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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 L. Valentik

Many attempts have been made during the last 40 years to evaluate the performance of gravity separation equipement, that is, the effectiveness with which light and heavy particles are separated. The most comprehensive treatment of the subject was made by Cerchar at the 1st International Conference on Coal Preparation held in Paris in 1950. The methods suggested by the Conference were accepted and very widely used in the last two decades. This paper discusses an improved method of evaluation in the light of the now-accepted standard presentation. The float-and-sink analysis of the product is presented on a Gaussian distribution curve, resulting in an easier visualization of the inherent difficulties of separation. The ogives of the distribution curve me then plotted, giving a quantitative measure of the deviation from perfect separation as an error distance instead of an error area. Illustrations of the new method are given both for gravel and for coal preparation, but the content is valid and applicable to other types of minerals which are separated by gravity methods. Many attempts had been made during the last forty years to evaluate the performance of heavy-media separation (HMS) equipment, that is, the effectiveness with which floats and sinks are separated.'-' The most comprehensive treatment of the subject was made by Cerchar at the 1st International Conference on Coal Preparation held in Paris. 6 The primary aim was the thorough understanding of the mechanism of separation and the unified presentation of data on gravity separation so that the evaluation and comparison of washery performance could be made from all over the world. No strict overall standardization has been achieved, but after the conference a more or less uniform presentation of performance was accepted, which, during the last two decades, has been very widely used. In this paper, illustration of the old methods and an improved method of evaluation will be given. HEAVY-MEDIA SEPARATION (HMS) PERFORMANCE CRITERIA In the ideal HMS process, all material lower in density than the specific gravity of separation (SGS) would be recovered as floats and all material of higher density would appear as sinks. In order to evaluate the misplaced material, the washery products are tested at the density at which the washing unit is operated. The original type of plot1,7, 8 is shown in Fig 1; this was developed primarily for coal cleaning units. The curve for raw coal represents the cumulative percentages of sink material. The refuse curve is also plotted as a cumulative sink, the percentages being expressed in terms of raw coal. This diagrammatic representation of the results of washing units has the merit of easy visual observance of the degree of separation obtained. The error areas (cross-hatched) are a measure of the amount of misplaced material and therefore they can be used to characterize the quality of separation. The ideal and actual separating performance between floats and sinks can be best seen from the partition curve developed by Tromp,2 where the ordinate is the percentage recovery of the sinks, and the abscissa is the specific gravity (Fig. 2). It can be seen from the shape of the curve that as the SGS is approached, the proportion of material reporting to the improper product increases rapidly. In fact, the SGS can be defined as the density of the material in the feed that is distributed equally between float-and-sink products. When the upper half of the curve is inverted, a shape similar to that of a Gaussian error distribution curve is obtained and therefore the analysis of gravity separation may be carried out by using the law of probability. The shape of the curve in Fig. 2 is determined partly by the density composition of the feed, and partly by the sharpness with which the unit separates floats from the sinks.9, l0

Jan 1, 1970

By S. T. Yuster

An analysis has been made of the factors responsible for tilted fluid contacts in petroleum reservoirs. The factors are static and dynamic with the former being controlled by those variables responsible for the capillary rise of fluids, and the latter include rate of formation tilt and hydraulic circulation. The explanation that rate of formation tilt may be responsible for tilted contacts appears untenable. The role of some of these factors in the migration, fractionation. accumulation and possibly the prospecting for oil is indicated. INTRODUCTION While it is generally considered that the segregation of gas, oil, and water in a petroleum reservoir results in approximately horizontal planes separating these phases. there are factor; which modify this simplified picture to a very great extent. Some of these factors are static. and the departure of the fluid interfaces from horizontal may represent a static equlibriun. Some of these factors may be dynamic and the interface positions may be non-equilibrium and represent a steady .state condition. Of course combinations of these two situations may also exist. The reasons most commonly given for this behavior are hydraulic circulation of fluids, change in character of the formation, and a rate of tilt of the formations more rapid than the rate at which the fluids may re-establish an equilibrium. Russell's Principles of Petroleum Geology' contains an extensive discussion of tilted fluid interfaces and their importance in the migration and accumulation of petroleum. Russell cites examples of tilted water tables at Lance Creek, Wyo.; Rock River, Wyo.: Cut Bank. Mont.; Cushing, Okla.: and Graham; Okla. Also given was the Wasson Field of West Texas which has saucer shaped oil-water and gas-oil interfaces with the saucer being deeper in the case of the oil-water contact. The Bradford Field in Pennsylvania has a tilted water table. San Ardo. Coalinga None and some other California field.; have tilled contacts. A recent paper by King Hubbert discuses the effect of hydraulic circulation of the water underlying the oil in a given stratun and it- implications in the accumulation of and drilling for the oil. The foregoing would indicate that tilted fluid interfaces are not uncommon and that it would be of importance to underbtand the forces which are responsible. Further. it would be of interest to examine certain idealized models of situations which may cause tilting with the thought in mind of deriving relatinnships between the important variables. These relationships may only hold exactly for the model* assumed but the results may apply semi-quantitatively to actual formations and at least indicate trends. The discussion will be divided into the effect of static factors and the effect of dynamic factors. STATIC FACTORS It has already been mentioned that one reason given for tilted contacts is a variation in formation properties. Specifically this is a change in the pore size of the formation capilaries. If the internal surface of the reservoir is preferetially wet by water, capillarity will cause the water 10 rise to a greater extent above the free water table in a small capillary than in a large one. Consequently the water-oil contact will be higher in the lower permeability sands than in the higher permeability sand.;. The free water table may be defined as the position the oil-water interface would take if capillarity were absent. Since the phenomenon is the capillary rise of water in an oil environment, a derivation of this shold give a relationship between the variables. Fig. 1 is an idealized model of the situation with a uniform bore circular capillary ubstitttting for the tortuous non.circular formation pore. The upward force.; on the column of water will be equated to the forces downward to give the equilibrium situation. forces upward = force downward where r is the radius of the capillary in ceritimetera. a is the interfacial ten4on oil-water in dynes per centimeter, 0 is the

Jan 1, 1953

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By Alton B. Cook, G. B. Spencer, F. P. Bobrowski

