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By M. R. Tek, F. F. Craig, J. O. Wilkes, C. S. Goddin

The waterflood performance of a water-wet, stratified system with crossflow is computed by a finite difference procedure. The effects of five dimensionless parameters on tile oil displacement efficiency, water saturation con-tour.7 and crossflow rates are evaluated in the absence of gravity forces. Crossflow due to viscous and capillary forces is shown to exert a significant effect on oil recovery in a field-scale model of a two-layered. water-wet sandstone reservoir. The crossflow is at a maximum in the vicinity of the front advancing in the more permeable layer. Under favorable mobility ratio conditions, the comparted oil recovery with crossflow always is interrnerliate between that predicted for a uniform reservoir and that for a layered reservoir with no crossflow. INTRODUCTION The important erects of reservoir heterogeneity on waterflood performance are commanding increased attention in the technical literature. Much of this attention is centered on two categories of layered reservoirs: those in which layers are non-communicating and those in which crossflow of fluids occurs between the layers. In the first category, the reservoir is assumed to consist of discrete layers, each uniform within itself and differing from the others only in such properties as thickness, porosity and absolute permeability. The performance within each layer is calculated by one-dimensional flow theory, and the performance of the total reservoir is obtained by summing individual layer performances. Capillary and gravity effects usually are not considered. Representative publications dealing with thi5 type of reservoir are those of Stiles,' Dykstra and Parsons,' Hiatt,3 Warren and Cosgrove' and Higgins and Leighton." Prediction of performance for reservoirs in the second category is considerably more difficult since viscous, capillary and gravitational forces all play important roles in causing crossflow between layers. A number of authors have investigated the simpler problem of two-dimensional displacement flow in a stratified system with a mobility ratio of unity and negligible capillary and gravity effects.'; Others have considered two-dimensional, non-steady-state flow of a single, slightly compressible fluid in a stratified reservoir. A limited number of laboratory oil displacement tests in layered models with crossflow have been reported. Miscible floods (with resultant zero capillary forces) in layered five-spot models were conducted by Dyes and Braun," who studied the effect of mobility ratio with zero gravity forces, and by Craig et al. 12 who studied the effect of gravity forces at constant mobility ratio. Waterfloods in layered five-spot models (with cross-tlow due to capillary, viscous and gravity forces) were conducted by Gaucher and Lindley,"' who showed the effect of gravity forces in causing underrunning of the injected water and by Carpenter, Bail and Bobek, 14 who demonstrated the reliability of Rapoport's" dimension-less parameters for scaling layered systems. Waterfloods in rectangular layered models were conducted by Richardson and Perkins."' who investigated the effect of velocity at constant mobility ratio and with zero gravity forces, and by Hutchinson," who studied the effects of varying mobility, layer permeability and layer thickness ratios. The differential equations which rigorously describe waterflooding in a heterogenous porous medium are non-linear and do not facilitate analytical solution. By using finite difference approximations it is possible to obtain a solution to any desired degree of accuracy. Such a solution, using an alternating direction implicit procedure (ADJP), is described by Douglas, Peaceman and Rachford.18 In the present study, a computer program using ADJP explores systematically the effects of important parameters on waterflood performance of a two-dimensional, two-layered, field-scale model of a water-wet sandstone system. Particular attention is given to evaluation of the water saturation contours and crossflow rates at the interface between layers to gain improved understanding of the crossflow mechanism. PROCEDURE BASIC: FLOW EQUATIONS The basic flow equations for two-dimensional, two-phase, immiscible, incon~pressible flow in a porous medium are:

Jan 1, 1967

By P. H. Turnock, R. D. Pehlke

The effects of mutual interactions between elements on the solubility of nitrogen in liquid iron alloys containing chrormium, columbium, molybdenurn, nickel, or silicon have been determined. The equilibrium nitrogen solubilities in the liquid iron alloys were measured by the Sieverts method. The second-order effects caused by the presence of chrormium, columbium , or silicon in the melt were found to be significant. The solubility of nitrogen in liquid iron alloys containing several alloying elements has also been measured as a function of melt temperature and nitrogen pressure. The heat of solution of nitrogen in microcomponent iron alloys has been found to be a function of the logarithnz of the activity coefficient of nitrogen, irrvespectilje of the composition of the melt. The heat of solution of nitrogen in pure liquid iron was determined to be 1265 ± 450 cal per g-atom of N over the temperatxue range 1600° to 1800°. Sieverts ' law was obeyed for all melt compositions studied in the pressure interval 0.4 to 1.0 atm. The solubility of nitrogen in liquid pure iron and in many dilute binary liquid-iron alloys has been the subject of many investigations. Pehlke and Elliott' made a comprehensive investigation on this subject in which they summarized and compared previous researches. However, the practical application of these solubility studies requires prediction of the nitrogen solubility in the multicomponent alloys encountered in operating practice. The interaction parameter as defined by wagner2 has been used to predict the behavior of a solute in a complex alloy, and a modification of this approach has met with reasonable success in several instances.'1"5 The necessity for extending the nitrogen solubility data on binary alloys is caused by the lack of direct measurements of the solubility of nitrogen in molten alloy steels. A direct comparison between measured solubilities and those predicted for multicomponent alloys based on data in binary systems has been made in only a few instances, and most of these were reviewed by Langenberg,6 who developed a graphical technique for predicting nitrogen solubilities in multicomponent iron alloys. The solubility of nitrogen has also been studied over the entire Fe-Cr-Ni ternary system by Humbert and Elliott.? Both studies compared the solubilities computed from binary iron alloy data with those measured in ternary alloys in the liquid state at 1600°C. Most of the nitrogen solubility measurements referred to above were for iron alloys at 1600°C; thus, the ability to predict nitrogen solubilities in molten iron alloys has been restricted primarily to alloys at 1600°C. Recently, Nelsson8 devised an approximate method for calculating the change in nitrogen solubility in molten iron alloys as a function of temperature, but an assumption of regular solution behavior limits the applicability of the method. Chipman and Corrigan9,10 have developed an empirical correlation. based on the activity coefficient of nitrogen in the iron alloy at 1600°C, which facilitates the estimation of nitrogen solubilities at higher temperatures. This method also has limitations, due to the necessity of calculating the activity coefficient for nitrogen in a multicomponent iron alloy at 1600°C from the nitrogen solubility data for binary iron alloys. The shortcoming of such a straightforward approach to the problem of predicting nitrogen solubilities is the disregard of mutual interactions between elements in a complex iron melt. This investigation was conducted in an attempt to provide a more reliable method of predicting nitrogen solubilities in multicomponent iron alloys. The effects of the mutual interactions between chromium, nickel, silicon, molybdenum, or columbium in iron were studied, using the Sieverts' technique1,7 to measure the effects of alloy composition, temperature, and pressure on the solubility of nitrogen in ternary liquid iron alloys.

