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By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By A. N. Crownover, H. T. Kennedy, E. P. Miesch, C. H. Bowman

The paper presents correlations of (l) molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C,-plus fraction; (2) shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and (3) bubble-point pressure with temperature, composition and characteristics of C, plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sul-fide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psis, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. he equations resented are all explicit in the dependent variable, and require no iteration on the digital cow puter. INTRODUCTION The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer arc useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy The van der Waals equation is modified to make a and b functions of temperature instead of being constants for each material.This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between a,,, and b,,, for mixtures and the a, and b, for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. For normal mixtures, however, the area may be added to any of the bounding areas without substantial error. The new relationships employed are

Jan 1, 1966

By M. M. Wong

Salt mixtures consisting of KC1, BaC12, and HfCl4 with RbCl or CsCl were investigated as electrolytes for refining hafnium. The presence of RbCI or CsCl in the electrolyte appeared to suppress the volatility of. Best electrorefining was obtained with an electrolyte containing 50.7 percent KCl, 27.l percent BaCl2, 15.7 percent CsCl, and 6.5 percent HfCl4. In this electrolyte, hafnium metal with an average oxygen content of 470 ppm was produced from an anode feed containing l,600 ppm oxygen. All metallic impurities were lowered, except titanium, manganese, and tin.

Jan 1, 1966

By C. J. Thompson

This Bureau of Mines study describes the preparation of sulfur compound concentrates boiling from 225° to 400° C, and reports the sulfur types detected in these concentrates by low-voltage mass spectrometry (LVMS). Existing LVMS methods were extended; the procedures described should be generally applicable to high-boiling petroleum distillates and concentrates as a preliminary means of narrowing the number of factions to be considered for more detailed separation and identification studies. The following major sulfur compound constituents of petroleum are indicated by the data: benzothiophenes, dibenzothiophenes, naphthanothiophenes, naphthenobenzothiophenes, and homologs and isomers of these. Cyclic and chain sulfides comprise a significant portion of the gas-oil range sulfur compound types. The presence of some classes of sulfur compounds containing two sulfur atoms per molecule was indicated.

Jan 1, 1966

By James Paone

The Bureau of Mines studied the behavior of rocks at the initial state of crater formation that results from the stresses created under a drill bit to determine which mechanical properties of rock are important in rock fragmentation by drilling. Although a definite relation between the drilling strength and relevant mechanical properties has not been established, maximum yield strength of rock is apparently a parameter of drillability of rock. The strengths of rock were considered from the Mohr-Coulomb criterion from which the surface of failure was constructed. The results from previous tri-axial tests on Solenhofen limestone were adopted to verify the criterion of failure. Inelastic behavior of some rock types was observed under a low-velocity impact of a hemispherical bit and under static indentation with a similar bit. Quantitative determinations of strengths of Solenhofen limestone) Indiana limestone, and Tennessee marble were made under static indentation. The maximum yield strength estimated from the average stress over the indented area was used as the crushing strength of rock under a drill bit.

Jan 1, 1966

By H. Evans

It is well known that iron-ore pellets are considered one of the best blast-furnace burden materials used today. The demand for pellets is demonstrated by the increase in pellet output from one million tons in 1955 to approximately 37 million tons in 1964. This growth continues as new plants are placed on-stream each year. The consumer generally specified (1) the acceptable content and range of chemical constituents, (2) a minimum strength determined by some standard testing procedure, (3) the size range of pellets, and (4) perhaps a measure of reducibility.

