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By G. A. Vissac, R. G. Minet, N. E. Sylvander

R. G. Minet—The authors' description of the remarkable progress made in the last few years in applying the fluidized solids technique to the problem of lignite drying and carbonization clearly demonstrates that engineering techniques available today may make many processes practical and profitable which a few years ago were considered otherwise. As pointed out in the article, the future of the carbonization step hinges on the value and utilization of low temperature tar. On paper, at any rate, this tar looks like a valuable raw material for the chemical industry to use. Some 50 to 60 pct may be converted to pitch for electrodes, roofing, road tars, and other valuable products; the 25 to 30 pct tar acids could conceivably form a basis for a new low cost resin or plastic of the phenolformalde-hyde type. Yet these materials are so new and dissimilar from available sources that much work must be undertaken by the chemical industry before they will be accepted. Now that the work of Dr. Perry and his colleagues has made a large supply of low temperature tar a real possibility, I would expect the chemical industry to accelerate its work in this field. On the basis of certain data available in the literature it appears possible to produce a more aromatic tar, although in smaller yield, by operating at temperatures in the range of 1300" to 1500°F. Operating a fluidized bed process for lignite at these conditions should be technically possible, at least, and could produce a tar having more familiar characteristics. I wonder if Dr. Parry would care to comment on such a possibility. Incidentally, in our own work on carbonizing coking coals in fluidized beds, using Ohio, Pennsylvania, and West Virginia high volatile bituminous coals, we have obtained yields which agree with the correlation given for tar yields vs moisture and ash-free volatile Btu. Our data are slightly under the line, but certainly in the range of the correlation. We have also obtained evidence in support of the authors' statement as to the effect of air on the process. In our pilot plant all the heat required for carbonizing is released by internal combustion of char in the fluidized bed in normal operation. We are also equipped to obtain all carbonization heat by external electric heaters on the shell of the carbonizer while introducing only an inert gas to the process. We note no difference in tar yield or characteristics between the two operations. In the case of the gas, however, it appears that some hydrogen is consumed by the air combustion. We would be interested in hearing in a little more detail about the hot dust and char handling problems at Sandow. Have the authors found char subject to spontaneous combustion? Have they ever tried a coking coal in their pilot plant? V. F. Parry (author's reply)—Production of a more aromatic tar by operation of the carbonizer at 1300" to 1500°F does not appear to be economical. 1) The capacity of a reactor operating at 1500°F would be 30 to 50 pct less than the capacity at 932 °F and the cost of processing would increase materially. 2) The cracking of tar vapors in a reactor requires appreciable time to complete the reactions and it is doubtful that considering the very short time of residence of tar vapors within the reactor (4 to 10 sec after evolution) the basic character of the tar would be changed significantly. This is indicated from the data reported in Table XIV. 3) General studies have shown that it is advisable to operate at the minimum temperature to produce the maximum tar and minimum gas. 4) Operating problems and the maintenance of vessels and reactors, and the hazards of handling hot char, increase with the temperature of carbonization. It is technically possible to operate at temperatures as high as 1500°F, but in my opinion it is not economical or desirable. We believe that the primary tar must be won in the simplest way and then processed alone to change its character for production of desired products. It is interesting to have confirmation of our observations on the reaction of air with the products of carbonization. The major reaction is with the char, fol-

Jan 1, 1957

By F. X. Tartaron

The comparison of actual energy of comminution with theoretical surface energy presents a wide gap. On the other hand, Solid State Theory presents a viewpoint that places actual energy of breakage in understandable relationship with the theoretical strength of materials. Therefore the physical background of comminution theory favors Kick's Law. A11 discussions of comminution theory appear farfetched when comparison is made of the actual energy of crushing with the energy input called for by thermodynamic theory. Quoting Taggart:' "The work required to crush halite was of the general order of 0.10 kg cm per sq cm of new surface produced (based on air percolation) whereas the theoretical energy of this new surface, based on thermodynamic calculation by a number of investigators is 1 x 10'4 kg cm per sq cm or the work expended was 1000 times the new surface energy — an indicated crushing efficiency of 0.10 pct." It is frustrating to probe into comminution theory with the prospect that the energy one is measuring is 99.9 pct waste energy. Do the laws of comminution deal with energy consumed by mineral breakage or with waste heat energy? There seems to be something wrong. Solid State Theory may provide the answer. The following statement is particularly apt to the situation: "The fundamental fact about metals and indeed all materials, is that they are much weaker than they should be. By this, we mean that if the stress required to cause a given plane of atoms to slip past a neighboring plane is calculated from basic atomic and Solid State Theory, the resulting number is some 1000 times too large to be accounted for by errors in approximations or assumptions. We know now that this is due to dislocations, and we even have a fair understanding of the details of the process by which dislocations make a crystal weak. An intriguing possibility which suggests itself, results from the discovery of very minute metallic crystals which are apparently free of dislocations and which have a strength approaching the ideal value for a perfect crystal." Here we have an extraordinary reversal of the situation. The actual energy for breakage is only one-thousandth the theoretical instead of 1000 times as given by Taggart. But the theoretical energy presented by Solid State Theory is the binding energy between atoms (or ions) in a crystal lattice. This is the kind of energy envisaged by Kick's law. The surface energy or the other hand corresponds to Rittinger's law. Comparison of theoretical with actual, on the basis of surface or on the basis of Rittinger's law, seems to present an absurdity; yet Rittinger's law is confirmed by an impressive array of experimental evidence. Comparison of theoretical and actual on the basis of Solid State Theory or, in other words, on the basis of Kick's law seems reasonable; yet there is not a scrap of evidence to verify Kick's law. The situation appears paradoxical, but the developments in the next section of this paper show that the paradox is a hint to a strange turn of events. ENERGY-WEIGHT FRACTION FUNCTION charles3 has presented a final equation showing the relation of energy consumed in comminution to size of product n{-1) a-n + 1 E is energy, C is proportionality constant, a and n are constants and k is the coarsest size in the ground product (size modulus). In the course of study of a large amount of experimental evidence, Charles discovered that in the general case, a-n + 1 approximated zero. For some reason, a and n differed only by unity. But if a—n + 1 = 0 within experimental error, then it is obvious that Eq. 1 states that it requires an infinite amount of energy to grind any sample to any size. This is a case where nature gives an absurd answer to a man-made mathematical equation, hence something is wrong with the equation. An adjustment must be made to fit the equation with experience. TO reveal the nature of the adjustment, the differential equation preceding the second integration in Charles' group of equations is given When Charles integrated the quantity xa-n it was almost impossible for him to realize that he was dealing with a special case of integration and that