Jan 1, 1967

By W. N. Miner, R. O. Elliott

Electrical-resistivity )measurments were made be-trueetz room temperatrive and 1.5 oK on five different stocks of cerium metal, and the results were correlated with the types, amounts, and distribution of the impurities present. Magnesium, which appeared to be distributed as a solute throughout the cerium matrix, was found to have a large effect on the residual resistivity, 1 at. pct Mg being sufficient to increase the residual resistivity by about 10 microhm-cm. The formation of ß by repeated thermal cycling between room temperature and liquid-helium temperature is attributed to the deformation and faulting that occurs during the ? D a transformation. In preparation for starting a proposed study of cerium-rich alloys, we examined samples from severa1 stocks of cerium metal in order to choose the purest stock for future use in making the alloys. Low-temperature electrical-resistivity data were used to gain initial information about the purities of the stocks. Additional information was subsequently obtained from chemical analyses, density measurements, optical metallography, and electron-micro-probe analyses. Cerium that has been annealed at high temperature and cooled to room temperature has the fee crystal structure (? phase) with a = 5.16Å. When cooled further, in the region between about 250" and 150°K, some of the fee phase transforms to the double hcp form (ß phase) with a = 3.68 and c = 11.92Å. The remainder of the room-temperature fee form (and perhaps some of the hexagonal phase) transforms electronically in the vicinity of 100° K to the more dense or "collapsed" fee form (a phase), a - 4.85A, by transferring about 0.5 electron per atom from the 4f level to the valence band. Very little work related specifically to the effects of impurities on the physical properties of cerium has been reported in the literature. Gaume-Mahn1, 2 has studied the effects of calcium, magnesium. iron, silicon, and tantalum on the electrical resistivity and magnetic susceptibility of cerium between 60o and 300°K. Gschneidner, Elliott, and McDonald3 have discussed the effects of total impurity content on the hysteresis of the a —? (reversible) transformation and on the formation of the 4 and "a-? intermediate" phases. Smith and Morrice* have reported the effect of total impurity content on the resistivity of cerium at 4 and 293°K. In none of these reports, however, is it apparent that the distributions of the impurities were determined, L.r., whether the impurities were present in inclusions or in solid solution in the matrix is not mentioned; nor does it appear that the phase purity of the cerium was always considered. In the present study, five different stocks of cerium were involved. One was represented by a single sample of electrowon cerium, which was all that had remained from a stock of high-purity material obtained from the U.S. Bureau of Mines, Reno, Nev., in 1959. The other four stocks were recently purchased from commercial sources and were specified to be 99.9 wt pct pure. EXPERIMENTAL Cerium stocks designated as #1, #2, #4, and #5 were obtained from commercial suppliers for the specific purpose of finding a reliable source of high-purity cerium. Although the purity level of the cerium was specified to be 99.9 pet, the specifications did not include limits as to the amounts of various impurities that would be acceptable. Consequently the chemical analyses of the different stocks varied widely. Stock #3, which had been obtained from the U.S. Bureau of Mines and which was the purest on the basis of chemical analyses, consisted of a single specimen of electrowon cerium. It was included in the examination for purposes of comparison. Table I contains the chemical and spectrographic-

Jan 1, 1968

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967

By S. K. Mitra

A refinement of the Seeger model for intersection process is investigated which is in better agreement with experimental observations than the original. It is shown that, in single crystals, the strain hardening in Stage II is mainly due to the short-mnge interactions when intersection is the rate-controlling process. It is also demonstrated that the creep curves, as predicted by this theory, are in good agreement with the experimental observations. MOTT: Cottrell? and Seeger have developed an approximate theory for plastic deformation of single crystals over the range of variables where the strain rate is controlled by the rate of intersection of dislocations. Although it is now generally agreed that the low temperature deformation of many pure metals is controlled by the intersection mechanism, various dictates of the over-simplified Seeger model are not in good agreement with all the experimental facts. It is the purpose of this paper to reveal that by appropriate extensions of the Seeger model, particularly those suggested by Basinski: a much more reliable theory results. The refined model to be presented here will be shown to account, in a satisfactory way, for the effect of stress, temperature, and strain on the creep rate under constant stress and for the effect of temperature and strain on the flow stress in constant strain-rate tests. EXPERIMENTAL METHOD To Check the theoretical deductions, both creep and tension tests were conducted on single crystals of high-purity Al (99.994 pct Al) so oriented that both the active slip plane and the Burger's vector of the operative dislocations on that plane made angles of about 45 deg to the tension axis. Single crystals of aluminum (5/8 in. by 1/10 in. by 8 in.) were grown in a graphite mold under an inert atmosphere using the Bridgman method. The chemical composition of the aluminum is given in Table I. A common seed was used for all crystals and their orientation is shown in Fig 3. The extensometry consisted of two differential transformers with matched outputs mounted so as to measure the extension in a 2 in. gage length. The amplified difference in output of the two transformers was recorded by a potentiometer. The amplification was calibrated before each run so that one chart division of the recording potentiometer indicated a 105 shear strain on the specimen. Stresses were measured to the nearest 1 x l04 dynes per sq cm. ACTIVATION VOLUME The concept of Basinski that the activation volume is not constant but is a function of the force that aids thermal fluctuation in effecting the cutting of dislocations will be adopted in this section. The force acting due to an applied shear stress on the dislocation being intersected is where L is the mean spacing between the forest dislocations, is the Burger's vector and T is the back stress. A detailed discussion about the origin of back stress will be taken up later in this report. As shown by Basinski, the activation energy, U, that must be supplied by a thermal fluctuation in order to effect intersection, is equal to where x is the distance through which the dislocation must be translated for complete intersection, and Fm is the maximum force encountered in intersection. When the applied stress is decreased abrupt ly F also decreases and the activation energy increases correspondingly as documented in Eqs. [ 1 ] and [2]. The Seeger equation for the strain rate when the deformation is controlled by rate of intersection of where the shear strain rate (per sec) N = the number of points per unit vol at which intersection can take place

