Search Documents

By B. Wilhelmi, W. H. Somerton

Simultaneous measurement of pore and elastic properties of socks under a wide range of triaxial stress conditions may be made with equipment and methods developed in this paper. Tests were run on three outcrop sandstones at several confining pressures and axial stresses up to approximately 80 percent of failure stress. The greater reduction in porosities and permeabilities occurred in the hydrostatic loading portion of the stress cycle, but substantial reductions in both properties did occur upon application of deviator (triaxial) stress. Triaxial elastic moduli were calculated from strain gauge measurements. Both Young's moduli and shear moduli were found to increase with increasing confining pressure. Poisson's ratios increased with axial stress but showed no consistent change with confining pressure. Only very general relations were observed between pore and elastic properties. The lesser decrease in porosity and permeability at higher stress values is related to increase in rigidity of rocks at higher stresses. INTRODUCTION Many investigators have studied the effects of hydrostatic stress on the properties and behavior of rocks. A few have studied the effects of triaxial stress fields on individual physical properties of rocks. To our knowledge no one has measured simultaneously pore and elastic properties of rocks under a wide range of triaxial stress conditions. This is the purpose of this work. Rocks exist in the subsurface under what Jaegerl refers to as "polyaxial" stress conditions (all principal stresses unequal). When two of the three principal stresses are equal, this is referred to as triaxial loading. The triaxial method of loading is most commonly used in modern testing work because experimental difficulties in measuring physical properties of rocks are greatly reduced over polyaxial testing. Although triaxial loading may not reproduce subsurface conditions precisely, subsurface stress conditions are never known precisely anyway. Triaxial testing would seem to be more realistic than testing under hydrostatic loading (all principal stresses equal) for application of results to subsurface problems. The objectives of this work were threefold: (1) to develop methods of measuring simultaneously pore and elastic properties of rocks under triaxial stress conditions, (2) to determine whether changes in these properties are of sufficient magnitude to be considered in subsurface calculations and (3) to attempt to relate changes in pore properties and elastic properties since they will have been measured at the same time under identical loading conditions. REVIEW OF EARLIER WORK PORE PROPERTIES Several investigators have studied the effects of stress on the physical properties of rocks. Fatt and Davis2 showed the reduction of permeability of rock with hydrostatic loading. McLatchie et al.3 and Knutson and Bohor4 related permeability reduction to compessibility of reservoir rock, again under hydrostatic loading. Wble,5 and later Redmond,6 evaluated the effects of applied radial pressure on conductivity, porosity and permeability of sandstones. In this latter work, no axial stress was applied. Dobrynin7 reviewed much of the previous work done . on the effects of overburden pressure on physical properties of rocks. He concluded that changes in physical properties are controlled to a large extent by pore compressibility of the rock. Several sets of curves developed from empirical relations are presented. These curves permit estimation of change of properties with net overburden pressure, knowing the pore compressibility and porosity of the rock. Net overburden pressure is defined as (Pe - 0.85 Pi ) where Pe is the

By T. K. Perkins, L. E. Bartlett

Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenonema This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young's moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy me generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. INTRODUCTION The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface). In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young's Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50-12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry.1 An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith6 has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1.