Jan 1, 1962

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

"The largest variety of asphalt and related bitumen deposits in this country is found in Utah. Utah is one of the few places in the world where the hydrocarbon minerals, gilsonite or uintaite, wurtzilite (trade name elaterite) and ozokerite are produced. These bitumens occur in an area embracing nearly 10,000 square miles in eastern Utah near the Colorado line. This area is largely in the western part of the Uintah basin. The bitumens are in the Tertiary horizon in the various divisions of the Eocene series.Gilsonite is an asphaltite derived from petroleum, wurtzilite is an asphaltic pyrobitu¬men derived from petroleum, and ozokerite is a native mineral wax resulting from the met-amorphosis of paraffinaceous petroleum.Gilsonite is produced by the Gilson Asphaltum Company, a subsidiary of the Bar¬ber Asphalt Company, at Watson, Utah. A narrow guage railroad, seventy miles in length and with a 7 1/2 percent grade over the Book Cliffs on Baxter Pass, was constructed by the company from the Denver & Rio Grande Western railroad main line in order to open up the gilsonite deposits. The veins range from narrow upward to 18 feet in width. The Rainbow vein at the present wokings is eight feet wide, vertical, and has sandstone walls. This vein has been opened up for a distance of about three miles and in some places four hundred feet deep. Forty men usually are employed with a production of eighty tons per day."

Jan 1, 1925

By R. Bakish, C. S. Barnett

IN experiments on tantalum strained in tension, Bechtold did not observe deformation-twinning even at a temperature as low as that of liquid air.' This is an unexpected behavior for a metal of body-centered-cubic structure. Therefore, it is desirable to determine whether the lack of twinning is an inherent characteristic of this particular metal, or whether the reluctance to twin can be overcome under suitable conditions. The following experiments were performed under conditions favorable to twinning and cleavage in their competition with slip, namely, with impact loading on large-grained sheet at low temperatures. The crystallography of cleavage in tantalum sheet was also investigated carefully because of the remarkable ductility of tantalum at low temperatures and because recent tests on oxygen-embrittled tantalum had disclosed unusual cleavage behavior for a metal of this structure: cleavage primarily on (110) planes and only occasionally on {100}.2 The tantalum, supplied by Fansteel, was of 99.9 pet purity, with the chief impurities being iron (0.03 pet) and carbon (0.03 pet). Coarse grains were produced by the strain-anneal method, the anneal being 4 hr at 2000°C in a vacuum of 10-3 mm Hg, followed by furnace cooling. Impact deformation was applied in various ways: a) by hammer blows on an anvil, the specimen and anvil being immersed in liquid nitrogen ( —196°C), b) by driving a precooled center-punch into the sheet, and c) by bending around a crystallographically determined axis with a hammer blow. The impact-deformation produced bands and slip lines on the surface, Fig. 1. The bands have every appearance of being deformation twins, a) They are tilted with respect to the untwinned surface. b) They have the appearance of Neumann bands in iron, thin lens shape, some having serrated edges. c) The orientation in each is different from that of the surrounding matrix and uniform within a given band, see slip lines within them in Fig. 1. d) Upon repolishing and etching, the difference in orientation and the resemblance to Neumann bands is again evident, Fig. 2. (In this micrograph the slight bend in the bands as they cross grain boundaries was noted frequently and results from the high degree of preferred orientation in the sheet.) e) The bands persist after annealing treatments that would have removed them had they been a low-temperature martensitic phase, e.g., after an anneal of 1/2 hr at 900°C. When back-reflection Laue data were plotted for single-surface analysis of several grains, every trace of the bands in each grain could be explained by (112) planes. In addition, two of the bands were located in space by traces on two surfaces, and these also were found to lie on (112) planes within the error of the stereographic plot. Since (1 12) is the anticipated composition plane for deformation twins in body-centered-cubic metals it is felt that the observations listed above are conclusive evidence for the identification of the bands as twins. Similar tests with impact at —77° and at 25°C produced no twinning. It is concluded that the critical shear stress for slip at the rates of straining used was always low enough to prevent the applied stress from reaching the value required for twinning at these temperatures. It was noted that the serrations along the edges of the twin bands exhibited parallel crystal facets. Several similarly oriented notches are visible in Fig. 1, and a remarkable set is shown in Fig. 3. It appears from Fig. 1 and similar areas that notches are frequently associated with the intersection of a slip line with a twin, although not all such intersections are at notches. In some instances a slip line appears to enter the twin, cross it, reflect from the opposite side and recross it, producing a pattern resembling a notch but without producing the notch itself, see Fig. 1. It is suggested that the stress concentration at the end of a slip line is responsible for these details. The strain energy associated with the pile-up of dislocations at a twin boundary may be lessened by untwin-ning or failing to twin a portion of the twin band, or

Jan 1, 1959

By AIME

VERSATILITY is perhaps the outstanding characteristic of the subject of this sketch. He is author, golf-player, musician, public speaker, philatelist, German scholar, and has been a school teacher; but these are incidental. Oliver Ralston's professional forte might be described as beneficiating solid minerals and he has dealt in an important way with practically all of them. To this work he has brought a fertile mind stimulated by keen imagination but kept on the track by a sense of economic balance. An indication of his versatility is evidenced by his career with the Bureau of Mines, which he first joined in 1912, when the Bureau was just one year old. Except for two excursions into industry-Hooker Electro Chemical Co. (1917-20) and United Verde Copper Co. (1928 to 1935)-his entire professional career has been with the Bureau.

