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By J. E. Campbell, A. W. Wesner, M. Pobereskin

This paper summarizes the results of an investigation sponsored by The Coates Steel Products Company. The objective was to determine the relative effects of certain chemical and physical properties on the wear resistance of grinding balls when grinding cement. In making this study, a number of types of balls were used in both dry and wet grinding in commercial ball mills. The radioactive-tracer technique was used in separating the test balls from the rest of the mill charge and in sorting the different types of halls that were all tested at the same time for each of the grinding operations. PROCESSING OF GRINDING BALLS In order to determine whether the properties of grinding balls, namely, composition, microstructure and hardness, can be related to the rate of wear, the halls used in this study were selected to represent various combinations of these properties. It was recognized that the mechanism of wear was not the same in the wet mill as in the dry mill. Therefore, the types of balls tested in each of the two environments were not necessarily the same. However, all of the types of balls evaluated in the dry mill were tested simultaneously for one time period, while those evaluated in the wet mill were tested simultaneously for three different time periods. All of the test balls were separated from the charge when the mill was dumped. All of the balls were of 0.940-inch diameter when charged, and all but the regular production balls were finish ground to this size to eliminate the decarburized surface layers. The steels and processing methods used, as well as the micro-structures and hardness levels of the balls, are described as follows: Regular production forged SAE 1095 steel balls were used in both the wet and dry mills. They were forged to a nominal diameter of 0.940 inch and quenched in oil from the forging temperature. Each retained a partially decarburized surface layer from the forging bar stock; the maximum depth of this layer was about 0.030 inch and the decarburization was negligible where the ball was sheared from the bar. The hardness at the surface was 40 to 46 Rock-well C in the partially decarburized area and 57 to 62 Rockwell C in the areas not decarburized. The hardened zone extended to a depth of about one-third of the radius. Below the decarburized layer, the hardened zone consisted primarily of hard as-quenched martensite with varying amounts of retained austenite. This structure changed to fine pearlite at a depth of about one-third of the radius. In order to eliminate the effect of the decarburized layer, a set of production balls of SAE 1095 steel was forged to about a 1-inch diameter, quenched in oil from the forging temperature, and ground on ball-bearing grinding equipment to a 0.940-inch diameter to remove the decarburized layer. The balls' hardened zones were similar to those in the previous set. The hardness of the finished surfaces was 52 to 60 Rockwell C. A slight amount of decarburization apparently remained after the removal of about 0.030 inch from the surface. Balls of this type were tested in the dry mill only. Another set of forged SAE 1095 steel balls of 1-inch diameter was heated to 1500 F and quenched

Jan 1, 1961

By C. J. Beevers

Tlze influence of zirconium hydride precipitate mprphology on the fructure of Zr-H alloys tested at strain rates of 10- sec at 20° and - 196°C and at strain rates of -500 sec.-1 at 20°C has been inves-tigated. The critical stage in the embrittlement of these alloys was the fracture of the zirconium hyhide precipitates to form large interval cracks at a stress of 25,000 10 137,000 psi. In specimens con-temping up to 100 ppm H the preciptates existed as isolafed platelets in the zirconium matrix and their fracture as enhanced by low temperature (—196°C) and high strain rate (-500 set-f) loading. These resl~lts lead to the conclusion that the rate of strain hardening of the zirconium metal controls the frac-tzrm of the hydride platelets. Increased hydrogen contents of 500 to 2000 ppm resulted in an increase in the 1)volume fraction and size of precipitates and crlso led to crack propogation in the hydride at both 20 and —196C at the low strain rates (10'* sec-'). Quenching led to refinerment of hydride precipitate size and reduced the degree of embrittlement at — 196°C; this effect is attributed to the absence of fracture of the fine precipitates. The formation of zirconium hydride precipitates has been shown to be the cause of hydrogen embrittlement of zirconium.' Several investigators'-" have studied the problem in broad outline, demonstrating that impact-loading conditions, testing temperatures below room temperature, and increasing hydrogen content produce increased brittleness. For example, Muehlenkamp and schwope2 showed that the transition temperature for notched impact tests was raised from 150" to 350°C on increasing the hydrogen content from 45 to 490 ppm. The degree of embrittlement is also controlled by the morphology of the zirconium hydride precipitates. The solubility of hydrogen in zirconium decreases from 600 ppm at 550°C to 10 ppm at 20"C,~ so that the form of the zirconium hydride precipitates (ZrH2) can be modified by varying the cooling rate through the Zr-aZr + ZrH2 phase boundary.= Forscher showed that quenching a specimen containing 35 ppm H from above 315°C resulted in a reduction in area of 70 pct at -196"C, whereas slowly cooling from above 315°C resulted in a ductility of half this value. The role of the hydride precipitate in the fracture process has been examined by Young and schwartz6 and more recently by westlake.' From metallo-graphic observations on slowly cooled Zr-H alloys they have suggested that cracks are nucleated in the hydride precipitates by the interactions of twins in the zirconium metal with the hydride. The experiments reported in this paper show that crack propagation in the zirconium hydride precipitates is the critical stage in the embrittlement of Zr-H alloys. The factors influencing fracture of the hydride precipitates and crack propagation in the zirconium metal will be related to the problem of embrittlement. EXPERIMENTAL TECHNIQUES The zirconium used in these experiments was produced from an ingot of vacuum arc-melted iodide zirconium forged down to 1 in. diameter at 800' to 850°C. The 1-in.-diameter bar was surface-machined and cold-swaged to 0.375 in. diameter. After a vacuum anneal at 800°C for 1 hr the hardness was 60 to 70 Vdh. The total impurity content was approxi-

