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Discussion of the paper of E. S. Moore, presented at the Colorado meeting, Sep-tember, 1918, and printed in Bulletin No. 135, March, 1918, p. 687. W. F. SMEETH, * Bangalore, Mysore, India (written discussion ? )-Before dealing with the air blasts, I would like to clear up a geological point. The author states that the matrix of the conglomerate resembles a hornblende schist. This is a, misapprehension. The conglomerate

Jan 10, 1918

By George W. Mansfield

My plan in this paper is, first, to prove three general points, and then to take up the specific applications of the electric motor to nining work. The three poinb are: 1. The electric system is the simplest method known for transmitting and distributing any amount of energy from one locality to another, irrespective of the intervening distance. 2. The electric system with its applications is not in its infancy.

Jan 1, 1888

By W. A. Backofen, F. de Kazinczy

FRACTURING under conditions of particular interest is identified with the junction of curves relating tensile yield and fracture stresses to test temperature; the intersection point gives the lowest stress, for brittle fracture (at the ductility transition temperature). An expression for is found in Cottrell's brittle-fracture analysis, Eq. [15],1 while measurements of this stress and temperature have been reported for a low-carbon steel heat treated to differ-

Jan 1, 1962

By R. H. Cox, A. S. Allen, James Paone

The southwestern Illinois communities of Belleville and Maryville lie within the greater metropolitan area surrounding St. Louis. Missouri. They also lie within that part of the Illinois coal basin where the Number 6 coalbed has been mined for more than a century. About half the coal was left as pillars to support the ground surface. Years later, however, damaging movements are affecting buildings, streets, and public utilities in some areas. They are generally believed to be related to abandoned mine workings. The threat of continued or increasing incidence of damage raises the need to explore other subsidence-control measures for protecting affected areas with high population density. Because of experience gained in a subsidence-control program of backfilling abandoned coal mines in the Applachian region and in Rock Springs, Wyoming, the Bureau of Mines was called upon to investigate the subsidence occurrences at Belleville and Maryville, and recommend protective measures. Funds ware appropriated for the Bureau to initiate subsidence-control projects at two residential sites in Belleville and one in Maryville. Subsurface investigation of the sites by diamond core drilling revealed two conditions that differ from those encountered at most sites of previous subsidence-control projects. The mine workings were found to be dry and the mine floor consisted of soft underclay which characteristically loses strength with increase of moisture. It had been anticipated that water would have percolated into the mine workings at one .or more of the sites through cracks resulting from subsidence. Under such conditions Bureau engineers believed that injection of mine waste by the pumped; slurry technique3 would provide support and stabilize any movements initiated by the softening of the clay. With discovery that the underclay deposits at the three sites have apparently not been exposed to water since the mines were operating, hydraulic backfilling of any type was considered inadvisable on the basis of present knowledge. To avoid introducing water, a portable pneumatic system is being devised for injecting minus 0.01 27 m (1/2 in.) mine waste into the mine workings. Machines for pneumatic backfilling have been used in Europe not only for subsidence protection but also for strata control, for reducing spontaneous combustion and methane accumulation, and as a means of waste disposal. The Bureau experimented with a pneumatic machine in the Northern anthracite field of Pennsylvania in the 1950's. Previously pneumatic machines have been installed in active mine workings discharging from horizontal pipelines which conveyed air- borne material into rooms to be filled. In the present adaptation to abandoned mines, the machine and air compressor will be operating at the surface, to impel material vertically down injection boreholes with sufficient air pressure to disperse fill material laterally in mine workings at the base of injection holes. Large diameter access and ventilation boreholes will be provided at one site for entry into mine workings to observe backfilling progress. The Belleville and Maryville projects are part of the Mined Land Demonstration Program of the Bureau of Mines. The Illinois State Geological Survey and Department of Mines and Minerals are furnishing technical support.

