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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 L. Zwell, H. A. Wriedt

X-ray Lattice parameter and bulk density measurements were made at room temperature on solid solutions of nitrogen in purified a, iron, containing from 0 to 0.053 wt pct N. When nitrogen is dissolved in a, iron, the fractional increase in unit cell volume (X-ray diffraction) and the fractional increase in volume per gram of iron (bulk density measurement) are the same within experimental error. The two sets of results when averaged show that the unit cell edge of a, iron increases linearly by 3.2 X 10-2 A per wt pct N dissolved and that the partial gram-atomic volume of nitrogen at infinite dilution in a, iron is the same as it is in nitrogen-martensite, that is, 5.90 cm3. RECENT reviews17' of literature dealing with the lattice parameter of ferritic iron-nitrogen alloys indicate that the dilating effect of dissolved nitrogen on the bcc unit cell of a iron is not known with confidence. Five investigations3-7 either revealed no effect of nitrogen or were inconclusive. Among other investigations, where quantitative data were obtained, the results of Osawa and Iwaizumi8 indicate too large an effect, and those of Eisenhut and Kaupp9 show the lattice parameter of ferrite varying with the nitrogen content at concentrations far beyond the known solubility limit. It is not clear in Burns'10 data what value should be used for the lattice parameter of nitrogen-free ferrite in calculating the dilation. Burdese11 shares with Burns the shortcoming that the iron-nitrogen alloys were solution-treated and quenched with undissolved nitride present. The consequence is that the un- certainties in the solubility limit1 are added to those in the lattice parameter measurements when the variation of lattice parameter with nitrogen content is computed. For a system of such widespread interest, we felt that a new investigation was merited. Both X-ray diffraction and bulk density measurements were used to determine the dilation of the , a iron lattice by dissolved nitrogen. EXPERIMENTAL PROCEDURE Material. The bulk density and X-ray diffraction experiments were both made with specimens of a purified iron (denoted as "B iron")- from Battelle Memorial Institute. The impurity contents were as follows: As, C, Cu and Pb—50 ppm; Ag, Al, Co, Ga, 0, Ti-11 to 50 ppm; B, Be, Ca, Cd, Cr, Mg, Mn, Mo, N, Ni, S, Sb, Si, Sn, V, W-10 ppm or less. The vacuum-cast ingot was hot-forged and annealed. Pieces of the forged stock were machined and cold-rolled to give strip stock 0.08 and 0.002 in. thick for density and for X-ray measurements, respectively. Preparation of Specimens. Starting with a piece of the cold-rolled iron stock, the general sequence of operations, after an initial recrystallizing anneal, was to measure the density or lattice parameter, nitrogenize, remeasure the property, age or denitrogenize, and again measure the property. Duplicate analyses for nitrogen were made by a modified Kjeldahl method on portions of the actual density specimens and on pieces nitrogenized to equilibrium alongside the X-ray specimens. Annealing of the density specimens was performed by sealing the pieces with the as-rolled surfaces removed by filing into evacuated "Vycor" capsules and treating for 1 hr at 750°C followed by furnace cooling. (TO check the effect, if any, of annealing procedure, a specimen also was

Jan 1, 1962

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By B. H. Kear

All the possible ways of forming simple two-dislocation boundaries in multiple slip orientations are deduced. It is shown that the principal differences in work hardening behavior of crystals plastically deformed in these orientations can he accounted for in terms of the likelihood of formation of diffuse boundaries, or deformation bands, consisting of the products of dislocation reactions of the Lomer type. Also, it is pointed out that the break-up of boundaries under the applied stress is more likely to yield interstitial jogs than vacancy jogs, whereas glide dislocations cutting throuqh dislocations trapped in particularly stable boundam'es can acquire both types of jogs. USING Frank's' grain boundary formula, Ball and Hirsch2 determined the parameters of all the possible boundaries that can be built from two sets of glide dislocations in the fee structure. This paper deduces the geometrical possibilities for the formation of these two-dislocation boundaries in the different multiple slip orientations, and discusses the role of boundaries in work hardening and in jog formation. Formation of Two-Dislocation Boundaries in Mutiple Slip Orientations. The parameters of the possible two-dislocation boundaries for any crystal orientation can be deduced most conveniently using the boundary formulae due to Amelinckx,3 in conjunction with the stereographic projection shown in Fig. 1. Suppose that slip occurs in a-BC and ß-CA. According to Amelinckx, when the two systems of glide dislocations are parallel, the rotation axis, u, of the boundary is parallel to (a x ß) and the unit normal, u, defining the boundary plane is parallel to (a x ß) x (BC x CA). On the other hand, when the glide dislocations form a crossed grid, u is parallel to (BC x CA) and u is parallel to (a x CA) x (ß x BC). In Fig. 1, (a x ß) is the pole of the great circle passing through a and ß, so that u is parallel to DC, i.e., parallel to [110]. Furthermore, (a x ß) x (BC x CA) is the pole of the great circle passing through DC and 6, so that u is parallel to [110]. Hence, when all the glide dislocations are parallel, the boundary is pure tilt with parameters u = [110], v = [ 110]. Similarly, it may be shown that the corresponding crossed grid of dislocations is a mixed boundary with u = [111], u = [111]. Consider the case of a crystal compressed in the [001] orientation. In this orientation, according to Fig. 1, there are eight available slip systems. In what follows, the different types of two-dislocation boundaries that are possible in this orientation will be examined by taking different combinations of two slip systems out of the available eight, with a-BC always one of the systems. Case (i)—Slip Systems a-BC and d-CB. The formation of a tilt boundary in (101), which consists of a crossed grid of edge dislocations with vectors BC andCB, is illustrated in Fig. 2(a). As the figure shows, slip is required in the system a-BC in one part of the crystal and in d-CB in the other part, with both sets of dislocations entering the boundary from opposite sides. The rotation axis of the boundary lies in (101), depending on the relative densities of the two sets of edge dislocations in the boundary. Case (ii)-Slip Systems a-BC and ß-CA. The two possible boundaries are shown in Figs. 2(b) and (c); boundary (b) is tilt with u = [110], u = [110], and