By L. L. Handy

The development of a theory for miscible liquid displacement requires evaluation of the variables which affect growth of the mixing zone between solvent and displaced oil. Factors which appear to be important are individual fluid viscosities, viscosity ratios, flood rate, fluid densities, flow characteristics of the porous medium and molecular diffusion coefficients of the fluid components. The primary purpose of this paper is to evaluate diffusion effects. Theoretical treatments to date have been limited to floods for which the viscosity ratio is one. Two principal theories have been proposed. Von Rosenberg adapted for porous media a theory derived for capillary tubes by G. Taylor.' ,' In this theory molecular diffusion perpendicular to the direction of flow is a primary factor in sharpening the flood front. Slow floods give sharper fronts for a given distance traveled than fast floods. An alternative theory considers miscible liquid displacement as a statistical problem.3,4,5 Diffusion is not an important factor in this theory, but it leads to the same general type of equation as von Rosenberg's. Both theories predict S-shaped concentration profiles with the same dependence on distance traveled. The statistical or "dispersion" theory predicts rate independence, however. To supplement rate studies a direct measurement of a diffusion effect would be helpful in evaluating which of the two proposed mechanisms best describes miscible liquid displacement for one-to-one viscosity ratio systems. No quantitative theory has been proposed for floods in which a low-viscosity fluid displaces a high-viscosity fluid. It might be anticipated, however, that the extensive fingering observed in floods with adverse viscosity ratios would increase opportunities for an exchange of components between displaced and displacing liquids by a diffusional process. Even if molecular diffusion were not an important mixing mechanism for one-to-one viscosity ratio systems, it could be significant in systems with adverse viscosity ratios. METHOD FOR EVALUATING DIFFUSIONAL MIXING In solvent flooding the displacing liquid can become mixed with the displaced liquid by a number of processes; in general, either mechanical or diffusional in character. To evaluate the contribution of diffusion, a method was sought that would distinguish diffusional mixing from mechanical mixing. Suppose two soluble tracers are added to the displacing liquid and that one tracer has a diffusion coefficient much greater than the other. Then, if diffusion is important during miscible liquid displacement and if diffusional transport is primarily transverse to the direction of flow, substances with high diffusion coefficients will have sharper concentration profiles than those with comparatively low molecular diffusion coefficients. In order to have material balance the profiles for the two tracers must intersect. For one-to-one viscosity ratios the intersection would occur at the 50 per cent concentration point. It is generally assumed that diffusion in the direction of flow is negligible. This assumption appears reasonable because flow velocities are ordinarily orders of magnitude greater than diffusional velocities. If this is not a valid assumption, however, the shapes of the fronts will be further degraded by longitudinal diffusion. The effects of rate and molecular diffusion coefficients are the opposite for longitudinal diffusion to those for lateral diffusion. Higher rates or lower diffusion coefficients would tend to give sharper fronts. The double tracer method offers several unique advantages in evaluating effect of molecular diffusion. First, the method gives a direct measure of the effect of diffusion on mixing zone size. Second, the effect of a difference in diffusion coefficients is determined from a single experiment. Comparison of several experiments at different rates is not required. Third, the method is applicable for any viscosity ratio. Fourth, the method is unaffected by density differences between the two fluids which might result in rate dependent gravity effects. EXPERIMENTAL PROCEDURE Suitable tracers are substances whose diffusion coefficients differ as widely as possible, but whose adsorptions on rock surfaces is negligible. The two tracers selected were methanol and sucrose in water solutions. The approximate diffusion coefficients for methanol and sucrose, as given in the International Critical Tables, are 1.3 X 10-5 and 0.3 X 10-5 m2/sec, respectively. Concentrations in the water solutions were 200 gm/liter of solution for both methanol and sucrose. These high

By J. A. Putnam, A. D. K. Laird

In laboratory research on the behavior of oil, gas and water in porous materials, no direct method has been devised to measure saturation without disturbing the flow. Indirect methods involving various forms of radiation have been developed for measuring one or two components. The X-ray absorption method for two components has been described previously1-3. The possibility of three component measurement has also been mentioned1. Since two component measurement still requires considerable care to insure accuracy, the fact that three components can be measured satisfactorily is not generally appreciated. The fraction of the energy of an X-ray beam of one wavelength transmitted through a material is given by the transmission factor. in which 1 is the beam's path length through the fluid. p is the fluid density, and 1,. is its mass absorption coefficient. Eq. 1 implies that all parts of the beam pass through equal amounts of the fluid. Practical applications are, therefore, limited to systems in which the fluid is distributed so that I varies negligibly over the cross-section of the beam. Typical variations of the transmission factor with X-ray tube potential arc shown in Fig. 2 from which experimental points have been omitted for clarity. The X-ray absorption of low pressure gases in a core is practically zero so it cannot he distinguished from that a vacuum by instruments that will differentiate between liquids. The transmission factor of a gas in a core is. therefore, unity. Consequently, the saturation of only one gaseous component can be found. If two fluids completely fill a core, their two saturations add to unity and, therefore, only one value of the transmission factor, T, is needed to determine both of them. When two liquids do not completely fill the core, their saturations do not add to unity and transmission factors at two wavelengths must be measured. At one of these wavelengths, 7 for one liquid must be different from T or the other liquid. The change of T for one liquid us the wavelength is changed between the two values must be different from the corresponding change of T in the other liquid. The two values of fluid saturation will also give that of the gas because the three saturations must add to unity. In Fig. 2 it can be seen that there are many large differences of T between various oil solutions and water solutions at any one potential, and between potentials for any one solution. Consequently, conditions for optimum accuracy of measurement of the saturations of a gas and two liquids can be chosen. Once the operating potentials have been selected, however. it is more convenient to cross plot the data from Fig. 2 on transmission factor-solution concentration coordinates for the chosen potentials, as shown in Fig. 3. Fig. 3 was used to plan the experimental procedure for Core N-38-1. Since the voltage control at 45 kv was good, the slopes of the curves in Fig. 2 at this potential would cause little error. At low potentials, however, the voltage control was not good, so 33 kv was chosen because the small slopes of the curves made voltage control less critical. The lowest strength beam that could be measured reasonably at 33 kv corresponded to a minimum T factor of 0.385. Fig. 3 shows that both 4.80 weight per cent of cadmium chloride in water and 24.0 per cent of iodobenzene in crystal oil had this T value, and, consequently, were indistinguishable to the X-rays at 33 kv. Thus, at 33 kv, the liquid saturation was given by the same curve regardless of the relative amounts of oil and water solutions present. This simple calibration curve from which the gas and liquid saturation can be read, is shown in Fig. 4. Fig. 3 also shows that at 45 kv, T for the aqueous solution is 0.610. and that T for the oil solution is 0.220. These values were transferred to Fig. 4 to give the triangular calibration plot from which the brine and oil saturations can be found, after the gas saturation has been determined at 33 kv.