In estimating production gas/oil ratios and oil recoveries from reservoirs containing highly volatile oils it is highly important to include condensate that may be recovered from the gas produced from the reservoir. The volume of the hydrocarbon liquid condensed from the production of the solution gas that has been liberated. in some reservoirs may equal or even exceed the volume of recoverable stock-tank oil as estimated by present methods. The usual procedure1, 2, 3 in estimating future reservoir performance includes use of relative permeability data of the reservoir rock to gas and oil and includes material-balance calculations utilizing data on the volume of the reservoir fluids, oil and gas production and reservoir pressure decline, and data on the physical properties of the initial reservoir fluids. The inaccuracy in the procedure results from the false assumption that all of the free or liberated gas that enters the well bore of reservoirs containing highly volatile oils remains in the gaseous phase as it is produced. This paper presents a method for estimating future reservoir performance and oil recoveries based on special labora. tory analyses of reservoir-oil samples and recognition of the additional volume of hydrocarbon liquid that will be recovered at various stages of depletion from a solution.gas.drive reservoir. The method also includes calculations of the volume and composition of the hydrocarbon liquids that can be recovered by processing the produced gas in a natural-gasoline plant. The development of the method resulted from a study of laboratory analyses of reservoir samples and of field data obtained from two reservoirs containing oil of the highly velatile type. Relatively high pressures and temperatures prevail in oil reservoirs discovered at the greater depths of present-day drilling. The contained fluids may have high saturation -Dressures and large volumes of gas in solution. The oils and gases under these conditions may be almost identical in compositions and densities.4,5 Also, engineers have noted that, for a number of oil reservoirs and especially the deeper reservoirs, the API gravity of the stock-tank oil increaees as the production gas/oil ratios increase. They attributed this increase in API gravity of the stock-tank oil to the formation of condensate as the liberated gas in the reservoir is being produced. SOURCE OF DATA FOR CALCULATIONS Subsurface oil samples and well-test data were obtained from the E. Constantin-Lambert Well No. 1 in the Elk City Field, Okla., to demonstrate the need for and a method of calculating future reservoir performance when consideration is given to the recoverable hydrocarbon liquid from the production of solution gas that has been or will be liberated in a reservoir. The Lambert well is located in C, SW 1/4, SW 1/4, Set- 18, T-l0-N, R-20-W, Washita County, Okla. At the time of completion it was on the east edge of the development and Was producing from conglomerate through 30 perforations in the 5 1/2-in. casing at a depth of 9,859 to 9,864 ft. The well Was completed on July 9, 1949, and subsurface oil samples were obtained July 29 and August 1, 1949. Production gas/oil ratio data were obtained during the operation in series of two Separators at high and low-pressures of 314 and 44 psia, respectively, and at an average temperature of approximately 60°F. The flowing bottom-hole pressure at the time of sampling was 3,934 psis. The static bottom-hole pressure was not obtained at the time of sampling, as the well could not be shut in long enough for testing because gas produced from the well was used for fuel at an offset drilling well. However, the initial reservoir pressure was calculated to be 4,364 psia from knowledge of pressure gradients in other wells in the field and the depth of the casing perforations in the Lambert NO. 1 well.

Jan 1, 1951

By J. F. Held

In a study of the influence of cold rolling on mechani cal properties of steel, it was found that the specific rolling procedure influenced crystallographic orientation. Properties developed by several rolling modes were determined and related to crystallographic orientation. Sanzples were cold-rolled various amounts on a laboratory mill. When palm oil was used as a lubricant, the crystallographic orientation was homogeneous throughout the thickness of the samples. Other samples were rolled without lubrication. Variations in intensity of the recrystallization texture components persisted throughout more than 50 pct of the volume of these samples. When the average plastic strain ratio, which is dependent upon crystallogvaphic orientation, was plotted as a function of percent reduction, a maximum was found at 40 pct in the samples which contained the observed texture variation. No maximum was found for the samples with the homogeneous texture distribution. Other mechanical properties, such as tensile strength and yield strength, were not influenced by the variation in crystallopaphic orientation. MECHANICAL properties of steel sheets depend, in general, upon the structural properties of the steel. For example, the Petch equation describes the relationship between yield strength and grain size. Other properties, such as hardness, vary with chemical composition. The plastic strain ratio, or R value, has been found to be dependent upon crystallographic orientation . In the course of investigating the effect of cold rolling on mechanical properties, it was found that a previously reported relationship between percent cold reduction and R value was not always observed. Published data had shown that the optimum cold reduction for best R values is 70 pct for aluminum killed steel.' However, by altering the rolling conditions, the optimum reduction can be shifted to much lower values, or it can be moved to very high values. This paper describes the rolling conditions that lead to shifting of the optimum cold reduction. The effect of rolling conditions on the various structure parameters and the resulting mechanical properties are evaluated. EXPERIMENTAL PROCEDURE Samples of three low-carbon aluminum killed steels were cold-rolled various amounts on a 9-in.-diam 2-high laboratory mill. Hot-mill thermal practice and steel chemistries are listed in Table I. Steel A was rolled with palm oil lubrication and heavy reductions on each pass; i.e., a total reduction of 75 pct was ac- complished with a maximum of five passes. Steel B was rolled without lubrication, and light reductions were given on each pass. After approximately 75 pct reduction, it was necessary to use a small amount of light oil to achieve any additional reduction in thickness. Following cold reduction, the samples were box-annealed at 1300°F for 10 hr. The heating rate between 800" and 1300°F was 50°F per hr, and the cooling rate following the soak period was 50°F per hr. Tensile specimens were machined from the annealed material and these were used to measure yield strength, tensile strength, and the plastic strain ratio (R value). Recrystallization textures were determined by an inverse pole figure technique.*'3 Integrated intensities of the (110), (002), (112), and (222) reflections were recorded for those planes lying parallel to the sheet surface. Examinations were made on both surfaces of each sample, and also at various levels beneath each surface to approximately 0.010 in. depth by etching techniques. RESULTS R Values. The R values obtained in steels A and B are shown as a function of percent cold reduction in Fig. 1. No optimum cold reduction was observed in steel A, rolled with palm oil lubrication. It is likely, however, that an optimum reduction would have occurred had higher reductions than 88 pct been employed. The optimum reduction in steel B occurred at 40 pct. The behavior in both of these steels is quite