Jan 1, 1962

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By Pedro L. Lizaur

INTRODUCTION The degree of success of an association between parties in establishing a new venture ultimately depends on three factors: a. the venture's underlying economic strength, which is based on the complementarity of the comparative advantages brought by each party to the negotiating table; b. the ability to reach an agreement which satisfies each party's objectives and constraints; and, c. the capacity to design and implement a funding structure which is consistent with the project economics. A thorough assessment of the venture's profitability and associated risks under alternative technical and economic scenarios is the basis for a sound "go" or "no go" decision. In-depth evaluation of the risks and rewards to each of the parties involved under alternative legal and financial structure must be the foundation for a long lasting "how to go" decision. The allocation of risks and rewards should be consistent with the objectives and constraints of all parties and the sharing mechanisms, established in the contract, should be flexible to assure the long-term stability of the agreement. Rapidly changing economic conditions during the last decade have had a dramatic impact on the envisaged allocation of risks and rewards between host countries and private investors. The effects of these changes, and the fact that the relative strengths of the parties involved may shift during the life of a project (e.g. before and after major capital investments have been made), have forced the renegotiation of a multitude of contracts. Therefore, the present and future stability of an economic agreement would depend not only on the originally designed provisions, but also on provisions which allow for the automatic adjustment of rewards to project sponsors under a variety of future economic situations. A pre-condition for the allocation and quantification of risks and rewards is the definition of standards of measurement used by each of the parties. This is critical in international negotiations when one of the parties represents the national interests of a country. The understanding and use of different standards for the measurement of rewards for risk taken between a government and private enterprise facilitate the negotiation of a satisfactory agreement. This is possible because certain trade-offs between the negotiating parties may have different relative values. STANDARDS OF MEASUREMENT OF REWARDS FOR RISK TAKEN The negotiating process takes a step forward when the parties are able to focus on their interests, explore different alternative solutions and then base results on a set of objective standards. Unfortunately, the parties frequently put more effort into "staking out" and defending positions, than into understanding their intrinsic interests. Moreover, when one party, such as a governemnt owned corporation, represents a country's national interests, the negotiation process increases in complexity. Private firms focus on commercial profitability, using discounted cash flow techniques such as NPV, IRR, or ROE. In contrast, the government is also concerned with the project's impact on the local socio-economic environment. Without entering into a discussion of alternative economic development theories and approaches, there exist several possible measures that could be pragmatically utilized by each party in evaluating the socio-economic impact of a project. The more complete measure is the National Profitability (NP). The NP is a discounted cash flow procedure similar in structure to IRR or NPV but in which the project's financial cash inflows and outflows and discount rates are adjusted to take into consideration the local conditions. The NP is calculated on an unlevered basis and all taxes and duties are removed from the project