By W. van der Knapp

A theoretical and experimental ana1ysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The result enable one to deduce directly the effect of large increlents in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical rules surface, the generating lines of Which have a slope according to the solid rock compressibility. Analytical expression for such a ,surface is very simple. It follows that the bulk and pore compressihilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be conduded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could he related by means of a simple empirical formula. Results from the described study find a direct applicxtion in material balance calculations and in prob1ems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equatiorls for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 1.5 to -10 prr cent porosity that laboratory measured porosities may differ from those lender reservoir conditions by about I per cent of their value. The difference for low porosity limestotnes can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to he very small. General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot1, Gassmann2 and Geertsma.2 Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension. It has been known for a long timei that the stress-strain relations of a packing of spheres are essentially noninear. Our experiments show that for almost all reservoir rocks which arc elastically deformable the relation between volume and loading is also a nonlinear one, resembling that of a packing of spheres very closely. The behavior of these media is often described by using the linear stress-strain relations for small incremental stresses and strains in the vicinity of a pre-stressed condition." The present study differs from these considerations in that it enables one to deduce the effect of large increments in the stresses directly. In analogy to the stress tensor for a homogeneous body the stress tensor for a porous body can be written in the conventional way: where the tensor components, o, and t, represent the total forces acting on the faces of a unit cube of porous material. This tensor can be split into two parts. a hydrostatic and a deviatoric part, as follows2,3,1 where the component of the hydrostatic stress system, a. equals The hydrostatic stress causes a change in volume whereas the deviatoric stress system gives rise to a change in shape only. One of the difficulties in describing changes of volume occurring in reservoir rocks is that the relations connecting these volume changes with external and internal stresses are essentially non-linear. A complete description requires the bulk volume, V,,, as well as the pore volume,V,,. to be known as a function of both the changes in pore fluid tension (v) and the hydrostatic tension on the outer boundary.

By R. R. Harvey

Recent evidence has indicated that the films forming at crude oil-water interfaces are the result of naturally occurring su,rface-active components in the crude oil rather than oxidation products resulting from exposure of the oil to air. Since the presence of such films may strongly affect the displacement of oil from porous media, a knowledge of their composition and formatiorz is of fundamental importance. In this study, without the assumption of a specific mechanism, film formation is considered to involve the transfer of a weakly surface-active species in solution in the oil to the oil-water interface. The film gas law and the Gibbs adsorption equation may thus he applied to the system. The rigid films which form upon decrease of the oil-water interfacial area are considered a result of the very slow rate of re-solution of the film material into the oil. When the shrinkage of the interface is very rapid, the amount of film material leaving the interface is negligible, and the system may then be treated in the same manner as an insoluble film. The combination of these treatments leads to a new concept of the film factor in which it may he quantitatively related to the concentration of film-forming material at the interface. Suitable experiments can then yield the following information. 1. Original concentration of surface-active species in the oil. 2. The change of concentration with time. 3. Concentration of surface active species at the interface. 4. The change of this concentration with time. 5. Interfacial tension of the system at any time and its variation with time. 6. Equilibriunz concentrations for a given set of conditions. 7. Concentration requirements for solid film formation. 8. Molecular diameter of the adrorbed species. These calculations may be made solely from data taken from measurements on the original oil. While using the pendant drop method of interfacial tension measurement of crude oil-water systems, Bartell and Niederhauser' remarked on the thin, transparent, pliable, solid films or membranes which were often formed at the interface between crude oil and water. As a result of their observations of these films, Bar-tell and Niederhauser concluded: 1. The films are formed by material from the oil adsorbed at the interface rather than by a reaction at the interface. 2. The adsorption of the film-forming material is a rather slow process. 3. There are good indications that the process is reversible; i.e., the film constituents may re-dissolve into the oil. 4. The film will spontaneously spread over any new surface formed. 5. The process of adsorption at the interface is accompanied by a decrease in the interfacial tension of the system. Although they had proved that film formation was not due to a reaction at the interface, Bartell and Niederhauser were unable to demonstrate conclusively whether these film-forming constituents were present in the original reservoir oil or whether they were formed as oxidation products after exposure of the oil to air. Recent evidence seems to point to their presence in the original oil. Although the true nature of the film-forming constituents is still uncertain, these conditions would be fulfilled by the assumption of the presence of a slightly soluble surface-active component in the original oil. This component would migrate to a freshly formed interface because it would thereby lower the free energy of the system. The component at the surface constitutes an expanded monolayer which would become compressed, upon retraction of drop, due to the slow rate of re-solution of the film components into the bulk of the oil. It is possible, by involved extraction processes, to separate or at least concentrate this film-forming fraction. However, using the assumptions made above, the technique of monolayer film study may be applied to reveal much of the nature of the adsorbing material without resorting to an actual separation of the film-forming constituents.