Jan 1, 1968

By F. P. Bobrowski, G. B. Spencer, Alton B. Cook

In estimating production gas/oil ratios and oil recoveries from reservoirs containing highly volatile oils it is highly important to include condensate that may be recovered from the gas produced from the reservoir. The volume of the hydrocarbon liquid condensed from the production of the solution gas that has been liberated. in some reservoirs may equal or even exceed the volume of recoverable stock-tank oil as estimated by present methods. The usual procedure1, 2, 3 in estimating future reservoir performance includes use of relative permeability data of the reservoir rock to gas and oil and includes material-balance calculations utilizing data on the volume of the reservoir fluids, oil and gas production and reservoir pressure decline, and data on the physical properties of the initial reservoir fluids. The inaccuracy in the procedure results from the false assumption that all of the free or liberated gas that enters the well bore of reservoirs containing highly volatile oils remains in the gaseous phase as it is produced. This paper presents a method for estimating future reservoir performance and oil recoveries based on special labora. tory analyses of reservoir-oil samples and recognition of the additional volume of hydrocarbon liquid that will be recovered at various stages of depletion from a solution.gas.drive reservoir. The method also includes calculations of the volume and composition of the hydrocarbon liquids that can be recovered by processing the produced gas in a natural-gasoline plant. The development of the method resulted from a study of laboratory analyses of reservoir samples and of field data obtained from two reservoirs containing oil of the highly velatile type. Relatively high pressures and temperatures prevail in oil reservoirs discovered at the greater depths of present-day drilling. The contained fluids may have high saturation -Dressures and large volumes of gas in solution. The oils and gases under these conditions may be almost identical in compositions and densities.4,5 Also, engineers have noted that, for a number of oil reservoirs and especially the deeper reservoirs, the API gravity of the stock-tank oil increaees as the production gas/oil ratios increase. They attributed this increase in API gravity of the stock-tank oil to the formation of condensate as the liberated gas in the reservoir is being produced. SOURCE OF DATA FOR CALCULATIONS Subsurface oil samples and well-test data were obtained from the E. Constantin-Lambert Well No. 1 in the Elk City Field, Okla., to demonstrate the need for and a method of calculating future reservoir performance when consideration is given to the recoverable hydrocarbon liquid from the production of solution gas that has been or will be liberated in a reservoir. The Lambert well is located in C, SW 1/4, SW 1/4, Set- 18, T-l0-N, R-20-W, Washita County, Okla. At the time of completion it was on the east edge of the development and Was producing from conglomerate through 30 perforations in the 5 1/2-in. casing at a depth of 9,859 to 9,864 ft. The well Was completed on July 9, 1949, and subsurface oil samples were obtained July 29 and August 1, 1949. Production gas/oil ratio data were obtained during the operation in series of two Separators at high and low-pressures of 314 and 44 psia, respectively, and at an average temperature of approximately 60°F. The flowing bottom-hole pressure at the time of sampling was 3,934 psis. The static bottom-hole pressure was not obtained at the time of sampling, as the well could not be shut in long enough for testing because gas produced from the well was used for fuel at an offset drilling well. However, the initial reservoir pressure was calculated to be 4,364 psia from knowledge of pressure gradients in other wells in the field and the depth of the casing perforations in the Lambert NO. 1 well.

Jan 1, 1951

By G. T. Pruitt, T. L. Irby, P. B. Crawford, H. Ferrell

In water flooding peripheral, center-to-edge, line-drive or water-encroachment patterns the question has arisen, "when should a producing well be converted to a water-injection well?". It is realized that, if the producing well is shut in when water breakthrough occurs, some oil could be left in an unswept area. Yet, operation to high water-oil ratios may require processing much additional water. If a well is shut in, "where should the allowable be transferred?". A review of the literature indicates that very few data are available to the engineer to assist him in answering these questions. It is the purpose of this paper to present information which may be of value in selecting the flooding technique and the injection and producing wells and in scheduling injection and production rates. Certain phases of these problems can be studied in the laboratory. The Potentiometric model is well suited for studying many waterflooding problems. This model assumes that steady-state flow exists, that the mobility ratio is equal to one and that gravitational effects are neglected.'-' The three-phase sand model also has been recognized as an effective means for studying certain reservoir problems. Both models were used in making the study reported here. This paper discusses seven cases utilizing various waterflooding techniques. Data for the first five cases were obtained on the potentiometric model. Data for Cases VI and VII were obtained by constructing and flooding an unconsolidated sand pack (a three-fluid-phase system) and by determining the swept area and cumulative oil recovery for various types of operations. APPARATUS AND PROCEDURE The potentiometric model reservoir was 30 in. long X 10 in. wide by about 1/2 in. deep. Four wells were equally spaced in a line array along the lateral center line. (See Fig. 1.) Well No. 1 initially was an injection well for each of the patterns reported. The cases studied with the potentiometric model and sand model are described herein. The laboratory sand model reservoir was a 30- 10-in. rectangular Lucite vessel packed with sand to a depth of about 0.65 in. Four wells were equally spaced in a line array along the lateral center line. The reservoir material was an unconsolidated sand into which the reservoir fluids were mixed to yield fluid saturations of 55 per cent oil, 25 per cent water and 20 per cent gas. The water was added to the sand and the material mixed, after which the oil was added. Kerosene and water, the fluids used, gave a viscosity ratio of 1.64:1. In packing the reservoir, care was taken to assure constant fluid saturations and constant porosities. A new mixture was prepared for each run. During water flooding, a colored water was injected by a constant rate pump. The injection rate was 1.1 B/D/ft of sand thickness. For this series of tests, each of the producing wells was open to the atmosphere and, as in the potentiometric model study, Well No. 1 initially was an injection well for each of the patterns. KESULTS OF POTENTIOMETKIC MODEL STUDlES Two cases (Cases I and 11) involving equal pressure injections were studied, with the following results. Case Water injection was initiated at Well No. 1; the producing wells (Nos. 2, 3 and 4) were operated at constant and equal bottom-hole pressures. When water broke through at Well No. 2 and achieved the selected water-oil ratio, Well 2 was converted to a water injection well, resulting in two injection and two producing wells. The injection pressures at Wells 1 and 2 were maintained equal and constant; pressures at the producing wells were held equal, but they were lower than those at the injecting wells. A similar process was repeated when water broke through at Well No. 3. The flood was terminated when

