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By J. W. Graham

For many years the author has been cognizant of the difficulty encountered by some in treating with the water influx formulas for unsteady-state fluid flow as pertain to the material balance equation. This has particularly applied in establishing reservoir performance and identifying reservoir pressure, which to the practicing engineer has entailed a trial-and-error procedure, and for others has necessitated resorting to computing devices and reiteration processes. In retrospect this difficulty stems from the fact that reservoir pressure in the material balance formulas, as well as associated with the water influx equations, is an inexplicit term, and the work reported in the past is irrefutable. However, what will be presented in this paper is another approach to the problem, whereby the entire material balance equation will be treated by the Laplace transformation, and reservoir pressure which hereto has been inexplicit, can now be isolated by mathematical procedure to relate that parameter with all the factors contributing to its change. This is the simplification entailed, that treats first with an undersaturated oil reservoir as an integrated effect from the inception of production. The second phase pertains to saturated oil reservoirs that encompass a survey traverse. Although both methods of approach are necessarily different in aspect, the most interesting fact is that the mathematics so deduced are identical. Both the linear and radial water-drive systems are incorporated. for which an illustrated factual example is offered for the latter, treating with a saturated oil reservoir. INTRODUCTIO N What is performed in this work is the simplification of an involved computation by advanced analysis. Although such may be construed as a contradiction when one treats with higher mathematics; nevertheless, when direction is given to such an undertaking the results car. be most revealing. Likewise, it is to be mentioned that the bases for these mathematics have been developed on the expediency of the occasion. This is not to be inferred as a qualification of this work, but rather the demands frequently placed upon the author in his private prac- tice in meeting a time limit. A situation, instead of being fraught with hazards, often has given emphasis to creative thought. What will be entailed in this work is the simplification of the material balance formulas by the Laplace Transformation., Although this reveals entirely new horizons that will be given expression in a forthcoming tract, it suffices in the present instance to limit our attention to this phase of the development that treats both with an undersaturated and saturated oil reservoir. To orient the reader's thoughts as to what is involved in this simplification is the recognition that reservoir pressure, as such, is an inexplicit term in the material balance equation. This is the independent parameter that defines the total history of performance in the author's' unsteady-state water influx formulas, as well as the basis for the physical dependency of fluid behavior within the formation as prescribed in the Schil-thuis' material balance equation. Therefore, to isolate reservoir pressure, which is the most essential factor in any reservoir study, is rather a cumbersome procedure entailing either a trial-and-error calculation for the engineer; or as some prefer, a reiteration process performed on a computing device. However, once such an equation can be transcribed as a Laplace transformation, this inexplicitness so expressed can be alleviated to identify reservoir pressure as an explicit function of all the factors contributing to its change. This is the simplification encompassed, that will treat first with an undersaturated oil reservoir as an integrated effect from the inception of production, and secondly, with a saturated oil reservoir as a survey traverse. Although the two approaches are necessarily different because of the uhvsics involved. it is an interesting commentary that the mathematics are identical, showing the interdependency of the two methods. In order to acquaint the reader with this development, the simplest case will be treated first; namely, an under-saturated oil reservoir subject to a linear water drive. However, what may be construed for this example as an idealistic case is actually a most practical application in certain parts of the world, where the size of the fields are so large that radial water-drive approaches the configuration of a linear drive. Further, to avoid the repetition of much symbolism, frequent references will be made to the work of the author and an associate on Laplace Transformations3,

By R. W. Smith, R. J. Charles

Fractions of glass particles in the size range 0.5 to 5.0 µ were prepared by an elutriator that operates in a centrifugal field. Although mean sizes of commercially graded abrasive powders were ten times greater than those of samples prepared by the elutriator, frequency size plots for elutriator samples compared favorably. Efficiency of separation was low and amounts of material recovered by the elutriator were small, but the method should find use in preparation of small amounts of sized materials for laboratory investigations.

Aug 1, 1956

By Orville R. Lyons

THE continuous vacuum filter, whether it be a vertical or horizontal disk, inside or outside drum, when properly applied is a very effective device for dewatering fine solids. Because of the number of variables that affect its performance, however, it is not possible to obtain consistently maximum moisture reduction in an operating plant. This paper presents a method for determining the average cake moisture and the variations in cake moisture to be anticipated when dewatering fine solids by continuous vacuum filters under normal operating conditions.