By G. D. Boozer, W. H. Somerton

RESEARCH CORP., LA HABRA, CALIF. Thermal diffusivities of some typical sedimentary rocks have been measured by a rapid unsteady-state technique. Thermal data including diffusivity and conductivity are presented for the temperature range of 200" to 1,800°F. Diffusivities calculated from steady-state conductivity rneasurernents compared favorably with unsteady-state data at the lower temperatures. Unsteady-state data are less reliable at higher temperatures; reported values may be as much as 20 per cent high at temperatures in excess of 1,500°F. This is caused partly by the simplified method used in calculating diffusivity from experimental data and partly by the many thermal reactions which occur at the higher temperatures. The marked decrease in thermal diffusivity and conductivity at elevated temperatures indicates the importance of considering the temperature dependence of thermal properties in subsurface heat-transfer calculntions. Knowledge of the effects of liquid saturation, overburden and pore pressures, and heats of reaction of reservoir materials will be required before complete subsurface thermal analyses may be made. INTRODUCTION Heat-transfer calculations are becoming increasingly important in the analysis of in situ combustion and underground nuclear explosions. Thermal data for natural rock materials at elevated temperatures are generally unavailable. Calculations at high temperatures may be grossly inaccurate if temperature-dependent thermal properties of rocks are not considered. It is known that the heat capacities of rocks increase with temperature. Heat capacities may be calculated from chemical or mineralogica1 analyses of the rock system. Thermal bulk expansion of rocks is believed to be small, although few data are available. Thermal conductivities of most natural rock materials decrease with increased temperature. Thermal diffusivity, defined as the thermal conductivity divided by the product of the heat capacity and the bulk density of the material, is used in unsteadv-state heat-transfer calculations. It is apparent that thermal diffusivity decreases markedly with increased temperature. A new method, which gives a nearly continuous record of thermal diffusivity within the temperature range of 200° to 1,800°F and requires less than 1.5 hours for the run,' was used to measure the diffusivity of several sedimentary rocks. Thermal conductivities were calculated from measured bulk densities, heat capacities calculated from chemical analysis and the measured diffusivity values. Thermal conductivities were measured at lower temperatures by a steady-state technique1 to test the agreement of data obtained by the two methods.

By J. M. Smith, D. Kunii

Effective thermal conductivities of sandstones filled with stagnant fluids were measured using a steady-state technique. Data were obtained for seven sandstone samples, taken from four different locations and ranging in permeability from 18 to 590 md. The measurements with gases (helium, nitrogen, air and carbon dioxide) covered a pressure range from 0.039 psia to 400 psig. Data were taken for four liquids — n-heptane, methyl alcohol, 79.8 weight per cent glycerol-water solution and pure water at atmospheric pressure. The experimental results were used to evaluate the theoretical equations for predicting stagnant conductivities developed earlier 4 The low-pressure measurements permitted evaluation of the consolidation parameter bpDp/ks (necessary to utilize the theory) for the various types of sandstones. Using these characteristic values, the tbeoretical equations correlated well with the experimental conductivity data for the several fluids and rock samples. INTRODUCTION An aspect of heat transfer in solid-fluid systems of considerable current interest is the effective thermal conductivity of porous media. The stimulus for study of the subject arises from the need for sound procedures for designing thermal methods of petroleum production. The general system occurs when there exists a flow of fluid through the pores of the solid material. However, a logical starting point in developing a theory for predicting the effective thermal conductivity in the general system is to attack the special case when the porous solid is filled with stagnant fluid. Since the flow rates anticipated in thermal production processes are very low, such stagnant conductivities k,O are also of practical significance. Kunii and Smith4 recently reviewed the existing data for stagnant conductivities and proposed a theory for heat transfer in porous rocks. This leads to equations for predicting the stagnant conductivity as a function of the properties of the fluid and solid phases. The existing experimental information1-3,5,7,8 covered a range of porosities and agreed well with the theory. However, the available data were insufficient to examine critically the effects of two important properties on koe, — the thermal conductivity of the fluid and the pressure. The objectives of the present study are twofold: (1) to measure the effect on koe of (a) the pressure for gases, and (L) the thermal conductivity of the fluid kg for bloth gases and liquids; and (2) to determine for rocks of different porosities and permeabilities the apparent solid conductivity ks and the consolidation parameter bpDp/ks required in applying the theoletical equations. Measurements extrapolated to zero pressure are helpful in evaluating ks and the consolidation parameter. However, the extrapolations must be based upon data obtained at low pressures because in small pores the molecular conductivity of the fluid may be unusually depressed. This occurs when the mean free path of the molecules is of the same order of magnitude as the pore diameter, that is, in small-diameter pores at low pressures. The phenomenon has been studied recently by Schotte6in beds of unconsolidated fine particles. With particles in the size range of 45 to 200 microns, a significant reduction of kg with pressure was found even at absolute pressures greater than 1 atm. In the sandstones employed in the present investigation, pore diameters lower than those experienced by Schotte are likely, so that the effect would presumably be greater. SCOPE OF MEASUREMENTS Stagnant conductivities were measured for four types of sandstones using a total of seven samples. The characteristics of the samples, including porosity and permeability values, are given in Table