Jan 1, 1985

By R. B. Basham, C. W. Macune

Very small anomalies in oil well temperatures are detected and measured by recording the difference in temperature existing between two thermally sensitive elements which are Spaced several feet apart on a small diameter carrier and lowered into the bore hole. The elements operate in a balanced electrical circuit, sending only a reference signal to the surface as long as normal gradient temperatures are encountered. When either element enters a temperature disturbance, the circuit is unbalanced and produces large recorder deflections for minute anomalies. The system is highly sensitive to small changes in thermal gradients caused by gas or fluid movements and to the boundaries between beds of different thermal conductivities. Typical logs show successful applications of the process to locating gas and water leaks in casing, gas entry. and gas-oil contact. INTRODUCTION Temperature measurements in oil wells have been made for many years in the search for additional sub-surface data. It has been generally agreed that many conditions in the bore hole cause temperature anomalies which, if located and measured, could yield useful information. But it has been recognized also that many of the irregularities, such as those produced by small water and gas leaks in casing, might be very small and therefore difficult to detect with certainty.' Although tem-perature measurements have been made which show anomalies of less than one degree deviation from normal gradient temperatures, the results are usually uncertain and unconvincing. The general practice, therefore. has been to apply temperature surveys only to well conditions known to produce appreciable disturbances, such as large gas movements and cement hydration. The recent demand for additional data has focused attention on the problem of making dependable temperature measurements in the many instances when anomalies are small but none the less significant. It was for the purpose of detecting these minute irregularities in bore hole temperature that the program described in the following text was undertaken. It is emphasized that this presentation is not offered as a complete study, for the process is still partially experimental. But it is believed that the results obtained thus far will be of interest to the industry and will indicate some of the system's potential usefulness. DIFFERENTIAL MEASUREMENT The chief value of differential measurement lies in the fact that a difference between two factors can be measured with a scale of values best suited to that difference, a scale that might be cumbersome or impractical if applied to the factors themselves. When it is known that all factors will be nearly equal in value, and therefore the differences consistently small, it is possible to select a scale which will permit very accurate measurement of the differences. This advantage is in contrast to the difficulty of measuring small increments of a single variable, where the increment must be measured by a large scale which is suitable for measuring the entire factor. Gradient temperatures are usually measured under this latter condition where temperature measuring apparatus must have a scale extending over the range of expected temperatures, say 50' to 25O°F, and it becomes almost impossible to detect small irregularities of less than one degree. The use of large strip chart recorders and divided multiple ranges tend to amplify the small anomaly and make it more pronounced. But the instability of instruments, both

Jan 1, 1952

By C. S. Barrett

The torsional after-effect in polycrystalline cadmium is interrupted by an abnormal twisting when the film is removed by etching. This is accounted for by the pile-up of dislocations beneath anodic or other oxide films during the original twisting, and the relief of the residual stresses from these by elastic and plastic processes during etching. WHEN an iron or zinc wire coated with oxide is plastically twisted and then released, it untwists according to a law of equal increments in equal intervals of log time, but if the oxide is suddenly removed by etching this normal after-effect is interrupted by a transient, and thereafter the untwisting is slower.' Etching may even reverse the strain temporarily. Related effects caused by hydrated oxide films on cadmium in creep tests have been observed by Phillips and Thompson:' definite transient strains caused by the removal of the film from single crystals of cadmium were observed; however, negligible effects were obtained with polycrystalline wires. Pronounced effects of both transient and steady nature were observed by Phillips and Thompson when anodic films 10-4 cm thick were etched off, and weak effects, transient only, occurred with hydrated oxide films 3x10 cm thick such as were formed by standing in water for 10 min. It was estimated that 10.' cm films, formed in water in 1 or 2 min, could be detected in the apparatus of Phillips and Thompson. Since abnormal after-effects were observed by the torsion method equally well with polycrystalline and monocrystalline iron and zinc wires,' it was anticipated that the torsion method would also disclose them in polycrystalline cadmium, in spite of the fact that analogous effects had not been observed in tensile creep tests on polycrystalline zinc by Pickus and Parker3 r on polycrystalline cadmium in tensile studies by Andrade and Randall." Because of its high sensitivity, particularly its sensitivity to surface conditions, the torsion method was thought to merit further study as a method of investigating thin films of various types and the action of various reagents on these films. Materials and Methods Cadmium wires were cold-drawn to a diameter of 0.039 in. from a stock that was determined spectro-scopically to contain 0.05 pct Bi, 0.005 pct Cu, 0.008 pct Pb, and 0.007 pct Si. The wires were cut to about 17/8 in. lengths and were annealed 1 hr in air at 290°C, after which the grain size was such that there were 5 to 7 grains across a diameter. The wires were then mounted as indicated in the insert in Fig. 1, one end being fastened with laboratory wax into a small diameter brass tube and the other end being waxed to a thin glass fiber which supported, on its upper end, a small galvanometer mirror. The wires were waxed with care to avoid straining or annealing, for it was found that the after-effect rate was sensitive to prior cold work in a wire. The assembly was then clamped above a beaker into which the reagent could be poured. The lower end of the wire was held in the hand while the wire was twisted 180"; it was then released immediately. Since precision timing of these manipulations was not attempted, the different wires cannot be compared as to exact rates of untwisting. The length subjected to plastic strain was 15/8 in. The surface coatings studied were those produced by the annealing in air, by anodic treatment of