Jan 10, 1951

"The Southern Cross mining district was discovered during the early rush of gold seekers over Montana following the discovery of gold in 1861. Placers were worked near the Atlantic Cable mine in 1866, and soon attention was turned to quartz lode mining. High grade ores were discovered in the North Atlantic claim, adjoining the present Southern Cross group. The early metallurgical treat¬ment of these ores was by means of arrastres, a crude form of amalgamating mill, illustrated on the page opposite. This old arrastre located by the roadside on Warm Springs creek, was built by Barker Bros. in 1879. Further discoveries overtaxed the capacity of this plant, and in 1875 Thomas' Stuart employed a contractor named Jeptha J. Corner to convert the old Wilson & Fifer sawmill located at the Big Spring into an up-to-date gold quartz mill. 'For this trans¬formation Corner received the sum of $1,400.00. The illustrations give a good idea of the nature of its construction. Practically no iron was used in the mill, excepting for the stamps, dies and cams and cam shafts. Whether or not the saving attained reached the limits of present day perfection is not known. There being no steam boilers available, the early prospectors believed in the principle of conservation of fire wood, water power was therefore used, generated by a ""direct-connected"" over-shot wheel. Water for power purposes was supplied by the nearby spring. History fails to record the tonnage treated in this relic of early Montana milling practice.The ores of the Southern Cross district have not proved readily amenable to mill treatment, but being largely composed of iron oxides, they are most desirable fluxing ores for smelter operations. The B. A. & P. Ry. extends into the district. Electric power is furnished by the Flint Creek 'station, three miles distant."

Jan 1, 1913

The John Fritz Medal for the year 1917 has been awarded to Professor Henry Marion Howe for his investigations in metallurgy, especially in the metallography of iron and steel. Record of the John Fritz Medal. The John Fritz Medal Board of Award has published a book giving a history of the Medal, the Rules of Award, biographical notices of the medallists illustrated with portraits, etc. This beautiful book, designed, engraved and printed by Bartlett Orr Press, New York, may be obtained by addressing the Secretary of John Fritz Medal Board of Award, Engineering Societies' Building, New York. Price $3 per copy.

Jan 3, 1917

* Phosphate from the Maiden Rock deposits in the Missouri River Basin, Mont., are to be developed by the Victor Chemical Works of Chicago. A $5 million plant for processing the rock into elemental phosphorus is to be constructed in the vicinity of Butte. The plant will receive power from the Bonneville Power Administration. * Tests are being made to determine whether iron pellets from taconite concentrates will boost blast furnace and open hearth output at the Campbell Works of the Youngstown Sheet & Tube Co. About 35,000 tons of iron pellets have been shipped from Minnesota for this purpose.

Jan 2, 1951

By Sam Rosenblum

The anomaly ratio is obtained by dividing the analyzed value of an element by the anomaly threshold value of the element. The sum of anomaly ratios for all anomaly elements in a sample may be compared with similar sums for other samples, so that samples having the greatest anomaly- ratio totals can be recognized easily. In partial or full suites of ore elements the we of anomaly ratios is more meaningful than use of analyzed value because the ratios quickly indicate how use of analyzed values because the ratios quickly indicate how anomalous some elements are, and call attention to samples and

Jan 1, 1982

By E. T. Cox

The peninsula of Florida is remarkable for the uniform character and simplicity of its geological structure. Major Henry Whiting, of the U. S. Army, was one of the first to give an account of the physical features and rocks of Florida, in an article published in 1839, in the American Journal of Science (vol. xxxv., p. 47). He says: " The rocks found in situ are all calcareous, though siliceous boulders are occasionally seen, and nodules of hornstone are here and there mingled with the limestone, which elicit sparks and are sometimes used by the Indians for flints."

Jan 1, 1896

By H. E. Mauck

The many factors that control bumping must be carefully studied for each coal seam where bumps occur, and specifications known to exclude bumping should be incorporated in the mining plans. This calls for complete knowledge of the seam's characteristics and its adjacent strata, and in many instances these characteristics are not revealed until the seam is actually mined. Pressure and shock bumps, the two general types, occur jointly and separately. In this discussion no differentiation will be made. Whether pressure or shock, they are treated as bumps, and both must be eliminated.

Jan 9, 1958

By Merlyn B. Buhle

FOR the past 20 years electrical earth resistivity exploration has been used in Illinois in many phases of study undertaken by the State Geological Survey, chiefly in locating and outlining deposits of water-bearing sand and gravel from which to obtain ground water for municipal and industrial supplies. At least 43 municipalities in the state derive their total water supply from deposits of sand and gravel discovered by resistivity methods. These deposits occur in both Quaternary and preglacial valleys and within much of the glacial drift which covers .a large portion of the state

Jan 4, 1953

By Robert C. Bates

Published information on costs of radon daughter control in uranium mines was analyzed to develop estimates of the cost per ton for any level of radiation exposure control. All data were converted to 1967 cost of living index to provide a common analysis base. Re- of the analysis show that the cost per ton increases exponentially as the radiation level is lowered. A linear relationship with the cost of living index is assumed, and equations and graphs are provided to estimate control cost per ton for any exposure control level and cost of living index.