Jan 1, 1946

By AIME

A present the colleges and universities are struggling to meet the responsibilities placed upon them by the return of the veterans from the armed forces to the educational institutions as well as the youth graduating from the high schools. The problems of meeting these responsibilities are complex and upon the shoulders of the educational administrators lies much of the burden. One of those educators who is in the midst of this situation is James Rowland Cudworth, dean of the College of Engineering of the University of Alabama and Chairman of the Mineral Industry Education Division, AIME, both for 1946 and 1947. He was born at Norwich, Conn., on Sept. 23, 1897, and like his father before him went to the Massachusetts Institute of Technology where he received his Bachelor's degree in 1921. His studies at MIT were mainly in the fields of geological and mining engineering. Why a New Englander studies mining is anybody's guess, but it may be due to a love of traveling to far places which so many New Englanders do. After graduating tinder the famed Waldemar Lindgren. Jim trekked to Mexico where he worked at Pachuca for the Cia. Real del Monte and at Charcas with the American Smelting and Refining Co.

Jan 1, 1946

SUCCESSFUL development of a new process for heat hardening of pellets made from taconite concentrates was announced by Arthur G. McKee & CO., steel plant engineering and construction firm of Cleveland, and Allis-Chalmers Mfg. Co. An order for the design, engineering, and materials for a plant incorporating the process, has been received by the McKee Co. from the Reserve Mining Co. for its new E. W. Davis Works at Silver Bay, Minn. It is estimated that this plant will cost around $19 million and when in full operation, will turn out 12,000 tons of pellets per day.

Jan 10, 1954

Since this paper was written, some changes have taken place, materially reducing the cost of iron-making as estimated in the text. These are chiefly reductions in the prices of ore and fuel. The charcoal used is now made in bee-hive ovens, and the price is con-

Jan 1, 1895

By A. Schild

The effect of heating a producing well on the rate of oil recovery has been analyzed in the simple case of a well producing oil by a radial drive and in the steady state. Differences of production rates with and without borehole heating have been calculated and plotted; these measure some of the benefits of the thermal recovery process. A striking feature is that the production increase tends rapidly to a constant value for large production rates. Some concrete examples, including a rough comparison with field data. are discussed. Heating requirements have been calculated and plotted on the assumption that the heaters used are 100 per cent efficient. Heating has been thought of as applying only to low volume wells producing heavy oils. However, the calculations suggest that the thermal process considered might be profitable even for some wells producing large quantities of light oil, especially in unconsolidated formations where fracturing is not possible. In the case of wells producing other fluids with the oil or of wells producing partly or wholly by gravity drainage, the theory developed does not apply in detail. It can be expected, however, that any general qualitative be-havior will remain valid. Under normal temperature conditions, high viscosity emulsions sometimes form around the wellbore, lowering the permeability in the vicinity of the well and impeding the production of oil. Borehole heating often prevents such emulsification. This important effect is not easily amenable to mathematical analysis and has not been included in the theory presented here. It should therefore be kept in mind that the benefits due to borehole heating may in fact exceed the values given by the following calculations. INTRODUCTION The recovery of viscous, low gravity oils can often be stimulated by applying heat to the production zone. The higher temperature lowers the viscosity of the oil, increasing its mobility, and therefore its rate of production. One thermal method of recovery 1,2,3,4. consists in operating a heater inside a producing well and, at the same time, producing oil from the well. In this paper a simple theoretical model is analyzed to study the effect of such heating on the recovery of oil. The reservoir mechanics of the process is the only aspect of the problem which is considered here. The details of the heating system are ignored, and it is simply assumed that the heater raises the temperature in the immediate vicinity of the producing well to a pre-assigned temperature T w. Although heating requirements are calculated, these refer only to the heat supplied to the formation and to the oil being produced; they do not include heat losses due to the inefficiency of the heater. A short outline of the theory follows: The heat supplied to the producing well flows out into the formation by means of thermal conduction. At the same time, the flow of oil carries heat by convection from the formation towards the producing well. After sufficient time has elapsed, a steady-state is reached where the temperature, the velocity of the oil, etc., no longer vary with time but are functions of position only. In the steady state the temperature decays like an inverse power from the high value Tw at the wellbore to the original reservoir temperature T. at some distance away from the well. The effect of the high temperature and low oil viscosity near the producing well is the same as if the oil were produced at reservoir temperature To but through a producing well of a larger radius. From this point of view, the energy and money being expended to provide heat

