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By R. D. Vaughn

The analysis of laminar flow of power-law non-Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journa! bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annul us would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7. 5 per cent. INTRODUCTION Non-Newtonianism and eccentricity occur simultaneously in two engineering problems: (1) flow of lubricants in journal-bearings and pressure-reducing bushings, and (2) flow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character — often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publicationsl-4,6,7 have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda 1 and Redberger and Charles 2 have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Ca ld well 3 and Bairstow and Berry,4 which is reported by Dryden, et al. 5 Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles2 show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (k < 0.5); however, for large diameter ratios (k + l), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden,5 Tao and Donovan6 and Piercy, et a1.7 Tao and Donovan examined the case of flow in narrow, eccentric annuli (k + 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et a l. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles2 and the experimental proof of Tao and Donovan6 both suggest that the region of large diameter ratios (k + 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. This model has many disadvantages which have been pointed out; nevertheless, its simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Bird8 and Savins9 have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli.

Jan 1, 1966

By Harry R. Nicholls

Preliminary tests on presplitting rock in the presence of an in situ static stress field were undertaken to study the influence of a horizontal static stress field on the creation of a vertical presplit fracture plane. These tests indicated that it is easier to fracture the rock parallel to the in situ maximum compressive stress than in other directions. Instrumented shots indicate that the interaction of stress waves generated by the detonating charges is probably responsible for starting tensile fractures between shotholes and that expanding gases may propagate these initial cracks by a wedging action. The hole spacing for presplitting appears to be equal to the half wavelength of the stress wave. However, wider hole spacing appears feasible if the initial fracture is started by closer hole spacing.

Jan 1, 1966

By Donald W. Mitchell

Certification tests for urethane-foam systems and techniques for apply-ing foam safely in mines are described. Fire hazard from foam exists if flame propagates beyond the ignition source or penetrates the foam. Foam that passes the certification tests can be applied on stoppings, continuous sections of ribs of relatively wide passageways (with no foam on the roof), short sections of roof such as overcasts, roof cavities, and intersections (with no foam on the ribs), and between buntons on one wall of a shaft. Foam on the ribs and adjoining roof presents a fire hazard. Stoppings covered with foam passing the certification tests are resistant to penetration of heat, flame, and smoke than similar stopping without foam. Flame propagation can be arrested by water sprays. Spontaneous ignition of foam can be prevented.

Jan 1, 1966

By H. V. Fairbanks

It is estimated that millions of tons of coal fines are unsaleable each year due to difficulty of drying them economically with conventional mechanical dewatering and thermal drying equipment. The difficulty is due to the fact that coal of small particle size presents a large surface area with polar groups which have a great affinity for water. In order to remove this water thermally, a high temperature is necessary which oxidizes the surface of the coal. This substantially reduces the heating value of the coal. If drying could be satisfactorily carried out at a lower temperature, much more of the heating value of the coal fines could be retained. It was conjectured that acoustic energy applied during the drying process might prove to be of value since acoustic energy has the property of producing cavitation at a liquid-solid interface when the intensity is sufficiently great. This cavitation process produces water at room temperature which can be carried away from the solid surface by a flow of relatively cool air. Hence, moisture removal is made possible at a lower temperature.

Jan 1, 1966

By John Nagy

The Bureau of Mines adapted thermal theories explaining combustion of gases to correlate parameters affecting ignition of dust dispersions. The dust dispersions were ignited in a Godbert-Greenwald furnace at atmospheric pressure. Ignition temperature and the concentrations of fuel, admixed inert powder, and atmospheric oxygen were related mathematically. Values for these parameters obtained in laboratory experiments for cornstarch agreed with theory. The developed equation permits extrapolation; the predicted upper igni-tion limits correspond with limited experimental data from laboratory and large-scale tests. Explanation of the effect of fineness of dust on ignition parameters is attempted by introducing a surface-area constant to modify the activation energy. Arguments are presented to show that the ignition process is a solid-gas phase reaction rather than an ignition of prevolatilized gases.