Jan 1, 1954

By A. M. Gaudin, D. W. Fuerstenau

IN concentration of certain ores by soap flotation, prevention of quartz flotation is desired; the contrary is true in treatment of some oxide iron ores. Experimental study of the flotation of quartz goes back at least a quarter of a century.' Clean quartz does not float with fatty acids or soaps but does float when activated by one of many metallic salts. Control of pH is important. Broadly speaking the problem of quartz flotation has been approached from the empirical side, as was the related topic of flocculation or dispersion of quartz suspensions? Empirical studies indicated the existence of critical relationships between the additions of collector and activator. These additions were not stoichiometric for the formation of soaps of the activator cation. For example, Gaudin and Rizo-Patrona found optimum quartz flotation at pH 10.6 using barium activation and oleate collection when the molar ratio of oleate to barium was 1 to 1 instead of 2 to 1, as would be called for formation of Ba(OL),. Cooke and Digre" ' found that if calcium is the activator, a minimum quantity of that agent is required for effective flotation when the pH is 11.5. In other words, if the concentration of Na' exceeds 10 -2.5 mols per liter or if the concentration of H exceeds 10-11 mols per liter, the concentration of Ca++ in solution required for quartz activation is increased. This suggests that H+ is much more effective than Na+ on 10-2.5 quartz, perhaps in the ratio ofp or 108. Schuh- mann and Prakash6 studied anew the activation of quartz by barium, calcium, aluminum, and ferric iron. Salts of these metals are activators provided they are in stoichiometric excess over the collector used with them. Alkaline-earth salts are effective only in alkaline circuits. Important as they are in giving data on the effect of various agents on quartz, all these studies fail to give information on the detailed structure of the quartz-solution interface. A beginning in this direction was made by Gaudin and Chang,? who measured the adsorption of radioactively marked barium and laurate ions at quartz surfaces, and by Gaudin. Spedden, and Laxen,8 ho measured the adsorption of radioactively marked sodium at quartz surfaces. Work has also been done by Bell0 n measurement of the adsorption of sodium ion and chloride ion at quartz-solution interfaces. In all these experimental measurements of adsorption, the solid was centrifuged or filtered from the bulk of the liquor with which it had been associated; and the composition of the solid surface was ascertained by analysis, after allowance was made for the ionic composition of the liquor included with the centrifuged solids on the assumption that it is identical to the bulk liquid. Adsorption measurements give only the total amount of collector adsorbed at the quartz-solution interface; they give no indication of the distribution of these adsorbed ions at the interfacial layer. It is the ionic structure of the solid-solution interface and its importance to flotation that is the subject of this paper. The structure of this interfacial layer can be investigated by means of electrokinetic methods so that by combining electrokinetic studies with adsorption measurements, a more complete picture of the quartz surface may be obtained. The following studies were made to ascertain how electrolytes used in the soap flotation

Jan 1, 1956

By I. Fatt

The chromalographic effect refers to the separation of constituents in a moving fluid phase which occurs when the phase is passed over a stationary phase, either solid or liquid, or large areal extent. In performing chemical analyses, the large surface contact areal is provided in the case of gas-solid chromatography by-passing the gas over a porous solid and for gas-liquid chronla tog rap hy by-passing the gas over a porous solid which has been coated with a nonvolatile liquid. The porous medium is usually placed in a cylindrical tube, although it may be a relatively flat sheet as in paper chroma-tography. According to one theory,' the separation results from the difference in time spent by various components in the stationary phahe. A gaseous component which is conlpletely insoluble in the stationary phase, or is not adsorbed on the solid, proceeds unimpeded through the column. The versatility and power of the various types of chromatogruphy for the analysis of complex mixtures are evident from their widespread use in performing chemical analyses and from the large number of symposia, books, and papers devoted to the subject in recent years. Associated developments are the application of chromatography to the determination of heats of solution, heats of adsorption, solubilities orK-values, etc. Gas-liquicl chromatography analyses may be characterized by the manner in which the samples are introduced and displaced from the column'. The three techniques used are known as (1) frontal analysis, (3) displacement analysis, and (3) elution analysis. The frontal analysis is performed by displacing an inert gas from the column by a continuous stream of the sample. As indicated in Fig. l(A), all but the first fraction leaving the column represent mixtures rather than pure components. The displacement analysis is conducted by filling the column with a sample, then displacing it with a more strongly adsorbed or absorbed vapor. The resulting chro-matogram is illustrated by Fig. 1(B). Finally, in the elution analysis a small sample of the mixture to be analyzed is introduced as a "plug" into a Rowing stream of carrier gas to give an elution-type chromato-gram. Fig. l(C). The three techniques may be used to provide models to which Row patterns in other physical situations may be compared. PURPOSE OF THE INVESTIGATION The purpose of this investigation was to determine whether natural reservoir rocks, when coated with crude oil, provided sufficient surface areas to give rise to a chromato-graphic separation of light hydrocarbon constituents. The tests were conducted with the light hydrocar-bons in the gaseous state. SANDS TESTED Two sands of widely different permeabilities have been studied: (1) Ventura core (16 md), and (2) Torpedo sandstone core (578 md).Table 1 gives a description of the cores that were tested. With the exception of one frontal-type flow arrangement which was performed on Core 3, the tests were of theelution-type in which a methane-propane mixture was eluted through the core by means of helium. The Ventura core, when impregnated with a weathered crude from the same field, became so impermeable to gas flow that it was necessary to conduct the tests on the granulated cores (Cores 2 and 3).