Jan 1, 1982

By Peter J. Huck, Madan M. Singh

IIT Research Institute has investigated the potential of high pressure water jets for rapid rock excavation. During this study, an attempt was made to correlate the extent of breakage effected to the mechanical properties of rocks. Six rock types were used in these experiments and nine properties were determined for each rock variety. A regression equation using the two most significant rock properties and one jet parameter (pressure) was established. Although tests were conducted to specific pressures of 35, no minimum in the specific energy consumption was noted.

Jan 1, 1971

By Elmer R. Kaiser

Cooperative research is an established and important activity of modern business by which whole industries can advance on a broad front. The economy of jointly sponsored research as well as the limited research talent available direct attention to the advisability of projects in which a number of companies participate. After outlining the growth of industrial research, the paper discusses one successful method for organizing and financing group research programs. A systematic procedure is advocated by which engineers and scientists can bring to management practical plans for cooperative research and development programs.

Jan 3, 1950

By Donald L. King

This paper has been prepared with the objective of providing basic information on thickening equipment as applied to mineral processing plant design. Thus, by design, the content is elementary, yet sufficiently informative to advise the reader concerning the thickening and clarifying process, equipment configurations, installation and operation. Practical considerations are provided for slurry samples for testing, evaluation of testing, preliminary sizing, duty classification, and thickener selection to enhance operation, see icing and control. Illustrations are provided to both inform and demonstrate present state of the art features and capability.

Jan 1, 1978

By G. Campbell

The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff’s theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which

Jan 1, 1984

By C. P. Parsons

Caliper logging is a practice of measuring the variations in the diameter of the open hole in a well. This information is useful for many purposes, among which are: Determining the volumetric capacity of the portion of open hole to be cemented; the amount of gravel to be used for gravel-packing a well; the size and location of seat for a packer to be placed in a well; studying the effects of nitroglycerin shots; studying the effects of acidizing; studying the cause of drill-pipe failures; studying drilling technique; geological correlations. This is a new practice in oil fields and is eliminating considerable guesswork. Introduction Caliper logging of the open hole in oil wells, recently introduced and now showing initial results in many sections of the country, is providing information that is filling a long-felt need in oil-well cementing and in numerous other oil-field practices. Briefly, it measures the variations in diameter, of the open hole in a well. This direct physical measurement of the strati-graphic profile has considerable value for subsurface interpretations by the geologist, engineer, driller and others charged with the responsibility of properly completing and repairing oil and gas wells. The caliper shown in Fig. I is run into a well in closed position. The four arms are released when logging is to start. These arms are independent of each other. As the calipers are pulled upward through the open hole, the arms are like nimble fingers feeling the changing profile of the hole. This mechanical action is in turn converted into an electrical circuit, which is connected to a recording mechanism at the surface. a. Lowered into well in closed position. b. Arms released. Readings are made while caliper travels upward. Direct recording is made at surface, in inches. The recording of the diameter of the hole is directly in inches.

Jan 1, 1943

By C. P. Parsons

Caliper logging is a practice of measuring the variations in the diameter of the open hole in a well. This information is useful for many purposes, among which are: Determining the volumetric capacity of the portion of open hole to be cemented; the amount of gravel to be used for gravel-packing a well; the size and location of seat for a packer to be placed in a well; studying the effects of nitroglycerin shots; studying the effects of acidizing; studying the cause of drill-pipe failures; studying drilling technique; geological correlations. This is a new practice in oil fields and is eliminating considerable guesswork. Introduction Caliper logging of the open hole in oil wells, recently introduced and now showing initial results in many sections of the country, is providing information that is filling a long-felt need in oil-well cementing and in numerous other oil-field practices. Briefly, it measures the variations in diameter, of the open hole in a well. This direct physical measurement of the strati-graphic profile has considerable value for subsurface interpretations by the geologist, engineer, driller and others charged with the responsibility of properly completing and repairing oil and gas wells. The caliper shown in Fig. I is run into a well in closed position. The four arms are released when logging is to start. These arms are independent of each other. As the calipers are pulled upward through the open hole, the arms are like nimble fingers feeling the changing profile of the hole. This mechanical action is in turn converted into an electrical circuit, which is connected to a recording mechanism at the surface. a. Lowered into well in closed position. b. Arms released. Readings are made while caliper travels upward. Direct recording is made at surface, in inches. The recording of the diameter of the hole is directly in inches.

