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By Edward N. Trump

EXTENSIVE beds of rock salt occur in New York, Michigan, Kansas, and Texas. Wells are drilled through the beds, cased, and equipped with a suspended center tube. By circulating water through such a well, the soluble saline is dissolved and a brine produced. Operation of a well results ordinarily in the formation of an inverted conical cavity in the saline, inasmuch as the dissolving action of the fresh water is more rapid at the top of the bed than at the bottom. Under continued operations, the side wall of the cavity becomes so flat that a blanket of mud is deposited thereon and if the bed is overlain with shale or a soft rock caving follows. Three methods of operating wells have been employed-the "Tully plan," "the Detroit plan," and "the Trump plan." Both the Tully plan and the Detroit plan involve the formation of the aforesaid conical cavity with constant caving of shale above and deposition of mud on the side wall; the Trump plan was developed to avoid both these circumstances and thus materially prolong the life of a well. Details of the three plans follow. THE TULLY PLAN In the Tully plan, the water passes down the annular space between the casing and the center -tube, the brine rising in the center tube (Figs. I and 2). An inverted conical cavity is formed, the side wall of which relatively soon becomes so flat that it is blanketed by mud and impurities from the rock salt; this blanket limits dissolving action to the perimeter of the base of the cone, situated at the top of the saline bed. Caving of the overlying strata follows, and the total production of brine from the well is comparatively small. THE DETROIT PLAN In the Detroit plan, the water passes down the center tube, the brine rising in the annular space between the center tube and casing (Figs. I and 2). Initially, this flow forms a pear-shaped cavity in the bottom of the salt bed, but this cavity soon changes in shape to that of an inverted cone, as under the Tully plan, with the attendant disadvantages inherent in that plan. Application of the Detroit plan is limited to salt beds 300 ft. thick as a minimum. This depth of bed is necessary to prevent fresh water of lower specific gravity than the brine from rising in the

Jan 1, 1944

By Edward N. Trump

Extensive beds of rock salt occur in New York, Michigan, Kansas, and Texas. Wells are drilled through the beds, cased, and equipped with a suspended center tube. By circulating water through such a well, the soluble saline is dissolved and a brine produced. Operation of a well results ordinarily in the formation of an inverted conical cavity in the saline, inasmuch as the dissolving action of the fresh water is more rapid at the top of the bed than at the bottom. Under continued operations, the side wall of the cavity becomes so flat that a blanket of mud is deposited thereon and if the bed is overlain with shale or a soft rock caving follows. Three methods of operating wells have been employed—the "Tully plan," "the Detroit plan," and "the Trump plan." Both the Tully plan and the Detroit plan involve the formation of the aforesaid conical cavity with constant caving of shale above and deposition of mud on the side wall; the Trump plan was developed to avoid both these circumstances and thus materially prolong the life of a well. Details of the three plans follow. The Tully Plan In the Tully plan, the water passes down the annular space between the casing and the center tube, the brine rising in the center tube (Figs. I and 2). An inverted conical cavity is formed, the side wall of which relatively soon becomes so flat that it is blanketed by mud and impurities from the rock salt; this blanket limits dissolving action to the perimeter of the base of the cone, situated at the top of the saline bed. Caving of the overlying strata follows, and the total production of brine from the well is comparatively small. The Detroit Plan In the Detroit plan, the water passes down the center tube, the brine rising in the annular space between the center tube and casing (Figs. I and 2). Initially, this flow forms a pear-shaped cavity in the bottom of the salt bed, but this cavity soon changes in shape to that of an inverted cone, as under the Tully plan, with the attendant disadvantages inherent in that plan. Application of the Detroit plan is limited to salt beds 300 ft. thick as a minimum. This depth of bed is necessary to prevent fresh water of lower specific gravity than the brine from rising in the

Jan 1, 1948

By T. Inoue, T. Imaizumi

A simulation model has been developed to find out the possibility of improving the industrial closed-circuit wet grinding operations. The model involves a continuous tumbling mill in combination with a hydrocyclone to recycle the oversize material back to the mill. The mill is described by the breakage, i.e. the selection and the distribution, functions, co-ordinated with the diffusional mixing along the axis. The cyclone classifier is characterized by the partition function with allowance for the non-selective separation of part of the feed material into the underflow. The computer program developed incorporates an interactive capability to modify the operating conditions of the system whenever needed. The results are analysed for the operational conditions characterizing the mill and the classifier. Besides the steady state conditions some observations are also made about the dynamic responses of the closed circuit grinding system.

