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By T. Sterry Hunt

But little was known of the coals of Southeastern Ohio until the present survey of the State under Dr. Newberry began its work. The results of the geological investigations of Prof. E. B. Andrews in this region, and of the chemical investigations of Prof. T. G. Wormley, both of which appear in the reports of the survey for 1869 and 1874, and more recent special reports by the former, together with some data for which I am indebted to the kindness of Dr. Newberry, and my own limited observations, have served me for the preparation of the following notice of the coals lying on the western border of the great Appalachian coal-basin in the region drained by the Hocking River and its tributaries, and belonging to the Lower Coal-Measures. Some uncertainty exists as to the place in the suc- ' cession of the lower coals to be assigned to the seams known and mined in the Hocking Valley. It is the opinion of Prof. Andrews that the inequalities of the original surface were such that we cannot identify in that region the lowest coals known in Northwestern Pennsylvania and the contiguous parts of Ohio, but that we must rather count from above downwards. These conclusions Dr. Newberry is not prepared to accept, and further researches will be necessary before certainty can be attained in this matter. Meanwhile it seems, from a study of its relations to the Pomeroy or Pittsburgh seam, that what is known as the great vein of the Hocking Valley, occupies the horizon of the Upper Freeport coal, E of the Pennsylvania survey, or No. 6 in Dr. Newberry's enumeration, counting from the base. This seam, in the region in question. assumes certain characteristics which, taken in connection with its geographical position, give it a great importance among the coals of the State. The area to be noticed includes the whole or parts of several townships in Perry, Hocking, Vinton, and Athens Counties, lying near the margin of the basin over which the vein in question assumes the character of a dry-burning or splint coal, and has a thickness varying from six to ten and even twelve feet. Its precise limit southward cannot at present be clearly defined, but it has been found as far south as the line of the Marietta and Cincinnati Railroad, with a thickness of six feet, and is mined at various points along the valley of the Hocking River, near Nelsonville, where it attains six or seven feet. To the northward, along the tributaries of this river, Sunday and Monday

By C. W. Gennet

Announcement was made in the spring of 1926 that the Boston & Maine R. R. Co. had contracted with the well-known German steelmakers, Messrs. Fried Krupp, for the manufacture of 15,000 tons of basic open-hearth steel rails at the Rheinhausen Works, for delivery to Boston, Mass. The manufacture of rails in the United States has for many years been almost a national pride, and as this feeling is chiefly the result of a long-time liberal and consistent patronage of American rails by American railroads, it is not strange that this somewhat unusual announcement should arouse more than ordinary interest. Since the end of the World War, the importation of foreign rail has been fairly large, principally because the newly created economic conditions have rendered some American competition more difficult, but the tonnage imported, for the most part, has been made up of small orders for miscellaneous use; and the contract referred to constitutes the largest single importation of foreign rail in over ten years. In 1915, the Algoma Steel Co. of Sault Ste. Marie, Canada, supplied the Illinois Central R. R. with 30,000 tons of rails,' and various other American roads with smaller amounts. In 1902, 1903 and 1904, large tonnages of rail from abroad were purchased, the Louisville & Nashville R. R. alone obtaining 30,000 tons from German mills. It is the object of this paper to present, in what is believed to be a new and concise form, figures showing the production and consumption of rails in the United States, and to record some of the testing and inspection results of the recent Krupp rails; also, to direct attention to two quite unique departures from American practice that were regular features of the Krupp process and which are worthy, it is thought, of careful study. Production and Consumption of Rails in the United States Table 1 shows the tonnage of rail produced in the United States and the amount imported, exported, and consumed by years since 1849. That, evidently, was the first year of record, for the statistics of the American Iron and Steel Institute and its predecessor, the American Iron and

By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy's law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity' factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By G. C. Wallick, W. R. Foster, J. G. Savins