By Glenn C. Waterman

Richard Strong (Oliver Iron Mining Div., U. S. Steel Corp.)—Mr. Waterman states (p. 59, Trans., January 1954): "Core-sludge combining factors have been calculaied for any combination of core-sludge recovery on the basis of several logical assumptions: 1—The sludge sample loses reliability geometrically as sludge recovery drops. 2—The sludge sample should not be used if the percentage of sludge return is less than the percentage of core recovered. 3—A core sample should receive a weighting at least equal to the percentage of core recovery." Assumptions 1 and 2 seem justified at Chuquicamata and most geologists would agree to the validity of assumption 3. However, contrary to the statement quoted above, the core sample does not in general receive a weighting at least equal to the percentage of core recovery when the Chuquicamata methgd is used. Furthermore, the basic Chuquicamata method is identical to the Longyear or relative volume core-sludge assay combining method. Finally, the Chuquicamata method does not, in its present form, reflect true geometric loss in sludge sample reliability according to the relationship L = AR (N-1) The basic equations representing the two steps of the Chuquicamata method can be combined algebraically as follows (using the symbology of the original article except as noted): Vol A + B Assay 2 = ASA = Assay 1 Vol A VolB Core Assay [I] Vol A CA.F + ASA (100 —F) Combined grade =[21 100 Pct where F and (100 — F) are the core and adjusted sludge assay factors from Fig. 3. Substituting Eqs. 1 and 2 and collecting terms Combined grade = Vol B Vol A + B CAF (100—-F) + Assay 1 (100-F) Vol A Vol A 100 pct Eq. 3 is a unified and general statement of the Chuquicamata method. The true core factor includes not only the factor F from Fig. 3 but also the quantity VolB ------------- (100 — F), which is implicit in the value of Vol A the adjusted sludge assay. This quantity is real and positive for all values of F and core recovery less than 100. Therefore the true core factor is always less than F except when F is equal to 100. If sludge recovery is 100 pct, Eq. 3 can be further simplified as follows: Let F = percentage of core recovered. Let Vol A = Vdh (100 Pct — Pct CR) where Vdh is the total volume of the sampled interval and let Vol B = (Vdh — Vc.) Pct CR where V, is the core volume in the sampled interval at 100 pct core recovery. Then combined grade = Vo V. CA Pct CR- + Assay 1, 100 Pct — Pct CR Vdh Vdh [4] 100 Pct Eq. 4 shows that when sludge recovery is 100 pct the laboratory sludge assay receives significant weight in the Chuquicamata method, even at 100 pct core recovery. The maximum weight assigned to the laboratory sludge assay depends on drillhole size, as follows: Eq. 4, with suitable changes in symbology, is identical to Royce's formula 8,' which is a statement of the Longyear or relative volume method of combining core and sludge assays. If Mr. Waterman's assumption 3 is of paramount concern to the geologist, the Royce method (for core recoveries of 60 pct and above) or a method employing the percentage of core recovered as a core weighting factor are the only recognized methods known to the writer which achieve the desired result. A modification of the latter method embodying Mr. Waterman's assumptions 1 and 2 would result from applying the factors from Fig. 3 directly to the laboratory core and sludge assays.

Jan 1, 1956

By M. Semchyshen, G. A. Timmons

The predominant orientation in both straight-rolled and cross-rolled molybdenum is the {100} [110] texture. Upon complete recrystallization, this same texture predominates, but there is less spread about the ideal orientation. A secondary orientation about the [111] direction as the axis develops in cross-rolled sheet. Compression-rolled sheet exhibits random orientation in the plane of the sheet. Some mechanical properties were measured at varying angles to the rolling direction to determine the effect of preferred orientation on anisotropy in molybdenum sheet which had been straight, cross, or compression rolled. THE development of the arc-cast process has made available large ingots of molybdenum from which it is possible to roll sheet of considerable size. It is anticipated that such sheet will be further fabricated by spinning, drawing, stamping, or forming. Anisotropy of physical properties caused by the preferred orientation developed in the sheet during rolling may be expected to affect the behavior of the metal when subjected to these fabricating operations. To produce a sheet which will be most amenable to the fabrication of a given shape by a particular operation, consideration should be given to the directions and magnitudes of plastic deformations produced in the operation. When possible, the rolling schedule should be controlled to develop a texture which favors the required deformation. The existence of preferred orientations in rolled molybdenum sheet has been reported by Jeffries,' Konobejewsky,' Fujiwara," Goss,' and Ransley and Rooksby." None of these investigators obtained sufficient X-ray data to permit the construction of pole figures; instead, they based their conclusions upon Debye-Scherrer patterns of a limited number of positions. Ransley and Rooksby devoted some attention to transcrystalline cleavage at 45" to the rolling direction, indicating that it is appreciable in polycrystalline material only when the crystals are in the ideally preferred condition, and that this condition is only approached if the metal has been rolled successively in two perpendicular directions. In a recent paper, Custers and Riemersmao introduced the first pole figures to describe the textures of straight-rolled and cross-rolled molybdenum sheet. To increase the knowledge concerning the generation and effects of preferred orientations in molybdenum sheet, an investigation was undertaken to determine the effects of variations in rolling schedule and annealing treatments on preferred orientation, and to correlate preferred orientations with some mechanical properties. The orientations of straight-rolled, cross-rolled, and compression-rolled sheet have been determined by X-ray analysis, both as-rolled and after recrystallization. Pole figures have been constructed to describe the textures produced by these various rolling procedures. Texture of Cast Molybdenum Ingots In the arc-cast process, molybdenum powder is pressed into a vertical column which is sintered to increase its strength as it proceeds downward into a water-cooled mold, where the metal is melted in an alternating-current arc established between the end of the formed powder electrode and the metal bath at the top of the growing ingot. Since the solid-liquid interface moves continuously upward in the mold, the crystal axes are not normal to the cold surface of the mold but have the curvature shown in Fig. la. X-ray analysis reveals that the cube axis is the fiber axis and that it is normal to the cold surface of the mold; that is, the [loo] direction is parallel to the longitudinal axis of the ingot. This substantiates recent work by

