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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

By P. F. Gnirk, J. B. Cheatham

Single bit-tooth penetration experiments under static load were conducted on six rocks at confining pressures of O to 5,000 psi using sharp wedge-shaped teeth with included angles ranging from 30 to 120° In general, the force-displacement curves for all rocks exhibit an increasingly nonlinear and discontinuous behavior with decreasing confining pressure. The confining pressure at which a rock exhibits a macroscopic transition from predominantly ductile to predominantly brittle behavior during penetration vmies from about 500 to 1,000 psi for the limestones to greater than 5,000 psi for dolomite. The correlation between calculated values of force per unit penetration based on plasticity theory and experimental values is quite encouraging, even at confining pressures as low as 1,000 psi A qualitative correlation between volume of fragmented rock per unit energy input for a single bit-tooth and drilling rate for microbits appears to exist over a confining pressure range of 0 to 5,000 psi. INTRODUCTION Laboratory experiments utilizing a small-scale drilling apparatus have demonstrated that penetration rates are reduced considerably as a result of increasing the confining pressure from atmospheric to a few thousand psi?-3 This undesirable situation can, in general, be attributed to a combination of decreased efficiency of chip removal at the bottom of the borehole, increased rock-failure strength, and a possible change in the mechanism of chip generation and rock fragmentation with increasing confining pressure. To more fully understand the principles underlying the last circumstance, it is the purpose of this investigation to experimentally study the mechanism of single bit-tooth penetration into dry rock at low confining pressures and, in particular, to establish the confining pressure at which the penetration mechanism may undergo a brittle to ductile transition for various rock types commonly encountered in drilling. Confining pressure as used here refers to the differential pressure between the borehole fluid pressure and the formation-pore fluid pressure. EXPERIMENTAL PROCEDURE Using an experimental apparatus previously described: a single, sharp wedge-shaped tool was forced under a "statically" applied load into an effectively semi-in finite dry rock sample subjected to a prescribed confining pressure. To prevent the invasion of the con fining-pressure fluid into the pores of the rock sample during penetration, the exposed surface of the rock was jacketed with a layer of silicon putty.* Electrical instrumentation incorporated into the apparatus yielded a graphical plot of force on the tool as a function of penetration or displacement of the tool into the rock during an experiment. During the course of the experimentation the following conditions were maintained constant: (1) pore pressure — atmospheric (i.e., the rock was dry); (2) temperature — 75F; (3) rate of loading — essentially static (approximately 0.002 in./sec); (4) bit tooth — a sharp wedge-shaped tool loaded normal to the rock surface; (5) rock surface — smooth and flat; (6) drilling fluid — hydraulic oil; and (7) maximum depth of penetration — approximateiy 0.1 in. In addition, each experiment was performed on a different rock sample so the rock surface is free of a layer of cuttings and of any previous indentation craters. The influence of the corners of a borehole was neglected, since each rock sample was cemented inta a section of aLuminum tubing to simulate a semi-infinite body. Indentation experiments were made on a sandstone, two limestones, a marble, a dolomite and a schist with a 60' bit-tooth over a range of confining pressures from atmospheric to 5,000 psi and at a constant confining pressure of 1,000 psi for a variety of bit-teeth with angles ranging from 30 to

Jan 1, 1966

By Wilbert T. Malenka

In its search for a highly productive mining system for anthracite beds pitching from 100 to 200, where conventional mobile equipment cannot be used) the Bureau initiated a longwall project by introducing a shearer drum cutter loader of European origin. Because of the undulating nature of the roof and floor and changing bed thicknesses, the machine proved inflexible and extra work was required in lifting bottom coal and blasting top coal.

Jan 1, 1966

By Edward E. Johnson

The U.S. economy boomed in 1965, completing its fifth consecutive year of expansion. Although the advance was somewhat irregular, previous records for production, sales, employment, and income were topped. During the first few months of 1965, as the economy recovered from the depressing effects of the automobile strikes of late 1964, increases were unusually large. The gains moderated in early spring, but were stimulated at midyear by sharply rising capital outlays, excise tax cuts, in? creased Social Security payments, and accelerated Viet-Nam defense expenditures. Gross national product (GNP) in cur-rent dollars rose $49.5 billion or 7.8 percent, to a total of S681.2 billion. In constant dollars (effects of price changes eliminated), GNP increased 5.9 percent, a rate considerably higher than the historical postwar annual average growth of 3.5 per-cent. Demand increased in most final markets and was especially strong for business fixed investment and consumption expenditures. With the exception of construction, most of the increases in GNP were real, since prices increased less than 2 percent.

Jan 1, 1966

By Adrian E. Scheidegger

Recently, a new theory of the subsidence of rock masses has been advanced by Litwiniszyn and coworkers, which is based on the notion that the individual rock particles perform random walks. It is shown in the present paper that the final equations of the random walk theory can be justified from general principles of statistical mechanics in which no specific theoretical model of particle behavior has to be made. The theory appears to account appropriately for subsidence phenomena.