Jan 1, 1980

By E. J. Horwood

The varying physical character and large extent of the Broken Hill lode necesarily involve the employment of a variety of underground methods. The lode had its origin in an extensive fault plane traversing metamorphosed schists conformably, as a rule, with their beds of stratification. The underground waters carrying minerals in solution deposited their contents in the original cavities formed by the faulting action, and in the enlargements of these cavities due to dynamic forces brought to bear on the rocks, more especially on the hanging-wall side of the fault. This deposition was supplemented by metasomatic replacement of a portion of the original rock contents by the argentiferous sulphides of lead and zinc which form the staple products of the district. Although the orebody is practically continuous throughout the mines, its width varies greatly, ranging from a few feet to about 350 ft. The widest portions occur in conjunction with huge folds in the inclosing country rock, almost exclusively on the hanging-wall side. The ore in these folds pitches to the south in the southern half of the field, and to the north in the northern half; there are, however, undulations in these ore channels evidently due to compression of the rocks in the direction of the channels. In the earlier days, before the orebodies had been opened up, vertical cross-sections across these bulges in the hanging wall gave the lode the appearance of the "saddle formation," so well exemplified at Bendigo in Victoria; but subsequent development of the ore channels has long since proved that the formations in the two districts are entirely different. The depth reached by the zone of complete oxidation of the sulphides varies from about 259 to 550 ft, from the original outcrop, while partial oxidation extends in places below the 1,000-ft. level. The result of oxidizing influences has been the production of ore of every grade of cohesive-ness, from that of dry sand to that of hard compact rock. The methods of mining followed in this field, and even in individual mines, are varied in accordance with the character of the ore. The general practice of the field is to sink vertical shafts, generally on the foot-

Jan 1, 1916

By G. H. Pardue, L. H. Gollwitzer, J. H. Moran, R. L. Morris

Experimental and theoretical studies of casing-borne signals have provided data on the attenuation efect, compressive strength and shear modulus for different types of cement. These data resulted in the establishment of a definite relationship between the cement compressive strength and the Cement Bond log reading. The relationship is influenced by the casing dimensions, but is independent of the type of cement and the curing conditions. The theoretical analysis provides a mathematical statement of the phenomenon and shows that the attenuation rate is basically a function of the shear modulus of the cement and the thickness of the casing. The lab tests provided a connection between the shear modulus and the compressive strength, and permitted a comparison of the experimental and theoretical work. The results of the experimental and theoretical study have provided means of quantitative interpretation of the Cement Bond log. This interpretation is made more convenient with the use of a nomograph. INTRODUCTION Past interpretation of Cement Bond logs has been essenlially based upon a qualitative comparison between the log response in the zone of interest and the responses in the "fully cemented" and the "uncemented" intervals. Most of the variables influencing the magnitude of the signals were recognized in an earlier paper'; however, insufficient laboratory data were available at that time for quantitative evaluation of these variables. Early attempts to use the numerical amplitudes of the signals without full knowledge of their significance resulted in erroneous comparisons between various types of cement. An extensive program was undertaken to evaluate, both experimentally and theoretically, the attenuation phenomenon and to study the effects of the more common variables. A major objective of the experimental program was to obtain data on the relationship between cement-bond-tool response and physical property standards used by the industry so that practical interpretation methods could be devised. The studies included a comparison of attenuation rate with these properties as a function of time, temperature and pressure, using common sizes of casing. The main result was that a definite relationship was established between the compressive strength of the cement in inti- mate contact with the casing and the response of the cement bond tool. For a given casing thickness, regardless of the type of cement or the curing conditions used, the attenuation rate is a function of the compressive strength. A theoretical analysis showed that the attenuation rate for casing-borne signals should be a function of (among other things) the shear modulus of the cement and the thickness of the casing. The relationship between the compressive strength and shear modulus for curing times similar to those encountered in the field was determined from laboratory tests. Using this relationship, the computed attenuation rates showed reasonable agreement with the measured attenuation rates. The purpose of this paper is to report the results of the experimental and theoretical investigations and to present the first practical method for a quantitative interpretation of Cement Bond logs based on known variables. This method is applicable where the casing-borne signal is not affected by high-velocity formation arrivals. DESCRIPTION OF LOGGING TOOL The Cement Bond logging tool shown schematically in Fig. 1 has been described previously.' The tool consists of two sections: acoustic and electronic. The acoustic section contains a transmitter and a receiver, usually spaced 3-ft apart. Sonic energy emittted by the transmitter travels through the casing and is detected at the receiver. The electronic section measures the amplitude of the