By Robert E. Green, Kenneth Reifsnider

A microscopic X-ray diffraction technique was employed for the simultaneous study of the behavior of several families of lattice planes, whose local orientatiotz changes are manufestations of internal distortions resulting from specimen deformation. Photographs taken using aluminum were single crystals 1/64 in. In diam are presented which illustrate the appearance of various types of deformation- or growth- induced structural variations. Slip and lattice bending were detected in tensile tests for strains as small as 0.1 pct. Evidence of deformation bands, lineage structure, and void formation wns also shown. AmONG the most important methods of studying internal stresses in metals is the utilization of various X-ray techniques. The general subject of X-ray metallography has been treated in a most excellent manner by Taylor,1 and the use of X-rays for the direct observation of imperfections in crystals has recently been reviewed in an article by Newkirk2 and in the book edited by Newkirk and Wernick.3 Since the inception of metallographic X-ray analysis, there have been numerous technological developments and refinements, each with its particular advantages and disadvantages and, acrording to these, its particular applications. X-ray diffraction techniques can be divided into two general categories, that of X-ray diffraction microscopy and that of X-ray diffraction macroscopy. In the former are included such methods as those of Berg-Barrett, Lang, and Schultz2,3 which are concerned with microscopic imperfections such as dislocations. The second category includes all work concerned with the study of the condition of a crystal lattice structure as indicated by the marroscopic detail in its diffraction patterns. An example of this is the study of the diffraction manifestations of inhomogeneous plastic deformation as manifested by formation of deformation bands and inhomogeneous lattice rotations. The method used in the present investigation was an X-ray diffraction macroscopy technique. The geometry and analytical aspects of the method were similar to those of Julien and Cullity.4,5 The source was collimated with a single slit in a manner simi- lar to the "parallel beam'' method of Barth and Hosemann6 except that a continuous spectrum of radiation was employed. The apparatus produced large-beam transmission Laue patterns of thin cylindrical aluminum-wire crystals, which were deformed either in tension or torsion. Although the conventional X-ray target and interposed slit were not capable of the high resolution obtainable with a fine-focus X-ray source as employed in a microfocus apparatus, resolution was a secondary consideration in our technique, and was sacrificed to obtain sufficient intensity along a sizable length of the specimen. By using a grid indexing technique similar to that of Barth,7 we were able to study several diffraction lines from various planes simultaneously. The results of these tests give additional information with regard to the inhomogeneous deformation of single crystals, and the indexing procedure used provides a correlation between portions of the test specimen and portions of a diffracted beam. EXPERIMENTAL TECHNIQUE The experimental arrangement used is shown schematically in Fig. 1. A source of continuous X radiation from a vertically mounted Machlett X-ray tube possessing a copper target and operated at 20 kv and 10 ma was passed down a horizontal lead tube 80 cm long which terminated in an adjustable vertical brass slit. The slit opening was adjusted to correspond with the diameter of the test specimen. In front of the brass slit it was possible to place a screen wire mesh, one horizontal strand of which was a lead wire which served as a fiduciary mark, the screen itself serving as an indexing system as will be described later. Behind the screen was the test specimen which consisted of an aluminum single crystal wire 1/64 in. in diameter and 3 in. long. These 3-in.-long crystals were cut from

Jan 1, 1965

By E. A. Gulbransen, K. F. Andrew

Weight loss measurements were made using a sensitive microbalance operating in a high vacuum system. The Langmuir equation was used to Calculate the vapor pressures of the several metals and alloys. Aluminum lowered the vapor pressure of i9,on in a 5.4 Al-94.6 Fe alloy, and of iron and chromium in a 4.8 Al-21.5 Cr-73.7 Fe alloy. The influence of oxide films formed on the alloys on the effective vapor pressures of the alloys was also studied. These studies were used to aid in the inte9,pretation of the high temperature oxidation of alloys based on iron, chromium, and aluminum. RECENT studies on the oxidation of chromium1 and the heat resistant alloy 5 Al-22 Cr-73 Fe showed transitions in the rate of oxidation at 900o and 1050oC respectively. The transition for chromium occurred at a temperature where the rate of evaporation of chromium from oxide-free surfaces equalled the rate of chromium atoms reacting with oxygen. This paper presents new vapor pressure studies on iron, chromium, and the specially prepared alloys 5.4 Al-94.6 Fe, 21.9 Cr-78.1 Fe, and 4.8 Al-21.5 Cr-73.7 Fe. The ternary alloy is similar in basic composition to the patented heat-resistant commercial alloy known as Kanthal. The binary alloys were studied to show the individual effects of aluminum on the vapor pressure of iron and of iron on the vapor pressure of chromium. The purpose of the proposed studies was to test the influence of metal volatility on the oxidation behavior of heat-resistant alloys based on iron, chromium, and aluminum. Since oxide films formed on the metal may limit metal transfer to the surface, the influence of oxide films on metal volatility was also studied. LITERATURE A) Vapor Pressure. The vapor pressure of iron has been studied by Jones, Langmuir, and Mackay,' Dornte and Nrton. Edwards. Johnston. and Ditmar. and McCabe, Hudson, and Paton. Stull and SinkeT have calculated a heat of sublimation at 298° K of 99.83 kcalper g atom. The vapor pressure of chromium has been reported by Bauer and Brunner,' Speiser, Johnston, and Blakburn, Gulbransen and Andrew,'' Vintaikin,o McCabe, Hudson, and Paton, and Kubaschewski and Heymer.12 Good agreement was obtained except for the early work of Bauer and Brunner.' Stull and Sinke7 calculate a heat of sublimation at 298°K of 95.0 kcal per g atom. Vapor pressure measurements on aluminum have been made by Brewer and Searcy,13 Bauer and Brunner,aand Farkas.I4 Stull and Sinke,7 giving Brewer and Seary's' data the most weight, derive a heat of sublimation of 77.5 kcal per g atom at 298 oK. B) Method. Two methods15 are used for measuring the vapor pressure of metals: 1) The Langhuir free evaporation method, and 2) the Knudsen effusion method, In the Langmuir method, used in the present work, the vapor pressure of the metal P is given by the equation: Here M is the molecular weight of the vapor species. T is the absolute temperature. (dw/dt) is the rate of sublimation in g per sq cm per sec and a is the condensation coefficient. a is a measure of the efficiency of condensation of molecules striking the metal surface from the vapor. If condensation results from each collision a is unity. This coefficient has been found to be unity,a, le for metals. These results establish the general validity of the Langmuir free evaporation method as applied to metals. EXPERIMENTAL A) Vacuum Microbalance Method. A modification of the Langmuir free evaporation method was used. Strip specimens were suspended from a sensitive microbalance operating inside of a high vacuum system. For alloys, microbalance methods17 must be used on large area samples at relatively low temperatures to minimize composition changes. The