Jan 1, 1966

By J. H. Elledge

Hydraulic Transportation of Phosphate Ore from, a 40,000 Cubic Yard per Day Strip Mine IMC is transporting 1500 yards per hour of phosphate ore in a water slurry a distance of approximately five miles from a strip mine to a flotation beneficiation plant at their Noralyn Operation. in Barrow, Florida. This ore, which consists of approximately 1/4 phosphate, 1/2 silica sand, and 1/4 clay slimes, is being pumped through a 20 inch O. D. pipeline using seven 20 and 18 inch GIW metal pumps direct connected to electric, motors. This paper details some of the problems involved and the specific methods used to accomplish this bulk material handling requirement.

Jan 1, 1966

By Constantine C. Popoff

This report reviews and analyzes, by a simple analytical and logical reasoning, the conventional methods of reserve computations of mineral deposits described in various domestic and foreign publications. It brings together, formulates, and evaluates the principles underlying interpretation of exploration data; and ties such principles to the proposed classification of methods. The material is discussed in sufficient detail to allow general application.

Jan 1, 1966

By W. G. Bearden, G. C. Howard, J. W. Spurlock

An investigation of the factors af-fec.ting the inter-zonal flow of fluids in the casing-wellbore annrc1rt.s of an oil or gas ivell is presented Laborntory tests revealed that failure of the caring-cement bond allows communi-cation of fluid at pressure differentials near 1.000 psi. Perforating with a 11011011: carrier gun does not shatter or crack the cement sufficiently to allow communication through these cracks and does not seriously affect the casing-cement bond failure pressure. The pressure to cause communication at the casing-cement bond can he increared to 3,000 psi by. limiting pipe deformation during cementing and subsequent operations. Communication can be prevented, however. up to pressures sufficient to cause the cement to fail or the casing to col-lapse, by attaching to the casing a seal ring of deformable ruhber molded between two steel flanges. When installed, one flange is attached rigidlv to the casing to serve as back-up for the gasket While tile other flange is movable. To date, these gasket seal rings have been field-tested in 27 Wells. Althotrgh communication has been noted in two wells, inter-zonal flow has been prevented in other wells in the same area by installing more seal rings between the communicaring zones. INTRODUCTION The inter-zonal flow of fluids behind casing cemented in oil wells during normal production or stimulation operations is a major operating problem. If it cccurs during production operations. it can seriously limit the pressure to which a reservoir may be depleted without harmful invasion of unwanted fluids. If it occurs during stimulation operations, it may preclude the possibility of stimulating the desired zone. This communication can be caused by failure of the bond between the casing and cement, failure of the bond between the cement and formation, or failure of the cement itself. This paper presents the results of an investigation of factors affecting com-munication at the casing-cement bond and methods which aid in preventing it. LABORATORY INVESTIGATIONS The laboratory tests performed in this study were divided into three phases. The first phase consisted of tests to determine if perforating would shatter and crack the cement sheath so severely that communication would occur through the cement itself. The second phase consisted of tests to determine more precisely the cause for the casing-cement bond failure. The third phase consisted of tests to evaluate the effectiveness of various de-formable seals attached to the casing in preventing communication. EFFECT OF PERFORATING, The effect of perforating was invest~gated in tests performed with apparatus shown on Fig. 1. Cement was poured into the annulur space hetween 5%-in. casing and 8%-in. casing and allowed to cure for 72 hours. The apparatus was then perforated with a hollow carrier gun containing eight duPont 26-A shaped charges. Bull plugs were placed over the perforations in the 8 5/8-in. casing and hydraulic pressure was applied inside the 5 1/2i-in. casing. The pressure to cause fluid communication past the cement sheath was observed and termed the "bond failure pressure". Several different cement compositions were included in these tests, the results of which are shown in Table 1. In Tests 1 through 4 of Table 1, bond failure occurred at- the inter- .