Jan 1, 1953

By E. W. Cawthorne, R. I. Jaffee, C. M. Craighead

SOLUTION of a solid metal or alloy in a molten metal bath is used daily in melting operations, extractive metallurgical processes, and in brazing. It is generally recognized that temperature, time, agitation, and the composition of the solute metal and the solvent bath all affect solution rate. However, there is little information available in the literature on the kinetics of the process or the relative effect that these variables have on solution rate. In connection with an aluminum brazing study, data on the solution of aluminum in an A1-Si* bath to promote rapid solidification. The chemical analyses were made on drillings taken from the cast plates. The results of this work are listed in Table I. The thermal-analysis data were obtained on 200 gram samples cooled at approximately 1.5" per min. A calibrated chromel-alumel couple was used. The thermal arrests were recorded autographically on a General Electric photoelectric potentiometer recorder. The instrument was calibrated to 22.5 pct. The thermal emf was bucked with a Leeds and Northrup semiprecision potentiometer so that 1 mv represented the full scale of the GE recorder. Referring to Table I, it will be noted that the analytical results tend to be lower than the intended compositions by about 0.3 pct Si in the higher ranges. In view of the known difficulties in obtaining accurate silicon determinations by wet analysis when the silicon content is high and in view of the care that was employed in weighing and preparing the alloys, the intended compositions are believed to be more accurate than the analyses. Furthermore, when the thermal-arrest data are plotted against the intended compositions, a smooth curve is obtained, as shown in Fig. 1. This is not the case when the data are plotted against the analytical results. It will be noted from Table I that the 12.5 pct Si alloy (melt 4) showed a primary arrest at 577.6"C and the eutectic at 576.l°C. The metallographic examination of this chill-cast plate sample showed a small amount of primary silicon. These results, Fig. 1, place the eutectic at slightly less than 12.5 pct Si and are in rather good agreement with the unpublished Hanford data. In all of the subsequent work, the composition of the A1-Si dipping baths was determined by thermal analysis (spread between the primary arrest and the eutectic temperature) employing 12.5 pct Si and 577.2 °C as the composition and temperature of the eutectic. Material Preparation and Selection of the Techniques: At the beginning of this work, it was anticipated that, owing to oxide film present on the surface of the aluminum, difficulty would be encountered in obtaining rapid uniform wetting of aluminum specimens dipped in the A1-Si bath. The following etchants were investigated as possible methods of providing a thin uniform oxide film on the specimen surface: 1—phosphoric acid (H³O4), 2—fluoboric acid (HBFI), 3—sodium hydroxide (NaOH), and 4—hydrofluoric acid (HF). Tests with sheet .specimens (2x½x0.06 in.) of 2s aluminum prepared with these etchants indicated that the fast uniform wetting required for this work could not be obtained if any oxide film existed on the specimen surface. Tests were then conducted by dipping similar specimens etched in 5 pct NaOH and given a thin