Jan 1, 1962

By P. T. Bail, J. E. Bobek

In reservoirs containing soft shales interbedded with oil-producing sands, it is possible to have water movement from the shales into the sands during reservoir depletion. This paper presents the results of scaled flow-model tests performed to investigate the efficiency of oil displacement by this vertical influx of water into oil-producing sands. In these model tests, the effects of rate of influx and rock wettability were considered. Oil recoveries by shale-wafer influx and by water flooding were cornpared after 0.4 hydrocarbon volume of water entered the producing sand. This comparison was made for water-wet and oil-wet systems. In water-wet sand, shale-water influx produces slightly less oil than conventional water flooding; in oil-wet sand, shale-water influx produces about one-half as much oil as conventional water flooding. In another type of comparison, it was found that shale-water influx followed by water flooding recovers less oil than water flooding alone. This is true for both water-wet and oil-wet sands. A comparison of tests run at different rates of shale-water influx shows that oil recovery is insensitive to rate in water-wet sand; in oil-wet sand, oil recovery decreases with decreasing rate of influx. INTRODUCTION Localized subsidence of the earth's surface has accompanied the depletion of some oil reservoirs, particularly in California,1, 2 along the Texas Gulf Coast,3 4 and in the Bolivar Coastal fields of Venezuela. Subsidence occurs when fluid withdrawals reduce the pressure in the reservoir. The reasons for subsidence accompanying a reduction in reservoir pressure are not known with certainty.10° However, there is considerable evidence that compaction of soft shale beds adjacent to producing oil sands can be a major cause of this subsi-dence.3, 6, 10-12 When the shales compact, a limited amount of water moves from the shales into the producing sands. A schematic illustration of this oil-producing mechanism is shown in Fig. 1. As the pressure in the sand declines due to oil production, a predominantly vertical pressure gradient develops at the sand-shale boundary. This causes water to move from the shale into the sand as indicated by the solid arrows. This paper reports the results of scaled flow-model tests to investigate the efficiency of oil displacement by the vertical influx of shale water into producing sands. The model tests were not performed with the aim of duplicating the recovery behavior of any specific reservoir. The primary purpose of the tests was to obtain a better understanding of oil displacement by shale-water influx. A knowledge of the oil- and water-production characteristics of even a simplified reservoir system should be of value to engineers estimating the performance of reservoirs where shale-water influx is occurring in conjunction with other production mechanisms. The following limitations and assumptions apply to the model work. 1. The sand of the prototype reservoir is homogeneous and horizontal. 2. The shale-water influx is uniformly distributed along the top and bottom of the sand member being studied. 3. No effects of edge-water drive or dissolved-gas drive that might accompany shale-water influx are considered. PROTOTYPE RESERVOIRS Scaled-model tests were performed to study oil displacement from three prototype reservoir sections. The reservoir sections modeled consist of single sand layers out of a sequence of -sand and -shale layers, as illustrated in Fig. 1. Each prototype represents a homogeneous, high-permeability, unconsolidated sand layer. In the field, the prototype is oriented in such a manner that one end is at the radius of drainage of a producing well and the other end is pointed toward the producing well (Fig. 2). The sand and fluid properties and the dimensions of the three prototypes are given in Table 1. The capillary pressure relationships for the three prototypes are presented in Figs. 3, 4 and 5. The oil-water per-

By H. A. Fisch, A. J. Opinsky, J. L. Bartos

Fort?-six- two-grain bounduries were studied in doped tungsten 1amp wire that had been heated to 3450°K very vapidly. Back-reflection Laue photograms were taken of the grain boundary partners and solved, using a computer. The resulting distribution of large-grain orientations was analyzed. Rotational axes were calculatedfor each grain boundary pair. The axes of least rotation show an anisotropy of rolalional angle. WhILE the orientations of large grains in straight doped tungsten wire have been studied extensively, little has been done to characterize the boundary that separates them. Rosi.1 upon seeing the jagged interlocking boundary in doped tungsten wire. inferred that the grains should have a preferred orientation, and proved it. He interprets his data as indicative of a single ideal orientation—(531)— being parallel to the wire axis. Rieck2, 3 and Mannerkoski' have essentially confirmed this finding. Opinsky, Orehotsky, and Siegle argue that the data suggest that (211)—a plane-is parallel to the wire axis instead. This (211 ) contains the (531). and hence would appear to be a more general case.5 Ahlborn and wasserman6 report that their orientation data stretch from (110) through (531) to (311). This path is the locus of {211 Recently. Opinsky has suggested that the data can be interpreted as a series of ideal orientations that can be related by coincidence relationships to the (110) fiber texture. All these investigators have determined the orientations of the large grains by the back-reflection Laue technique, and they have all obtained similar results. Only Rieck5 as methodically looked at the large grains along a wire. He was apparently not concerned with the relationships of the large grains across their common boundary, but only with their individual orientations. This research was undertaken to fill this gap in the under standing of the mechanical properties of tungsten wire. Only the crystallographic aspects of the problem will be reported here. In addition, the large number of large-grain orientations, which was accumulated in this study. will also be analyzed. EXPERIMENTAL MATERIAL AND TECHNIQUES All of the data were obtained from four pieces of the same 7-mil-diam General Electric tungsten lamp wire. Twelve-inch lengths of the cleaned wire were heated in vacuum by the flick of a switch to 90 pct of the amperes necessary for fusion (a temperature of approximately 3450°K) and held for 1 min. On the basis of other data. it is estimated that the rise time is of the order of 0.5 sec. The four pieces of wire could have come from anywhere within about 18 ft of wire. Consecutive segments of each piece of wire were mounted in bakelite and polished metallographically The polishing procedure followed that described by woods. "nly boundaries between two grains that each occupied the entire cross section of the wire were photographed and X-rayed. The metallographic sample was mounted accurately with respect to the X-ray unit. Steps were taken to read the films as accurately as possible with the conventional Greninger net. The data were then entered into computer programs that solve the Laue film by precisely the same techniques that are used in the solution of the film by means of the stereographic projection. The use of the computer has probably shifted the main source of error from the stereographic plot to the reading of the film. On the basis of several experiments, it is thought that the error associated with the entire process, from mounting the sample through the computer solution, is of the order of about one-half degree. The output of the computer is the direction cosines of the fiducial direction (the wire axis) and the locations of the three cube axes. The former data were used to calculate the differences in orientation between the two grain boundary partners, and the latter were used in the calculation of the rotational axes that could bring the two grains

