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By Mary S. Esfandiary

This is a revision of a directory of coal research organizations throughout the world that was first published in 1961 as Bureau of Mines Information Circular 8008. Because of the wide acceptance of the first edition, a revision which would supply up-to-date information on coal research and which would facilitate communication among organizations of similar interest seemed important. This compilation includes the names and activities of organizations of various types-government, university, private, and industry. The areas of investigation that each organization is engaged in are indicated in broad terms: Analysis and constitution, mining and geology, preparation, briquetting, combustion, high-and low-temperature carbonization, gasification, conversion to solid and liquid fuels, and health and safety. Publications issued by and describing the work of each organization are cited; almost all of the organizations also publish results of their investigations in the technical press. Selected technical and trade publications that publish information on the science and technology of coal and are not published directly by any of the organizations listed are cited in the pages following the list of organizations in each country. Information that would improve coverage and accuracy of the next revision of the publication will be welcomed by the Bureau of Mines.

Jan 1, 1966

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.'a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.' However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By Bernard Porter

The rate of the heterogeneous reaction between high-purity uranium metal and uranium tetrafluoride in molten lithium fluoride was measured. The apparent heat of activation for the reaction is 16.91 kilocalories per mole of UF4. A surface-controlled mechanism is suggested in which UF4 is adsorbed on the uranium metal surface. Additional UF4 reacts with the adsorbed species and the metal site to form an activated complex that decomposes to the product UF3. The reaction is an important source of metal loss in the electrowinning of uranium metal.

Jan 1, 1966

By James R. Dunn

The nature of water and clay in carbonate rocks is currently being investigated at Rensselaer Polytechnic Institute by various thermal and sorption techniques. Two basic concepts 'led to the present research. (1) To explain the expansion and contraction on wetting and drying of some unsound argillaceous carbonate rocks, it was postulated that the pore space around each clay particle is such that when water is sorbed by the clay, force is exerted against the pore walls. (2) The clays in expansive rocks are rejected from the growing dolomite crystals during their growth, and form a more or less connected network, thereby becoming "wettable," or available to water. New quantitative cold differential-thermal-analysis (electrocalorimetric) equipment was designed and constructed to check the "limited space" and "wettable clay" concepts and to determine the thermal nature of the transition of water to ice in rocks. This DTA equipment can detect the release of heat in freezing of less than 0.001 per cent water in a rock. Twenty-three rock cores (nine sound and fourteen unsound) and 4 procelain cylinders for standards were studied. In the nine sound rocks and in all the procelain cylinders, the rapid freezing of from 50 to 100 per cent of the water was readily detectable after 7 to 10° C of supercooling. No further freezing could be detected to -20° C. However, in eleven of the fourteen unsound rocks, no freezing was detected to as low as -40° C; in the other three, less than 50 per cent of the water froze. As a check of the DTA measurements, adsorption isotherms were determined for all materials. Calculations of theoretical freezing points for sorbed water again demonstrated that the least sound rocks had the most nonfreezable water. "Frost" sensitivity in these carbonate rocks is, therefore, probably not the result of the force of expansion of water to ice. The disruptive force is believed to result from expansion of sorbed, ordered water on clay surfaces. The relationship between the unfilled rock pores after 24-hour water saturation and the water sorbed at 85 per cent humidity at 30° C (i.e., the theoretical nonfreezable water delineates the sound and unsound carbonate rocks.

Jan 1, 1966

By Severn P. Brown

Cement plants in the central Hudson River valley utilize limestones of the Helder-bergian Series of the Lower Devonian. Chiefly calcilutites, calcarenites, and cherty calcisiltites, these rocks represent progressively deeper environments, from lagoonal to neritic, with scattered reef deposits. Stratigraphic continuity is marked, and a layer-by- layer analysis shows strikingly constant chemical compositions. The structural picture varies from flat-lying and relatively unfaulted beds on the northwest, through gently folded and faulted beds on the north, to complex overturned beds with closely spaced imbricate faults on the south. Operating techniques are simpler in the north, where grade control is effected chiefly by the initial layout of the faces. In the south, grade control requires flexibility and frequent adjustment of faces or scheduling. A system of quarrying along strike has been developed, grade being computed from a cumulative foot-per cent graph of the critical oxides in each mappable layer. Balancing shovel production among the many faces is simplified by comparing production requirement ratios with ratios of the various types of rock in each face. Drilling and blasting limits are geologically controlled if warranted, or large blasts embracing several rock types are shot and the resulting pile of broken rock is staked along shovel limits.

