with some degree of consistency. Final grinding is accomplished in one of two closed circuit ball mill-classifier systems allowing simultaneous processing of two basic types of ores. High acid consumers may be leached separately in the required environment. Part of the free acid remaining can then be utilized by an ore stream entering later whose component ores require much less free acid for leaching.

Jan 11, 1958

By M. Muskat

Calculations are reported on the differential sensitivity of the updip invasion of oil strata of varving permeability to the driving pressure differential. It is assumed that the water-oil interfaces advance with sharp fronts, or that the microscopic displacement efficiency is independent of rate and capillary pressure effects. It is found that, under such conditions, limitations of withdrawal rates will not greatly inhibit the "fingering" and bypassing tendency through high permeability strata unless the differential fluid head across the original oil column is of the order of or exceeds about 80 per cent of the driving pressure differential. In practice, such restrictions will be feasible only for oil reservoirs and aquifers of high permeability and dip, but may develop automatically under combined gas injection and water drive operations. INTRODUCTION A commonly expressed view regarding the intrusion of edge-waters into oil producing formations is that the geometry of such advance is rate sensitive. Specifically, it has been suggested that high rates of advance, stimulated by rapid withdrawals, will lead to "fingering" and an irregular type of invasion, whereas at low withdrawal rates the water encroachment will be more uniform. Two factors tend to support this view. One is the resultant effect of capillary pressure and gravity gradients in the displacement processes&apos; involved in water intrusion, which are magnified at low rates of flow so as to improve the recovery efficiency. The other is the direct retarding effect of the rising water head as it advances upslope into the producing area. Capillary pressure forces give rise to a rate sensitivity of the oil recovery by water displacement in uniform strata as well as differential effects in non-uniform formations. These are basically independent of the effect of gravity and would also occur in horizontal beds or when the oil and water have the same density. Unfortunately, however, the fundamental equation describing the displacement process under the action of capillary pressures can be solved only by numerical or graphical procedures, and moreover the solutions are sensitive to the character of the capillary pressure and relative permeability curves.* On the other hand, the direct effect of gravity can be given a formal analytical solution if the simplifying assumption is introduced that the water advances with sharp fronts in the individual uniform strata. It depends on the absolute permeabilities of the water invaded zones and hence results in a rate sensitivity of the differential invasion in stratified media. Although a tieatment of this factor alone will not give a complete evaluation of the effect of rate on water intrusion in non-uniform pays, it should provide at least a semiquantitative measure of the sensitivity of "fingering" to withdrawal rate. Such a treatment will be presented in the following sections. GENERAL THEORY The basic element of the theory is the history of water advance updip in a uniform stratum (Fig. 1). In contrast to the assumption of constant flow rate, generally made in the analysis of displacement processes, we shall assume here that

Jan 1, 1951