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor's thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the 'rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor's thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the 'rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

The Joint Committee (consisting of the chairmen of the several society committees), formed under the authority of the five societies, in order to facilitate the carrying out of the organization of an engineer reserve as part of the military forces of the United States, for which work it was appointed, now begs leave to report as follows: .The Committee has been in personal communication with the Secretary of War, the officers of the General Staff, the officers of the War College, and with the Hon. George E. Chamberlain, Chairman of the Senate Committee on Military Affairs, and the Hon. James Hay, Chairman of the House Committee on Military Affairs. As the result of these interviews there has been incorporated in the draft of the legislation proposed by the Secretary of War and included also in the bills drawn by the committees of the Senate and of the House a provision for the organization of an officers reserve on broad lines, including an engineer reserve. As now drawn these bills provide that an officer shall be commissioned for a period of five years with rank up to and including that of major, after passing such requirements of character and qualifications as shall be prescribed by the President. The bill also provides that a certain amount of duty with pay shall he performed each year by the officers in the reserve. . The Committee is waiting for the Navy Department to formulate its plans for the increase in the naval forces, and as soon as a decision has been reached by that Department and the Committee is in possession of the facts, the Committee will take up the question of the organization of an engineer reserve for the navy, similar to that contemplated for the army.

Jan 2, 1916

By J. Mackintosh Bell

The history of the South Lorrain mining camp is given and comparisons are made between the local topography and general geology and that of the Cobalt camp. The character of the silver-bearing veins and their analogy to those of Cobalt are given and the theory regarding the cause of the deep seated oxidation in South Lorrain, particularly at the Keeley Mine, is outlined. The oreshoots are described, also the conditions governing their occurrence and position. The mining and metallurgical practice are briefly considered. IN THE numerous districts subsidiary to Cobalt, and carrying mineral deposits similar in character to that world-famous mining camp, the most interesting recent developments have occurred in South Lorrain. The district, the center of which lies about 16 miles southeast of Cobalt, was the scene of a rush in 1907 but, in spite of the success of the Wettlauffer mine, the locality soon lost its popularity, largely on account of the unsavory early history of the Keeley mine. In recent years, following the successful development of this property by the London operators, who acquired it from the liquidator of the original company, and the later conspicuous progress made on the properties of the Mining Corporation contiguous to the Keeley on the north, the district has again come into prominence and, at present, is doing much toward maintaining the gradually declining production of Cobalt itself. Apart from the Mining Corporation of Canada and the Keeley Silver Mines Limited, the principal concerns now operating in South Lorrain are the Lorrain Consolidated, the Trout Lake Mines (operated by English interests associated with the Mining Corporation) and the Canadian Lorrain Silver Mines (operated by the Huronian Belt Co., of London). A number of minor prospects are also active. The Wettlaufer and Currie, on both of which considerable work was done some years ago, are now closed.