Jan 1, 1966

By Jr. Karr

The Bureau of Mines studied the influence of carbonization method, temperature, and carrier gas on the composition of eight different low-temperature tars produced from a Colorado subbituminous coal. A fluidized bed was compared with an entrained bed, temperature was varied from 500° C to 650° C, and external heating using recycle gas as the carrier gas was compared with internal heating using oxygen-containing gas. The entrained bed yielded significantly more m-cresol and m-ethylphenol, indicating that thermodynamic equilibrium was more nearly approached in the system. Increasing the temperature greatly increased the yield of benzenes and naphthalenes, while paraffins, olefins, and total tar acids were reduced. Using oxygen in the carrier gas decreased the yield of low-boiling phenols and increased that of paraffins and olefins at 650° C.

Jan 1, 1966

Major activities of the Bureau of Mines Explosives Research Center during fiscal year 1965 (July 1, 1964, to June 30, 1965) are reviewed briefly. Part 1 summarizes significant accomplishments of the projects that were active during the report period. Part 2 presents short abstracts of the publications that appeared in the Bureau series and in other media during fiscal year 1965. Publications issued after June 30, 1965 are noted where pertinent in footnotes but are not abstracted. ACKNOWLEDGMENTS The Bureau of Mines gratefully acknowledges the support given through cooperative agreements by the following organizations to investigations con¬ducted by the Explosives Research Center during fiscal year 1965: Dow Chemical Company Manufacturing Chemists' Association Monsanto Chemical Company The Sulphur Institute

Jan 1, 1966

By Chas. L. Emery

"The laws of rock mechanics apply equally well to all rock structures, and open pits are not exceptions. The concepts and some arguments about the emphasis to be placed on various aspects of open-pit design are discussed in this article.RocksROCK can be described as a granular material consisting of grains and glue. The grains may be fragments of other rocks or polycrystalline aggregates. The glue may be ferruginous, calcareous, argillaceous, siliceous or other material connecting the grains. In a crystal intergrowth, the outer layers of the crystals in contact with each other may be considered to act as a glue. Water may be a glue in clay or a grain in a crystal structure. Air and other fluids or gases are grains if they occupy spaces in a granular mass. Such grains are functional either chemically or mechanically or both."

Jan 1, 1966

By B. E. Shaw

This paper describes the use of the Free Piston Valve, and a simple hoist brake control system, which has been developed over the last two years, greatly improving the performance of low-pressure brake engines. The basic control system is outlined, with sections devoted to emergency trips and differential braking, and the application of the system to deep shaft hoisting is discussed.

Jan 1, 1966

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966

By S. Kaiman

This paper describes flotation test work conducted over the past several years at the Mines Branch, Ottawa, on the radioactive quartz-pebble conglomerate ores of the Elliot Lake area of Ontario. The purpose of this work has been to produce a uranium flotation concentrate for sub-sequent leaching operations. The results of earlier investigations are summarized and correlated with the results of mineralogical studies of the ores and flotation products. The results of recent pilot-plant investigations by flotation, as well as by gravity concentration followed by flotation of the gravity tailings, are given. The principal collector used for uranium flotation was a tall oil fatty acid, and the indicated total cost of all reagents ranged from 21 to 31 cents per ton of ore treated.