By R. A. Salathiel, A. D. Kaiser, P. H. Monaghan, B. E. Morgan

The productivities of many hydrocarbon-bearing for-rnntions appear to be reduced during drilling, completing and repairing operations. The reason for these othcarwise unexplainable low productivities may be a drastic reduction of formation permeability immediately surrounding the borehole. A possible cause of the reduced permeability is swelling and dispersion of clays present in porous media when contacted by fresh water or mud filtrates. Hence, the invasion of fresh water or mud filtrate into hydrocarbon-bearing formations that contain clays may cause low productivities as a result of formation damage. Present laboratory investigations have yielded results which supplement existing literature on formation damage. An expanded-type clay, montmorillonite, way found in hydrocarbon-bearing formations not previously analyzed. When sand columns and formation cores containing montmorillonite were contacted by fresh water, their oil permeabilities were reduced. This reduction in oil permeability way restored partially but not completely by a repair procedure, i.e., flooding with kerosene containing organic agents or flooding with water containing electrolytes. Hence, where montmorillonite is present in formations, prevention of formation danzage was indicated to be the only complete solution to the problem. To prevernt formation damage, results suggested use of an approximately 1 per cent solution of calcium chloride or stronger solutions of sodium or potassium chloride. In conventional rotary drilling operations the wall of the hole is exposed to drilling mud for days, weeks, and in some instances for as long as several months. During this time, drilling mud filtrate seeps slowly into formations surrounding the hole. The permeability and stability of many formations, especially those containing clayey materials, are impaired by the mud filtrate. Often interaction between the mud filtrate and the formation causes drilling and production difficulties. Serious reduction in productivity of oil and gas formations during drilling, completing and repairing wells has been noted often in recent years. Cases are known of development wells which produced only small volumes of fluid upon completion. However, after a period had elapsed, they began to produce oil or gas in commercial quantities. In other cases, results of drill-stem tests taken during the drilling of deep wells have indicated good production should be obtained from shallow formations. Later difficulty has been experienced in obtaining production from these shallow formations which had remained in contact with drilling muds for an extended time. In yet other cases wells have failed to attain the productivities expected from previous performance after the use of drilling mud as a circulating fluid during workover operations. It is evident from the field behavior cited that the productivities of certain oil- and gas-bearing formations have been damaged by exposure to drilling muds. This reduction in well productivity, called "formation damage", causes serious consequences. In development wells, expensive remedial operations are incurred. In wildcat wells, good formations may appear to be marginal or even non-productive. The importance of formation damage has been recognized by a number of investigators1-s who have considered the effects of fresh water, saline solutions and aqueous mud filtrates on the permeabilities of formations. A general conclusion from such studies is that interaction between water and formation clays reduces permeability of reservoir rock and that the permeability decreases as salinity of the water decreases. Data in these references, however, concern the permeability change with only a single fluid present. A more pertinent and direct consideration in the production of oil and gas from wells is the permeability change when two fluids, oil and water, are present. Recognizing this, Nowak and Kreuger2 and Bertness1" considered several ways in which mud filtrates and saline solutions caused reductions in the oil permeability of formation cores. Investigations discussed here were designed to supplement information in the literature on changes in oil

By R. J. Wygal, J. Naar

An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by 1/pc2 = CS*. The evolution of an oil-gas system imbibing water from Swi to(Sw,imb )max is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturation. When the gas satuation cannot be reduced further, the system evolves along a line of constant Sg with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. INTRODUCTION Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper,1 a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model: (1) an analytical expression of oil isoperms; (2) oil isoperrns as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by 1/PC = CS*; and (3) evaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson1 for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid. The following expressions were derived from the model. 1. The amount of oil blocked by the invading water is