Jan 1, 1966

By R. W. Van Dolah

The Bureau of Mines t.ced its investigations into sympathetic detonation of ammonium nitrate (AN) and ammonium nitrate-fuel oil (AN-FO) to define the scaling law for safe separation from detonating AN-FO. Both missile- and non-missile-producing AN-FO donors, weighing up to 5,400 pounds, were employed with acceptors of the same size. The usual cube-root scaling law was not confirmed; exponents for the relationship S = f(Wx) for AN were 0.51 with non¬missile-producing donors and 0.61 for missile-producing donors. For AN-FO an exponent of 0.80 was indicated in the missile-producing case. AN-F0 in polyethylene bags appeared somewhat more easily initiated than bulk AN-FO. The efficacy of barricades in protecting AN charges was investigated. detonation distances were reduced from one-third to one-seventh when filled barricades were employed. The investigation was extended to dynamite with both types of donors. With 1,600-pound missile-producing donors and an equivalent weight of dynamite, initiation would be expected in 50 percent of the trials at 167 feet. The corresponding value in the non-missile case was 67 feet. The data developed in this program of sympathetic detonation will allow the development of a rational set of safe separation distances for AN, AN-FO, and explosives.

Jan 1, 1966

By H. R. Babitzke

To develop alloys suitable for use at elevated temperatures, columbium and tantalum were combined with tungsten, hafnium, vanadium, zirconium, and titanium, and the resulting alloys were evaluated with respect to fabricability, hardness, Electrical resistivity, strength at elevated temperatures, oxidation resistance, and bend transition. Of the 23 compositions tested, Cb-2OHf-5W-10Ti exhibited superior high-temperature properties. A recrystallized sample of this alloy was fabricable at room temperature, had a strength of 44,000 psi at 1,200° C, and had an oxidation rate of only 7.7 mg/cm2/hr at 1,000° C.

Jan 1, 1966

By C. R. Kyle, R. L. Perrine

A transparent model of a reservoir has been used to study some characteristics of instability in miscible displacement. The linear model dimensions are 1/4 in. x 91/2 in. x 10 ft. The model is packed with spherical glass beads. Thee groups of experiments have been performed. The objectives were to measure, respectively, the rate of growth of the transition zone, flow velocity variations in the transition zone, and the effect of a graded viscosity zone on stability. All experiments were compared, where possible, with theory. The transition zone grew almost linearly with distance traveled, regardless of flow rate, where adverse viscosity ratios were used. At very adverse viscosity ratios and large distances traveled, some reduction below linear growth was noted. This could be attributed to the effects of mixing. General similarity in flow pattern was commonly shown in different tests, although exceptions occurred at the higher viscosity ratios. Injection of tracer spots permitted direct experimental measurement of velocity variations. Statistical methods were used to compare observed velocity variations with recently published theories. Surprisingly good agreement with some theoretical predictions was obtained. In the experiments using an initially graded viscosity zone, macroscopic stability was reached before predicted by theory. Under conditions theoretically considered to be slightly unstable, any fingering tendency was too slight to become observable within a 10-ft long system. The general correlation of all experiments with published theory was good, and suggests that theoretical predictions can be extended to reservoir problems. INTRODUCTION Early laboratory studies of miscible displacement demonstrated the high recovery efficiency possible with this method. Linear laboratory models showed that, under some circumstances, all in-place hydrocarbons could be recovered using as little solvent as 5 per cent of the pore volume. These results led to a series of pilot field projects. Under realistic conditions, however, other laboratory studies showed that a small solvent bank may not recover much more oil than a conventional gas drive. The cause of this lack of efficiency is unstable viscous fingering. The size of the solvent bank required to give optimum recovery is, therefore, a question of great economic significance. The object of the experiments described in this paper was the quantitative measurement of unstable flow parameters, the verification of present theories on the miscible displacement process, and correlation of these theories with ex peri mental observation. Of the theories which have been advanced, those by Dougherty, Koval and Perrine show promise of predicting reservoir performance with reasonable accuracy.l-7 The present experiments were correlated, where possible, with the theories of Koval and Perrine. Dougherty's theory was not used because of the additional computational difficulty it presented and the belief that no further information would result. EXPERIMENTAL EQUIPMENT A transparent reservoir model, consisting of a vertical reinforced plexiglass column, was used for the experiments. The column was packed with glass beads, which served as the porous medium. To induce a known velocity disturbance in the flow, a double cosine wave restriction in the transverse cross-section was placed at the top of the column. To mark the flow field and provide a means of measuring the local fluid velocity, a dye-spot injection system was provided. The column was 10 ft high by 1/2 in. wide by 1/4 in. deep. The cosine restriction was placed 16 in. from the top of the column. The glass beads were smooth and spherical and had a mean diameter of 0.0102 cm. Liquids entered the top of the column through a manifold allowing three points of entry (left, center, and right, or any combination of these). A positive-displacement pump with variable-speed drive was used to control liquid flow rates. The pump transferred viscous oil from a reservoir to an accumulator, which displaced the test liquid into