Jan 1, 1965

By L. A. Roe

Magnetic separation of iron ores is one of the fastest-growing segments of the minerals beneficiation industry. The tonnage of taconite ores processed annually by magnetic separation will, in a few years, reach 100 million. Magnetic separation occupies an attractive position in the field of ore beneficiation. It is a simple yet effective method, used for some 150 years and steadily growing more important. This type of beneficiation orginated in 1792, when William Ful-larton was issued a British patent covering the separation of iron ore by magnetic attraction. What is magnetism, and why are some materials capable of being magnetized and others not The study involves many unknowns, and even a partial answer to these questions would be a dissertation in solid state physics and perhaps other fields of science. But the last two decades have revealed basic facts as to why certain materials are magnetic and what happens to them when they are magnetized. Some of the newer studies in solid state physics have developed a theory that can be applied to studies of magnetism. It is claimed that magnetism stems fundamentally from the spin of electrons in atoms that tend to go in pairs, spinning in opposite directions. The atom as a whole can act as a magnet only when there is an imbalance of electronic spin. Whenever an atom has an odd number of electrons, therefore, this imbalance exists. This neutralizing effect explains why a piece of material that contains atomic magnets is not necessarily magnetic. The physicists tell us that iron is composed of many small magnetized regions called domains, which consist individually of millions of atoms. The piece of iron becomes magnetized when an external force lines up these domains in the same direction. Fundamental data developed by physicists working in fields far removed from minerals beneficiation are now available for developing better magnetic separators for ore processing. More Data Needed on Magnetic Properties of Minerals: There is less information on magnetic properties of minerals than there is for certain aspects of magnetic separator design. When the data on magnetic properties is available, it is often directed toward the study of powders for tape recorders and other highly scientific endeavors that are of little use to the beneficiation engineer. W. R. Crane's table of tractive forces, published in 1902, is still a guide in the study of magnetic minerals. Bits of other information regarding electrostatic conductivity, dielectric constant values, and permeability of various minerals have also appeared but are of small practical value in magnetic separation of ore. It is extremely important to obtain pure mineral specimens for making investigations and to record results that may be of use in studies of magnetic processes. Reference to the large volume of data developed by those concerned with analysis and design of permanent magnets soon reveals that these people have extensively evaluated the effect of various impurities on magnetic properties. Much of the science of the ferrite industry is based upon spinel-type structures which are varied by substitution of selected elements or even subtraction of elements, leaving vacant sites in the space lattice. Magnetic separators are used to beneficiate a wide variety of industrial minerals. In this application the relatively large volumes of nonmagnetics are usually the commercial products. The amount of mag-