Jan 1, 1962

By H. L. Hartman

The estimation of the magnitude of pressure changes which occur in mine ventilation circuits is of primary importance to the mining engineer in making changes in an existing mine or in projecting the ventilation requirements of a new mine. It is a formidable task in many cases, because no adequate theory is available and empirical data are unreliable or even lacking. The common practice of increasing one's estimate of the mine static pressure by an arbitrary "safety factor" to compensate for the unknown is a poor substitute for accuracy. Generally little difficulty is encountered in calculating friction losses in mine airways. As long as the friction factor can be reliably estimated, the well-known Atkinson formula gives accurate results. However, it is in the determination of shock losses that the ventilation engineer encounters difficulty and is apt to resort to an arbitrary allowance. Shock losses may constitute as little as five or as much as twenty-five percent or more of the overall pressure drop in the mine, and such allowances are generally completely unsatisfactory. Since other shock losses have been covered by McElroy (1), this paper deals with a long-neglected source of shock and pressure change in ventilation circuits, divergence and convergence of airflows, here referred to by their more common mining terms, splits and junctions. PREVIOUS WORK There is practically no fundamental information available in ventilation literature on the splitting and junction of airflows, either in mining or mechanical engineering periodicals or handbooks. Fluid mechanics textbooks seemingly avoid the subject of divergence and convergence, except for brief empirical treatment. The only investigation reported for mine ventilation systems was by Weeks, et a1 (21), in 1933. Although applicable to the case of line brattices in coal mines, it cannot be applied to the general case of mine splitting and junctions involving change of direction with little or no area change. In dealing briefly with the subject of shock losses at splits and junctions, McElroy (1) suggests only that they be considered comparable to bends, with losses at junctions being increased 50 pct to allow for interference of merging streams. He recognizes the importance of quantity ratio but concludes that exact quantitative data are lacking to compute losses at splits and junctions. A very capable summary and analysis of the state of knowledge in industrial ventilation and fluid mechanics regarding losses due to divergence has recently been reported by Gilman (3). In considering all earlier work dealing with both air and water as fluids, he compares results on a common basis and obtains good empirical agreement. For divergent flow, the controlling variable in each branch is the quantity ratio, although the deflection angle is of secondary importance. Empirical equations are presented for straight and 90-deg branches with varying velocity ratios, assuming branches smaller than the main duct. These formulas are modifications of the Borda equation for abrupt contraction and expansion. The only information available on shock losses in convergent flow are approximate experimental data presented by Alden (4) and the Manual of Recommended Practice for Industrial Ventilation of the American Conference of Governmental Industrial Hygienists. Alden considers the effects of both quantity ratio and deflection angle. The data indicate an effect opposite to that observed in divergence, the shock loss varying directly with quantity ratio. SHOCK LOSS THEORY Because pressure losses due to shock have been found to bear a constant relation to the mean velocity of flow in a given conduit, they are frequently expressed as a dimensionless function of the velocity head, termed the shock loss factor. For airflow in ducts and mine airways, the shock loss may be represented by the formula (1): Hx - XHv, (1)

Jan 1, 1961

By R. P. Alger, M. P. Tixier, D. R. Tanguy

In the combination induction-electrical log used at present in the field, the induction logging tool is appropriate for the investigation of moderately invaded formations. A new induction sonde with a radius and investigation about twice as large has been developed recently for the case of deep invasion. It has very nearly the same vertical resolution as the present sonde so that thin beds are defined as accurately as before. The characteristics of the new tool are described, the corresponding interpretation charts are given and field examples are discussed. The design of the sonic logging tool has been modified to improve the calibration and the reliability. The fact that porosity can be accurately recorded by means of the sonic log has prompted new interpretation procedures for saturation estimation, wherein the data concerning the various permeable beds in a given well are correlated. One approach consists of plotting transit time vs true resistivity, with an appropriate scale. With this approach, saturations can be estimated conveniently even in cases where formation water resistivity is not well known. In another approach, a comparison is made of the values of the formation waters computed from the re- sistivity and sonic logs. Using the concept of continuity, this procedure makes possible a quick determination of zones of saturation in shaly sands and/or in case of appreciable variations of formation salinities with depth. It has been found that the comparison of porosity from the sonic log with the apparent porosity computed from a short-investigation resistivity log may reveal, in many cases, the presence of residual oil and thus detect potentially productive formations; this procedure is valuable when the true formation resistivity and the resistivity of the formation water are in doubt. INTRODUCTION During the past year, the efficiency of log interpretation has been vastly improved. The improvements have largely resulted from the introduction of a deep-investigation induction device and from the application of new interpretation techniques that utilize sonic vs resistivity readings. Since the new interpretation techniques depend, in part, upon good values of true formation resistivity, the new induction log will be discussed under Part I. The sonic interpretation techniques will be studied under Part 11. Early in 1959, the 6FF40 induction equipment was introduced in the field. This device was designed for a better approach to true formation resistivities in deeply invaded zones. The greatly improved radial investigation of the 6FF40 equipment has been achieved without sacrificing vertical resolution. The first combination induction-electrical log, the 5FF40, was introduced as a standard tool in 1956 for the logging of wells drilled with fresh muds. The tool has received wide industry acceptance in the United States. 'The 5FF40 induction log has a radial investigation sufficient to overcome average depths of mud filtrate invasion. At 5d invasion, for example, the 5FF40 induction log will read about 1.4 R. in a water sand where R., = 10R,. At 10d invasion, such induction log would read 2.45 R. in the same water sand. In either case, the effects of invasion would not be sufficiently great to cause a water sand to be mistaken for a shale-free oil- or gas-producing zone. Some formations, however, invade deeply — in excess of 10d. Such water zones could be mistaken for oil-or gas-saturated sands unless the porosity balance' can clearly make the distinction. It is for these deeply invaded formations that the 6FF40 was developed. CHARACTERISTICS OF THE 6FF40 Radial Investigation Characteristics To describe the comparative responses of the 5FF40