Jan 1, 1924

By H. D. Outmans

In steady vertical flow, the interface of an immiscible liquid-liquid displacement is horizontal for any flow rate below the critical. In nonvertical flow, however, the shape of the interface in the steady state does depend on the flow rate, and the purpose of this paper is to calculate the unsteady interfaces during the transition of one steady state of flow to another. A knowledge of these transient interfaces is of considerable importance in reservoir engineering where the calculation of breakthrough recovery depends on the instant the interface reaches the producing wells and on the shape of the interface at that time. Although the emphasis is put on transient interlaces, which eventually approach stable equilibrium, it is shown that if the displacement exceeds a critical rate no equilibrium is possible. The interface is then unstable and viscous fingers are formed during the displacement. The critical rate and the shape of the transient and equilibrium interfaces are affected by the effective interfacial tension; but since this effective interfacial tension appears in the calculations only in combination with the inverse square of the thickness of the medium, its effect in the reservoir would appear to be negligible compared to its significance in model experiments. INTRODUCTION Stability criteria and the early growth of interfacial disturbances in a plane parallel to the boundaries of a dipping formation in which oil is displaced by an incompressible fluid were described in a previous paper.l This type of instability is significant in thin reservoirs. However, if the reservoir has appreciable thickness, then interfacial stability in vertical planes, normal to the upper and lower boundaries, also becomes important (the displacement is supposed to be parallel to these vertical planes). The difference between the two stability problems is that, in the first case, the intersections of the interface with planes parallel to the boundaries are normal to the direction of the displacement; in the second case, the intersections, this time with vertical planes, are not normal to the displacement. Instead, they are tilted at an angle which depends on the displacement rate. The tilt of steady interfaces was calculated by Dietz2 who also determined the critical rate of displacement for stability in the vertical plane by assuming that this rate would coincide with an interfacial tilt equal to the dip of the formation. The critical rate thus calculated is the same as has been found for thin reservoirs (see Eq. 1.1 of Ref. 1 and of the present paper). Dietz's calculation of the stable tilt was verified by laboratory experiments and the agreement was found to be fairly good.3 It is doubtful, however, that stable tilts actually exist in the reservoir because a change in production rate is not followed by an instantaneous adjustment of the interface to the new rate but, rather, by a transition period during which the interface changes from one equilibrium tilt to the other. The principal objective of this paper has been to describe these transient interfaces without putting any restrictions on the flow conditions or the shape of the interface, as had been done previously. The second objective was to compute the critical velocity, taking into account capillary effects, and the third was to evaluate, at least qualitatively, the shape of the front at rates above the critical, again without making the simplifying assumptions introduced by previous investigators.2,3 In the following sections two examples are given of the calculation of interfacial motion. The first describes this motion for an initially horizontal interface in a dipping layer, and the second for a vertical interface in a horizontal layer. The mathematical formulation of the problem is nonlinear in the boundary conditions, and this prohibits its solution in closed form. Instead, the solution is obtained in the form of higher-order approximations. 1 Before proceeding to a description of the mathematical model, however, we define two quantities

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.' The U. S. Bureau of Mines2-' described and later improved the apparatus for a now widely used method generally known as the "Boyle's law" method. In the present form of the Washburn-Bunting method,' the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle's law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle's law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle's law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By W. G. Whildin