Jan 1, 1979

By E. L. Bruce

THE district of. Patricia, in the province of Ontario, lies northwest of the Albany River and extends northward to Hudson's Bay. Formerly this was the unorganized district of Keewatin, the southern part of which was divided in 1912 between the provinces of Manitoba and Ontario. The interprovincial boundary now runs north from Lake of the Woods for 275 mi. and thence northeast 375 mi. to Hudson's Bay. This district is comparable in size to all the older part of Ontario south of the Canadian Pacific Railway east of Lake Huron-thus it is roughly one-third of the whole of the present provincial area. The central part of this great triangle is one of the least accessible parts of Canada. From it streams flow southward to the English River, southeastward to the Albany, northward to Hudson's Bay and the Hayes River, and westward to Lake Winnipeg. None of the streams is large and canoe travel is not easy. The only industry it has ever had is the trade in furs. Until the development of the airplane on a commercial basis, the only means of travel was by canoe or dog-train. There is not a mile of railway in the whole district. The two areas to be dealt with lie in the southwestern part of Patricia. Red Lake is 50 mi. east of the Manitoba boundary and 75 mi. north of the transcontinental railway from Cochrane to Winnipeg. Woman Lake is 50 mi. farther east and slightly farther north. The late Dr. D. B. Dowling, of the Geological Survey of Canada, visited Red Lake and spent some time there during his exploration survey from Lac Seul to Berens River in 1893. He also visited the Woman Lake basin during the same journey, but his examination of it was much less detailed, the great area covered by him during the one field season making it impossible to make more than a hurried reconnaissance. Some prospecting in the Red Lake district followed Dowling's exploration, but the distance from railway was too great for any systematic work to be done.

Jan 1, 1928

By A. J. Lynch, E. V. Manlapig, J. H. Fewings, D. J. McKee

Progress in the development of an automatic control system for the chalcopyrite flotation circuit at Mount Isa Mines Limited is discussed. Preliminary studies have shown that the operating grade/ recovery curve for a sulphide flotation circuit is established by rougher-scavenger behaviour and the operating point on that curve by cleaner-retreatment behaviour. The control strategy of the rougher-scavenger banks involved regulation of xanthate to maintain recovery and control of air to seek the optimum grade/recovery curve. Control of the cleaner circuit to maintain the correct operating point of the plant relative to the ore entering it will be by air. Pulp levels will be used as an additional controllable variable in due course. Sensing instruments include a “Courier” on-stream analyser and several mass flow metering systems each of which contains a magnetic flow meter and a gama gauge. Measurements of concentrate grades and recoveries are made as early as possible in the rougher bank so that a change in the ore entering the plant can be detected as soon as possible. Over a period of six months from initial control systems application, computer control of xanthate resulted in an overall reduction in consumption of 10%. Experimental work has indicated that improved metallurgical performance will result from the introduction of additional air and level control loops.

Jan 1, 1976

By Marc Lemieux

Computer pit design techniques generally make use of models in which the deposit is represented by a regular array of data. Using a regular system, the number of data points required to represent the air, waste and mineralization in a large deposit become excessive. The number of blocks used to describe the deposit is dependent upon the block size. The quality of the pit wall slope design also is dependent upon the block size used and the method of defining the slope. The error associated with reserve calculations becomes greater with increasing block size. A deposit model consisting of variable sized air and mineralized blocks has been developed at the University of British Columbia and improved upon at Climax for pit design work. The method permits put- ting the entire model in core for rapid data processing. This permits the use of a versatile cone generation technique which allows close adherence to variable slope constraints in all directions. The conical shape is approximated by rectangles on each level which equal the area of the ideal conical intersection. The shape of the intersection may vary from approximately circular to elipsoidal. The approximate cone shape is controlled by the slope constraints applicable at the point of intersection on the bench. The overall modeling technique greatly assists the pit design engineer in developing a high quality pit design.

Jan 1, 1977

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

P,, and v, may now be solved for by trial and error between Eqs. 2 and 3, by assuming time approaching zero and equating PI, to P12. Observe that the pressure under the slug, P12 of Eq. 3, does not remain equal to the P1, at the valve in Eq. 2 as the slug proceeds up the hole. To plot the profile of pressure vs depth, it is necessary to express P12 in terms of P11. To do so, the extent to which the original submergence length S changes with respect to time must be analyzed. At the end of time t after injection, the actual value of L in Fig. 3 is The fall-back v,(t) is now distributed in the gas and exerts pressure on the bottom. This, in addition to the weight of the gas, amounts to the difference in pressures from point to point. With the average pressure profile calculable, a true numerical value for the average pressure in the tubing may be obtained. The value of v, must be obtained experimentally, and since v,, S and D are known, the basic Eq. 1 may be solved for the amount produced. Knowing P, and the actual volume of tubing occupied by gas (vat), it is possible to calculate the volume of gas at standard conditions which is present in the