Jan 1, 1956

By D. O. Wyble

Five water-driver fields, for which pressure predictions had been made within a few years after discovery, were re-studied when four to five years of additional pressure and production data became available. It was fortnd that forecasts of the pressure in water-dri~fe reservoirs may be subject to considerable unccrtainty. Predictions car be erroneous when there is insufficient presswe history to define the cllaracteristics of the aquifer, and when there are errors in the pressure, production or geologic data. INTRODUCTION The efficient operation of an oil or gas reservoir requires that the important characteristics of the reservoir be determined soon after its discovery. It is especially desirable to evaluate the pressure-production relationship quickly, for this relationship provides a basis for deducing the type of production mechanism that is operative, and for making pressure predictions. The pressure predictions, in turn, provide a basis for calculating efficient rates of production, determining whether water or gas should be injected, etc. The importance of pressure prediction is such that forecasts should be made as accurate as possible, and the limits of error well defined. Historically, pressure forecasts for some fields have proved very accurate, while for others the forecasts were so erroneous that they resulted in the adoption of wrong, or at best, unnecessary production practices. Pressure predictions made for water-drive fields are especially subject to error. Accurate forecasting for these fields requires that much be known not only about the reservoir proper but about the adjacent water-filled rock as well. The water-containing rock, or aquifer, may extend for many miles, and often there is only meager data regarding its thickness, permeability and porosity. Much of the information must be inferred from the previous pressure behavior of the reservoir. A brief pressure history may provide little information about the characteristics of the aquifer. Hence, pressure predictions made early in the life of water-drive fields can be incorrect. The work described in this paper was done to determine the degree of reliability which can be expected of pressure predictions made within a few years after water-drive fields are discovered. Five fields, for which the original pressure predictions had been based on less than seven years' history, were re-examined with the aid of four to five years of additional pressure data. Where the predictions were inaccurate, the reasons for failure were ascertained. The studies were accomplished by use of the electric reservoir analyzer.' The analyzer was first adjusted to repeat the original pressure-production match using the same values for the various parameters as were used in the original study. Then, the actual production rates experienced during the time elapsed since the initial study were set into the analyzer, and the pressure behavior indicated by the machine for this period was compared with that which actually OCcurred. Where the pressure profile traced out by the analyzer deviated from the observed field behavior, the analyzer was readjusted to obtain a better over-all match. The old and the new solutions were compared to determine the reasons for any differences. COMPARISON OF PREDICTED RESERVOIR PRESSURE BEHAVIOR WITH ACTUAL PERFORMANCE Field A The original pressure-production match is entirely adequate as evidenced by the pressure match of the field's history subsequent to Jan., 1952 (see Fig. 1)'.

By L. L. Gray, D. W. Reed, F. Morgan

A flowMeter has been developed at Gulf Research and Development Co. and tested in the field for measuring the flow of gas in well bores. It has been used in a study of the injection capacity of different horizons in gas injection wells in Oklahoma. The flow sensitive element of the meter is a semi-conductor having a very high temperature coefficient of resistance. Advantages possessed by this meter are the result of that property and the high specific resistance of the element. The instrument possesses a sensitivity considerably higher than any reported previously. In the application described here the element is heated to a temperature considerably above ambient by an electric current, which is supplied by a voltage source at the surface. When fluid flows through the meter the rate of dissipation of heat is increased and the temperature of the element decreases. Because of the negative temperature characteristics of the resistance element such a decrease of temperature will be accompanied by an increase of resistance which, under flow conditions ordinarily found in wells, is of such a magnitude that it can be directly measured or recorded in terms of a change in voltage at the surface. In practice, rate of flow is measured in terms of the drop in voltage in the resistance element. All the metering and control apparatus remains at the surface while the thermal element is lowered into the well on a single conductor cable, consisting of an insulated wire and sheath. The meter is calibrated by passing known quantities of gas through it either at the surface or in the hole at a point immediately above the region in which gas is lost to the formation. In case calibration is made at the surface, the ambient temperature in the hole may readily be obtained by a second resistance element which is operated at a current so low that effectively no heating occurs. The instrument has been adapted to con-tinuous recording, but the velocity of the meter relative to that of the gas must be low unless corrections are made. Curves giving data obtained in actual field tests are shown' The meter can also be used to determine the distribution of flow capacity in a gas producing well. A differential form of the meter has been designed and built in which the local flow or injection capacity of the formation is obtained directly. Introduction When fluid is injected into a well in a secondary recovery or pressure-maintenance operation the question of its most effective use invariably arises. Although the core log, when available, will show the regions of good permeability and oil saturation, there is normally no assurance that the fluid actually enters the formation in zones where injection is deemed desirable. In view of the uncertainties involved in such programs, it is generally conceded that measurements of permeability for a formation in place are more significant than those obtained by the core-sampling technique. A subsurface meter has been developed at the Gulf Research and Development Co. for measuring flow of fluids at different horizons in a well bore, and field tests have been made on the instrument in Cooperation with the Tulsa Division of the Gulf Oil Corp. In this paper the meter is de-