Jan 1, 1958

By C. N. Garman

Homestake-New Mexico Partners operate a 750-tpd carbonate leach uranium concentrate mill near Grants, N.M. The highly mineralized water available as process water leaves much to be desired. The 628 ppm as CaCO 3 makes the use of raw water very troublesome in pipes and on filter cloths. However, the residual sodium carbonate in the final filter cake going to tails makes an ideal softening agent. To take advantage of this fact, all makeup water used in the mill is first used as tailing slurry dilution water and comes to the mill from the tailings pond. The 5-acre tailings pond serves as a thickener and 100 to 150 gpm of nearly clear solution is decanted to a pump to be returned to the mill. Since this tailings water has small quantities of uranium in the solution an ion exchange scavenger unit was installed to remove as much uranium as possible. The ion exchange raffinate is then used as final filter wash ahead of the tailings slurrying step. In spite of the large settling area this return water is not clean enough for ion exchange feed. The solids present are very fine and composed of approximately 15 pct (by weight) burnable carbonaceous material common to the sandstone uranium ores in the area, 40 pct SiOz plus 45 pct CaC03. Laboratory work showed that this material responds very well to flotation. Before deciding to use flotation, various clarifying systems such as pressure leaf filters, sand filters, and continuous vacuum pre-coat filters, were considered. Each of these could have solved the problem but with much more operating labor, more reagents and greater installation costs than the flotation step. About 100 to 150 gpm of fouled water is fed to two 66-in. Fagergren cells, in series. Reagents used at the beginning were Arquad 2HT75 and Arquad C50, at the rate of about 1% lb per 8-hr shift, or about 0.0053 lb each per ton of ore. This did not completely remove the solids but does an acceptable job. Approximately 75 pct of the slimes are a size that can be caught on a 41-Whatman Paper are removed. Removal of these slimes also allows much better settling of the coarse nonfloatable material. Advantage is also taken of this fact in a small settling tank ahead of precipitation. Removal of this amount of the slimes makes the ion t:xchange feasible. PREGNANT SOLUTION CIRCUIT The carbonate? leach-caustic precipitation method of uranium concertration does not provide for any process purification step ahead of precipitation. Therefore, any fine solids getting into the pregnant solution through the filter cloth show up in the final concentrate. This, of course, lowers the grade, and, at times, the slimy nature of these very fine solids rendered final filtration of the concentrate difficult if not impossible At Homestake-New Mexico Partners a 75-ft thickener was available for gravity clarification of 100 to 120 gpm of this pregnant solution. However this did not sufficiently remove the slimes. Laboratory investigation of the whole range of flocculants that were suggested by literature, salesmen, and friends failed to turn up anything of consequence. A continuous vacuum pre-coat filter would do the job and was investigated. The capital cost and the operating labor and materials made this a last chance choice. Following work done in the metallurgical laboratory on the tailings return water, it was found that some changes in the reagent strengths and combinations made a very definite decrease in the solids in the pregnant solution. Concentrate grade improved about 5 pct anti the final product after drying had an appreciably greater bulk density. Compared to a cost of about 2.2e per ton for pre-coat filter opelation for cleaning just one circuit, flotation costs less than 1.0 per ton of ore for cleaning two circuits. While a pre-coat filter would do a more thorough job, the flotation does all that is required for either circuit. Gravity causes the froth produced to run back into the leach circuit. This does not appear to result in a build-up of objectionable slime. No extra manpower is required; the operators in the separate areas can observe the operation of the cells and mix the small quantities of reagents as needed. Normally the 66-in. Fagergren cell requires 15 hp per cell, but this very dilute slurry needs only 10 hp for both cells. Originally, a combination of the two Arquads mentioned previously served as frothers and promoters. As further testing

Jan 1, 1962

By Jun Hino, P. G. Shewmon, P. A. Beck

THE investigations of Crussard,' of Guinier and Tennevin,' and of Dunn and Daniels," indicate that the subgrains formed in a cold worked and annealed metal are capable of growing at each other's expense during annealing, if the temperature of annealing is sufficiently high and the time is long enough. The results of Dunn and Daniels are particularly convincing in showing that subgrain growth is essentially the result of the free surface energy associated with the subboundaries. In subgrain growth, as in ordinary grain growth, energy is gained as a result of the decrease in total subboundary surface area per unit volume. Recently, Wood and Scrutton4 found that the rate of subgrain growth upon annealing increased very considerably, if simultaneously a creep strain was applied to the specimen at a low strain rate. Working with 99.98 pct pure fine-grained aluminum, these investigators found that the continuous X-ray diffraction back-reflection rings of material strained at room temperature remained continuous after heating for ten days at 250 °C. However, when heated at the same temperature under a stress of 1000 psi even for only three days, the formerly continuous X-ray diffraction rings broke up into numerous dots, which were fairly clearly separated from each other. The continuous X-ray diffraction rings were interpreted as indications of a very small subgrain size, not resolved by the X-ray diffraction method used. The breaking up of the continuous X-ray diffraction ring during annealing under stress was taken as an indication of a great increase in subgrain size, so that the individual subgrains could then be resolved. The effect of simultaneous strain at a low strain rate in accelerating subgrain growth, discovered by Wood and Scrutton and designated by them as "cell growth," is of fundamental importance. The experiments described in this note were carried out in order to confirm Wood and Scrutton's results by direct metallographic observation. Also, information was sought as to the minimum creep strain necessary to produce this effect. A fine grained high purity aluminum strip was prepared by alternate 33 pct rolling and annealing treatments for 1 hr at 350°C. Specimens cut from this strip were subjected to a relatively fast creep strain of 7.2 pct in 3.5 min at 300°C under a constant load initially corresponding to 1185 psi. The subgrains set up were large enough (about 0.015 to 0.03 mm) to be clearly observed (Fig. 1) at X200 magnification with polarized light, after electrolytic polishing and anodic etching, producing a fine oxide film." The corresponding X-ray diffraction pattern is shown in Fig. la. After the fast creep strain treatment a portion of the specimen was subjected to a creep strain of 8.3 pct in 44 hr at 350°C under a constant load initially corresponding to 320 psi. Another portion, annealed under the same conditions, but not strained, served as control specimen. The subgrain size of a typical area of the specimen annealed under strain and of the one annealed without strain is shown in Figs. 2 and 3 (X-ray diffraction patterns, Figs. 2a and 3a). Annealing without strain produced clearly observable subgrain growth (subgrain size: about 0.03 to 0.05 mm). The effect of simultaneous strain was to increase greatly the rate of subgrain growth (resulting in a subgrain size of approximately 0.05 to 0.13 mm), in accordance with Wood and Scrutton. In another experiment, the effect of the amount of simultaneous strain was studied. The initial subgrain structure was set up by fast creep, as described previously. The specimen was then heated at 350 °C under a constant load initially corresponding to 320 psi, as above, for 2.2 hr (0.24 pct strain), and 8.8 hr (0.58 pct strain). Comparison with the corresponding unstrained control specimens by means of X-ray diffraction showed that 0.58 pct strain definitely had an effect, but the effect of 0.24 pct strain was doubtful.