This paper will be confined to a discussion of the methods in use in the property of the Lehigh Coal & Navigation Co. in the Panther Creek valley. Only the methods used in mining the Mammoth vein will be .considered, as the methods in use in the smaller veins are adaptations of the same. Typical cross-sections of the coal basin are shown in Figs. 1, 2, and 3. The Mammoth vein varies in thickness. It is 21 ft. at one colliery, 50 to 125 ft. at another, and over 200 ft. at still another. Its normal thickness is 35 to 40 ft. At some points in the Panther Creek basin the Mammoth vein is made up of three splits-the Bottom, Middle, and Top, while in other portions the dividing strata between the benches amount to only 1 ½ to 2 ½ ft., and the vein is practically in one. The section of the Mammoth vein shown in Fig. 4 was taken at the Greenwood colliery, and shows a thickness of 60 ft. The miners know it by benches, as follows:. The Three-Foot, the Four-Foot, the Eighteen-Inch Slate, the Bony, the Grey Slate, the Grain Clear, the Five-Foot, the Seven-Foot, the Slaty or Dirty benches, the Blue Slate, and the Top bench. The present-day methods of mining are an outgrowth of the experiences of the last 100 years in this territory. The first attempt at mining, according to the company's maps, was made at Summit Hill in 1792, when open cuts and pits were made. Later the pillar-and-breast method was introduced. This and other methods will be discussed hereinafter. Drifts, slopes, and shafts, according to the requirements and physical conditions, are the main openings, from which the gangways are driven. The gangways (haulageways) and airways are driven along the strike of the vein; the gangways in the various veins on the same level being connected by tunnels through the intervening rock. The gangways and airways in thick veins are heavily timbered ;throughout. The sets of timber, consisting of a collar and two legs, are spaced 5 ft. apart, and later, after the ground :has settled, additional sets, called "liners" or "relief sets," are placed between, to relieve the strain on the original timbers, so that the result is a set of timber every 2 ½ ft.

Jan 12, 1914

By R. A. Thomas, R. L. Solbod

The importance of transverse diffusion on the finger development in a miscible-phase displacement at an adverse mobility ratio of tbree was studied in a porous plate 1/4-in. thick, 3-in. wide and 18-in. long. Fast displacement rates (29 ft/D) and slow rates (1.6 ft/D) were used to determine the effect of residence time on the geometry of the fingers. The shape of the fingers was observed directly by use of the X-ray technique. At fast rates numerous narrow fingers were observed, but at slow rates a single somewhat bulging finger was produced. The amount of material moved transversely by diffusion across the plate was sufficient to modify the finger geometry in the slow-rate run because of the long residence time. These results are in contradiction to some of the postulates in the literature. The composition of the effluent stream, however, was not affected by the flow rate. This result is not inconsistent with the observed change in the shape of the finger in a short model, but it seems likely that a short model does not offer adequate and proper scaling of the reservoir. The model used was probably a valid one for studying the effect of transverse diffusion on the finger geometry, but a longer model would be needed for proper scaling of the effect of the change in the finger shape on the efficiency of displacement as measured by the composition of the effluent stream. INTRODUCTION Fingering can be defined as the uneven advance of the injected phase as it moves into a porous medium displacing the resident phase from the pore spaces of the rock. The use of this term is usually restticted to the situation in which the displacing phase is less viscous or more mobile than the fluid being displaced. Under these conditions, not only are fingers formed, but the length and width of the fingers grow with distance traveled in the porous medium. This subject has become one of great interest to the oil industry because of the present trend toward the use of various forms of miscible-phase displacement to increase oil recovery. Since in nearly all of the known modifications of the miscible-phase displacements an unfavorable mobility ratio exists (the displacing phase has a lower viscosity than that of the crude oil), the conditions are proper for fingering to develop. An appreciable amount of fingering appears to be a severe handicap to these processes for it increases the volume of agent required for the process to be a success, and such an increase puts a severe strain on the economics of the proposed processes. In some cases, such as for a mobility ratio of 200 unfavorable, it has already been demonstrated that the proposed process would not be economic if the fingering in the field were to be of the same magnitude as that observed in the laboratory. A number of aspects of fingering have been studied and reported in the literature. While the phenomenon of fingering cannot be regarded as a completely understood subject, considerable information exists on the effect of the path length and the mobility ratio on the growth of fingers. Less-complete data are available on the effect of the diameter of the flow path on the character and amount of the fingering, and even less agreement in results exists on the effect of rate of flow on the nature of fingering. This paper deals with one aspect of this latter subject. OBJECTIVE The objective of this study was narrowed down to one rather specific feature of the behavior of fingers in miscible-phase displacement in porous media. The variable studied was the effect of rate of flow on the nature and the development of fingers. It should be made clear at this point that, while rate was the apparent variable, the real variable was residence time; that is, at low rates the fluids are present at a given spot in the porous medium for a longer time interval than at fast rates. The purpose of the study, therefore, was to determine the changes which occur in the fingering and the possible benefits which might accrue from a longer residence time during that period when fingers are