Inasmuch as the differentiation and integration methods represent different modes of rheological analyses, a dual scheme of analysis using both methods should lead to a generalized method of data analysis. A dual differentiation-integmtion method of analysis is applied here to the Poiseuille flow of a variety of ideal Generalized Newtonian and viscoplastic models. Using machine-processing techniques, the result is a spectrum of response patterns which are expressed in terms of certain derivative functions. It is shown that these characteristic functions form the basis of a highly-sensitive analytic technique for optimizing the selection of the most appropriate functional relationship between shear rate and shearing stress. INTRODUCTION In the first paper of this series, Savins, Wallick and Foster1 presented an historical review of the salient features of the differentiation method of rheological analysis in Poiseuille flow, and also indicated how the method could be applied to problems involving plane Poiseuille flow. It was shown that the differentiation and integration methods, although basically not incompatible, do represent different modes of rheological analysis. This suggests that valuable background information regarding the probable response characteristics of real data obtained with the differentiation method can be obtained from an integration method-differentiation method analysis of the response of a variety of ideal rheological models. The present paper describes how this dual method of analysis has been applied to suites of idealized models representing a wide variety of Generalized Newtonian and viscoplastic behavior which have received attention at various places in the literature.

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By A. L. Holley

The general usage of engineers, manufacturers, and merchants, is gradually, bat surely, fixing the answer to this question. In every country rails, boiler-plates, and machinery bars, whether hard or soft, are almost universally called steel, when they are made from cast ingots. Other names for the softer steels, such as " homogeneous metal,'' "Bessemer iron," " Martin iron," and the like, have failed to obtain general recognition. The meaning of the term steel, before it was enlarged to cover newly developing varieties, has been traced, by a recent writer, down through Percy, Shakspeare, and the Bible, in a most interesting manner, from an archœological point of view. Undoubtedly, it did characterize hardness arid other qualities imparted by carbon. It is within the memory of most of us, that all steels were tool steels, and that the soft, structural varieties were introduced—varieties which harden but little, which bend cold, and which, in many physical properties, are akin rather to wrought-iron than to tool-steel. But, since both the hard and the soft steels are made by the same processes, and have their great, distinguishing structural feature in common, viz., homogeneity resulting from fluidity, it has come to pass, despite every other proposed nomenclature, that all the compounds of iron which have been cast in malleable masses, are called steel, the term wrought-iron being still confined to malleable iron made from pasty masses, and hence laminated in structure. No inconvenience has been found, so far, in distinguishing between the more or less carburized products, in general, by the terms " highsteel," "low-steel," "tool-steel," etc., and, in particular, by prefixing the percentage of carbon and other ingredients, to the terra steel. Steels which contain distinguishing ingredients other than carbon, are called "chrome-steel," "titanium-steel," and the like, just as variously compounded bronzes are called " phosphor bronze," " aluminium bronze," etc. Thus the combination of several words or symbols, and figures, may completely disclose the characters of the metal, in terms that are subject to no misunderstanding. But inasmuch as several high metallurgical authorities and clever writers have of late proposed to disturb this natural and somewhat settled nomenclature, it seems important to consider the claims of the various classifications. I shall attempt, in this paper, to show

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By J. N. Sicking, F. H. Brinkman

A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium-ratio data for reservoir studies of condensates and volatile crude-oil systems. The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and variom reservoir pressures. Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems. In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir. INTRODUCTION As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids—thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated. Unfortunately, because of the complex nature of hydrocarbon mixtures, accurate K-values are hard to obtain. The equilibrium ratios for a particular component will vary not only with the temperature and pressure, but also with over-all composition of the system. The importance of composition is quite critical at elevated pressures, but becomes negligible at pressures below about 300 psia. Therefore, because most phase behavior problems involve the high-pressure region, each fluid system becomes a special case. Experimental programs to determine characteristic K-values are quite difficult and time-consuming. Thus, it is often necessary to resort to approximations of the K-value data. Charts giving K-values for various mixtures and classes of mixtures are available in the literature. However, there are two major difficulties in using them: (1) the K-values of the "plus" component (that mixture of components heavier than the last one analyzed) must be obtained by extrapolation from the K-values of the other components; and (2) the K-values obtained must finally be adjusted by trial and error to agree with observed volumetric data. To eliminate these difficulties, a new method of determining equilibrium ratios was developed. Briefly, after the composition of the system as a whole has been analyzed, the method uses empirical correlations and the gross fluid properties of the system (relative vapor-liquid volumes and densities) to calculate K-values. Because the calculative procedure is long, it is best solved on a digital computer. About one hour of machine time on an IBM 650 computer is required to develop a K-chart for the fluid being examined. DEVELOPMENT OF THE METHOD OF OBTAINING K-VALUES Equilibrium ratios are defined as the ratio of the mole fraction of a component in the vapor phase to its mole fraction in the liquid phase. This statement is expressed in Eq. 1. A typical plot of equilibrium ratios for a particular system is shown in Fig. 1. It should be noted that, at pressures near the saturation pressure, the K-values appear to converge to a common point. This apparent convergence point is called the convergence pressure and is a characteristic of the system involved. Various empirical correlations of K-values have been noted. It has been observed that an isothermal plot of