Jan 1, 1966

By John M. Gomes

In the repetitive electrowinning of tungsten from scheelite, the calcium impurity buildup in the molten electrolyte results in decreased metal purity, metal recovery, and current efficiency. Periodic addition of B2O3, which reacts with the lime liberated from the scheelite, more than tripled the life of the electrolyte in winning 99.9-percent-pure tungsten and also reduced the number of units of electrolyte required per unit of tungsten recovered from six to four.

Jan 1, 1966

By J. C. Ingles

"A new technique is in the process of revolutionizing inorganic chemical analysis. Galled atomic absorption spectrophotometry, it combines the use of a special light source, a flame, and the equipment of conventional spectrophotometry, to provide a quick, reasonably accurate method for the determination of a large number of elements.This paper outlines the principles on which it is based, describes the commercial instrumentation"" available for exploiting it, and. summarizes current applications in process metallurgy."

Jan 1, 1966

By M. N. Collison

"In 1960, with the opening of the Chisel Lake mine near Snow Lake, Manitoba, the Hudson Bay Mining and Smelting Co., Limited, commenced a new phase in their mining operation -that of bringing ore to Flin Flon over 100 miles of railroad.The schedule of operations required to accomplish this, together with an outline of some of the problems of handling ore at 40° and 50,0 below zero, are discussed. The facilities required to thaw and unload from twenty to fifty cars per working day are also described."

Jan 1, 1966

By M. C. Fuerstenau

Flotation data indicate that sulfonate and dodecylamine adsorb physically on Mn02 at ambient temperature. Oleate also adsorbs physically if the zero-point-of-charge of the Mn02 is sufficiently high. Chemisorption of oleate apparently occurs between pH 8 and 9, and this phenomenon is enhanced considerably at elevated temperature.

Jan 1, 1966

By John M. Gomes

Two molten salt systems were evaluated as electrolytes for the repetitive recovery of tungsten from tungsten oxide (W03) made by calcining commercial-grade ammonium paratungstate. Using a sodium chloride-sodium fluoride-potassium aluminum tetrafluoride electrolyte at 800° C, 1 pound of 99.8 percent tungsten was recovered for each 2.7 kilowatt-hours of energy consumed. The metal contained 1,100 ppm carbon, was in dendritic masses of spherical grains, and had an apparent bulk density of 5.41 g/cm3. T ngsten of 99.9 percent purity was won from a sodium pyrophosphate-sodium tetraborate-sodium chloride electrolyte at 1,000° C; 6.0 kilowatt-hours of energy was consumed for each pound of metal recovered. The metal contained 120 ppm carbon, was in dendritic masses of hexagonal acicular crystals, and had an apparent bulk density of 7.25 g/cm . Each metallic impurity--aluminum, calcium, copper, iron, nickel, and silicon--in the two tungsten products was 16 ppm or less.

Jan 1, 1966

By Frank B. Fulkerson

A study was made of scrap iron and steel in the South Central States in order to determine trends in processing, shipment, and consumption if this important commodity. These data were derived in part from statistical sources and in part by visits to scrap yards and steel mills. Trends in the industry were reviewed. Dealers in 1963 supplied 1.8 million tons of iron and steel scrap to steel mills and foundries in the south-central area, compared with 2.1 mill ion tons in 1955. Most of the scrap was processed and shipped within 200 to 300 miles of consuming centers. Exports provide a principal outlet for dealers along the gulf coast. Most of the scrap that fills these orders is loaded onto freight cars at yards in Texas and Louisiana and is shipped to ports for direct transfer from railroad car to ship. The tonnage exported varies greatly from year to year. The largest scrap operations are in or near large cities which are heavy scrap generating areas, steel mill sites, or port cities for export of scrap. A tentative analysis indicates that the short-run supply of prepared scrap is inelastic to price changes; therefore, buyers probably are in a strong bargaining position at times of declining demand. One technological development in the iron and steel scrap industry is the use of large presses which can take complete automobiles with frames, wheels, springs, and other heavy parts still intact and reduce them to bundles. At Houston, Tex., and Kansas City, Mo., shredding plants are in operation that reduce car bodies and other light scrap into flat pieces 4 to 6 inches in size.