Jan 1, 1970

By S. T. Wlodek, John Wulff

Dense, adherent, and ductile coatings of chromium can be applied to Molybdenum by selectively freezing out the chromium solute from a supersaturated copper-or tin-rich liquid alloy. The successful exploitation of this technique depends on the control of variables common to any freezing process. Under the most favorable combimtion of supersaturation, nucleation, and mass-transfey, coatings as thick as 0.004 in. can be obtained. In exploratory experiments it was found that a coating of chromium may be applied to molybdenum by immersing the molybdenum body in a supercooled copper-chromium or tin-chromium melt and selectively freezing out the contained chromium onto the molybdenum body. Supercooling of the liquid metal plating bath can be achieved by cooling, or the maintenance of thermal or concentration gradients in the melt. The technique is similar to conventional dip-plating procedures where the sample is immersed in a molten bath of the pure plating medium, except that in these studies, the plating medium consisted of a dilute solution of chromium in liquid tin or copper. The success of this method requires that the base material to be plated be isomorphous with the coating and insoluble in the plating bath. In addition, the plating bath, while having an appreciable solubility for the coating component, must have negligible solid solubility in the solid plate. Such relationships exist in the molybdenum-chromium, chromium-tin, and chromium-copper systems. Liquid tin and copper are satisfactory as the plating solvent, because although chromium is appreciably soluble in both of these liquid metals, solid inter-solubility is almost negligible, and no compound formation occurs. The same relationships exist between molybdenum and copper or tin except that the solubility of molybdenum in liquid tin or copper is insignificant. It is this combination of solubility relationships, as well as the completely isomorphous nature of the molybdenum-chromium system, which allows the formation of a chromium coating on molybdenum by the selective freezing mechanism. Since the main deterrent to the widespread use of molybdenum for high-temperature structural applications is its poor oxidation resistance, the formation of a dense and ductile chromium coating on molybdenum may well be of commercial significance. In addition, the basic principle of coating formation by selective freezing should be applicable to other metallic or even nonmetallic systems. The precipitation of the solute from a liquid metallic solution, for the formation of a protective coating, has not been previously considered in the literature. Frequently, however, a similar phenomenon has been described in the corrosion of metallic heat exchangers by liquid metals1 wherein temperature gradients in the liquid metal heat-transfer medium result in the formation of layers or deposits of metallic residue2 in the cooler portions of the system. Impregnating techniques using liquid baths have been tried as a plating process. Semchyshen and Barr, for instance, have successfully diffused chromium into molybdenum by immersing the molybdenum specimen in a liquid tin-chromium or copper-chromium alloy. This simple holding technique fails to produce a layer of pure chromium and requires prolonged immersion to allow for the diffusion-activated enrichment of the molybdenum. During the course of this investigation, most of the phase relations published for the copper-chromium4 and molybdenum-chromium4 systems, were found reliable. It was necessary, however, to investigate the solubilities of chromium and molybdenum in liquid tin as well as the solubility of molybdenum in liquid copper. These determinations were made by a simpie weight loss technique on materials of the same purity as used in the plating studies. The results of these solubility studies are given in Tables I and I1 and indicate that although the solubility of molybdenum in liquid

Jan 1, 1961

By M. P. Tixier, A. Poupon, M. E. Loy

Simple qualitative methods are explained for identifying those shaly sands in a well that are most likely to contain oil. A need for more precise measurement of the variables that enter shaly sand analysis is indicated. Field examples are given to illustrate the methods. A theoretical discussion of the quantitative interpretation of shaly sands is given as a basis for discussion and as a guide for the future. While not generally capable of practical application at the present time because of the lack of sufficient accuracy of the electric log data, these methods may become more feasible in the future as the result of the improved logging methods now being introduced. INTRODUCTION Experience has shown that for porous formations containing only a negligible amount of clayey material, reliable information on the fluid saturation and porosity of the reservoir rocks can usually be derived from the electrical logs. The interpretation is based on empirical formulae relating the true resistivity of a porous formation to its lithologic character, to the resistivity of the interstitial water, and to the proportions of water and hydrocarbons in the pores.' If the resistivity of the interstitial water is not known, its approximate value can be derived from the SP curve.2,3 The porosity can usually be determined to a good approximation from a MicroLog, or a MicroLaterolog.4,5 When the reservoir rocks contain an appreciable percentage of clayey material, an additional factor is introduced into the analysis. In a clean formation, the matrix is an electrical insulator, so that the ability of the formation to conduct current is due only to the conductivity of the electrolytes in the pores; in a shaly formation, the shale constitutes a part of the rock matrix able to conduct current, and influences the resistivity of the formation. On the other hand, the spontaneous emf's and the circulation of the SP currents are also responsive to the presence of the shaly material. All other factors being the same, the deflection of the SP curve opposite a shaly permeable formation is smaller than the deflection which would be observed if the formation were clean. The effects of the presence of shale on the resistivity and on the SP curves in a shaly formation are functions of the amount, of the specific resistivity, and of the geometrical distribution of the shaly material within the formation. The presence of shale therefore constitutes an important complication in electrical log interpretation. It is easy to realize, for example, that the presence of a large amount of clayey material in a sand may have such a predominant effect that the resistivity of the sand will not change very much, whether the pores are entirely filled with connate water, or contain a high saturation of hydrocarbons. Important research projects have been undertaken to investigate the influence of shales and to find a way to allow for this influence in the interpretation of a log. The problem of the SP in shaly sands was analyzed mathematically by H. G. Doll"' for the case of sands with shale laminations. Formulae expressing the resistivity of shaly formations were proposed by Patnode and Wyllie8 and de Witte.9 Other quite interesting theoretical and experimental results have been published by various authors.l0,ll,12,l3,14 The purpose of the present paper is to discuss an approach to electrical log interpretation in shaly sands. This approach is based partly on some of the theoretical and experimental data available in the literature and partly on observations made on actual field logs. Comparatively simple methods for qualitative and semi-quantitative analysis are described. These methods depend principally upon information provided by the electrical logs.

Jan 1, 1955

By Leonard L. Melton, Calvin D. Saunders

The design and performance of many operations common to the petroleum industry depend upon the unique properties of a class of materials known as non-Newtonian fluids. The art of measuring and describing these properties, called rheology, has fallen far behind the field applica-tion of these fluids in this industry. Empirical methods are still employed although theoretically sound methods of analysis are now available. This paper illustrates a completely general method of analysis of the rheological properties of non-Newtonian fluids which id independent of the type of viscometer employed and also the rheological type of fluid encountered except those of a thixo-tropic or rheopectic nature. Values of the rheological properties of a fluid obtained using this method of analysis are based upon an absolute scale of measurement, eliminating the necessity of employ-jng arbitrary concepts of the flow properties of non-Newtonian fluids, The fundamental nature of this method of analysis is further demonstrated by evaluating the precision with which measurements have been made of these rheological properties by employing a dimensionless criteric: —the Fanning friction factor-Reynolds number correlation. INTRODUCTION Non-Newtonian fluids are not new in the petroleum industry. Particular properties of non-Newtonian materials have been recognized and used to advantage in drilling fluids and have found excellent application in the hydraulic fracturing process.'.' While usage of these fluids is not new in this industry, the art of measuring and describing their rheological properties is still in its infancy. This is reflected in the accepted method of evaluating drilling fluids, API RP 29, (1950), which recommends a one point "viscosity" measurement. These shortcomings are recognized by various groups in the industry and more adequate methods have been prposed.3,4 The efforts Of these people are to be commended; but, at the same time, the limitations of their method of analysis and viscometer must be appreciated. This method Of analysis is applicable Only to Bingham plastic fluids as is pointed out early in their articles. The consistency of a Bingham plastic fluid must also lie within the range of the viscometer which is also well defined by the author. It is believed that the apparent simplicity of this method of analysis and the utility Of Operation Of their viscometer will soon make the terms non-Newtonian fluid and Bingham plastic fluid synonymous as used in this industry; a tendency which has already been encountered. Application of this method of analysis to a non-Newtonian fluid other than a Bingham plastic can lead to erroneous results. The field of rheology has long been hampered by the adherence to arbitrary concepts of Of of the flow properties Of non-Newtonian fluids. This has resulted in the design and operation of viscometers so as to fulfill these concepts rather than following the more logical method of analyzing experimental data so as to yield a fundamental truth. completely Bingham proposed the concept Of plastic flow and yield asu rement. data presented by Buckingham could hardly be interpreted so as to substantiate this theory; but rather succeeded in establishing the fact that compliance with this flow concept could never be realized in the capillary tube vis-cometer.5 Bingham, in reply, sug-gested "Rather than complicate our formula, it would seem to me a much better plan to so change the conditions of flow that the formula will be linear... Reiner0 stated .This plan has been followed by me in collaboration with Miss Riwlin. . . . From the present paper (Reiner and Riwlin, 1929) it will be seen that it is possible to choose the conditions of flow so that the formula based on Bingham's law of plastic flow remains linear. This is realized in the rotation viscometer," Thus, a viscometer, with design and operation based on the Reiner and Riwlin equation for plastic flow, is restricted to a specific range of flow