By M. G. Benz, J. F. Elliott

A. J. Goldak and J. Gordon Parr (U)iuersity of Alberta) —Margolin and Ence's paper reached us only a few days after we had submitted a paper on the structure of Ti2Cu to the AIME. Here, however, we only wish to point out an error in the paper (page 321): "Karlsson has reported the crystal structure of the first intermediate phase occurring in the Ti-rich portion of the Ti-Cu system to be face-centered tetragonal." Karlsson actually reported the structure of Ti3Cu (i.e., "the first intermediate phase") to be primitive tetragonal with four atoms per lattice point: Cu at 0, 0, 0; and Ti at 1/2, 1/2, 0; 0, 1/2, 1/2; and 1/2, 0, 1/2. Thus, Karlsson suggests a primitive lattice with an ordered arrangement of atoms located at corners and face-centers: Ence and Margolin suggest a random body-centered tetragonal structure—-with which our results agree. E. Ence and H. Margolin (authors' reply)— We do not agree that Karlsson has not reported the structure of Ti3Cu as face-centered tetragonal. The fact that Cu atoms are located at the corners and titanium at the face-centers does not indicate that the lattice is not face-centered. We are pleased that the discussers' results agree with our own.

Jan 1, 1962

By H. Margolin, E. Ence

A. J. Goldak and J. Gordon Parr University of Alberta) —Margolin and Ence's paper reached us only a few days after we had submitted a paper on the structure of Ti2Cu to the AIME. Here, however, we only wish to point out an error in the paper (page 321): "Karlsson has reported the crystal structure of the first intermediate phase occurring in the Ti-rich portion of the Ti-Cu system to be face-centered tetragonal." Karlsson actually reported the structure of Ti3Cu (i.e., "the first intermediate phase") to be primitive tetragonal with four atoms per lattice point: Cu at 0, 0, 0; and Ti at 1/2, 1/2, 0; 0, 1/2, 1/2; and 1/2, 0, 1/2. Thus, Karlsson suggests a primitive lattice with an ordered arrangement of atoms located at corners and face-centers: Ence and Margolin suggest a random body-centered tetragonal structure—-with which our results agree. E. Ence and H. Margolin (azlt1zo.l-s' reply)— We do not agree that Karlsson has not reported the structure of Ti3Cu as face-centered tetragonal. The fact that Cu atoms are located at the corners and titanium at the face-centers does not indicate that the lattice is not face-centered. We are pleased that the discussers' results agree with our own.

Jan 1, 1962

E. M. BROHL. It seems as though the physicists in this crowd in the case of the cartridge cases have been a little in advance of the chemists in the crowd. What I am curious about here, and the way this appears to me, without too much study, is that in season cracking we get an atomic distortion so that both by sound means and by magnetic means we are finding a reluctance of the atomic planetary system to line up in accordance with the so-called good metal. The point that is brought up, or rather that has not been brought up-and I think perhaps we could think of that from the chemical point of view-is that this season cracking as I am used to the stress-corrosion cracking, appears to act much as though it were copper oxide. You remember when YOU take copper oxide films in which we again use this distortion of the atomic system to allow currents to pass selectively in one direction only, we get results almost identical with what we saw on the oscillograph report. In other words, on the one section of this season cracking we had a trace of one phase and if you notice on the sections three and four of the numbered oscillograph trace we had what appears 180 deg. out of phase.

Jan 1, 1945

There is no simple answer to the question, "What is the meaning of life?" The expressions of life are so multiple that life has different meanings for different spheres of thought, such as art, science, or philosophy; and it conveys a different significance to different persons, according to their individual development and interests. Life is complex from a philosophical point of view. The meaning of life is superficially positive and unmistakable only when approached from a mechanistic view- point; namely, that of biology or biochemistry, since these deal with the physicochemical basis of life processes. However, such a purely mechanistic or biochemical approach to the significance of life and the interpretation of man's behavior on the basis of purely physical laws is certain to run into trouble. Similarly, a concentration of effort upon materialistic advances in world progress is extremely dangerous. The possible consequences of splitting the atom, development of guided missiles, and possible bacterial warfare are timely examples. Man becomes more self-reliant as he extends his scientific and technologic discoveries and learns how to shape natural conditions to his own desires. When man will be able to travel to other planets in atomically propelled space ships and destroy whole worlds by pushing a button, a possibility which now seems to be within the realm of the predictable future, he will need the strong-