By A. S. Odeh

ABSTRACT A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs fram pressure build-up and/or drawdown plots. INTRODUCTION The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard,l Freeman and Natanson,2 and Samara.3 The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results,4 Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a fractured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. TO understand the behavior of the pressure buildup and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions: 1. The matrix blocks act like sources which feed the fractures with fluid; 2. The net fluid movement toward the wellbore obtains only in the fractures; and 3. The fractures' flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures' bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady -state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. la this paper, the fundamental equation of flow

Jan 1, 1966

By J. Geertsma

The relationship between porosity and the speed of propagation of acoustic waves in fluid-saturated porous rocks as measured by the Sonic log and by ultrasonic tecbniques is analyzed. Biot's continuum theory 1 is used to explain the difference in acoustic wave propagation between a dry and a liquid-saturated porous material. The porosity is a variable in this theory. However, the acoustic wave propagation in the dry rock depends too on porosity, and this dependence is not predicted by the theory. Frequently in dry sandstones, a nearly linear relationship between reciprocal acoustic wave velocity and porosity is observed in the low-porosity range. The physics behind this behavior is outlined. An empirical relationship of the form, 1/v = A + F, applies accordingly for many porous dry rocks, provided the porosity is the only variable. The presence of a liquid in the pores changes the value of B, and this change is found to be in agreement with the Biot theory. The time-average relation introduced some years ago2 results in an equation of the same type — 1/V = F/Vf + (1 - F)/Vr — but is not based on a sound physical picture. Still, this relation sometimes predicts approximately correct A and B values. Carbonate rocks with their complicated pore structures sometimes show a different relationship between wave velocity and porosity, unfavorable for log interpretation. Examples are presented. The simultaneous presence of calcite, dolomite and anhydrite, with their different grain densities and matrix compressibilities, complicates acoustic-log interpretation in carbonate rocks still further. Other complicating effects of acoustic-log interpretation are discussed. They are related to the influence of shale streaks and natural fractures on the average wave velocity observed by the logging tool and to the effect of adsorption phenomena on wave propagation in unstressed rocks particularly in sandstones. INTRODUCTION The velocity of propagation of sound waves in porous sediments as a function of depth is a quantity frequently measured. Velocity loggers of various d-sign may be used, for which velocity is defined as the. distance between a wave generator and a wave detector (one-receiver system) or the distance between two wave detectors (two-receiver system), divided by the shortest time required for a vibrational pulse to cross this distance. Velocity loggers ale used to assist in seismic prospecting, to differentiate between the various types of sedimentary rock layers, and also to determine rock porosity and pore fluid content. This paper is especially concerned with the relation between velocity and porosity and the effect of the pore fluid. Most velocity-log interpretation in terms of porosity is based on a formula advocated by Wyllie, et al,2 suggested earlier by Hughes and Jones,3 and known as the "time-average relation". This formula app1ies for a model consisting of a layered system of parallel alternating slices of a solid and a liquid, crossed by the wave path perpendicular to the interfacrbs. This must be an unsuitable model for the derivation of wave propagation properties of liquid-saturated porous media. It suggests that only rock matrix and fluid properties influence the wave velocity. The surprising fact, nevertheless, is that applications of this formula to clean sandstones under specific conditions (sufficient effective stress) results in porosity predictions which are close to reality. Other authors, such as Gassmann,4 White and Sengbush,5 Brandt,6 and Hicks and Berry,7 make use of more realistic models to arrive at a wave velocity formula for porous sediments. Their models consist of various liquid-saturated packings of frictionless spherical grains and are, therefore, also highly idealized. A number of experimental results obtained in the laboratory can be better explained with these model theories than by the time-average relation. A study of a general character, not depending a priori on a special model of the porous structure, was still lacking.

In deposits in which the secondary zones are well defined a layer of rich oxidized ore is frequently found immediately to overlie the enriched sulphides, from which it is derived by direct oxidation in place. In deposits that contain oxidizing precipitants particles and masses of residual oxidized ore are likely to be scattered through the leached zone, having been precipitated during migration before reaching the zone of enrichment. This precipitation hinders secondary enrichment and in extreme cases prevents the formation of such concentrations. Residual ores are precipitated by various reagents. Carbonates are formed through the action of the carbonic acid contained in surface waters, and also directly through the replacement of calcite, especially where the containing rock is limestone. Native metals, such as copper, gold, and silver, are formed by the action of reducing agents, among which organic matter and ferrous sulphate are prominent. Kaolin, gouge, and certain shales occasionally act as powerful precipitants through adsorption. Silver is often found as residual chloride, formed through precipitation by the chlorine contained in surface waters. Residual ores are often the result of incomplete solution, the relatively insoluble minerals being left behind during the migration of associated metals; incomplete oxidation and solution often leave residual masses of unaltered, or partly altered, sulphides in the oxidized zone. Such residual particles or masses have commonly been enriched by additions from circulating, metal-bearing solutions. During oxidation under conditions that permit reprecipitation, such as the oxidation of sulphide deposits in limestone, a scat-