Jan 1, 1966

By W. D. Macleod

This paper describes a mineral dressing process for the upgrading of tin ores. The process described is called 'agglomeration' and. is similar in many respects to flotation. Many variables have been examined experimentally both on batch and continuous operations and are reported upon herein... Using a Mt. Pleasant tin ore, assaying 0.5% Sn, an upgrading to 8% Sn, with a recovery of 95% could be obtained by this process.

Jan 1, 1966

This report describes the activities and publications of the Bureau of Mines Health and Safety Research and Testing Center, Pittsburgh, Pa., for the fiscal years 1960-65. It includes a discussion or work being conducted on roof control, dust explosions, ventilation, health, coal mine fire control, and electrical-mechanical testing, and an abstract of each paper published during the report period.

Jan 1, 1966

Jan 1, 1966

By G. G. W. Thom, A. A. F. Schuldt

At The Steel Company of Canada, Limited, iron oxide dust from the basic oxygen open hearths is being collected by means of electrostatic precipitators. The utilization of this dust, which has been hampered by the presence of zinc and lead oxides and sulphur compounds, is made possible by direct reduction in a rotary kiln. The description of the dust collection system and the results of kiln tests are presented.

Jan 1, 1966

By Jack G. Croeni

The Bureau of Mines developed a method to extrude low-density tungsten powder billets into rods and sheet bar with high-energy-rate forming equipment. Billets were compacted and sintered in an atmosphere of hydrogen to obtain a density of approximately 60 percent. Extrusion was conducted at reduction ratios of 6.25 to 1 and 9 to 1 at 1,800° C to prod e high-density, sound material. Yield strengths obtained were higher than those of material produced by conventional powder-metallurgy techniques, but ductility was lower at high temperatures.

Jan 1, 1966

By Edward C. Peterson

Recent studies indicate that the United States halt substantial reserves of ilmenite, one of the major titanium minerals. However, the studies showed that sources of rutile, another important source of titanium are limited. This paper summarizes and evaluates results and conclusions reached by the various investigations initiated by the Bureau of Mines and others pertaining to the titanium mineral resources of the Nation. Domestic occurrences of ilmenite that are economically exploitable by present-day beneficiation methods are found in Florida, New Jersey, New York, South Carolina, and Virginia. These deposits are estimated to contain 50.3 million tons of titanium dioxide (TiO2). Occurrences of ilmenite that cannot be processed economically under present technological conditions are found in California, Colorado, Minnesota, Montana, Oklahoma, Oregon, Rhode Island, and Wyoming. These reserves amount to 51.1 million tons of TiO2. Reserves of rutile found in the United States are estimated to be 1.8 to 2.1 million tons of TiO2. Other than occurrences in Florida and South Carolina, rutile is found either in small scattered bodies or in deposits where the mineral cannot be recovered economically by present beneficiation methods.