Jan 1, 1966

By R. T. Sorensen

Research and testing in a small scale equivalent of a commercial flota-tion plant was completed on four low-grade, iron-bearing materials from the western Mesabi range. Closed circuit-flotation of calcium-activated silica with fatty acid collector developed data for comparison with the batch process and highlighted problems not evident from previous bench testing. The four ore samples contained from 27 to 39 percent Fe and were equally represented by nonmagnetic taconite and semitaconite type materials. Iron concentrates containing 6.0 percent, or less, SiO2 were made 5, all four samples. Of the two material types, the semitaconite was the ore amenable to treatment, yielding iron recoveries of about 90 percent as cc pared with 70 to 80 percent for the other. Pilot plant tests showed that concentrate grade made in batch tests could be duplicated in the closed circuit and demonstrated that the amount of recoverable middling iron varied considerably between ore samples. The continuous tests also showed that water temperature strongly influenced results in the treatment of one ore but apparently was of indifferent consequence in another. Progress in thickening and filtration of flotation concentrates was made through introduction of tapioca flour to serve the dual role of iron mineral depressant and flocculant.

Jan 1, 1966

"Since all gold mills must sooner or later be cleaned up for permanent shutdown it was felt that a record of what was done at one mill might be of some help to those who will have to do the same job in the future,In cleaning up the mill of Delnite Mines Limited, I had an advantage that most mill superintendents will not have in that I started up the mill and was there until it was shut down, It was also known for two years approximately when the shutdown would be and for a year almost the exact time. This, of course, made careful planning possible and enabled me to get advance information that wouldn't have been available had the shutdown come unexpectedly,Early in 1964 calculation of ore reserves and the known number of working places available indicated that the mine would run out of ore sometime in August or September but not later than October, The time of course would vary with the number of competent miners that could be retained until the shutdown. Since the mining method used exclusively on the ore then remaining was cut and fill, it was known that once mining operations ceased it would require at most two days to crush and grind the last of the ore.In March 1 964 I took samples of the concrete floor under the precipitation presses, in the flux room and furnace room of the refinery and from the assays obtained proved that there would be no profit in breaking up the concrete to recover the gold from it, Samples taken from the top half inch of the concrete floors assayed less than 0, 10 oz per ton,"

Jan 1, 1966

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.' They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan'gin' using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By Paul C. Lingo

Two recent antitrust cases, coming from widely separated areas, different industries and involving wholly different facts were decided by the Supreme Court on June 7, 1965. The decisions in there two cases may well prove to be the most important and far-reaching decisions in the field of labor law that have been handed down in the last 24 years. These cases, although quite dissimilar factually, had one common element. In both, the gravamen of the antitrust violation was bottomed on the terms of labor agreements negotiated by a multiemployer group. These cases are usually referred to as Pennington1 and Jewel Teat. Since a number of references will be made to the antitrust laws, it may be well to state briefly the applicable portions. Section 1 of the Sherman Antitrust Act makes "every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several states, or with foreign nations, is declared to be illegal...". Section 2 imposes criminal sanctions against "Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce among the several states...". Under Section 4 of the Clayton Act a person who sustains damages as a result of a violation of the anti¬trust laws is entitled to recover treble damages plus costs.

Jan 1, 1966

By W. A. Gibson, A. D. Trujillo

The Santa Rita copper deposit first served as a source of native copper for Indian implements and weapons. In 1801 Santa Rita copper, trans- ported by mule train to Chihuahua, began to be used commercially for making coins. It was a small- scale operation made difficult by Indian raids, transportation costs and depletion of the higher grade ores. There was, moreover, no known method for economically extracting copper from the under- lying low grade sulfide ores. Originally, copper and copper oxide ores were mined by underground methods, but there was virtually no development of the deposit-which became United States territory after the Treaty of Guadalupe Hidalgo in 1848-for almost a hundred years. A number of small underground mines had been started during that time, but it was not until 1873 that all the principal claims were consolidated under one control.

Jan 1, 1966

By J. R. Fisher

"Uranium may be leached to some extent in situ from the Blind River conglomerate uranium ores by using the products of bacterial activity from the bacterium Thio-bacillus ferrooxidans his paper describes some of the laboratory techniques used to investigate the characteristics of the bacteria, and to utilize their properties in uranium leaching. The application of some of the laboratory results underground at the Milliken mine of Rio Algom Mines Limited are de-scribed, along with the method of uranium recovery from the mine waters."