Jan 1, 1950

During the year Jan. 1 to Dec. 31, 1916, 962 applications for member-ship in the Institute were received, as compared to 558 during the corresponding period in 1915. The lines along which the Committee has, worked during the year, group themselves under seven principal heads. Large Companies.-Early in the year a letter was addressed to each member of the Institute who is the executive head of an organization, pointing out to him the advantages that would accrue to that organization through having as many of its subordinate members as were qualified participating in the activities of the Institute. This was followed by a second letter to those who made no reply to the first. The response to these letters was very gratifying, 12 new members having been secured at a single plant, and smaller numbers at others. This was effectively supplemented by our President, who wrote the executive heads of some of the largest mining and smelting companies, pointing out to them the advantage to be derived from sending some of the junior members of their staff to attend the Arizona Meeting. One organization sent 24 of its younger men, many of whom were not members of the Institute, but who, subsequently sent in applications for membership. It is to be hoped that the precedent thus set' will be acted 'on in -fuller measure in succeeding years.

Jan 2, 1917

By H. M. Howe, E. C. Groesbeck

Fig. 1 shows a volute aging break which developed spontaneously in a hardened and tempered steel helmet between 19 and 38 days after it had been tested ballistically. A similar break, shown in Fig. 2, developed spontaneously in a similar helmet about 40 days after the ballistic testing. In this case the rupture occurred abruptly and with a loud report. The path of rupture in this second case, though much the less regular, is the more interesting of the two, in that it is an approximation to two parallel volutes centered at the point of impact of the projectile, just below D. Several weeks later, after the photograph for Fig. 1 was taken, a similar doubling of the volute crack occurred in this helmet, starting from the end of the eyelash crack near A and spreading thence to the left contra-clockwise for about 1/2 in. The negatives from which these pictures are made have not been touched up in any way, save writing the letters on them. In both cases the trajectory of the bullet was normal to the initial surface at the point of impact, and in both the helmet passed the ballistic test without detectable cracking, under a velocity of impact not far below that which usually causes perforation. The initial surface itself was very nearly spherical throughout the region covered by the break.

Jan 1, 1920

In reply to inquiries and comments which have reached me since the publication of this paper, and in explanation of some seeming discrepancies between my statements in the text concerning the amount of displacement of the faults, on one hand, and certain figures in the plates on the other hand, I give here, with some additional remarks, my measurements of the displacements in the different sections, which it originally seemed unnecessary to print : By displacement, I mean neither the throw, i.e., the vertical distance apart of the two edges of a faulted bed (what Mr.

Jan 1, 1896

By R. J. Caro

The Anaconda phosphate plant was put into operation in the fall of 1923. Its present daily operating capacity is approximately 170 tons of treble superphosphate and 16 tons of phosphoric acid analyzing 42 pct P2 O5 and 52 pct P2 Os, respectively. As a result of the continued increased demand for phosphates, Anaconda decided in 1947 to expand the plant's daily output to 270 tons of treble superphosphate and 54 tons of phosphoric acid. The present daily plant intake is 335 tons of wet (footwall) phosphate rock analyzing 31.7 pct P² O5 and 0.28 pct V² O5. The rock is shipped from Anaconda's mine at Conda, Idaho, in open railroad cars, having been crushed to pass 3/8 in. mesh at the mine.' The expansion program will require an increased intake of 300 tons of rock per day. The hanging-wall rock anaIj-ses approximately 30.5 pct P2 O5 and 0.11 pct V² O5, and will be beneficiated in a new washing plant under construction