By C. Tom Blevins

The purpose of this paper is to discuss production and roof control problems associated with directional lateral stresses in an in situ stress field and the approach that Inland Steel Coal Company made in trying to cope with them. Before proceeding, a description of the mine location, product, geology, restraints, and mine history is in order. The mine is located in Hamilton County in Southeastern Illinois. It produces a high volatile metalurgical coal and is slated to produce 2.1 MTY. Product ion is in the Illinois No. 5 seam at a depth of 930 feet, approximately 490 feet below sea level. The scam height averages from 5.5 to 6.0 feet throughout the reserves with height increasing in the eastern reserve area to approximately feet and a 5 Foot average in the West. The scam tends to dip to the North, North East, but is locally very undulating. The Galatia channel washout outlines the eastern boundary of the reserves and there is a split coal area toward the central part of the property than runs south-southeast. The top above the #5 seam is laminated medium gray shale called Dykersburg. Individual shale bedding planes vary locally From ½ to 1" in thickness to a more normal thickness of 1 to 1 ½ with some areas being interlayed by thin carboncous material. The top normally must be considered as materially competent. Even though the mine is still relatively small in area with only 1.3 million tons of total production to (late, we have encountered dense zones of slicker sides and premining, stress cracks (joints). There are also areas of siltstone, that vary from a few inches to several feet thick, and areas of rider coal, clay instrusions, and rolls. We have crossed lineament concentrations that show strong evidence of corelation to localise top problems. These are being monitored closely to see their predictability on our present and future mining conditions. The face cleat runs N 55° E and butt cleat runs S. 25° E. On a regional basis, there are several anticlinal belts that trend in a northerly direction. The one major restraint is that Inland does not own surface subsidence rights. Therefore, a partial extraction mining plan is being followed. The Holland-Gaddy formula for pillar strength design is used to calculate theortical pillar sides. When production began in March of 1979, it was noted that ground control problems occurred as we drove north entries. East-west cross cuts tended to have better working conditions. This phenomia occurred from a couple hundred feet, but seemed to dispate as we got away from the men and material shafts. Once the production shaft was connected and enough entries extended for installation of belts, ground control problems were again experienced in north-south headings. It was also observed that when mining north-south headings with east-west crosscuts, if the crosscut was driven through ahead and supported, the intersection was stable upon entry connection. This held true even where fairly extreme ground control, problems were encountered. The reverse held true. when driving east-west headings with north-south crosscuts. At this time, we started searching in earnest for a working theory to explain this roof phenomia. It also became the first step of what eventually was a four step sequence to derive a workable solu¬tion to the problem. The combination of the many geological changes and the fact that north-south condition was at times intermitent, helped to disguise the stress field. The mine also being in a fairly virgin area with no mines in approximately 25 milt, radius, meant we didn't have a reliable case history to examine. Various theories were researched before it was concluded that our primary ground control problem was a directional lateral stress Field, with the major stress axis in an east-west direction. The second stop of the procedure was then to test. mining methods and determine if these stresses could be modified to a

Jan 1, 1982

By OÆGrady P

Finite element analysis is becoming a routine component of design of longwall extractions, now superseding more traditional somewhat intuitive approaches. Finite element modelling is relatively inexpensive and provides an adequate degree of similitude to give satisfactory analysis. The physical modelling of two decades ago is now largely replaced by numerical methods of which finite element is the best known. Important data for finite element work are physical properties, including creep aspects, introducing the non-linearity of stress response.Various computer packages are available and some were used to model two specific UK examples, using both linear and non-linear approaches. It appears that non-linear approaches will yield most benefit. The use of materially non-linear analysis is merited by the greater similitude it provides between model output and real mine situations.

Jan 1, 1991

Mining regulatory authorities worldwide mandate frequent inspection of winder ropes used in shaft-equipped underground mines and ski lifts. Visual inspections are effective in identifying and assessing the type and severity of damage found in the exterior of the rope. In addition, electromagnetic or permanent magnet-based methods are used to identify broken wires, corrosion damage and other anomalies that occur anywhere within the core of wire ropes made of steel, which is a ferromagnetic material. The magnetic methods yield the loss of metallic area due to wire breaks and other damage in the ropeÆs section as well as local flaws that give rise to discontinuities in the magnetic field. The quantitative measurement of the loss of metallic area is indirectly related to the loss of breaking strength that is commonly used as a rope discard criterion. The ropes used in a mine winder in the Goldfields of Western Australia are inspected using Meraster 120B permanent magnet-based rope tester and their condition is assessed against published discard criteria.

Jan 1, 2003

By Hon-Yim Ko

1972 constituted the second year of the projected five-year study on constitutive relations of coal. The schedule adhered closely to the five-year outline which is summarized in Table 1. This chapter is intended to serve as introduction and concise synopsis of the year's activities and results, which are presented in greater detail in the following chapters, which have been contributed by the individual researchers in charge of the various aspects of the project under study. Coal Sources, Material Procurement, and Sample Preparation Most of the studies performed during 1972 were done on coal from two sources: the Old Ben Mine #22 in Illinois, and the Bruceton Mine in the Pittsburgh seam of Pennsylvania, which may be considered typical of coal sources of economic importance in the Midwestern and Eastern part of the U.S. These two mines have proven to be reliable suppliers of coal material for our research. We have been able to establish good working relations with their personnel and feel that we can continue to count on their cooperation and help.