Jan 1, 1943

By Holbrook G. Botset

Experiments performed in this laboratory on the flow of gas-liquid mixtures through unconsolidated sands have been described and discussed in an earlier paper.4 In these earlier experiments a definite relationship was found between the liquid saturation of a sand and its permeability to the liquid or gas phase. Furthermore, the nature of the sand, the permeabilities of the sands over a range between 17 and 260 darcies, appeared to have a negligible effect upon the saturation-permeability relation. Likewise experiments indicated that the viscosity of the liquid, or the substitution of an immiscible liquid for the gas phase, had only a very slight effect on the permeability-saturation relation. This conclusion has since been definitely confirmed by the experiments of M. C. Leverett3 on the flow of oil and water through unconsolidated sands. The sands used by Leverett were of very low permeability (between 6.8 and 1.04 darcies), while the oil-water viscosity ratio varied between 90 and 0.057. Since the sands that constitute petroleum reservoirs are largely consolidated, although of widely varying degrees of consolidation, it was desirable to extend the experiments on gas-liquid mixtures to consolidated sand. In the study of consolidated sands additional variables are involved, but for the initial experiments the only new variable to be introduced was the cementing material. Experimental Procedure A comparatively limited assortment of sandstones was available for the selection of the experimental material. Of these, the Nichols buff sandstone appeared to be most suitable. It gives no visual evidence of any bedding planes, it has a firm structure, permitting easy handling, and its permeability is about 0.5 darcy. Its only disadvantage is the fact that it contains an appreciable amount of ferric oxide which, for experiments involving water, will hydrate and reduce the permeability. This

Jan 1, 1940

By Holbrook G. Botset

Experiments performed in this laboratory on the flow of gas-liquid mixtures through unconsolidated sands have been described and discussed in an earlier paper.4 In these earlier experiments a definite relationship was found between the liquid saturation of a sand and its permeability to the liquid or gas phase. Furthermore, the nature of the sand, the permeabilities of the sands over a range between 17 and 260 darcies, appeared to have a negligible effect upon the saturation-permeability relation. Likewise experiments indicated that the viscosity of the liquid, or the substitution of an immiscible liquid for the gas phase, had only a very slight effect on the permeability-saturation relation. This conclusion has since been definitely confirmed by the experiments of M. C. Leverett3 on the flow of oil and water through unconsolidated sands. The sands used by Leverett were of very low permeability (between 6.8 and 1.04 darcies), while the oil-water viscosity ratio varied between 90 and 0.057. Since the sands that constitute petroleum reservoirs are largely consolidated, although of widely varying degrees of consolidation, it was desirable to extend the experiments on gas-liquid mixtures to consolidated sand. In the study of consolidated sands additional variables are involved, but for the initial experiments the only new variable to be introduced was the cementing material. Experimental Procedure A comparatively limited assortment of sandstones was available for the selection of the experimental material. Of these, the Nichols buff sandstone appeared to be most suitable. It gives no visual evidence of any bedding planes, it has a firm structure, permitting easy handling, and its permeability is about 0.5 darcy. Its only disadvantage is the fact that it contains an appreciable amount of ferric oxide which, for experiments involving water, will hydrate and reduce the permeability. This

Jan 1, 1940

By E. G. Leonardon, C. Schlumberger, M. Schlumberger

In the search for practical geological problems amenable to solution by the potential methods, the geophysicist is led to study mathematically various theoretical cases. In these idealistic discussions, the media under consideration are generally supposed to be homogeneous and iso-tropic. The geophysicist, of course, realizes perfectly that these conditions do not occur in their entirety in reality. However, the assumptions made are justified, because very often they are necessary in order to render possible an exhaustive study of a given problem, which otherwise would be too complicated, and would not lend itself to a complete mathematical analysis. Of the above two assumptions, that concerning the homogeneity of a given geological formation is satisfactorily realized except in so far as isotropy is concerned, since this property is not often encountered in practice. As a consequence, it is very desirable for the geophysicist to have quite an extensive knowledge of the properties of anisotropic formations, and of the laws that govern the propagation of electric current therein. With such principles in mind, he will be able to decide whether the conclusions arrived at in simple, isotropic conditions are still correct in more complex cases, or in what way they must be modified or adapted in order to constitute a sound basis for the interpretation of the results obtained in anisotropic media. On the other hand, the fact that in anisotropic formations the mobility of the ions is greater along the strike than perpendicular thereto can be utilized for determining the direction of the dip by induction measurements. We therefore propose to study in three successive chapters the following points: 1. Propagation of the electric current in anisotropic media. 2. Some consequences of the anisotropy of geological formations with reference to the surface electrical measurements, and their interpretation. 3. Determination of the direction of the dip of anisotropic formations by surface induction measurements.

Jan 1, 1934