By W. M. Robertson

The rate of crack Propagation thvough a solid meta1 in the presence of a liquid metal has been calculated. The crack is assumed to propagate by solution of the solid in the liquid under the influence of an applied stress, with volume diffusion of the dissolved solute through the liquid controlling the propagation. The calculated velocities can be tens of centimeters per second or higher. THE embrittlement of normally ductile solid metals by liquid metals has been the subject of extensive study, as summarized in the book by Rostoker, McCaughey, and arkuus.' In experimental studies of liquid-metal embrittlement it is usually concluded that the observed crack-propagation rates are too high to be accounted for by diffusion processes. Diffusion is considered to be an unimportant factor and various other mechanisms are invoked to account for the experimental observations. The similarities of liquid-metal embrittlement to stress-corrosion cracking, to hydrogen embrittlement of steel, and to low-temperature embrittlement of bcc metals are frequently used as analogies for these mechanisms.1"3 The present paper assesses how rapidly a crack could propagate by a mechanism of volume diffusion through the liquid metal. We assume that the crack propagates by solution of the solid in the liquid at the crack tip under the influence of the applied stress and diffusion of the dissolved solute away from the crack tip. The model uses only macroscopic thermodynamic, kinetic, and elastic concepts. The calculations indicate that this dissolution-diffusion mechanism can give high crack velocities. In some previous treatments4'' of crack propagation in a liquid-metal environment the fundamental step has been the breaking of atomic bonds at the crack tip. The liquid greatly decreases the energy necessary to break these bonds. The present model assumes the crack is filled with liquid metal; the presence of the liquid is essential because diffusion through the liquid is assumed to control the rate of propagation. With proper modification this model could also apply to stress corrosion in a liquid environment. THEORY Consider a crack in a homogeneous elastic continuum, ignoring all the structural details of the solid. This neglects a host of metallurgical details which can be significant in the problem of liquid-metal embrittlement;' but this simple assumption is a useful approach in evaluating the role of diffusion through the liquid. The stress distribution around the crack tip establishes a gradient in the chemical potential at the tip, which causes a diffusion flux through the liquid away from the tip. The solid-liquid interfacial tension works against crack propagation, since propagation requires creation of interfacial area. From these two considerations we derive the diffusion flux, which then yields an expression for the velocity of the crack tip. The concentration of the solute in the liquid, C, is equal to the equilibrium concentration in the presence of an unstressed, flat surface, Co, plus the excess concentration due to the stress, AC(a), plus the excess concentration due to capillarity, AC(y): We calculate AC(o) and AC(y) and then obtain the diffusion flux. Consider (Fig. 1) a long flat crack of length 2L, thickness 2r, and tip radius r, where r remains constant as the crack propagates in the positive x direction. There is no stress ay in the y direction across the flat surfaces of the crack. The magnitude of the stress at the crack tip due to the applied stress, a,, is given by the relation6 ^=^[l-2^] 12] which, for long narrow cracks, becomes The stress increases the chemical potential in proportion to the strain energy.? The excess chemical potential due to the stress, Ap(a), is given by where 52 is the atomic volume of the solid and E the Young's modulus. Inserting Eq. [3] gives Now consider the crack to be filled with a liquid metal. The excess solubility due to stress, hC(a), is given by the excess chemical potential due to capillarity, Ap(y), is given by8 where y is the solid-liquid interfacial energy, and v1 and YZ are the two principal radii of curvature of any surface point. At the crack tip, r1 = -r and vz = m, so TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