Jan 1, 1972

By K. M. Myles

The vapor pressure of palladium over a series of Rlz-Pd alloys has been measured by the torsion-effusion method. The thermodynamic properties of the alloy system at 1575=K have been calculated from the vapor pressure data. The activities and the free energies of formation exhibit large positive deviations from ideal behavior. The enthalpies of formation are endother-mic. The entropies of formation are positive and larger than the ideal entropy of mixing. All of the thermodynamic properties suggest that a strong tendency toward phase separation exists in the solid solutions. The possible origin of the phase instability and the various factors that influence the thermodynamic properties are discussed. RECENT studies of the thermodynamic properties of alloys of palladium with nontransition elements have indicated that a significant contribution to the enthalpy of formation is related to the redistribution of the conduction electrons upon alloy formation.'-' The present work was undertaken to ascertain the importance of this contribution in Pd/transition-metal alloys. The Rh-Pd system was chosen for this investigation for several reasons: 1) The thermodynamics of the system were unknown. 2) Rhodium and palladium are completely soluble at high temperatures; below 1118OK the solid solution becomes immiscible.', 3) The difference in magnitude between the vapor pressures of rhodium and palladium permitted the use of an existing effusion apparatus. 4) Additional information was known about the alloy system that would facilitate the interpretation of the thermodynamic results. EXPERIMENTAL PROCEDURE The thermodynamic properties of the Rh-Pd alloy system were calculated from the vapor pressure of palladium over solid palladium and over several solid Rh-Pd alloys. The vapor pressure was measured by means of the torsion-effusion apparatus that has been described previously. In this method, an effusion cell is suspended from a tungsten filament inside a high-temperature furnace. Two orifices are located eccentrically such that the effusion of the vapor creates a rotational torque in the filament. The angle of rotation is directly related to the total vapor pressure within the cell. As the vapor pressures of rhodium and palladium are approximately five orders of magnitude apart," the total vapor pressure was considered to be effectively equal to the equilibrium vapor pressure of palladium. The effusion cells were made from high-purity alumina since auxiliary experiments indicated that essentially no reaction occurs between alumina and solid Rh-Pd alloys. Unfortunately, because the orifices were irregular, an accurate calculation of the Free- man-Searcy correction factors" could not be made. The constants were determined in an independent experiment where the vapor pressure of copper, as measured in the alumina cell, was compared with an accurate value of the vapor pressure, which had been determined previously.4 Depletion of palladium from the surfaces of the specimens was minimal as the deflection of the cell remained constant, for at least 15 minutes, at each of the experimental temperatures. Lattice parameter measurements of the postrun alloys also indicated that no changes in the composition of the surfaces had occurred. The alloys were prepared by arc melting the requisite amounts of the 99.99 pct pure elements. The four most palladium-rich alloys were remelted in a levita-tion furnace since complete melting of the components had not occurred in the arc furnace. All of the alloys were subsequently homogenized at elevated temperatures in sealed alumina thimbles. After heat treatment, the alloys were analyzed chemically and were in essential agreement with the nominal compositions. The thermal histories and nominal compositions of the alloys are given in Table I. Lattice parameters of the heat-treated alloys were computed, by means of the method described by Mueller et a1. ,I2 from X-ray diffraction powder patterns obtained with filtered copper radiation in a 114.6-mm-diam Straumanis-type Debye-Scherrer camera. The results, which are tabulated in Table I, exhibit a slightly greater negative deviation from Vegards' law than the values reported by Raub et al.13 The diffraction lines were sharp and well-resolved and thus indicated that the alloys were homogenous. RESULTS The logarithms of the individual values of the vapor pressure of palladium were fit, by the least-squares method, as a linear function of the reciprocal of the absolute temperatures. The constants of the equations are given in Table I along with the temperature range over which the data was accumulated. The latent heat of vaporization at 298.15"K for pure palladium, calculated by the third-law method,14 showed no systematic temperature dependence. The average value of 88,920 * 20 cal per g-atom agrees favorably with the average of the results obtained in the most reliable previous investigations.15"19 The activities of palladium were computed from the vapor pressure data at 1525', 1575", and 1625OK. Consistent with the mass spectrometric study of the atomicity of palladium vapor,lg the vapor was assumed to be monoatomic. The activities of rhodium were determined by integrating the Gibbs-Duhem equation with the aid of the a function.20 In the calculations, the activities of the pure solid metals were assigned the value of unity. From the activities, the partial and integral free energies, entropies, and enthalpies of formation at 1575° K were computed; they are assembled in Table 11.