Jan 1, 1959

By Norman F. Schulz

The technical excellence of separation achieved in a mineral concentration process, or any other process where two constituents of any kind are physically separated from each other, is expressed uniquely and quantitatively by the separation efficiency (E,): E. = (R - R,), where R is the percentage of the valuable constituent and R, the percentage of the waste appearing in the concentrate. The separation efficiency meets all the usual requirements of a true efficiency and is independent of the nature of the process used. It can be visualized as the percentage of the feed material that, in effect, actually undergoes complete separation while the rest of the feed is distributed randomly and unchanged into the two separation products. The problem of quantitatively assessing the results of a mineral concentration process recurs whenever one tries to decide which of two similar test results is more desirable. Although economic factors may greatly influence the eventual choice of process, they usually have very little to do with the technical excellence of a separation and are, therefore, not a consideration at this point. Concentrate grade and recovery, used simultaneously are the most widely accepted measures of performance, and if both the grade and the recovery are greater for one case than for another, the choice is simple. However, when the results of closely competitive operations are compared, it often occurs that one set of test results shows a higher grade and a lower recovery than another and the choice is no longer obvious. Laboratory investigations of a mineral concentration process applied to a given feed material can often be designed to yield successive paired values of concentrate grade and recovery over the practical range of the course of a separation process.' These results may be plotted as some combination of the cumulative values of grade, weight recovery, or unit recovery in the concentrate. The resulting correlations for two slightly different sets of conditions can then be compared qualitatively, or even quantitatively in particular cases.2 Such comparisons are not applicable, however, to individual concentration test results. The reduction of a separation test result to a single efficiency figure, preferably as a percentage of ideality, would afford the simplest and most precise means for comparing the results of competitive tests. The effective proportion of feed material that undergoes complete separation in any real concentration process, hereafter referred to as "separation efficiency," is such a figure. It is essily calculated from the usual feed and product data and can even be evaluated, in many cases, from data in publications describing various concentration processes. Mineral Concentration Processes and Their Evaluation Mineral Concentration Processes: The overall concentration process may be subdivided into a liberation process which severs the bonds between unlike mineral species, and a separation process, which sorts the resulting liberated particles into two products—a concentrate rich in mineral A and a tailing lean in mineral A. A perfect mineral concentration process is represented by the idealized scheme shown in Fig. 1 in which liberation and separation are not differentiated. The feed mixture consists of two mineral types which are completely liberated early in the process and then sorted by type. All the mineral particles of type A which respond uniquely to the selection forces acting in the ideal separator, report to the concentrate, while all the mineral particles of type non-A report to the tail-

Jan 1, 1971

By W. A. Scheuch

ORDINARILY secondary copper, unless electrolytically refined, is reclaimed directly as foundry ingots used in the manufacture of copper-rich alloy castings. This use does not require the elimination of the impurities to the degree required if the recovered metal is to be used for electrical purposes where a high electrical conductivity is of prime importance. However, as a part of the general policy of reusing its own scrap and by-products wherever possible, the Western Electric Co. at its Hawthorne Works is recovering its secondary copper as wire bars which are delivered to its own rod and wire mill and there processed into wire of high electrical conductivity. This departure from the usual recovery scheme has been accomplished through the careful classification and sorting of the material entering the furnace charges and the careful control of the subsequent melting and refining in a reverberatory furnace. Tests conducted over a period of approximately four years have shown that the quality of wire bars produced from selected secondary copper is equal to that of wire bars produced by the electrolytic refineries. The interest which has been exhibited in the process by those who have seen it has prompted the following general description. It is the authors' opinion that the recovery of secondary copper will become more and more an important factor in the copper production industry. The description is largely of the refining furnace and its operation, but it must be remembered that careful classification and sorting of the scrap materials to eliminate impurities are just as important as the furnace operation toward obtaining a satisfactory final product. Classification and sorting do not lend themselves easily to description; they must just be done. It should also be recognized at the outset that constant intelligent supervision is requisite to the success of the process because there are so many ways in which impurities can find their way into the final product.