Jan 1, 1966

By A. L. Barnes

Residual oil in watered-out reservoirs is a tremendous reserve which has been unrecoverable by established production methods. A study of the new recovery methods indicated that the forward combustion urocess might- recover oil from such reservoirs; however, no thermal recovery operating experience in a watered-out system was available. The Delaware-Childers pilot thermal test was undertaken to test the feasibility of thermal recovery in this watered-out reservoir. The pilot test consisted of a 2.22-acre, inverted five-spot in the 600-ft deep Bartlesville sand. The reservoir in the pilot area had a porosity of 20.6 per cent, a permeability of 118 md and an average sand thickness of 45 ft. The reservoir contains a 33' API, 6-cp oil. Combustion was started Nov. 22, 1960. The initial air injection capacity was 750 Mscf/D, but it was eventually increased to 2,000 Mscf/D. The test was surrounded by an active water flood; therefore, water production was initially high, but decreased as the heat wave moved toward the producing wells. Oil-bank arrival at an individual well was indicated by a drop in GOR and WOR, and an increase in oil production. Combustion-front arrival was evident at three of the pilot producers, and they were plugged. Cumulative oil production from pilot area wells war over 12,000 bbl. Operational difficulties were negligible and only conventional equipment was necessary. The combustion efficiency of this test averaged over 80 per cent. Results from coring showed that the leading edge of the combustion front tended to be wedge-shaped but a nearly complete sweep of the reservoir was eventually obtained. An isopach map based on evidence from 10 core holes and the existing wells showed that 126 acre-ft had been swept by the heat wave. Using this swept volume, an air requirement of 15.7 MMscf/acre-ft was calculated. It was calculated that 275 ,STB/acre-ft was consumed bv the heat wave. INTRODUCTION There is a large amount of oil remaining in reservoirs that have been water flooded. A study of ways to recover this oil showed that the forward combustion process might be applicable. Results from a number of forward combustion tests have been reported in the literature, but none of these tests were conducted in a watered-out system. The Delaware-Childers pilot thermal test was initiated in 1960 to define the operating characteristics of underground combustion in this watered-out Bartlesville sand reservoir, The purpose of this paper is to present the pilot test results in detail. FORWARD COMBUSTION PROCESS The forward combustion process consists of initiating combustion in the formation surrounding an injection well and driving this heat wave through the formation toward offset producing wells. As the combustion front progresses through the reservoir, oil and formation water are vaporized, driven forward in the gaseous phase, and recon-densed in the cooler part of the formation. These distilled liquids, water of combustion and gaseous combustion products, form a bank or three-phase region ahead of the burning front. This bank pushes mobile reservoir fluids toward the production wells. The rate of movement of the combustion front is controlled by the rate at which the nondistill able residue which serves as process fuel can be completely burned off the sand. The production performance from a heat wave conducted in a watered-out oil reservoir will differ from one conducted in a dissolved gas-depleted reservoir because of the difference in fluid saturations. The primary depleted reservoir contains connate water saturation, relatively high oil saturation and some gas saturation. The watered-out reservoir contains a highly mobile water saturation, residual oil saturation and little gas saturation. As the combustion front moves forward in either type of depleted reservoir, it drives the distillable oil, the water in place and the water of combustion ahead, and burns the nondistillable portion of the oil. The heat-wave process in a watered-out reservoir differs from the process in a

Jan 1, 1966

By Richard F. Link

A statistical technique, useful to analyze assay and other data characterized by location in three dimensions, is described in this Bureau of Mines report. If present, trends in the data are defined for the purposes of improving ore estimation, predicting ore beyond existing workings, and aiding geological interpretation. The technique is to fit linear and quadratic polynomial equations to the data through the statistical method of regression analysis. The fitted linear equations have the geometric form of hyperplanes; the fitted quadratic equations have the geometric form of ellipsoids or elliptic hyperboloids of one or two sheets. To visualize these three-dimensional forms, contour maps of a series of plane sections through the fitted surfaces are plotted. Both the fitting of the polynomial equations and the plotting of the con-tour maps are done by electronic computer to facilitate calculations and to obtain accurate results. Computer programs are described in appendixes. Methods employed are illustrated by an example analysis) based on data from a part of the Fresnillo mine) Zacatecas, Mexico.

Jan 1, 1966

By R. F. Merwin

Advancement in automation intensifies the need to remove tramp iron from bulk materials being processed and carried on belt conveyors. Although magnets have long been employed for this purpose, it becomes increasingly necessary that magnetic equipment of appropriate types and sizes be selected and advantageously installed -- if maximum benefits are to be derived Tramp iron present in bulk materials consists of ferrous trash, such as wire, bolts, nails, equipment parts, tools, and machine cuttings. The results, if the iron is not removed, are damaging to equipment having close clearances, explosions, or fire, En the case of flammable materials, production downtime losses, and contaminated products.