Jan 1, 1958

By Brown, R. W., G. H. Neill, R. G. Loper

All facets of ball sealer behavior must be known and understood to design for their optimum use in well treatments. The down-hole factors including the inertial forces, drag forces and holding forces have been discussed. Equations have been developed and presented for these forces. The use of these equations in this process will contribute to the most efficient use of an economical and proven ball sealer process. The urocedure presented has been used to successfully analyze field results indicating problems involving the use of ball sealers. These problems have been isolated and corrected in future treatments by using the procedure presented to revise the perforating program, the injection rate, the design of ball sealer stages and/or the type and size of ball sealers. The procedure presented also indicates that dislodgement of ball sealers occurs primarily in ultra slim-hole completions. INTRODUCTION The perforation sealing process has been proven highly successful and economical since it was introduced to the oil and gas industry in early 1956.' Since it has proved so successful in multistage fracture treatments at a much lower cost than conventional packers, the ball sealer process has become a byword in well completions.' Not only has it changed the design of fracture treatments, it has changed the concepts of selectively perforating and has greatly aided the success of the single-point and limited-entry techniques." Yet with all the advantages, there are still facets of ball sealer behavior that are not widely recognized. These must be known and understood to better design and execute the optimum ball sealer treatment. The down-hole behavior of ball sealers is influenced by a number of factors including an "inertial force", a "drag force" and a "holding force". These are considered in two phases—the initial seating of the ball and the forces tending to unseat the ball after contact has been made (see Fig. 1). This paper presents a theoretical study of these factors and formulas for predicting their influence. The authors acknowledge the fact that the flow equations presented herein describe the behavior of Newtonian fluids and do not cover the so-called power-law fluids. The assumptions made, however, are reasonable and well within practical limitations of the conditions encountered during field application. For example, it is assumed that the perforations are round with a discharge coefficient of 0.82. While this may not be exactly true, it has been verified within practical field limitations.' The discharge coefficient would not vary significantly even if the perforation size or configuration varied pronouncedly. The approach of assuming uniform perforation size is not as strained as it might first appear. Normally, a perforator contains charges equally spaced with the same number in each vertical (or horizontal) plane. If the perforating gun is not centralized, the holes in one plane will be smaller than average, while the holes in opposing planes will tend to be larger than average. The net result is that the two effects tend to balance. FACTORS AFFECTING CONTACT WITH PERFORATlON Ball sealers are injected into well treating fluids for the purpose of contacting and sealing those perforations which are accepting the fluid flow. The efficiency of the sealers is primarily influenced by: (1) the velocity of the balls down the pipe, and (2) the fluid velocity through the perforations. To divert the sealer to the perforation, the inertial force of the ball must be overcome by the drag force created by the fluid velocity through the perforation. BALL VELOCITY The final, or stable, velocity of the ball is the sum of the actual fall velocity and the fluid velocity. This will be

By Oren C. Baptist, Eliot J. White

Samples of four reservoir sands having different degrees of water sensitivity were subjected to several laboratory tests to determine differences in capillary behavior attributable to clay-mineral effects. The degree of water sensitivity was estimated by the difference between gas and water permeability. Unsaturated pore volumes determined with mercury injection were comparable to irreducible water saturations determined with the semipermeable bar-rier method only for the non-sensitive sands that contained small amounts of non-swelling clay minerals. Irreducible saturations were independent of salinity of the water, which suggests that most residual water is adsorbed 0.7 a film over solid surfaces and that internal retention by clay minerals is relatively insignificant. The water-sensitive sands imbibed water to higher saturations than did non-sensitive sands, and this result is believed to be a combination of the effects of clay minerals and preferential wettability; however, the relative importance of each of these effects is riot determinable. Thus it is concluded that the semipermeable barrier method is the best of the laborafory methods used for estimating formntion water .saturations in the sands studied. INTRODUCTION This investigation is a continuation of studies of the role of clay minerals in petroleum production in the Rocky Mountain area. Previous work has shown large differences in gas and water permeability in numerous reservoir sands; these water-sensitivity effects observed in the laboratory have been correlated with well behavior in the field, and the degree of water sensitivity imparted to reservoirs by the various clay minerals has been determined.'.' The effect of interstitial clay minerals on formation water3 saturations is not so well known. It has been reported that formation water saturations probably are higher in clayey than clean sands,' but this effect has not been evaluated in the laboratory, and the relative effect of the various types of clay minerals on formation water saturation has not been determined. The clay-mineral groups of most importance to this study and to petroleum production in general are kaolinite, illite, and montmorillonite. The minute layers of montmorillonite are loosely bound to one another so that water enters between them, causing great expansion of the particles. Kaolinite and illite do not exhibit interlayer hydration, but they do immobilize considerable amounts of water owing to their large surface areas, which are of the order of 15 to 97 m2/gm of clay.5 The four Wyoming sands used in this study were selected to represent a wide range of water sensitivities. These sands, with the number of wells and fields from which the samples were obtained, are: Second Frontier, five wells in two fields; Newcastle, six wells in one field; Tensleep, two wells in two fields; and Lower Muddy, five wells in one field. EXPERIMENTAL METHODS AND PROCEDURES Water-displacement data were obtained by the semipermeable barrier method," using both fresh water and brines having either 16,500 ppm sodium chloride or calcium chloride. A displacement pressure of 35 psi was found to be sufficient to obtain the practical irreducible water or brine saturation (IWS, IBS) in most samples. Mercury-injection data were ob-tained with equipment and pro-cedures similar to those described by Purcell.7 Exceedingly high pressures are required to attain complete mercury saturation by this method; however, since saturations in most samples change very little with large pressure increases above 1,000 psia, the maximum pressure used was 1,400 psia. To facilitate comparison of mercury-injection and water-displacement results, it is convenient to express mercury-injection data in terms of unsaturated pore volume. The abbreviation, (100 - SHg)min, is used to denote the pore volume unsaturated by mercury at 1,400 psia injection pressure. Gas permeabilities, ki, were deter-mined by the method proposed by Klinkenberg.8 Methods of determining types and amounts of clay minerals by X-ray diffraction analyses, as well as methods of determining water permeability, have been described previously.' The imbibition characteristics of