Jan 1, 1929

By L. A. Updegraff

Before discussing the application of capacitance for the measurement of moisture content in a moving stream of coal it might be well to first give a brief description of the process and then show how it can be applied to the coal industry. A capacitor may be described as a device having two conductors separated by an insulator, the conductors hereafter being designated as a test cell or test plates and the insulator as the dielectric. Capacitance, therefore, is a measure of the ability of a capacitor to store an electrical charge. Two basic factors that affect capacitance are the dimensions of the capacitor and the dielectric constant of the insulator. Capacitor dimensions which affect its capacity are the area A of the conductive surface, and the distance d between plates. Capacitance is inversely proportional to the distance between plates and directly proportional to area A, so if capacitance is indicated as C and the dielectric constant as K the equation for capacitance would be C = AK/d. The dielectric constant can be described as the ratio of the actual capacitance of any given material to that of a vacuum, which is unity. In industrial applications the area of the plates remains constant as also does the distance between them, leaving the dielectric constant as the only variable to affect the capacitance measurement. Figure 1 is a schematic diagram of an r-f excited capacitance bridge in which a test cell is part of the circuit. This bridge consists of four capacitors in two pairs connected across an a-c voltage source. In one side of the circuit the two capacitors are fixed but in the other side they are variable, one being the rebalance capacitor operated by the servo motor and the other the test plates between which the dielectric passes. Capacity of the plates is a function of the dielectric constant of the material between them and is measured at radio frequency. Within the recording instrument is an r-f oscillator and a 60 c ps modulator. The radio frequency signal is generated by the oscillator, modulated by a 60 cps wave, and sent to the bridge. Therefore the signal entering the capacitive bridge is a radio frequency carrier with a 60 cycle envelope, If the bridge is in balance as the signal enters there would be no voltage drop and so no output by the detector. As long as the dielectric constant remains the same the bridge will stay in balance. However, any change in the dielectric constant, which in this case would be a change in moisture content, would affect the bridge. Higher moisture increases the capacity of the test cell which causes less voltage to develop across it causing imbalance of the bridge. This in turn causes a radio frequency signal to appear at the detector. Output from the detector is a 60 cycle ripple which is in proportion to the imbalance of the circuit. A 60 cycle amplifier boosts the detector signal to enough power to drive the servo motor which positions the recording pen and also rotates the variable capacitor, to which it is mechanically connected, to bring the bridge back in balance. An increase in moisture causes the servo motor to rotate in one direction, but a decrease causes imbalance in the opposite direction, and thus rotates the motor in that direction. This brings the bridge back in balance and stops the motor. The bridge shown in Figure 1 has been modified so as to provide a wide range of adjustments. Coarse and fine span adjustments located in the recording instrument are set to govern the amount of pen movement for a given change in capacitance. A measuring head unit contains coarse and fine zero adjustments for

Jan 1, 1961

By Earl L. H. Sackett

Barite, although not a glamour mineral and probably little known to many of those in the mining business, is produced in the US. in very respectable quantities and is an important factor in the mineral economy of this country. The scope of the various uses of this mineral is perhaps one of the most misunderstood things about it, for it is surprising how many of those with a casual knowledge of the subject speak of its primary utilization in terms of paint pigments and barium chemicals. The life blood of barite utilization, however, is the petroleum industry by virtue of its dependence on this high specific gravity, inert mineral as the weighting material in its drilling fluids. From 80 to 85% of barite usage in the U. S. is accounted for in this manner-in fact, its role in oil well drilling is the only excuse for some of the large-scale barite production facilities which have been developed. Other uses are important and widely varied, but comparatively they are of small scale. They include fine crushed barite of low iron content as a component in glass manufacture, barite as a source material for manufacture of barium chemicals, finely divided barite as a component of some rubbers and ground, bleached barite in pigments. The formerly substantial use of barite in lithopone, however, has declined markedly because of replacement of lithopone by titanium pigments

Jan 5, 1962

CYRIL STANLEY SMITH, Chairman CARL E. SWARTZ, Past-Chairman ARTHUR PHILLIPS, Vice-Chairman E. E. SCHUMACHER, Vice-Chairman H. A. MALONEY, Treasurer FRANK. T. SISCO, Secretary 9 West 39th Street, New York, N. 1. Executive Committee 1944 1945 WILLIAM C. ELLIS C. S. BARRETT ALAN MORRIS T. A. WRIGHT KENT R. VAN HORN L. L. WYMAN

Jan 1, 1943

Jan 1, 1967

Official Program

Jan 8, 1950

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Jan 1, 1938

By H. DeWitt Smith

THE mine operated by the United Verde Copper Co. is situated near Jerome, Ariz., on the eastern flank of the Black Hills, at an elevation of approximately 5500 ft. (1676 m.) above sea level. The mine and the town of Jerome are located on a steep hillside, which slopes rapidly to the valley of the Verde River. The smelter town of Clarkdale is situated in the Verde valley 4.1 mi. (6.5 km.) distant in an air line from Jerome, and at an elevation of 3560 ft. The two towns are connected by the standard-gage railroad of the Verde Tunnel & Smelter R. R., a subsidiary of the United Verde Copper Co. This road is 11 mi. long and has a compensated 4 per cent. grade. At Clarkdale, it connects with the Verde Valley branch of the Santa Fe R. R. The narrow-gage (36-in.) line of the United Verde & Pacific Ry. was, until 1919, Jerome's only rail connection with a main trunk line. This road connects with a branch line of the Santa Fe system at Jerome Junction, after traversing 26 mi. of mountainous country. From the time of its location, in 1876, until its purchase by Senator W. A. Clark, of Montana, in 1889, the United Verde mine was worked on a small scale and shipments of high-grade gold-silver ore were made from the surface workings. Until 1894, when the narrow-gage railroad to