Jan 1, 1966

By H. E. Perlee

The concentration limits of flammability and autoignition temperatures of trichloroethylene in atmospheres of air, oxygen, and nitrogen tetroxide have been determined in a spherical vessel. The autoignition temperatures of TCE in atmospheres of air, oxygen, and nitrogen tetroxide were found to be 419°, 396°, and 221° C, respectively. The flammability zones of TCE-air, TCE-oxygen and TCE-nitrogen tetroxide mixtures at 100° C were found to be 10.5 to 41, 7.5 to 91, and 13.5 to 69 volume percent TCE, respectively. In addition, maxi-mum combustion pressures of 50 ps and 140 were recorded for constant volume combustion of the lower limit mixtures of trichloroethylene in air and oxygen, respectively.

Jan 1, 1966

By N. R. Morrow, C. C. Harris

The experimental points which describe capillary pressure curves are determined at apparent equilibria which are observed after bydrodynamic flow has ceased. For most systems, the time required to obtain equalization of pressure throughout the discontinuous part of a phase is prohibitive. To permit experimental points to be described as equilibria, a model of capillary behavior is proposed where mass transfer is restricted to bulk fluid flow. Model capillary pressure curves follow if the path described by such points is independent of the rate at which the saturation was changed to attain a capillary pressure point. Aemodified suction potential technique is used to study cyclic relationships between capillary pressure and moisture content for a porous mass. The time taken to complete an experiment was greatly reduced by using small samples. INTRODUCTION Capillary retention of liquid by porous materials has been investigated in the fields of hydrology,l soil science,2 oil reservoir engineering,3 chemical engineering," soil mechanics,5 textiles: paper making: and building materials In studies of the immiscible displacement of one fluid by another within a porous bed, drainage columnsl and suction potential techniques2 have been used to obtain relationships between pressure deficiency and saturation (Fig. 1). Except where there is no hysteresis of contact angle and the solid is of simple geometry, such as a tube of uniform cross section, there is hysteresis in the relationship between capillary pressure and saturation.2 The relationship which has received most attention is displacement of fluid from an initially saturated bed (Fig. 1, Curve R2), the final condition being an irreducible minimum fluid saturation Swr. Imbibition (Fig. 1, Curve A), further desaturation (Fig. 1, Curve R), and intermediate scanning curves have been studied to a lesser but increasing extent.2 ,3,9-12 This paper first considers the nature of the experimental points tracing the capillary pressure curves with respect to the modes and rates of mass transfer which are operative during the course of measurement. There are clear indications that the experimental points which describe these curves are obtained at apparent equilibria which are observed when viscous fluid flow has ceased; and any further changes in the fluid distribution are the result of much slower mass transfer processes, such as diffusion. Unless stated otherwise, this discussion applies to a stable packing of equal, smooth, hydrophilic spheres supported by a suction plate5 with water as the wetting phase and air as the nonwetting phase. The discussion can also be applied, in many

Jan 1, 1966

By Henry C. Meeves

The Bureau of Mines, between 1956 and 1963, examined 18 major pegmatite districts in Arizona, Colorado, New Mexico, South Dakota, Utah, and Wyoming to evaluate their content of beryllium, a material in short domestic supply that has become increasingly important to modern industry. This examination report includes the salient statistics on the production of pegmatite minerals other than quartz and feldspar; and brief descriptions of 170 specific pegmatite deposits.

Jan 1, 1966

Jan 1, 1966

By R. W. Van Dolah

An investigation was made of the distances over which sympathetic detonation of ammonium nitrate (AN) and ammonium nitrate-fuel oil (AN-FO) might be expected. Large-scale gap tests used two types of AN-FO donor charges in three sizes with AN, both at ambient and elevated temperatures, and AN-FO acceptor charges. Donor sizes were varied to test the validity of a scaling law commonly used in quantity distance tables. The up-and-down experimental design was chosen to determine the 50-percent initiation point efficiently. The acceptor charges were instrumented to indicate initiation and to determine detonation velocity. Other electronic techniques for measuring the rate of growth, stability of detonation, and detonation pressures were employed. Air shock and fragment velocities between charges were measured by electronic and photographic methods, and determination of side-on air-blast pressures and impulse duration were made for about half the shots. Separation distances between donor and acceptor were found to be larger than anticipated both for the AN and the AN-FO. With AN-FO acceptors and a 16-gage steel faced donor, one initiation occurred at a separation of 53 feet or nearly 16-charge diameters; with AN, initiation occurred at 4 to 5-1/2- charge diameters.

Jan 1, 1966

Jan 1, 1966

By R. F. Kendall

Only a limited number of mass and infrared reference spectra of high purity unsaturated hydrocarbons and oxygenates are presently available in the literature. To aid Bureau of Mines research programs requiring such references, 64 mass spectra and 70 infrared spectra were obtained and are reported. The individual compounds, acquired from commercial sources, were purified by preparatory gas chromatography. Purity determinations were made using a combination of analytical gas chromatography, microhydrogenation, and catalytic deoxygenation. These spectra will aid spectroscopists in the identification of compounds of the types reported.

Jan 1, 1966