Jan 1, 1969

By R. J. Fruehan, F. D. Richardson

Electrochemical measurements have been made of the activity of oxygen in copper and its alloys with silver and tin at 1100" and 1200°C. The galvanic cell used was Pt, Ni + NiO/solid ellectrolyte/[O] in metal, cermet, Pt The results do not support any of the equations so far designed for predicting the activities of dilute solutes in ternary solutions from activities in the corresponding binaries. If, however, a quasichemical equation is used with the coordination number set to unity, agreement between observed and calculated activities shows that this empirical relationship can be useful over a fair range of conditions. SEVERAL solution models have been proposed for predicting the activity coefficients of dilute solutes in ternary alloys from a knowledge of the three binary systems involved. Alcock and Richardson1 have shown that a regular model, and a quasichemical model,' in which the dissolved oxygen is coordinated with eight or so metal atoms, can reasonably predict the behavior of both metal and nonmetal solutes when the heats of solution of the solute in the separate solvent metals are similar. But when this is not so, neither model gives useful predictions unless coordination numbers of one or two are assumed. Wada and Saito3 subsequently adopted a similar model to derive the interaction energies for two dilute solutes in a solvent metal. Belton and Tankins4 Rave proposed both regular and quasichemical type models in which the oxygen is bound into molecular species, such as NiO and CuO in mixtures of Cu + Ni + 0. However, their models have only been tested on systems in which the excess free energies of solution of the solute in the two separate metals differ by a few kilocalories. Ope of the reasons why more advanced models have not been proposed is because few complete sets of data exist for ternary systems in which the solute behaves very differently in the two separate metals. For this reason measurements have been made of the activities of oxygen dissolved in Cu + Ag and Cu + Sn. Measurements on both systems were made by means of the electrochemical cell, Pt, Ni + NiO/solid electrolyte/O(in alloy), cermet,Pt [1] The activity of oxygen was calculated from the electromotive force and the standard free energy of formation of NiO, which is accurately known.5 Before investigating the alloys, studies were made of oxygen in copper to test the reliability of the cell and to check the thermodynamics of the system. Of the previous studies those by Sano and Sakao,6 Tom-linson and Young,7 and Tankins et al.8,7 have been made with gas-metal equilibrium techniques; those by Diaz and Richardson,9 Osterwald,10 wilder," Plusch-kell and Engell,12 Rickert and wagner,13 and Fischer and Ackermann14 have been made by electrochemical methods. EXPERIMENTAL The apparatus employed was the same as described previously,9 apart from slight modification. The molten sample of approximately 40 g was held in a high grade alumina crucible 1.2 in. OD and 1.6 in. long. The solid electrolytes were ZrO2 + 7½ wt pct CaO and ZrO2 + 15 wt pct CaO; the tubes 4 in. OD and 6 in. long were supplied by the Zirconia Corp. of America. They were closed (flat) at one end. In one experiment with Cu + O, both electrolytes were used in the cell at the same time. The reference electrodes inside the electrolyte tubes consisted of a mixture of Ni + NiO. They were made by mixing the powdered materials and pressing them manually into the ends of the tubes, with a platinum lead embedded in them. The tubes were then sintered overnight in the electromotive force apparatus at 1100°C. By sintering the powders inside the tubes (instead of using a presintered pellet9) better contacts were obtained between the electrolyte, the powder, and the platinum lead. Troubles arising from polarization9 were thus much reduced. The electromotive force was measured by a Vibron Electrometer with an input impedence of 1017 ohm; the temperature was measured with a Pt:13 pct Rh + Pt thermocouple protected by an alumina sheath. The couple was calibrated against the melting point of copper. The cermet conducting lead of Cr + 28 pct Al2O3, previously found to be satisfactory9 for use with Cu + 0 was also found satisfactory with Cu + Ag + 0 and Cu + Sn + 0. Superficial oxidation was observed, but it did not interfere with the working of the cell. The reaction tube containing the cell was closed at each end with cooled brass heads and suspended in a platinum resistance furnace. The tube was electrically shielded by a Kanthal A-1 ribbon which was wound round it, and the ribbon was protected by a N2 atmosphere between the furnace and the reaction tube. The cell was protected by a stream of high purity argon which was dried and passed through copper gauze at 450°C and titanium chips at 900°C. All the metals used were of spectrographic standard. Procedure. In studies of the system Cu + 0, be-

Jan 1, 1970

By S. L. Bessinger

Introduction Extensive testing in the past ten years has shown that where a uniform natural gamma background is present in the strata bordering a seam, the thickness of the boundary coal left in place after mining can be determined by measuring the attenuation of that radiation (Nelson and Bessinger, 1989). Measurements made by the authors in underground mines in Pennsylvania, West Virginia, Ohio, Illinois and Kentucky and by others in Wyoming and New Mexico have shown the presence of such a gamma background (Nelson. 1989). Natural gamma coal-thickness sensors of several configurations have been tested in mines owned and operated by the Consolidation Coal Company (Consol) in Pennsylvania and West Virginia (Nelson and Bessinger, 1988). This paper describes the installation of a natural gamma coal-thickness sensor on an operating continuous miner. Previous tests had shown that the NGB-1000 coal-thickness sensor manufactured by American Mining Electronics, Inc., of Huntsville. AL, is an accurate, mine-worthy instrument. This large gamma detector consists of a sensing head and a control panel. The sensing head contains thallium-doped, sodium iodide scintillating crystal, which is coupled to a photomultiplier tube. The control panel contains the electronic components required for calibration, count conversion and display to the operator. Methods Conditions at a Consol mine in northern West Virginia require that 10 to 15 cm (4 to 6 in.) of coal be left at the roof boundary of continuous miner development sections. This roof coal is required because the shale of the immediate roof is friable and unstable. In the past, operators have used a dirt band that is usually visible near the top of the seam as a guide in maintaining the proper cutting horizon. However, this is not always reliable. Earlier observation showed that the actual thickness of the coal left on the roof varied widely; further, it was noted that occasional, accidental excursions into the immediate roof required supplementary roof control measures, such as installation of planks or center bolts. Thus, it was concluded that operators needed a better source of guidance for control of the cutting horizon, and a roof-coal thickness sensor was scheduled for installation. The NGB-1000 sensor was installed on a Joy 12CM10 continuous miner in June 1988. The sensing head was mounted on the cutter boom of the miner, and the control panel was mounted in the operator's cab. Power for the sensor was initially derived from an intrinsically safe battery power supply. Initial measurements with the sensor showed that the calibration was the same as that used in earlier tests at two other mines, indicating the uniformity of the natural gamma background above the Pittsburgh seam. Operating personnel were initially skeptical of the instrument's accuracy, and were hesitant to use its readings as a guide in maintaining a proper cutting horizon. Because gamma attenuation, the instrument's operating principle, is somewhat abstract, attempts to demonstrate the instrument's accuracy by explaining that principle were generally ineffective. It was found, however, that an operator could usually be convinced of the usefulness of the instrument by placing a large piece of coal of fairly uniform thickness over the instrument's sensing head and allowing the operator to see that the instrument reading increased by an amount very near his estimate of the thickness of the piece. The mine was provided with seven battery power supplies and a charging station. The charging station was kept in the lampman's office, and the mechanic on each shift was instructed that he was responsible for two battery power supplies each day: a freshly charged one to be taken in at the beginning of his shift and a depleted one to be brought out at the end. This system worked well for a few weeks, but eventually some battery power supplies were left in use so long that their batteries were discharged too deeply to allow recharging. In addition, transport and recharging of the batteries represented an additional task for the mechanics, who were already very busy. Consequently, a request was filed with MSHA to allow the sensor to be powered through intrinsic safety barriers by an electronic power supply connected to machine power. The permit was granted, and the sensor was connected to machine power. After the sensor was connected to machine power, the only operating problem experienced was occasional failure of cables. A supply of the required cables was made and delivered to the mine so damaged cables could be quickly replaced. Much of the cable damage could be eliminated by slight modifications to the miner during a rebuild, so that cables could be installed in more protected locations. After the sensor had been in operation for about two months, a survey was made to determine its effect on continuous miner operations. In previous research, coal thickness measurements made in 88 locations by the natural gamma method were compared to measurements made in the same locations by observing drill cuttings and by inspections of drill holes with a borescope. That research showed that the gamma method is at least as accurate as the other two methods (Nelson and Bessinger, 1989) and is also much easier to use. The object of the survey described here was not to assess the accuracy of the natural gamma measurements. but rather to determine the effectiveness of the sensor output as a guide for the operator in maintaining control of the cutting horizon. Thus a smaller, hand-held gamma detector