Jan 1, 1953

By G. F. Leaming

The paper by R.V. Ramani and R.J. Sweigard is a wonderful description of the labyrinthine web that has been spun about the mining industry by energetic bureaucrats and politicians over the past 50 years. The remedy for the problem, however, is not more of the same, but less. That may be difficult for the industry to achieve, for it is not a technical solution but a political one. And the current fervor for more detailed planning at all levels of government and private enterprise has become deeply ingrained. The authors recommend the provision of more information about mining and mineral resources to "macro" (i.e., government) land use planners. They apparently overlook, however, the already strong tendency on the part of most government land use planners to consider themselves omniscient. Thus, giving them more information about the technical problems of mining will only make them want to get more and more involved in the "micro" (private, site specific) mine development and production plans of the individual mining firm. In fact, this has already happened at all levels of jurisdiction from municipal to federal government. Examples are legion. The most effective way to ameliorate the adverse impacts of government land use planning on existing and potential mining operations is to: (1) introduce greater flexibility in the definition of land use zones by local and state governments; (2) adopt realistic and relevant ambient environmental performance standards in governing relationships between mineral land uses and concurrent or subsequent nonmining land uses; (3) allow greater leeway for economic considerations in land use decisions in contrast to the explicit legalistic approach now in vogue; (4) recognize that all minerals are not the same and that sand and gravel mining should not be treated the same as underground metal mining, coal stripping, oil field production, or in situ leaching; and (5) eliminate the notion that mining operators should be responsible for determining in detail the use of land by subsequent owners of mined land. This last bit of conventional ethic really makes no more sense than requiring the builders of every shopping center or government office complex to provide detailed plans for the use of that land when its use for shopping or government is ended. Did the builder of Ebbetts Field plan for Brooklyn after the Dodgers went to Los Angeles? Should the developer of the Bingham Pit plan for suburban Salt Lake City after the copper mining goes to Chile? The nation's mining industry must address these questions before further bankrupting itself to provide more data to planners and spending thousands of dollars per acre to create land that when reclaimed is worth only a few hundred dollars per acre. ? Reply by R.V. Ramani and R.J. Sweigard We thank Mr. Learning for his valuable contribution. His views on the problems of land use planning and mineral resources are most welcome additions to our paper. As the title indicates, our paper was more concerned with the impacts of land use planning on mineral resource conservation than with the details of the planning process. On the whole, his five recommendations would be helpful for mineral resource conservation. However, we would suggest that the argument he presents for his final recommendation does not address the differences between mining as a land use and commercial or institutional uses. We believe that this difference is the crux of the issue. We share Mr. Learning's desire to ameliorate the adverse impacts of land use planning. Possibly the most detrimental impact is the loss of mineral resources. Any development, whether mineral or community, that does not give proper consideration to other resources can result in permanent loss or sterilization of resources. With proper planning, some of these losses can be avoided. As our paper indicated, one factor that limits the consideration of mineral resources, and ultimately leads to their sterilization, is the generally inadequate levels of resource characterization and understanding of the unique nature of mineral resources and mining operations. The last point raised by Mr. Learning is also important. In terms of reclamation and land use planning in mining districts, we certainly do not advocate spending more than what the results are worth. The main thrust of the paper was to explore the avenues for conserving the mineral resources so that, at some appropriate time, the issue of mining and reclamation can still be addressed. ?