Jan 8, 1920

By B. E. Warren

Jan 1, 1965

By A. M. Gaudin

Jan 1, 1962

By M. J. R. Morris

THE year 1939 has seen the iron and steel industry driving for efficiency with unabated zeal. "Efficiency" is here used in the sense of enabling the customer to do more with less, either supplying him with more economically priced steels or with higher priced steels that will do a job more economically. The plain carbon steels have been improved tremendously in quality be- cause of recent control tests. All steel companies have been urged to hold to .closer chemical control, closer standards, soundness, and more control on grain size, and now attention is being directed to closer control of hardening properties. Better control of open- hearth operations undoubtedly will result in an increase in the application of special carbon steel. Further, with a better understanding of quenching, the present trend to study the quenching of this class of steels will be ex- tended. These steels will then be used for purposes to which they are best suited. Utilization of special carbon bars and large shapes seems to be developing less slowly than special car- bon in the form of strip. There are many reasons for this and the future development of this trend will be important. Continued development of the manufacture of parts from strip and sheet to replace forgings, and of formed; structural members such as channels or welded pipe, is notable. Special carbon sheets with nonaging properties have been produced during the year; they maintain a higher degree of ductility over a longer time and are less sensitive to the changes which took place in the former product when stocked.

Jan 1, 1940

By R. J. Colony

MINING geology does not lend itself - very readily to a review embracing "improvements in methods," as perhaps do shop practices or laboratory procedures. The "methods" used in mining geology are simply the application of geology to mining; winning the ore, the handling of material, mechanical appliances, all belong strictly to mining proper, and have no place in a review of geology as applied to mining. A comprehensive review would necessarily cover a .very broad field, which could be subdivided into many -parts. Only a few of these can be discussed here. .Those that have been suggested to the chairman indude :

Jan 1, 1930

By Austin E. Dwight

IT has been shown by Oelsen and Wever' that the effect of a solute element on the allotropic transformation in iron is dependent upon the quantity

Jan 1, 1957

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt' studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger' discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and

By S. H. Ward

Since the advent of the first airborne electromagnetic system, it has been evident that such systems were inherently limited to shallow depths of exploration of the orderof 100 to 200 feet. Hence in 1948 the author and his associates commenced a study of the feasibility of applying natural audio frequency magnetic fields to investigation of the electrical properties of the subsurface in order to provide a system capable of overcoming this limitation. This research culminated, in the summer of 1958, in the development of a new airborne prospecting device — AFMAG. This device has detected surface massive sulphide bodies while flown at heights as great as 3000 feet. Hence, by inference, it is deduced that it could find similar sulphide bodies if they were buried 2500 feet below surface and the aircraft flown at 500 feet. Thus a considerable improvement over conventional airborne electro-magnetic systems is obtainable with AFMAG. Airborne exploration in mountainous terrain involving deep valley fill now becomes possible. Examples are presented of the results of actual airborne AFMAG test surveys over known deposits of massive sulphide mineralization. Interpretation of the data is discussed with particular reference to the knowledge of size, dip, depth, depth extent, and conductivity of causative bodies as deduced from the flight records. The possibility of mapping major geologic structures, for both mining and oil exploration purposes, is discussed with the aid of examples of airborne AFMAG data. INTRODUCTION Electrical prospecting with natural audio frequency electromagnetic waves as a source has, within the last three years, become a practical reality. Both airborne and ground survey instruments under the trademark "AFMAG" (for audio frequency magnetics) have been used successfully in the search for conductive mineral deposits. It is the object of this paper to discuss the principles of airborne AFMAG and to illustrate its application by means of examples obtained over known geological situations. WHY AFMAG? In view of the large number of good airborne electromagnetic systems available for purchase or contract surveying, one may well ask, "Why another new system?". Primarily the answer lies in the fact that AFMAG does not suffer from the very limited depth of exploration available with, and inherent in, any conventional airborne electromagnetic system. AFMAG is not conventional insofar as an artificial transmitter is not required. Only a receiving and detecting device is employed. The electromagnetic fields measured are those from millions of electrical discharges in the atmosphere (e.g;..- lightning strokes). Their random distribution in time and space make these fields difficult to employ and it is only with recent advances in the electronics of geophysical instrumentation that this has become possible. A second reason for AFMAG and one of its

Jan 1, 1961

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in