By Hugh Neill, O&apos

In previous papers,' the author has reported the results of experiments on the straining in tension of a single-crystal test piece, about 0.6 in. long, of vacuum-melted electrolytic iron containing 1.8 per cent. of silicon. The crystal was originally in the "as cast" condition, and was stressed slowly along a tetragonal axis so that slipping along conjugate gliding planes finally transformed the original cylindrical portion into a pair of fracture wedges. One of these fracture wedges was sectioned along the stress axis in a plane at right angles to the edge of the wedge. A metallographic study of this plane of section led to the conclusion that slip had taken place in the (111) direction along (112) planes making a V shape with the stress axis. The present paper describes the results of scratch-hardness tests conducted on the same section, in order to determine the distribution of strain hardness therein, followed by annealing, and considers the resulting variations in hardness. These observations supplement those made by Krivobok2 on similar material reduced 25 per cent. by hammering (i. e., by impact) in the cold. In order to investigate ageing effects, two small crystals of the same alloy were also tested. The Specimens Employed The principal specimen, A, was prepared for the metallographic examination leading to the determination of the slip planes of the crystal. Therefore the work described in this paper was conducted on metal which had been repeatedly etched and had been allowed to rest for about 30 months after straining. It consisted of a section of the fracture wedge and contiguous unstrained head of the test piece taken along a tetragonal axis parallel to the direction of stressing, the plane of section originally being not far removed from the (011). Several subsequent grindings

By C. van der Poel, R. L. Chuoke P. van Meurs

When an initially planar interface between two im-ttitcihle liquids is displaced at constant rate, U, nor-mat to the front, instability will occur for all rates greater than a critical rate. U, given by provided the Fourier decomposition of the spatial pertmrbcrtiott or deformation of the moving displacetment front contains modes with wavelengths. A, greater than a critical wavelength, given by tit there expressions, p, p and k, with the subscripts I and 2 distinguishing the two 1iquids under consideration, are density, viscosity and effective pemeability coefficients respectively; g is the absolute value of the acceleration due to gravity; and cos (zz') is the direction cosit7e between the vertical carlesian coordinate z' (positive upward) and the z coordinate norma1 to the initially plane macroscopic interface taken positive in the direction from Liquid I to Liquid 2. U is the average volumetric velocity (injected volume of liquid pet. unit time per unit of area normal to Z) and is positive for Liquid I displacing Liquid 2, negative for the reversc displacement and r2 is an effective inter-fucial tension (for displacements between parrallel plates, t0= s the ordinary bulk interfacial tension). further, there is a wavelength of maximum instability given by For natural perturbations, this wavelength will preclotninate and characterize the form of the instability as a quasi-sinusoidal deformation, i.e., viscous fitzgers of peak-to-peak separatiotr, A,,. Comparison of experitient with theory rei'eals tltat these considerations are recsonably valid for displacements in hoth parallel plate chantzels and nnconsoli-clutt'd glass ptnvder packs. These results are. tij particular interest for interpretation of data from laboratory experiments with regard to fielil applica/iotz.s. It is quite possible for A,, although st7zall relative to the large lateral dimension of the reservoir, to rxceed the greatr.st lateral extent of the lahoratory sample or model. If it does, frontal displace- ment occurs in the laboratory experiments, and oil INTRODUCTION Thc puposes of this paper are to present theoretical and experimental evidence for occurrence of macroscopic instabilities in displacement of one viscous fluid by another immiscible with it through a uniform porous medium and to compare available experimental data with some predictions of a theory of instability developed by the first author. The instabilities are referred to as macroscopic in the sense that spatially quasi-sinusoidal, growing fingers of the displacing liquid are formed, the width and peak-to-peak separation (wavelength) of which is large relative to a characteristic length of the particular permeable medium such as grain size. Visual models of two kinds have been used to obtain observations: displacement of oil by water-glycerine solutions through the flow channel formed by closely spaced parallel plates and displacement of oil by water with and without initial interstitial water through unconsolidated glass powder packs, employing the technique of matching indices of refraction. In all cases we have observed macroscopic instabilities or fingers under conditions predicted by the theory to be favorable for their occurrence. The phenomenon discussed here is not the production of streamers due to gross inhomogeneities such as permeability stratification of the porous medium. It is our object to show, on the contrary, that a quantitative prediction of finger spacing is possible in a porous medium known to be macroscopically homogeneous and isotropic throughout. The importance of the phenomenon in its influence on the configuration of oil and water with respect to oil production behavior was noted earlier by Engel-berts and Klinkenberg' who coined the term "viscous fingering". THEORY Necessary and Sufficient Conditions ior Instability anc Initial Kinematics There are several levels of increasing complexity in the theoretical description of instabiIity of fluid displacements in permeable media. Of these, the simplest description, ;tdapted to low permeability systems, is selected for presentation.' More inclusivc tlescriptions are reserved for separate publication.