Jan 1, 1992

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By B. A. Eaton, K. E. Brown, C. R. Knowles, D. E. Andrews, I. H. Silberberg

This paper presents the resitlts of an investigation of two-phase, gm-liquid flow in horizontal pipelines. Experimental data were taken in three field-size, horizontal pipelines, two of which were constructed for this purpose. The data were obtained using water, distillate and crude oil separately as the liquid phase, and natural gas as the second phase. Experimental pressure-length traverse, liquid holdup and flow-pattern data were collected for each set of flow rates. These data were used to develop three correlations that are presented herein. The liquid-holdup values correlated with various flow parameters without regard to the existing flow pattern. The same was true for the energy-loss factors. A new flow-pattern map is presented that appears to be quite reliable, but not required for the pressure-loss calculations. The liquid-holdup correlation and the energy-loss factor correlation are used in conjunction with a two-phase flow power balance, developed during this study, to predict the pressure losses that occur during gas-liquid flow in horizontal pipelines. A recommended calculational procedure is given, as well as a statistical analysis of the results. This procedure lends itself to computer application, since several small pressure decrements are needed to calculate a pressure-length traverse. The correlations are shown graphically, but may be curve fitted with existing curve-fitring computer programs. INTRODUCTION Due to the frequent occurrence of gas-liquid flow in pipelines and the desire to accurately calculate the pressure losses that occur in these lines, two-phase flow is of considerable interest to the petroleum, chemical and nuclear industries. In the petroleum industry, gas-liquid mixtures have been transported over relatively long distances in a common line due to the advent of centralized gathering and separation systems. Long two-phase flowlines are usually accompanied by large pressure drops which influence the design of the system. Gas-lift installations are designed on the basis of known tubing pressures at the wellheads. The horizontal flowline connecting the wellhead and the separator system must be correctly sized in order to minimize the horizontal flowline pressure losses and the wellhead tubing pressure. Practically all oilwell production design involves horizontal two-phase flow in pipeknes. All of the flow processes of oil and gas production must be studied simultaneously to insure good well design. Since the beginning of offshore oilfield development, long horizontal flowlines have been constructed. Because pressure losses greatly influence the performance of producing wells, a method is desired that can be used to predict such pressure losses and select optimum flowline size. Several types of gas-liquid flow exist, and many of these are discussed by Gouse The study of pressure gradients, fluid distributions and flow patterns that occur in horizontaI multiphase flow is made difficult by the great number of variables involved. The various flow regimes give rise to changing velocities of the fluid particles in all directions. These instabilities of the interface between the gas and liquid prohibit the determination of actual vector velocities of fluid particles in each phase. Also, it is practically impossible to arrive at correct sets of boundary conditions. Therefore, most investigators have concluded that a solution to the problem by the classical fluid dynamics approach, whereby the Navier-Stokes equationsM are formulated and solved, is far too complex. Other methods must be utilized to develop general correlations that will predict the behavior of gas-liquid horizontal flow systems. Multiphase flow studies have sought to develop a technique with which the pressure drop can be calculated. Pressure losses in two-phase, gas-liquid flow are quite different from those encountered in single-phase flow; in most cases an interface exists and the gas slips past the liquid. The interface may be smooth or have varying degrees of roughness, depending on the flow pattern. Therefore, a transfer of energy from the gaseous phase to the liquid phase may take place while energy is lost from the system through the wetting phase at the pipe wall. Such an energy transfer may be either in the form of heat exchange or of acceleration. Since each phase must flow through a smaller area than if it flowed alone, amazingly high pressure losses occur when compared to single-phase flow. Most investigators of horizontal two-phase flow phenomena have chosen to separate their experimental data into several groups of observed flow patterns or regimes.