Jan 1, 1967

By Robert H. Merrill, Raymond M. Stateham

Recently, the Denver Mining Research Center of the U.S. Bureau of Mines began tests to detect hazardous or potentially hazardous conditions in or around mines with infrared measurement devices. Among the many potential uses of infrared detection techniques are the location of misfires, underground mine fires, combustion in waste dumps, underground water courses and loose rock. However, the primary emphasis has been placed upon the detection of loose rock in roofs, pillars and faces in underground mines. The rock along the edge of an underground opening is subject to two temperature environments: the temperature of the air in the opening, and the temperature of the rock surrounding the opening. Assuming that the rock on the edge of the opening is solid, the rock will reach an equilibrium temperature that depends upon the temperature and flow of the air, the thermal conductivity of the rock and its ambient temperature. Presume that a loose rock exists among this solid rock; because there is a temperature barrier, to some extent, between the loose and the solid, the loose rock will be affected more than the solid rock by the temperature of the air. Therefore, depending upon the temperature differences between the rock and the air, the loose will be warmer or cooler than the solid.

Jan 1, 1970

By O. C. Wheeler

In past years the exploration of the oil possibilities of Colombia has been confined to parts of three distinct physiographic provinces; namely, the coastal plains area near the Caribbean Sea, the Magdalena Valley and the upper reaches of the Maracaibo Basin near the Venezuelan border. During 1935, little exploratory work and no drilling was carried on on the coast, but there was considerable activity in the other two areas. In the Magdalena Valley, the Tropical Oil Co. continued its producing and development operations on the De Mares Concession. The Socony-Vacuum exercised the option it acquired in 1934 on Sr. Luciano Restrepo's concession adjacent to the Tropical property and north of the Sogamoso River. No wells have been started on the Socony's lands although, according to the terms of the lease, drilling must be started within the next two years. West of the Carare River and adjacent to the Tropical's southwestern boundary, the Sociedad Nacional del Carare denounced the lands formerly held by the Union Colombiana, whose lease automatically lapsed during the year owing to the company's failure to comply with its drilling obligations. In the same area, the concessions held by Callejas et al. and the Société Européene des Pétroles are also understood to have lapsed for the same reason. Holdings of other interests in the Magdalena Valley were inactive during the year. Near the upper part of the Maracaibo Basin, the Gulf, through its subsidiary the Colombian Petroleum Co., continued active exploration and development on its Barco concession. Colombian Petroleum Co.—The following information and that presented in the accompanying tables relating to the activities of the Colombian Petroleum Co. was supplied through the courtesy of Mr. E. S. Bleecker, chief geologist of that company. Four wells were completed during the year on the north Petrolea dome, where an attempt is being made to define the limits of the field. On the south end of the Petrolea anticline, one well, Petrolea No. 3, which might be classed as a wildcat, encountered a heavy flow of salt water immediately below the oil zone and had to be abandoned. A second location has been made 1 miles south of No. 3 and somewhat higher on

Jan 1, 1936

By Ralph Nichols

The mines are near the town of Gilmore, in the Texas mining district. This district was organized in 1880. The present producing mines are near the terminus of the Gilmore & Pittsburg railroad. This railroad connects with the main line of the Oregon Short Line at Armstead, Mont. The distance from Gilmore to Armstead is 70 miles. The town of Gilmore is near the head of the Lemhi river at an elevation of 7,000 ft., while the mines are from 400 to 1,300 ft. higher. The range of mountains upon which the mines are situated forms the water shed for the Little Lost river on the west and the Lemhi river on the east. The winters are severe and the snow fall is heavy, but the mines ship right through the year. There is an abundance of timber suitable for all mining purposes in the immediate vicinity. Water is piped into the camp from a lake about 2.5 miles distant. This lake is about 1,400 ft. above the town of Gilmore. The water is exceptionally good for boiler and domestic purposes. The mining companies now producing are the Pittsburg Idaho Co., Ltd.; the Latest Out Mining & Smelting Co., Ltd.; and the Oilmore Mining Co., Ltd. Besides the above propertiea, there are a number of prospects in different stages of development. The producing mines of the district are fissures in limestone, with a general northeast-southwest course and a dip to the west of from 40' to 70°. These fissures are at about right angles to the bedding of the limestones. The veins are regular and the ore shoots strong, both laterally and in depth, so far as developed. The ore shoots have a rake or pitch to the south. The character of the formation is shown in Fig. 1, a section of the Latest Out mine. Character of Ore. The ores of the district are oxidized, carrying an excess of iron over the silica (insoluble matter). The vein filling is a mixture of limonite and hematite, which is replaced by shoots of lead-silver ores. The lead minerals consist of carbonate of lead principally, but with small quantities of sulphide, sulphate, and other lead minerals.