Jan 1, 1932

By C Gunther

In deposits in which the secondary zones are well defined a layer of rich oxidized ore is frequently found immediately to overlie the enriched sulphides, from which it is derived by direct oxidation in place. In deposits that contain oxidizing precipitants particles and masses of residual oxidized ore are likely to be scattered through the leached zone, having been precipitated during migration before reaching the zone of enrichment. This precipitation hinders secondary enrichment and in extreme cases prevents the formation of such concentrations. Residual ores are precipitated by various reagents. Carbonates are formed through the action of the carbonic acid contained in surface waters, and also directly through the replacement of calcite, especially where the containing rock is limestone. Native metals, such as copper, gold, and silver, are formed by the action of reducing agents, among which organic matter and ferrous sulphate are prominent. Kaolin, gouge, and certain shales occasionally act as powerful precipitants through adsorption. Silver is often found as residual chloride, formed through precipitation by the chlorine contained in surface waters. Residual ores are often the result of incomplete solution, the relatively insoluble minerals being left behind during the migration of associated metals; incomplete oxidation and solution often leave residual masses of unaltered, or partly altered, sulphides in the oxidized zone. Such residual particles or masses have commonly been enriched by additions from circulating, metal-bearing solutions. During oxidation under conditions that permit reprecipitation, such as the oxidation of sulphide deposits in limestone, a scab

Jan 1, 1932

By J. Mazia, H. Rosenthal

An investigation has been made of residual stress in the head and body of caliber 0.30 cartridge cases. The head was divided into four ring-lie sections which were cut off by a jeweler's saw. Spring-out was measured after a radial cut had relieved the circumferential bending moment. The residual stress corresponding to the observed spring-out was calculated by formulas in which the computed stress was a function of wall thickness. All rings sprang open, indicating compressive stress on the inner wall and tensile stress on the outer wall. The production stress-relief anneal of 475 F. for 45 min. reduced the stress to almost half. The priming and crimping operation, however, again raised the stress, especially in the flange section. The dect of stress-relief heat treatments on residual stresses in the body of caliber 0.30 cartridge cases was investigated by the split-ring method. Although this method did not reveal any large stresses in the body, the neck before mouth anneal was found to contain a computed stress of 30,000 psi. at the surface. This value was reduced to 15,000 psi. in 120, 30, and 15 min. at 400, 475, and 500 F., respectively.

Jan 1, 1945

By G. Sachs, G. Espey

IT is well known that high residual stresses are created in tubing by the sinking process, in which no internal tool or mandrel is used.1-4 In this process, the wall thickness is usually slightly increased.4,5 In tube drawing with a plug, the residual stresses are gradually reduced with increasing reduction of wall, and, by the conventional approximation methods of stress measurement, no stress is detected in tubing in which the wall reduction is over 50 per cent of the total reduction in cross-sectional area.1-6, It has also been observed that higher stresses are set up by the use of wide-angle dies than by the use of acute dies.2 The actual stress distribution in drawn .tubing has been investigated by a few workers,7-9 but has not been related to the conditions of the drawing process: Some attempts have been made to correlate accelerated cracking tests for stresses in brass products with the magnitude of the circumferential stresses and the condition of the metal.1-10 MATERIALS AND PREPARATION The material used in this experiment was commercial cartridge-brass (70 per cent Cu, 30 per cent Zn) tubing in the straightened and annealed condition.‡ This tubing was of various outside diameters and had a wall thickness of 0.032 in. It was sunk to 1/2-in. outside diameter by means of an experimental 10,000-lb. hydraulic draw-bench, with a maximum drawing speed of 8 ft. per minute. All dies were of 1/2 -in. diameter. Various die materials and contours were used in order to study the effect of die design on residual stresses in the tubing; the specifications for the dies are given in Fig. I. Castor oil was used throughout as lubricant. Chattering occurred in sinking some of the tubing, particularly when dies having the more acute angles were used, but the tubes showing chatter marks did not differ markedly from those with a smooth surface regarding the magnitude of residual stress. The source of the chattering has not yet been revealed. The wall of the tubing becomes thicker during sinking, as previously observed 4,5 The increases in wall thickness were 3, 7 and 9.5 per cent on the average for 6, 20 and 33 per cent reductions in diameter, no effect of the contour being noticeable. The reductions mentioned throughout this investigation do not consider this fact, but are reductions of the outside diameter. For the evaluation of the residual stress two fundamentally different methods were used. The approximation method1,11 of splitting a certain length of tubing was employed to obtain a bird's-eye view of the effect of various drawing conditions on the circumferential stress measured by the diameter change occurring on splitting. For the determination of the complete stress