Jan 1, 1986

By Michael A. Toole, O&apos

INTRODUCTION The tremendous capital investment required to produce a low grade ore deposit demands a reliable answer to the question: "How much does it cost to drill a well to produce the uranium that geologists have indicated is there in the ground?" However, you will find the answers given will be many and varied, depending on whether they come from the operating company, the drilling contractor, a geologist, a reservoir engineer, purchasing agent, or whoever. Each generally considers only a limited area of the total operation. The operating company usually depends upon the drilling contractors, service companies, and consultants to supply expertise. Because it is often difficult to see the "whole picture" or even to agree upon what the "whole picture" is, planning a well program and its costs is often done piecemeal. Frequently, costs "saved" in one area of the program are needlessly spent in another, because the effect of one area upon the other was overlooked. Since the drilling fluid is such an influential part of the drilling program, it should be given utmost consideration when planning the overall program. As W. D. Lacabanne wrote in 1954: "The drilling fluid system is understandably called the heart of the rotary oil drilling rig. Any other type of rotary rig.... should benefit by the incorporation of mud fluids in the drilling scheme." And G. R. Gray mentions that "The driller recognizes the drilling fluid as one of the useful tools available to solve drilling problems." However, in minerals drilling, only in recent years has the drilling fluid been considered as more than a tool to get through special problem areas. Although there are many similarities between drilling for oil and gas and drilling for minerals, the differences in the drilling equipment used justifies designing specific fluids for the minerals drilling industry. NL Baroid/NL Industries, Inc. has been a leader in introducing such fluids and in providing technical know-how to the minerals drilling industry. The purpose of this paper is: (1) to discuss the selection of drilling fluids to meet specific drilling conditions during both exploration and production and (2) to show the interrelationship among factors present in the exploration and production phases that influence total well costs. DRILLING FLUIDS FOR DRILLING PROBLEMS The drilling fluid is a tool that can be used to improve drilling performance by improving hole cutting, cleaning, stability, and formation productivity. Properly formulated and maintained drilling fluids enable the drilling operation to be carried out with increased efficiency and lower total (overall) costs. However, it should be noted that not all drilling problems can be solved by even the most carefully prepared and maintained drilling fluids. Of the many possible drilling problems encountered in a well before reaching target depth, this paper will discuss only those most likely to be present in the shallow [61 to 610 m (200 to 2000 ft)] drilling operations in South Texas. LOST CIRCULATION Loss of circulation is the most common problem encountered in drilling. Because the losses occur under varied conditions, it is often difficult to determine the exact causes. "Lost circulation" or "lost returns" means the partial or complete loss of drilling fluid to voids in the formation. "Loss of water" while drilling with water may take place into any permeable section and should be distinguished from "water loss" or filtration of fluid through the filter cake of mud solids laid down on a permeable formation. "Loss of water" can frequently be stopped by the addition of colloidal sized clay particles such as high yield bentonites, whereas "water loss" may be controlled with organic polymers. Subsurface conditions that lead to loss of circulation can be classified as: (1) natural fractures, (2) induced fractures, (3) unconsolidated or highly permeable formations (loose gravel), and (4) cavernous formations (crevices and channels). Loss of circulation may occur whenever the borehole pressure exceeds the formation pressure. The greater the differential pressure, the more likely it is that circulation may be lost. To stop loss of whole mud, voids must be bridged so that a filter cake can be laid down on the permeable section. The plugging material must be of the proper size and shape to offer greater resistance to the fluid flow around it than the flow up the annulus. A plugging composition that satisfies these requirements may not be able to be handled by the small rig pump available.

Jan 1, 1979

By AIME AIME

ALFRED WILLIAM GAUGER ??Al" or '?Doc" to his many friends in the coal and chemical industries- is known for his research talents and organizing ability. Appropriately the first public recognition of his technical ability was by the A.I.M.E. in the publishing of a paper by George A. Burrell and Alfred W. Gauger in the "Transactions" for the year 1916. "Al" Gauger was born at St. Paul, July 31, 1892. He graduated in chemistry at the University of Minnesota in 1914. A year later he began his initiation into the mysteries of coal mining when he joined the safety division of the U. S. Bureau of Mines at Pitts- burgh, serving from 1915 to 1917.

Jan 1, 1944

By J. C. Martin

A theoretical analysis of steam stimulation is presented for single sands. The analysis includes the effect of steam production and most of the effects of heat conduction. The results show the effects of a number of important variables on the performance of an idealized well under steam stimulation. Calculated responses are presented which indicate the effects of steam production, amount of steam injected, water production, formation thickness and formation damage. Results indicate that steam production can cause large reductions in the heat contained in the formation. This effect can be eliminated by drawdown control. Water production reduces the amount of oil produced during stimulation. The optimum amount of steam to inject depends on economic factors as well as the well response. In many cases, the increased temperature resulting from stimulation reduces oil viscosity near the well sufficiently to overcome the effects of formation damage even if the damage is not removed during steam injection. Calculated responses for thin sands are more favorable than anticipated. INTRODUCTION Little has been published on the theory of steam stimulation'-' despite the interest it has created and the wide variation in well responses. The results of the present analysis provide an insight into steam stimulation, and the methods employed provide a foundation for future work. Analyses presented in Refs. 1 and 2 are very limited and apply to gravity drainage conditions. Ref. 3 contains an analysis similar to the one presented here. The idealized models used and the assumptions made in Ref. 3 are different from those used in this paper. The analysis assumes that after steam injection has heated a small portion of the volume within the radius of drainage of a single uniform sand, a shut-in soaking period is allowed before returning the well to production. The effects of gravity, capillarity, transient pressure and water-sensitive sands are neglected. The injection and soaking times are assumed short compared to the stimulated production time. The initial temperature is assumed uniform; thus, the results apply primarily to first-cycle stimulation. The effects of gas production other than steam are neglected, and the water-oil ratio during production is assumed constant. Steam stimulation involves the simultaneous variation of the temperature, pressure and saturations. General mathematical equations for these variations are complicated and can be very difficult to solve. Simplified equations based on idealized models are used to reduce the mathematics sufficiently to allow approximate solutions to be obtained. DISCUSSION INJECTION An idealized model for which heat conduction is neglected is used to represent the behavior of a well during steam injection. The mathematics for this model is presented in Appendix A which also contains an approximate solution for the behavior of the no-conduction model. SOAKING During soaking, the well is shut in. Only the temperature, pressure and saturation distributions at the end of soaking are needed in the analysis. During soaking the heat is considered to be conducted in a uniform medium from an initially uniformly-heated circular cylinder confined to the producing interval. At the end of soaking the saturations and pressures are assumed to correspond to the cold zone. Analysis of the heat flow during soaking is included in the next section. The radius of the heated cylinder is calculated from the following heat balance (for constant quality steam injection). At the end of the soaking period it is assumed that little or no free gas is present near the well, and that the soaking period has been sufficiently long that the steam zone has had time to expand and the steam has condensed. The condition where there is no soaking is considered in the next section. PRODUCTION In this section, an approximate method is presented for solving the equations of heat and fluid flow associated with the production of oil and water during steam stimulation. Where initial pressure drawdowns are sufficient to cause steam to flow into the wellbore, steam production is assumed to occur within a short initial adjustment period (Appendix B). The production practices followed soon after the well is returned to production can have a large influence on the amount of oil produced during the stimulation cycle. Under most conditions, there is a period of time in which some or all of the water in the heated zone is converted into steam and produced. This flashing of hot water is caused by the pressure in the heated zone dropping below