Jan 1, 1914

By O. C. Wheeler

In past years the exploration of the oil possibilities of Colombia has been confined to parts of three distinct physiographic provinces; namely, the coastal plains area near the Caribbean Sea, the Magdalena Valley and the upper reaches of the Maracaibo Basin near the Venezuelan border. During 1935, little exploratory work and no drilling was carried on on the coast, but there was considerable activity in the other two areas. In the Magdalena Valley, the Tropical Oil Co. continued its producing and development operations on the De Mares Concession. The Socony-Vacuum exercised the option it acquired in 1934 on Sr. Luciano Restrepo's concession adjacent to the Tropical property and north of the Sogamoso River. No wells have been started on the Socony's lands although, according to the terms of the lease, drilling must be started within the next two years. West of the Carare River and adjacent to the Tropical's southwestern boundary, the Sociedad Nacional del Carare denounced the lands formerly held by the Union Colombiana, whose lease automatically lapsed during the year owing to the company's failure to comply with its drilling obligations. In the same area, the concessions held by Callejas et al. and the Société Européene des Pétroles are also understood to have lapsed for the same reason. Holdings of other interests in the Magdalena Valley were inactive during the year. Near the upper part of the Maracaibo Basin, the Gulf, through its subsidiary the Colombian Petroleum Co., continued active exploration and development on its Barco concession. Colombian Petroleum Co.—The following information and that presented in the accompanying tables relating to the activities of the Colombian Petroleum Co. was supplied through the courtesy of Mr. E. S. Bleecker, chief geologist of that company. Four wells were completed during the year on the north Petrolea dome, where an attempt is being made to define the limits of the field. On the south end of the Petrolea anticline, one well, Petrolea No. 3, which might be classed as a wildcat, encountered a heavy flow of salt water immediately below the oil zone and had to be abandoned. A second location has been made 1 miles south of No. 3 and somewhat higher on

Jan 1, 1936

By W. F. Boericke

The character of the Wisconsin orebodies must be clearly understood to appreciate the difficulties encountered in sampling and estimating them. Unlike the western vein deposits, they do not lie between regular walls, but form large, often highly irregular bodies, on a single floor in the so-called Galena limestone. The bottom of the ore is nearly always on the clay bed (a flat generally well-defined clay seam a few inches thick) which marks the junction of the base of the Galena lime and the top of the next formation, the Trenton lime. Above the clay bed, the orebodies make the unique pitch and flat formation described by Chamberlin.' Theoretically, we should find two pitches, one on either side of the top crevice, diverging as they go down, with the final flats a considerable distance apart on the clay bed. The area between, known locally as core ground, should thus constitute a single defined orebody, with the richer portions near the pitches and the leaner portion in the center of the core. Practically, we find few examples of this perfect orebody. Almost invariably one pitch is better defined than the other, and often the opposite pitch is marked only by a faint line of fracture showing stronger mineralization than the wall rock, or it may be totally lacking. But with an orebody of any size or richness, at least one strong pitch usually tends to follow an east-west trend, or a quartering course. Late mining developments in the rich New Diggings field indicate that these pitches often assume a horseshoe or crescent shape, the richer ore being in the heart of the crescent and the pitches showing less mineralization as they extend outwards. In the northern end of the field, on the contrary, the pitches maintain generally a consistent direction, and have been mined for thousands of feet from the shaft. The length of the orebody may be several thousand feet, the height varying from 10 to 60 ft. and the width from 60 to 250 ft. In fact, on the core side, there is no definite end to the ore. The mineralization simply gets thinner and thinner, and the limit of working depends on the cost sheet and the profit from the recovery.

Jan 1, 1923