Jan 1, 1950

By W. B. Wise, H. D. Attra, W. M. Black

The purpose of this paper is to illustrate a comparatively new approach for solving a problem that has plagued oil producers for many years—how to make the most money with available field production capacity. In a very basic operation such as a top-allowable one-well field, a computer and staff of engineers are not required to determine that the best operation is to produce that well at its maximum for as long a time as it will produce. However, as the problem becomes more complex and the number of wells and number of reservoirs increase, it probably will be a wise choice to devote some engineering thought and calculation time to determine the best way to operate that field on both an ultimate and day-to-day basis. Continued developments in the field broadly referred to as "operations research" have led to a number of useful engineering analyses for optimizing field operational problems. One of these techniques, termed linear programing, is parlicularly interesting because of its potential applications to the study of complex oilfield operating problems. Linear programing is concerned with the problem of planning a complex set of interde~endenl activities in the best possible (optimal) fashion. A field application of linear programing is being used to maximize daily income from a multi-reservoir producing operation. The initial results of this study indicate that the linear programing technique (I) can be applied effectively to field problems, (2) can be used to detect unsuspected avenues for improving operations and (3) can effect a significantly improved means of controlling field operations through the use of the highspeed computer. INTRODUCTION The usual approach for studying complex field operational problems has been to look in detail at several basic plans suggested by judgement and experience and, then, to choose the best plan from those investigated. This approach is entirely satisfactory provided: (1) that judgment and experience alone will reliably pick the best or near the best program as one of the plans to be investigated; and (2), and most important, that the factors which control field production will not change. This paper deals with the large group of field operations which are at least one-step removed from a satisfactory solution using the conventional method of analysis. Problems such as pipeline- and gathering-system design, transportation studies, large field development projects and multi-reservoir producing operations fall in this latter category. To find the best program for handling these problems when the best program is not obvious, a complete optimization study is required, and high-speed computers are required to continually update the program once it is selected. Operations of this type have an extremely large number of possible solutions. However, only one will result in maximum economic return and, more important, this one program must be re-evaluated and adjusted constantly to accomodate such changing field factors as the number of producing days, the price of crude, the discovery of new reserves, declining reservoir pressure with subsequent decline in production and a host of other factors which characterize specific operations. One of the most widely used, direct methods of optimization is a numerical procedure termed "linear programing", which is designed to investigate systematically each of the possible solutions involved in a given problem, determining rapidly and uniquely the optimum answer. As implied by the name, linear programing requires that all field variables be either defined or expressed in a series of interdependent linear equalities or inequalities. These relationships are solved simultaneously, using a form of matrix solutions to determine the optimum values for each producing variable that will maximize net profits. The solution techniques used in a recent field case study is termed the "simplex method" and is discussed in full detail in Ref. 1.

By Robert T. Howard, Morris Cohen

IT has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkin1 has shown that the compositions of two coexisting phases in a a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanalysis.3 Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantitative way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of, this research could not be treated satisfactorily by other quantitative tools, such as specific volume,4 magnetic,5 dilatometric,6 electrical resistance7 or x-ray measurements.8 It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. LITERATURE SURVEY Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1947

By P. Beardmore, B. W. Howlett, B. D. Lichter, M. B. Bever

The heats of formation at 273°K of the compounds Mg2Ge, Mg2sn, and Mg2b, the heats of fusion and melting points of Mg2Sn and Mg2Pb, and the heats of solution of magnesium, germanium, and lead in liquid tin have been measured. The excess free energies of the liquid alloys and the free energies of formation of magnesium-Group IVB compounds at their melting points and their standard free energies of formation at 298°K have been calculated. The stability and bonding of the compounds are discussed with reference to these properties. Some thermodynatnic aspects of the liquid phases in the systems Mg-Sn and Mg-Pb are also considered. THE compounds of magnesium with the Group TVB elements, silicon, germanium, tin, and lead, have often been considered to constitute a nearly ideal homologous series. In particular, their thermodynamic stability has been assumed to decrease with increasing atomic number of the Group IVB element.' The binary-phase diagrams of the magnesium-Group IVB elements given by Hansen and Anderko2 have the same form. Each system has a single con-gruently melting compound of limited homogeneity range. The structures of these compounds, which have the formula Mg2X, are anti-isomorphous with the calcium fluoride structure. A recent investigation has found evidence of a second compound in the system Mg-Pb.3 The solid compounds Mg2Si, Mg2Ge, and Mg,Sn are semiconductors, while the conductivity of Mg2Pb approaches that of a metallic conductor. This difference suggests that other properties may also show a discontinuity. The investigation reported here is concerned with the thermodynamic properties of magnesium-IVB compounds and particularly their variations with the period of the Group IVB element. The heats of formation at 273°K of the compounds MgzGe, Mg2Sn, and Mg2Pb and the heats of fusion and melting points of Mg2Sn and Mg2Pb have been measured. The results, combined with published data, are interpreted in relation to the stability and the bonding characteristics of the compounds. Some thermodynamic aspects of the liquid phases in the systems Mg-Sn and Mg-Pb are also considered. In the course of the investigation the heats of solution of magnesium, germanium, and lead in liquid tin have been determined. 1) EXPERIMENTAL PROCEDURES 1.1) Samples. Samples of the compounds Mg2Ge, Mg2Sn, and Mg2Pb, supplied by Professor P. Aigrain, Compagnie Générale de Télégraphie Sans Fils, were used in measuring heats of formation, heats of fusion, and melting points. Samples of Mg2Sn and Mg2Pb, supplied by Dr. V. B. Kurfman, Dow Metal Products Co., samples of Mg2Sn, prepared at the Air Force Cambridge Research Laboratories, and samples of MgzPb, prepared in this laboratory, were used for additional measurements of the heats of fusion and the melting points. The samples were stored in evacuated Pyrex capsules or under nonreacting liquids. 1.2) Heats of Formation. The heats of formation at 273°Kof the compounds Mg2Ge, Mg2Sn, and Mg,Pb were measured by tin-solution calorimetry. In this method, samples of the compound and of a mixture of the constituent elements are added alternately from 0°C to a tin-rich bath. The difference between the heat effects, corrected for the change in composition of the bath, is the heat of formation of the compound. Details of the method have been given elsewhere. 4 The bath was maintained at 350°C for the dissolution of the compounds MgzSn and Mg2Pb. Since at this temperature the dissolution of Mg2Ge was too slow, a bath temperature of 400" or 450°C was used with this compound. At least three calorimetric runs, each of approximately six additions, were made with each compound. 1.3) Heats of Solution. The determination of the heats of solution of magnesium, germanium, and lead in tin was included in this investigation because they were not well-established at the time this work was started. To obtain the heat of solution, the difference