By D. S. Choi, R. Stefanko

There are a number of complex factors that influence the effectiveness of anchorage to maintain tension in rock bolts. However, a plastic analysis of the anchorage site employing certain simplifying assumptions with application of the Mohr-Coulomb criterion appears to explain the observed phenomena. Such an analysis has been made and a correlation sought with field and laboratory tests. Field tests were made in an anthracite mine in eastern Pennsylvania and included pull tests and long-term tests of a variety of anchorage devices in two basic lengths, 30 and 42 in. in two widely differing seams. Performance is reviewed for wedge, expansion shell, and resin anchorage. Laboratory tests duplicated many of the field conditions but in addition compared the performance of shells with normal and reversed serrations. This performance was compared with the predicted results from the plastic analysis. One of the major problems in conducting long-term underground tests is the selection of suitable instrumentation. All installed bolts were fitted with spherical and hardened washers to insure the best possible torque wrench readings. In addition, commercially available load cells were used. Finally, the performance of a specially developed strain-gage-equipped ring cell is viewed. Rock bolting as a method of support continues to increase with applications in many other industries in addition to mining. Nevertheless, with nearly 55,000,000 roof bolts installed in coal mines alone last year, this remains as the single greatest use. While bolts have frequently supported ground where conventional timbering could not, there are relatively few design criteria; and trial-and-error procedures prevail. Furthermore, there has been a lag in development of suitable instrumentation that is simple to install and read out, sensitive, durable, reliable, safe, and economical in evaluating the effectiveness of a bolt over long periods of time. Therefore, the pull test continues to be the most popular method of evaluating the applicability of a certain type of roof bolt under specific installation conditions. At The Pennsylvania State University in the Dept. of Mining, research has been conducted for a number of years to measure bleed off in carefully controlled laboratory experiments as well as in underground investigations."-' Unfortunately, most of the instrumentation developed has been primarily suitable only for research purposes, not possessing all of the aforementioned characteristics desirable for routine underground use. Other groups also have met with restricted success. Therefore, while relatively crude, the torque wrench continues to remain as the most widely used load measuring device. While both field and laboratory tests continue to be con- ducted, analytical analyses are attempted to discover the more important design parameters in order that more efficient anchorage might be devised. Bolts are being used for a greater variety of purposes in mining. Suspending wire sideframe belt conveyors from roof bolts is a common application. The suspension of a monorail transportation system presents yet another. One such system has just been installed in a recently reopened anthracite mine and is presently being evaluated under production conditions. Preliminary studies revealed that a considerable cost reduction was possible by suspending the monorail on bolts anchored in the top. The monorail was to be installed under two widely differing conditions—a competent sandstone above the Buck Mountain seam and a softer shale top above the Skidmore. The type of anchorage device, length of bolt, and long-term performance, consistent with economy and safety, had to be established for the installation once the decision was made to suspend the system on rock bolts. This paper describes some of the testing procedures leading to a final selection. Theoretical Analysis of Expansion Shell Anchorage A detailed look at an expansion shell assembly might shed some light on the factors involved in the design of a suitable shell, Fig. 1. When a bolt is rotated, the tapered plug is forced downward, expanding the leaves laterally to grip the sides of the hole. Two friction surfaces are present: (1) the interface of the plug and leaf and (2) the interface between leaf and rock. The relationships of these friction planes, geometry of expansion shell, and properties of the rock are important in the design of an expansion shell. Therefore, an analysis assuming the rock to behave as a rigid plastic material with its yield governed by the Mohr-Coulomb criterion was made." Furthermore, the effect of friction between the leaf and rock produced by serrations was analyzed.

Jan 1, 1971

By K. H. Hiller

A rotational viscometer has been designed which perrnits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described. The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensiom at high temperatures and pressures, are presented. Data are also presented for the flow behavier of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. INTRODUCTION The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin.1 The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.' Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids. The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.3 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro- duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress 7 and the rate of shear D is given by the following equation: where is the plastic viscosity and 4 the yield point. If 4 = 0, the equation for simple Newtonian flow, 7 = pD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known. For this reason a high-pressure, high-temperature rhe-ometer has been designed to measure the plastic viscosity the yield point +, and the static gel strength S, at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress t at any given rate of shear D. This is possible only if t and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde." The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fie. 2. which revresents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. For measurements of dynamic flow properties, the rotating cup is driven by a 1/2-hp electric motor, which operates through a Vickers

By M. E. Shank, J. Wulff

At the present time, the designer of dies for metal powder pressing is handicapped by relative ignorance of stress distribution and frictional effects at the interior surface of the die. Unckell was the first to develop a method for the study of wall friction. He used three Brinell balls on which the die rested during pressing. The total frictional wall force was determined by the size of impression these balls left on a soft metal plate. Since the method does not give radial pressures, or distribution of such pressures, coefficients of friction could not be determined. Although Unckel measured density distribution, he was not able to determine radial or shear stresses. Shaler2 has proposed theoretical expressions for the stress and density distribution within cylindrical compacts during pressing, in accordance with the experimental results of Kamm, Steinberg, and Wulff.3 By application of Siebel's method,4 Kamm et a13 plotted stress trajectories for two compacts. From the stress trajectories they calculated coefficients of friction from point to point along the die wall. As pointed out by Shaler in the discussion of Ref. 3, these values are based on progressive point-to-point calculations on finite size grid squares across the compact. In the region of the die wall such calculated values may therefore have considerable cumulative error. The purpose of the present paper is to develop an experimental method by which the nonhydrostatic pressures and shears acting on the interior wall of a cylindrical die can be measured. Such measurements can then he correlated with existing data to aid in the explanation of the pressing process. The method used is based on the elastic: properties of the thick-walled tube used as the die. The principle of super-position of force systems on an elastic body is assumed to hold. Electric strain gauges were mounted in adjacent positions on the exterior die wall in order to get an exact measurement of the variation of tangential strain over the length of the die during pressing. While in this paper, measurements in terms of only tangential strains are considered, it is well to note that similar calculations may be set up for axial strains. The latter are not preferred, since they tend to be smaller than the tangential strains and therefore permit less sensitive measurements. Discussion in this work is restricted to compacts pressed from both ends, since the elastic deformation of the die is then more amenable to analysis. Before choosing the electric strain gauge method, a more direct line of attack was considered and discarded. The discarded idea was the insertion of a pressure gauge through a hole in the die wall.* The gauge would have been in the form of a small piston. If pressure were exerted against such a gauge, it would move outward along a radius of the die. One disadvantage of the scheme is its inability to measure shears along the die wall. Another more serious disadvantage is the disturbance caused by the device itself. It would serve to change the forces it was designed to measure. No matter how small the movement of the gauge, when pressure is applied a discontinuity would exist in the wall surface at that point. Due to the stress concentration caused by the hole, abnormal deflections of the die wall would occur around the gauge. During pressing, powder would be forced into the resulting depression. The depression would then become larger with increasing compacting pressure. Powder, not being a fluid, is capable of supporting shear. The ease with which it would flow into the die wall depression to further move the piston is an indication, not of the radial pressure at that point, but of the state of shear retarding the movement. Thus the "pressure" gauge is really a criterion of flowability, and of the capability of the powder to support shear. For these reasons, it was decided that the electric strain method, herein employed, was more reliable, if more indirect. The gauges and lead wires, mounted on the external die wall do not in any way affect the behavior of the metal powder or the die during pressing. Theory of the Method THE EFFECT OF RADIAL PRESSURE ON THE DIE WALL Effect of a Single Small Band of Hydrostatic Pressure Consider a die which is a thick-walled cylinder of outer radius R. and inner radius Ri. If over a small finite length L there is a normal pressure P, a tangential strain distribution at the outer wall results. This is shown schematically in Fig 1. The exact shape of the curve may he predicted by an extension of the theory of a semi-infinite beam on an elastic foundation.6 This

Jan 1, 1950