Jan 1, 1966

By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966

By Francis X. Cannaday

The Bureau of Mines developed equipment to measure the sonic velocity of pulses transmitted through rock samples varying in size from laboratory specimens to mine pillars in place. Pulses are produced by electronically excited piezoelectric ceramic transducers. Special equipment components were developed by Bureau facilities; other components are commercially available. The technique permits a nondestructive, repetitive, stable, shaped pulse to be used in place of explosive caps or hammer blows. Longitudinal wave travel time measurements were taken on an oscilloscope screen; transverse wave measurements were taken under special field conditions. Results were consistently repeatable within the accuracy of the oscilloscopes utilized.

Jan 1, 1966

Jan 1, 1966

Essential features of the role of the fill material in mechanized cut and fill mining are discussed, with particular emphasis on its dewatering and strength development after emplacement. The fill material is regarded as a chemically-reactive porous medium, the most important property of which is permeability. Methods are described for measurement of permeability and other fill properties and results of such measurements applied to develop an orderly approach to the operation.

Jan 1, 1966

By J. M. Singer

Quenching distances for flames of methane-coal dust mixtures were determined with air and oxygen-enriched air. Coals used were Pittsburgh, Sewell, and Pocahontas No.3. Quenching distances were greater for flames of hybrid mixtures of coal dust and methane than for methane flames of corresponding stoichiometry. From the data of quenching distances and methane-coal dust concentrations was calculated the quenching equivalence, which is the increase in coal dust concentration required to maintain a given quenching distance value as the methane concentration decreases. These equivalences could be useful in identifying hazardous methane-coal dust mixtures in mines.

Jan 1, 1966

By E. I. Radzinovsky, D. W. Dareing

This paper presents theory which is used to predict rock-bit bearing life reduction due to simple harmonic variations in bit forces. The theory is based on the premise that if a constant load acts for a certain fraction of the life which the bearing would have if that constant load were applied for its entire life, then the same fraction of thelife of the bearing is consumed. Total bearing life is related to simple harmonic variations in bearing life associated with instantaneous bearing loads. The results show that rock bit bearing life is not affected appreciably by forces commonly impressed upon a bit, but it is affecied appreciably by relatively large dynamic bit forces occasionally encountered during drilling. In addition, the results show that the life of sealed bearings is more sensitive to bit force variations than is the life of unsealed bearings. INTRODUCTION Roller bearings are important components in roller cone rock bits because they transmit a large portion of the drill collar weight to the formation being drilled. Unfortunately, they have a relatively short life under down-hole drilling conditions. Roller bearings are usually the first bit components to fail, and their failure leads immediately to failure of the entire bit. Short roller bearing life, and thus short bit life, is due mainly to high unit loads transmitted by the bit and to the adverse environment in which the bearings operate. The results of the study discussed in this report show how dynamic bit forces also affect roller bearing life. The purpose of this paper is to discuss theory developed to predict the effect of different magnitudes of periodic bit forces on roller bearing life. Theoretical results are used to compare the life of rock bit roller bearings subjected to steady forces to the life of rock bit roller bearings subjected to unsteady forces similar to the type of unsteady forces measured at the bit with a special downhole recording instrument. BACKGROUND AIanufacturers of bearings have conducted laboratory tests which show how bearing life is affected by steady bearing load. 1 The well-known empirical equation which defines bearing life follows from bearing test data. It is: where L = bearing life, hr P = bearing load, Ib C = constant q = exponent (constant). The effect of environment on bearing performance is manifested through the exponent q and the constant, C. King,2 in similar tests conducted on roller bearings used in rock bits, showed that, in addition to the load, the environment (abrasive materials, chemical components, etc.) greatly affects bearing life. His data, which show how the life of roller bearings in a 7-7/8-in. W7R bit rotating at 60 rpm is affected by bit weight and fluid environment, are displayed on a log-log plot by broken lines made up of straight line segments. Each broken line corresponds to a given environment. One segment (q = 1.4) of the broken line corresponding to a fluid environment of barite mud is shown in Fig. 1 along

Jan 1, 1966