By F. G. Jones, R. D. Pehlke, H. E. Gardner

The solubility of nitrogen in liquid Fe-18 pct Cr-8 pct Ni-0. 7 to 2.3 pct A1 alloys has been measured up to the solubility limit for the formation of aluminum nitride in the temperature range 1600° to 1700°C uszng the Sieverts' method. The solubility of nitrogen in 18-8 stainless steel increases with increasing aluminum content. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from the elements dissolved in liquid 18-8 stainless-steel alloys has been determined to be: ?G° = -42,500 + 20. IT in the range from 1600° to 1700° C. EVANS and pehlke1 have measured the equilibrium conditions for the formation of aluminum nitride, AlN, in liquid Fe-A1 alloys. The present study extends that work to the more complex solvent, liquid 18 pct Cr-8 pct Ni (18-8) stainless steel. Recent work by Small and pehlke2 has dealt with the effect of fourth-element additions on the solubility of nitrogen in 18-8 base alloys. They found the effect of aluminum additions, up to 0.74 pct, on the solubility of nitrogen to be small. The present study covered the range from 0.74 to 2.28 pct aluminum, and by extending the composition range may be used to better define the effect of aluminum on the nitrogen solubility in these alloys. EXPERIMENTAL PROCEDURE The Sieverts' method was used to measure the equilibrium solubility of nitrogen gas in liquid 18-8 stainless steel alloys containing 0.74, 1.49, 1.93, and 2.28 pct Al. The solubility was measured as a function of the nitrogen gas pressure at temperatures of 1600°, 1650°, and 1700°C. The apparatus used is the same as described by Small and Pehlke.2 The 100-g melts were made from Ferrovac-E high-purity iron, Crucible Steel Co.; 99.95 pct Cr, Union Carbide Corp.; 99.9 pct Ni, International Nickel Co.; and 99.99+ pct Al, Aluminum Co. of America. The aluminum was charged at the bottom of the crucible, surrounded by nickel and iron. The chromium was packed into the interstices to minimize vapor transport of the aluminum during initial melting. The hot volume of the system, measured for each melt with argon, ranged from 45 to 55 standard cu cm with a temperature coefficient of —8 x 10-3 cu cm per °C. The melt temperature was measured with a Leeds and Northrup disappearing-filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature calibration of the system by Small and pehlke2 was assumed. Two problems are involved in determining the solubility product of a solid, metal nitride phase in liquid iron alloys. These are: 1) establishing the point of departure from Henrian behavior at the solubility limit of the metal nitride phase; and 2) determining the composition of the solid nitride which is precipitated. Determination of the solubility product of AlN was made by admitting small amounts of nitrogen into the reaction bulb until the deviation from Sieverts' law was clearly evident in the form of a pressure halt. To obtain the solubility product at several temperatures during one run the following procedure was used: 1) add increments of nitrogen to determine the Sieverts' law line at the lowest desired temperature; 2) continue to add nitrogen to precipitate a small amount of the nitride phase; 3) increase the melt temperature 50°C to dissolve the precipitated nitride; 4) repeat step 2 until either a nitride formed or the system reached ambient pressure; if a nitride formed at 1650°C, the sequence was repeated at 1700°C. The composition of the precipitated phase was checked by an X-ray diffraction pattern obtained from powder scraped from the surface of the solidified 1.93 pct A1 melt. RESULTS AND DISCUSSlON Solubility Measurements. Fig. 1 is a typical nitrogen-absorption curve obtained from measurements on a 1.93 pct A1 alloy. Since the initial absorption of nitrogen follows Sieverts' law the nitrogen solubility is plotted as a function of the square root of the pressure of nitrogen gas in the reaction bulb. The results of the solubility measurements for all alloys studied are summarized in Table I. The slope of the Sieverts' law line for each alloy was determined. Since this is also the solubility of nitrogen at 1 atm pressure of nitrogen gas, the latter designation is used for the data. It should be noted. however, that in most cases the value lies above the solubility limit for AlN. Fig. 2 shows the effect of aluminum on the solubility of nitrogen at this reference pressure and as a function of melt temperature. The solid portions of the lines represent attainable solutions; the dashed regions lie above the limit for precipitation of AlN.