Jan 1, 1966

By James S. Browning

Research by the Bureau of Mines demonstrated that organic heavy liquid adhering to or adsorbed on fine mineral particles can be effectively removed by a novel method embracing pulping or displacement washing with hot water alone or in combination with a detergent. Displacement washing with steam alone or in combination with a detergent also was effective for removing the heavy liquid. In tests of sized minus 48-plus 200-mesh mineral charges, both the hot water washing with detergents and detergent steaming effectively reduced the heavy liquid losses on the particles to about 0.2 pound per ton of mineral or less. Centrifuging of the wash solutions permitted an almost complete recovery of heavy liquid from the solution as a pure heavy liquid product.

Jan 1, 1966

By J. C. Melrose

The contact angle is one of the boundary conditions for the differential equation specilying the configuration of fluid-fluid interfaces. Hence, applying knowledge concerning the wettability of a solid surface to problems of fluid distribution in porous solids, it is important to consider the complexity of the geometrical shapes of the individual, interconnected pores. As an approach to this problem, the ideal soil model introduced by soil physicists is discussed in detail. This model predicts that the pore structure of typical porous solids will lead to hysteresis effects in capillary pressure, even if a zero value of the contact angle is maintained. The model is generalized to situations in which the contact angle takes on values between zero and 40 degrees. For the imbibition branch of the capillary- pressure function, the model predicts a considerable departme ftom the usually assumed cos 0 relationship. In fact, according to the model, it is possible that a displaced wetting phase will not be able to reimbibe, even when the contact angle does not exhibit hysteresis. INTRODUCTION The subject of capillarity in porous media has long been of interest in many branches of engineering and applied science. The earlier investigators were those concerned with the physics of soils. 1-5 More recently, petroleum engineers and others dealing with the problems of petroleum production from reservoir rock have given much attention to the subject.6-10 Also, important additions to the literature of capillarity have been contributed from the field of chemical engineering.11-12 These attest to the wide range of industrial applications in which capillary phenomena play a role. The present paper is concerned with the role which wettability plays in capillary action in porous media. As is well known, capillary-rise (or capillary pressure) phenomena have frequently been interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This approach has enjoyed a certain degree of success in correlating experimental results.13 The generalization of this model, however, to situations which involve varying wettability, has not been established and, in fact, is likely to be unsuccessful. In this paper another approach to this problem will be discussed. A considerable literature relating to this approach exists in the field of soil science, where it is referred to as the ideal soil model. Certain features of this model have also been discussed by Purcel114 in relation to variable wettability. The application of this model, however, to studying the role of wettability in capillary phenomena has not previously been attempted in detail. In the present paper, additional features of the model are introduced. These features are critical in determining the quantitative behavior of the model. GENERAL FEATURES OF CAPILLARY HYDROSTATICS BASIC PRINCIPLES When the interstices of a typical porous solid are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. Hence, fluid-fluid interfaces are found within a certain fraction of the pore openings. The fundamental equation of capillarity specifies the configuration of these fluid-fluid interfaces. This is known as the Laplace equation, when derived from mechanics, and as the Gibbs-Kelvin equation when derived thermodynamically.15 Given two fluid phases, a and ß, in hydrostatic equilibrium, the Laplace equation states that the respective fluid pressures in regions close to the interface are related by Here oaß is the surface or interfacial tension and rl and r2 are the principal radii of curvature of the surface or interface. The pressure difference, Pa-Pß, is the capillary pressure, PC. As Buff15 has shown, Eq. 1 states the condition for hydrostatic equilibrium within the two-phase confluent region, which is referred to as the interface. It thus can

Jan 1, 1966

By James G. Tilton

Subsidence resulting from mining operations, has been the object of sporadic study for many years. Reports have shown that subsidence has ranged from minor settlement detected only by precise measurements to great slips where buildings are destroyed, roads disrupted, and large fissures opened at the surface. For years, a controversy has raged over the question of whether there is a positive or negative angle-of-draw. None of these questions can be given a flat answer for the variables controlling, subsidence are infinite. Generalizations can be made for various situations and areas but some means of control must be executed.

Jan 1, 1966