Jan 1, 1967

By John C. Calhoun, R. C. Newman

A report is made of experimental work performed on the capillary retention of water within porous solid systems, the displacement being accomplished with air and various organic liquids. A portion of the experiments were designed to measure the lowering of vapor pressure of water within a porous solid with subsequent conversion of such vapor pressure data to capillary pressure values. The form of the capillary pressure curve at high capillary pressures has been elucidated from this data. Certain theoretical approaches are presented to indicate the correlation between work done by previous investigators. The present work is correlated also with theory. Surface area values are calculated for the various core systems studied. INTRODUCTION Leverettl in 1941 presented a paper which gave the essential concepts of capillary behavior in porous solids. His presentation included both theoretical and experimental aspects of the problem. He defined the term "capillary pressure" and applied it to an ideal porous system. His work included the definition of a dimensionless quantity which was a function of fluid saturation and which could be correlated with porosity and permeability for clean, unconsolidated sands. His experimental work was performed by the drainage of water from packed columns of unconsolidated sands. Subsequently, other authors have presented experimental techniques which permit the determination of capillary pressure data on small core samples. Data have been presented on porous systems other than unconsolidated sand and with the use of liquids other than water. Notable among these are the works of Hassler, Brunner and Deahl,2 Bruce and Welge,³ Amyx and Yuster, and Purcell. Others have indicated the applicability of such data to field problems without regard to the theoretical aspects of the capillary pressure saturation function. Within the recent published literature there have also been reported studies of the correlations between capillary pressure data and other fundamental properties of porous solids. It was the intent of the present reported work to investigate the behavior noted by water and various other liquids within porous systems in an attempt to amplify existing correlations between capillary properties, surface properties, and other fundamental characteristics of porous systems. The experimental work described here was performed as two different investigations but due to its nature it is reported as separate phases of the same general topic. CAPILLARY PRESSURE AND VAPOR PRESSURE LOWERING It has long been recognized that the vapor pressure above the curved surface of a liquid is a function of the curvature of the liquid surface." The capillary pressure is also a function of the curvature of the liquid surface. Both capillary pressure values and vapor pressure lowering are, therefore, functions of the liquid saturation of a porous solid. A quantitative relationship between the vapor pressure lowering and the capillary pressure can be simply developed by considering a porous solid system containing water in equilibrium with its vapor. The capillary pressure at any height within the system is defined as Pc= Pv -P1.......(1) where PI is the pressure in the vapor phase and PI is the pressure in the liquid phase. Consider that both the water and its vapor are continuous phases within the system and that at any point the two phases are in equilibrium. The gradients in the liquid and vapor columns within the porous system are: PI = plgdh dPv = pvgdh By integrating these gradients from the point where h = 0 to the height h, values of PI and PI at the point h are found. Let the point where h = 0 be that where Pc = 0. At this point also Pv is equal to Pve, the equilibrium vapor pressure of the liquid above a flat surface. From the first of these integrations since p is independent of height: P = p1gh + P, From the second, by substituting pv = PvM/RT, where M is the molecular RT weight: Pv M Pvo- RT gh By combining the two last equations to eliminate h, one obtains: P1 RT Pv Substituting, values for Pv and Pi in equation (1) gives PyRT RT Pv which is approximately Pc=RT/Mp1 In Pvo/Pv .......(2) This equation relates the vapor pressure above a curved surface with the capillary pressure across the curved surface in terms of measurable quantities. The equivalent of this equation is given by Freundlich."

Jan 1, 1949