Jan 1, 1969

By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed. Flotation involves the selective levitation of mineral and its transfer from cell to launder. The flotation rate is the rate of this transfer. It may be defined by the slope of a recovery-time curve for any cell in a bank, or at any time in batch operation. The objective in flotation rate study is an equation expressing the rate in terms of some measurable property of the pulp. This can be either the concentration of floatable mineral in weight per unit volume1,2 or a relative concentration, which will be a function of the recovery." A rate equation for an actual flotation pulp will contain at least two constants, both to be determined from the data. One of these, the initial concentration or proportion of floatable mineral, is not necessarily equal to the feed assay because of nonfloatable oversize or locked particles." The other, a rate constant, is a measure of proportionality between the rate and the pulp property on which the rate depends. The value of the rate constant will be determined by the values of all variables which control the process and will be changed by significant changes in any of them. It is, therefore, a direct measure of performance. Where recovery or grade change continuously with flotation time, the rate constant will be independent of time and will characterize the entire course of the separation. Development of Rate Equations Rate equations can be developed either by analysis of the mechanism of the process or by direct fitting of equations to recovery-time data. Sutherland's attempt by the first method' suggests that the effect of particle size variation on the rate complicates the derivation of a simple equation applicable to an ore pulp. A further problem with an ore is the concentrate grade requirement, which usually involves a variable rate of froth removal. Thus the final rate for any cell may depend on the froth character and froth height, as well as on the pulp composition. This does not imply that each cell cannot reach a steady state2 in which the rate will depend ultimately on pulp composition. The second method is the fitting of rate equations consistent with the necessary boundary conditions* to experimental recovery-time curves. On the assumption that under constant operating conditions the flotation rate is proportional to the actual or relative concentration of floatable mineral in the pulp, a generalized rate equation may be expressed as follows: Rate = Kcn [I] where K is the rate constant, c is some measure of the quantity of floatable mineral in the pulp at time t, and n is a positive number. In previous rate studies, the value of n has been taken as 1, either by direct assumption," or as a result of the hypothesis that bubble-particle collision is rate determining.' A first order equation results, which after integration in terms of cumulative recovery R, leads to Loge A/A-R = Kt [2] The quantity A is the maximum possible recovery with prolonged time under the conditions used. No conclusive proof for the validity of this equation in flotation has been advanced. The evidence cited in its support consists entirely in the demonstration that it appears to apply to a limited number of recovery-time curves."' It will be shown subsequently that this procedure is not sufficient to establish the order of a flotation rate equation. The possibility that the equation may be of higher order therefore requires examination. If, in particular, the exponent in eq 1 is assumed to be 2, then after integration there results R = A2Kt/1 + AKt [3] with K again a rate constant and A the maximum proportion of recoverable mineral. Eq 3 may be

Jan 1, 1952

By J. S. Rinehart, W. C. Maurer

The mechanics of impact crater formation in rock, particularly sandstone, has been sutdied, the velocity range being approximately that normally associated with oilwell gun perforators. The bullets were small steel spheres having diameters of 3/16, 9/32 and 7/16 in; impact velocities ranged from 300 to 7,000 ft/sec. The craters have two distinct parts — a cylindrical hole (or burrow) with a diameter the same as that of the impacting sphere, and a wide-angle cup comprising most of the volume of the crater. The burrow is fornred as material in front of the projectile is crushed and pushed aside, forming a cylindrical hole surrounded by a high-density zone. The clip forms as fractures are initiated in front of the projectile and propagate along logarithmic spirals, approximaling maximum shear trajectories, to the free surface of the rock. A most significant observation (made for the first time) was that, below the base of the cup in one type of sandstone, there are a group of similar fractures, not extending to the surface, which are spaced uniformly a few millimeters apart. Each fracture follows roughly the contour of the base of the cup and appears to require a certain threshold impulse to initiate it. These fractures comprise a relatively high fraction of the total, newly exposed surface area. The volume of the material removed by crushing varies as the first power of the impact velocity and the volume removed by fracturing, as the second power of the impact velocity. Penetration varies linearly with the impact velocity and is inversely proportional to the specific acoustic resistance of the target material, the proportionality constant being dependent upon the shape of the projectile. INTRODUCTION Yield of oil from a producing well is frequently enhanced by firing bullets and shaped charges through the well casing into the oil-bearing rock, forming craters and fractures from which oil can flow more readily. The purpose of this investigation has been to develop a better understanding of the mechanics of impact crater formation in rock, particularly sandstone, the velocity range being approximately that normally associated with oilwell gun perforators. FORCES OPERATIVE DURING IMPACT When a projectile moving at considerable velocity strikes a- massive target such as oil-bearing sandstone, intense and complex transient stress situations develop within both the projectile and the rock or sandstone against which it is striking. Usually the struck rock fails, the missile or projectile penetrating into the rock to some depth where it comes to rest or is forcibly ejected from its burrow by expansion of a plug of target material compressed in front of it. When the impact velocity is very high, the projectile itself may fail, breaking apart or becoming distorted; this situation is not considered here, the discussion being limited to nondeforming projectiles. Many experimental studies'.' have been carried out to determine the nature of the mechanics of crater formation and the salient features of the forces coming into play, some of the earliest studies being the French Army experiments performed at Metz between 1835 and 1845.' The stratagem in most instances has been to make a post-mortem examination of the crater, measuring volume and depth of penetration and deducing force relationships from these observations rather than performing the more difficult (usually almost impossible) feat of measuring stresses during penetration. In many materials, the force acting during penetration of the projectile is found to be the sum of two components—(1) a constant force, independent of the velocity, representing some inherent strength of the target material; and (2) a component, proportional to the square of the velocity, representing inertial forces. For such materials, the average force per unit area acting on the projectile at any instant while it is in motion and being decelerated may be written F/A = a + bv2 . . . (1) where v is the velocity of the projectile at that instant, A is the cross-sectional area of the penetrating projectile taken normal to its trajectory, and a and b are constants which are dependent upon the target material and the shape of the projectile. It follows that the total penetration s is given by .........(2) where v, is the velocity of the projectile when it just strikes the target. Values of a and b for spherical projectiles impacting in a loose sand-gravel mixture and compacted earth were obtained in the Metz experiments. For sand-gravel, a and b are 620 psi and 0.0115 (psi) (ft/sec)', respectively; and for compacted earthworks, a and b are 432 psi and 0.0008 (psi) (ft/sec)'. Figs 1 and 2