By T. F. Witheree

The Fletcherville Furnace was built in 1864 and 1865, making its first blast from August until October of the latter year, when it was blown out to prevent its " bunging-up." Repairs were made in time to enable it to be blown in again December 12th, 1865, the blast ending October 7th, 1866. Total product 1921.15 tons iron, an average of 6.8.2.5 tons per day, from ores yielding 44.8 per cent. Consumption of charcoal 223.2 bushels per ton of iron. The furnace journal up to this time shows no record of furnace dimensions, or temperature of the blast, but as near as can be ascertained, they were as follows, viz.: Height of stack, 42 feet. Diameter of bosh, 11 feet. Angle of bosh, 71/2 inches to 12 inches rise, about 58°. Diameter of open tunnel head, 42 inches. Number of tuyeres 3 ; each 3 inches in diameter. Dam 15 inches high. Tuyeres 24 inches high. Tymp 224 inches high. Diameter of steam cylinder, 20) inches. } Diameter of blast cylinder, 64 inches. } Stroke 5 feet. The engine is direct-acting horizontal non-condensing. December 26th, 1866, the furnace was again put in blast, having been considerably altered in the crucible; the height of stack, bosh, and tunnel head remaining as before. Six tuyeres were put in, three in each of the side arches. The hearth or crucible was rectangular in form, 3 feet wide x 31/2 feet long x 64 feet high. Inclination of bosh 58°. Height of tuyeres 26 inches; nozzles 21/4 inches diameter. Temperature of blast estimated to be about 500°.

By R. H. Widmyer, G. M. Wood

This investigation was prompted by the absence of a simple, accurate method to predict optimum second stage separation pressure in three stage separation operations. Three stage separation as used here includes two separators plus the stock tank. The first stage pressure is usually fixed by gas sales conditions and the third stage is at atmospheric pressure. Thus, the second stage pressure is the only one that may be varied in-discriminantly during production operations. No variations in temperature were considered in this study, even though it will vary among systems, for a change in temperature has little effect on the optimum pressure. Optimum pressures may be determined from flash calculations, but these are tedious unless a computer is available. An early attempt to develop a simpler method&apos; yielded an equation which gave the optimum pressure only as a function of initial and final pressure. Experience, however, confirms theoretical relationships which show that composition as well as pressure and temperature must be a factor. This indicates that the basic relationship should be an equation of the form, where P, is second stage pressure, P, is first stage pressure, A is a function of P. (stock-tank pressure) and the system composition, and n is a function of the number of stages and the system composition. Fig. 1 shows the basic variation of P2 with P for a fixed system composition. A series of such figures clearly showed the effect of composition. The peak of each curve reflects that second stage pressure at which the stock-tank recovery (gal/MMcf) residue gas is a maximum value. DEVELOPMENT OF NEW CORRELATION Wellstreams having 17 different analyses, ranging from low gravity crude to condensate, were used to determine the effect of composition. Each wellstream was flashed through three stages to determine the optimum second stage pressure for each first stage pressure. Equilibrium vaporization ratios proposed by Latham and Campbell were used throughout. The heptane plus fraction, for simplicity, was assumed to have the properties of octane. The results were subjected to an empirical analysis in an attempt to develop a correlation- that would be (1) simple, (2) accurate, and (3) eliminate the need for any flash vaporization calculations. This analysis yielded two equations, one for wellstreams having a specific gravity greater than one (air = 1.0) and one for those less than one. For crude streams (specific gravFor condensate (specific gravity < 1.0),