Jan 1, 1958

By O. J. C. Runnals

The intermetallic compounds NpAl2, NpAl3, and NpAl have been prepared, and examined by X-ray diffraction methods. The compounds are isostructural with the corresponding U-Al compounds. NpAl3 is face-centered cubic with a = 7.785A and has the MgCu2 structure. NpAl is simple cubic with a = 4.2624 and has the AuCU3 structure. NpAl4 is body-centered orthorhombic with a = 4.428, b = 6.268, and c = 13.71A. The published description for the atomic positions in UAl, applies also to NpAl4 THE U-Al system has been examined by Gordon and Kaufmann.1 They identified the following intermetallic compounds: UAI2, UAl3, and a third, tentatively identified as UAl5. A structure analysis of the latter compound by Borie2 proved that the formula UAl4 was more consistent with the X-ray data. The crystal structures of UAl2 and UA have been reported by Rundle and Wilson.3 UAl2 was found to be isostructural with MgCu. The atomic positions in the simple cubic UA1, cell were found similar to those in the AuCu3 structure. Three analogous compounds exist in the binary system Np-Al. X-ray data for the compounds NpAl2, NpAl3, and NpAl4 are reported below. The neptunium used in the investigation was supplied through the courtesy of the Argonne National Laboratory as neptunium (V) nitrate. It was stated to have a radioactive content of 99.25 pct Np237. The impurity limits had been established by a spectrographic analysis given in Table I. Any titanium, boron, or bismuth impurity should be effectively removed during the fluorination of NpO2 to NpF4, and sodium, lithium, magnesium or strontium during the alloying procedure. The oxalate ignition technique, described by Westrum for the preparation of finely-divided reactive PuO2, was used.The neptunium (V) nitrate solution, containing 100 mg Np, was evaporated to dryness on oxalic acid crystals. The resulting oxalate was calcined to NpO, by heating in platinum at 650°C for 2 hr. An equimolar mixture of anhydrous hydrogen fluoride and purified hydrogen was passed over the NpO2 for 2 hr at 500°C. According to Fried and Davidson" the above fluorination conditions should produce the purple-black fluoride, NpF3 However, the light-green product showed only NpF4 lines on an X-ray diffraction pattern and contained only an estimated 5 pct of finely dispersed black NpF3 particles on microscopic examination. NpAl3: An intimate mixture of 50 mg of neptunium fluoride and aluminum powder (99.99 pct pure, —28 to $60 mesh) was heated to 900°C in a BeO crucible in vacuum by a tungsten coil for 2 hr, to allow the following reaction to proceed: NPF4 + 7Al + NpAl, + 4AlF. [1] The formation and sublimation of aluminum mono-fluoride in this system was verified from an X-ray diffraction analysis of the sublimate. The diffraction pattern was similar to one obtained in the aluminum reduction of UF4 to UF3,6 showing both Al and AlF3 lines. The resulting alloy was sintered at 1100°C for 1 hr. A powdered specimen of the crystalline product was sealed in a thin-walled quartz capillary for X-ray examination. The photograph was taken on a 14.32 cm General Electric powder diffraction camera, using filtered copper radiation. The films were calibrated in terms of a NaCl standard pattern. The wavelengths used in the calculations were 1.5418A for Cu K and 1.5405A for Cu K The powder diffraction pattern showed that NpAl is simple cubic with a = 4.262 % 0.005A, and is isostructural with UA13 where a = 4.27A1 or a =

Jan 1, 1954

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor's original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965

By F. Weinberg

In developing a mechanism for the solidification of metals from the melt, it has been proposed that solidification proceeds by the growth of platelets parallel to close packed planes. The evidence for this is based primarily on observations of decanted interfaces of lead1,2 and tin on which platelets 1 to 10 µ thick4 were observed. In recent observations of decanted eutectic alloys, 5,6 it was found that the eutectic structure on the decanted surface was markedly different than that of the bulk material, with the surface structure extending approximately 10 µ behind the interface.' This suggested that, at least for these experiments, a residual liquid layer 10 µ thick had been left on the decanted interface, which solidified subsequent to decanting. If a similar thickness of residual liquid was left on the decanted surfaces in the lead and tin observations referred to above, then it is questionable to what extent the observed platelets can be related to the solid-liquid interface before decanting. The purpose of the present investigation was to measure the thickness of the residual liquid layer on a decanted surface of tin, using relatively standard decanting procedures. The technique used was to add approximately 200 ppm of Tl204 (PI) to the melted portion of a high purity (99.999 pet) bar of tin, which was being progressively melted from one end, and then decant during melting. Since only the melt contained the radioactive tracer, the activity emanating from the decanted surface could be used as a measure of the thickness of the residual liquid layer. Progressive melting was carried out in the same fashion as single crystal growth, namely, in a horizontal graphite boat, in an argon atmosphere, using a moving furnace. The decanting was done in two ways; 1) removing the furnace and suddenly dropping the melt end of the boat, and 2) suddenly jerking the solid away from the liquid by the action of a falling weight (estimated peak acceleration 3 x 105 cm per sq sec), using a split graphite container. In all cases the melt was vigorously agitated by bubbling argon through it. The activity of the decanted surface was measured through an aperture 1.5 cm by 0.5 cm in a lead shield with an Anton tube geiger counter. Assuming that the active layer on the surface had the same concentration of Tl204 as the decanted liquid, the thickness of the layer could be determined from the measured activity of the decanted material, and the relationship between activity and material thickness. The latter was determined by rolling some of the decanted material into foil and measuring the activity of multiple layers of the foil. The activity At of material of thickness t (in mm) was determined to be A, = Ao(1 - e-22.5t) where Ao is the activity of the bulk material. The results of the measurements of the thickness of the residual liquid layer for six decants are given in Table I. The variation in t is attributed to variations in the decanting procedure and the rate of melting, the latter being difficult to control because of the vigorous agitation of the liquid. The rate of melting was in the order of 2 cm per hr, estimated from the position of the solid-liquid interface during melting. The results indicate that a residual liquid layer of the order of 10 µ in thickness is left on the decanted interface in agreement with the observation on eutectic alloys referred to above. If the mixing of the liquid during melting is not complete, as was

Jan 1, 1962