Jan 1, 1941

By William Griffith

THE purpose of this paper is to make public record of new information in regard to the sustaining power of artificial mine-roof supports (not timber props) the result of investigations recently made in the anthracite coal fields of Pennsylvania. First.-By the "Scranton Mine Cave Commission," appointed to investigate the mining conditions under the City of Scranton. Second.-By the "Pennsylvania Mine Cave Commission," appointed by the Governor to investigate the general subject of mine caves in the anthracite region of Pennsylvania. Third.-By the personal researches and tests made by the author in an effort to secure a better artificial mine-roof or surface support. During the progress of the work of the Scranton Mine Cave Commission, the Engineers for the Commission, Messrs. Conner and. Griffith, being aware of the general lack of exact information in the engineering profession as to the strength of the ordinary artificial mine-roof or surface support, and particularly the stronger kinds, such as mine cogs, rock piers, etc., had tests made at the. Fritz Engineering Laboratory at Lehigh University, to determine the sustaining power under various compressions of the several kinds of artificial mine supports in use in the anthracite region of Pennsylvania. A report of these tests was included in the report of this Commission, which was published as Bulletin No. 25 of the United States Bureau of Mines, Washington. A similar series of tests, more extensive and more elaborately-planned, were subsequently made for the Pennsylvania Mine Cave Commission at the U. S. Government Testing Laboratory at Pittsburgh, Pa. The report of this Commission was made to the Governor, but has not yet been published.

Jan 10, 1917

E.T. CONNER;. Scranton;. Pa-I had the honor of being associated with Mid. Griffith in an investigation of the Scranton mine cave problem several years ago; in the course of which we investigated rather carefully the bearing strength of various materials that might be utilized for, the support of over We found that there were no reliable data as to the resisting strength, for instance, of gob pillars or timber cogs or cribs, nor as to the amount of compression that might be expected under a given burden. We made a series of tests at the Fritz engineering laboratory of Lehigh University, from which we, reduced certain conclusions, subject, however, to further test before they could be definitely recommended. Onr study of the subject was later checked by a commission appointed by the Governor of the State of Pennsylvania, to investigate the same subject the subsidence of the surface, and the danger entailed thereby. The State, commission made a series of tests on a much more ambitious scale at Pittsburgh, in the laboratory of the U. S. Bureau of Mines, and their tests agreed quite closely with those that Mr. Griffith and I had made. As the result of our study, we determined that the most elastic support is the ordinary timber cog or crib, while the most rigid support is a

Jan 1, 1918

By H. A. Bedworth

ALLOYS of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry1 proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche3 and Corson.4 The constitution of the system has also been recently investigated by Matuyama,5 and in the laboratories of the American Brass Co. by Smith.6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of, the constitution of copper-silicon alloys, the solubility reaches its maximum value, 6.7 per cent. silicon, between 721° and 782° C. At 852° C. the solubility is 5.25 per cent., while at 400° C. it is only 4.1 percent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent. silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By T. L. Joseph

THE United States Bureau of Mines has been studying the blast-furnace process for, about ten years. An experimental furnace was developed by the bureau in cooperation with the Minnesota School of Mines Experiment Station, University of Minnesota. Many data have been obtained and published.1 Royster, Joseph and Kinney§(48) found that the particle size of ore had an important effect upon the blast-furnace, process. Kinney(28) stated: Economy in blast-furnace practice depends largely upon efficient gas-solid contact in the shaft of the furnace. If efficient work is not done in the shaft, the hearth and bosh will not function properly. A condition may be readily imagined where the particles of ore in the shaft are so large that the time entailed in the descent of these materials into the bosh is not sufficient to permit proper reduction and preparation prior to the time the ore enters the bosh of the furnace. Another condition may be pictured where the density of the stock column and the flow of stock is such that the ore will take one course and the gas another. Both of these examples will result in insufficient contact between the gas and the ore. Unreduced ore will reach the hearth, and the gas which has not been efficiently oxidized will reach the stock line. The result is the use of an excess of carbon in the smelting process. It is obvious that fine ore particles occurring in the ore as charged, or . formed in the furnace due to heat and mechanical action, place a definite limitation upon the efficiency of the operation. There is also an economic loss of fine material as dust.

Jan 1, 1930