Jan 1, 1966

By J. A. Jargon, H. K. van Poollen

Flow of slightly compressible fluids through porous media can be described by linear equations. Many mathematical solutions- are available for the boundary conditions of constant terminal pressures or constant flow rates, or a combination of both. Various techniques of formation evaluation use drastic rate changes, such as sudden shut-in. Other methods require that the well be produced at a constant rate. In practice, one is not always able m fulfill these rigid requtirements. This report shows a methor1 by which varying-rate data can be converted to a constant-rate pressure response, called the unit response function. After obtaining the unit response function, one may analyze it, using techniques described in the literature. The method uses tile principle of superposition. Necessary data is a time history of pressure and production. If pressure changes and/or rate changes are very drastic, the unit response function becomes erratic and oscillates The erratic and oscillating results are obvious, and under those circumstances, no answer can he obtained. It appears, however, that a response function without oscilla-tion will not contain any appreciable errors —- one gets either good results or no results. This report includes a mumber of examples of converting constant-rate data to constant terminal-pressure data and vice versa. In addition, a number of field-test applications are given. This method should be useful in converting mathematical solutions from one boundary condition to another. It already has proven useful in converting varying-rate data to constant-rate conditions. INTRODUCTION Pressure drawdown tests are performed on production wells to determine various reservoir characteristics, including permeability, distances to discontinuities, reservoir continuity and wellbore conditions. An ideal drawdown test is performed at a constant production rate with pressure observation during the drawdown period. A typical drawdown curve for a constant rate of production is shown in Fig. 1. In practice, a constant production rate cannot always be maintained. Fig. 2 shows a pressure drawdown curve for a varying rate. Usual methods of analysis are not applicable to tests such as this. It is, therefore, necessary to convert the varying-rate data somehow, before usual analytical techniques can be applied. This report describes a method of obtaining a response function. A response function can be defined as the relationship between pressure and time for a well producing at a constant unit rate. Such a response function can be analyzed by the usual analytical techniques. Hutchinson and Sikora' first approximated a resistance function (response function), and by applying the superposition principle, pressures were calculated using the varying rates. If no match was obtained, adjustments were made to the response function and the closer approximation was used again in an attempt to match calculated and observed pressure behavior. If a good match was obtained: the response function was then used to extrapolate the future aquifer behavior.

Jan 1, 1966

By P. L. Woolf

An investigation was conducted to evaluate the use of a formcoke as the total fuel in the Bureau of Mines experimental blast furnace. The formcoke performed very satisfactorily, and comparisons made with a metallurgical coke showed that the performance with the formcoke was somewhat superior under the experimental conditions used.

Jan 1, 1966

By H. S. Ten Eyck

The major underlying threat to man's successful survival and happy existence on this planet is our own prolification. This poses an even greater threat to the future of civilization than continued wars and even "The Bomb" itself. Just the predictions of the world's population trend are awesome and demand our serious thought. This trend has been given the now well-known term, "The Population Explosion" - and this is literally what is taking place throughout most of the countries around the globe. Today, the world's resources support approximately 3.3 billion people. Based on the present world population growth rate of 2.1 percent, there will be another 65, million just one year from today. Such an increase in one year means that the world will add a greater population than that of Mexico and Canada combined. Projecting at this remarkable, but unchecked, growth rate, 6.7 billion people will be competing for survival by the end of this century.

Jan 1, 1966

By B. L. Bessinger

Because of a, work stoppage at the Carlsbad plant, IMC faced the challenge of operating a 24-hour-a-day mine and plant with inexperienced maintenance and production crews. This is an underground mining operation, using the room-and-pillar mining- method. The mine was entirely, mechanized with conventional equipment, was hoisting an average of 13,539 tons off ore per 24 hours, and employed a, mine maintenance group of 100 men. The 100-man, mine maintenance group was equally divided between mechanics and electricians. In re-forming this maintenance group, two main objectives were to be achieved (1) a general upgrading off the intelligence level; and (2) the elimination of craft lines for greater flexibility.

Jan 1, 1966

By Albert R. Rule

Beneficiation studies were made by the Bureau of Mines to develop a process for concentrating phosphate minerals from the altered rock of the Phosphoria Formation. This report describes research on intermediate - and marginal-grade ores from southeast Idaho, The process developed consists of attrition scrubbing and sizing to produce a coarse concentrate; desliming at about 800 mesh (18.5 microns); flotation of the fine sands; roasting of the combined concentrates for removal of organic carbon and combined water; and leaching with SO2 for removal of magnesium and nonapatitic calcite. Results of continuous tests on three different ore types showed that approximately 80 percent of the available phosphate can be recovered at a grade suitable for phosphoric acid production. While leaching with SO2 is not necessary for all ore types, it is an important step in purifying concentrates containing excessive magnesium.

Jan 1, 1966