Jan 1, 1948

By F. Morgan, L. L. Gray, D. W. Reed

A flowMeter has been developed at Gulf Research and Development Co. and tested in the field for measuring the flow of gas in well bores. It has been used in a study of the injection capacity of different horizons in gas injection wells in Oklahoma. The flow sensitive element of the meter is a semi-conductor having a very high temperature coefficient of resistance. Advantages possessed by this meter are the result of that property and the high specific resistance of the element. The instrument possesses a sensitivity considerably higher than any reported previously. In the application described here the element is heated to a temperature considerably above ambient by an electric current, which is supplied by a voltage source at the surface. When fluid flows through the meter the rate of dissipation of heat is increased and the temperature of the element decreases. Because of the negative temperature characteristics of the resistance element such a decrease of temperature will be accompanied by an increase of resistance which, under flow conditions ordinarily found in wells, is of such a magnitude that it can be directly measured or recorded in terms of a change in voltage at the surface. In practice, rate of flow is measured in terms of the drop in voltage in the resistance element. All the metering and control apparatus remains at the surface while the thermal element is lowered into the well on a single conductor cable, consisting of an insulated wire and sheath. The meter is calibrated by passing known quantities of gas through it either at the surface or in the hole at a point immediately above the region in which gas is lost to the formation. In case calibration is made at the surface, the ambient temperature in the hole may readily be obtained by a second resistance element which is operated at a current so low that effectively no heating occurs. The instrument has been adapted to con-tinuous recording, but the velocity of the meter relative to that of the gas must be low unless corrections are made. Curves giving data obtained in actual field tests are shown' The meter can also be used to determine the distribution of flow capacity in a gas producing well. A differential form of the meter has been designed and built in which the local flow or injection capacity of the formation is obtained directly. Introduction When fluid is injected into a well in a secondary recovery or pressure-maintenance operation the question of its most effective use invariably arises. Although the core log, when available, will show the regions of good permeability and oil saturation, there is normally no assurance that the fluid actually enters the formation in zones where injection is deemed desirable. In view of the uncertainties involved in such programs, it is generally conceded that measurements of permeability for a formation in place are more significant than those obtained by the core-sampling technique. A subsurface meter has been developed at the Gulf Research and Development Co. for measuring flow of fluids at different horizons in a well bore, and field tests have been made on the instrument in Cooperation with the Tulsa Division of the Gulf Oil Corp. In this paper the meter is de-

Jan 1, 1948

By J. G. Kura, P. D. Frost, L. W. Eastwood

THE preparation and general properties of mag-nesium-lithium base alloys have been described in earlier papers.l,2 Lithium forms solid solutions with pure magnesium, lowers its density, and improves its formability. The improved isotropy and better formability of these alloys are attributed to the ability of lithium to convert the magnesium lattice from hexagonal (alpha phase) to body-centered-cubic (beta phase) structure. This change in structure is, however, accompanied by some limitations which make it difficult, if not impossible, to combine all the desirable properties in one composition. The most important of these limitations is the tendency of the high-strength alloys to overage and lose strength at temperatures of the order of 150" to 200°F. A study was made of the effects of composition and heat treatment on the age-hardening character- istics of the alloys. Stability of properties was determined by hardness and tensile testing of the alloys at room temperature after various periods of exposure to elevated temperatures. Precipitation-hardening curves are shown for a number of magnesium-lithium-zinc alloys in fig. 1. All the alloys were solution treated at 700°F and aged at 200°F. The reason for using the drastic quench, toluene at —105°F, was to reduce the rapid precipitation of the hardening phase which takes place at room temperature. Previous experience has shown that a hardness of about 90 to 95 Rockwell E is indicative of yield strengths in the range of 35,000 to 40,000 psi. This is a desirable strength level for magnesium-lithium base alloys with specific gravities of the order of 1.65 or less. Although the hardness level is raised by large zinc contents, a corresponding decrease in the cold formability of these alloys occurs with increasing zinc content. Thus, alloys containing up to about 10 pct Zn and having hardnesses of the order of 70 to 75 Rockwell E may be bent over a very small radius; however, the 16 pct Zn alloy requires a bend radius of more than 8T. The hardness relationships illustrated in fig. 1 can be explained by the partial phase diagram shown in fig. 2. The zinc-free magnesium-lithium alloys are entirely body-centered cubic (100 pct beta phase) when the lithium content of the binary is 10.3 pct or higher. When zinc is added, the boundary between the beta and alpha-plus-beta fields at 700°F is shifted to lower lithium contents. In addition, the solubility of zinc at 700°F decreases with decreasing lithium content. It is shown by a study of micro-structures that the limit of solid solubility of zinc in the 6Mg/Li* matrix at 700°F is about 19 pct. It is believed from a study of the aging curves that this limit is about 2 to 3 pct at 200°F. Zinc additions up to about 2 pct increase the hardness and strength of the magnesium-lithium base solid solution. Larger additions of zinc effect further hardness increases, but precipitate during prolonged aging at 200°F. Alloys having 14 to 20 pct Zn precipitation harden extremely rapidly during quenching, even when quenched in toluene at —105° F. The high-zinc alloys overage at 200°F but are capable of maintaining reasonably high hardnesses for periods up to 1000 hr.

Jan 1, 1951

By John Johnston

WHEN I was honored by being invited to give the Howe Memorial Lecture, I decided to read Howe's book, "The Metallography of Steel and Cast Iron," published in 1916-that is, about 25 years ago-in search of a text. I found the book written in fine, clear, attractive, yet precise style, as I expected, knowing that his father ¬Dr. Samuel Gridley Howe, his mother-Julia Ward Howe, and all of his four brothers and sisters had lived in a New England literary atmosphere and had written books. This leads me to suggest that many authors of metallurgical papers and books could well study Howe's writings with a view to the improvement of their own. I failed to find a specific text, but did find a subject, for in reading his book I was struck by the few instances in which time is considered explicitly as a factor in the phenomena examined, and by the fact that many of the hottest arguments would have been settled had time been taken properly into account. Indeed, Howe hardly mentions time except in a rather incidental way, as in a few references to lag; for instance: The lowering of temperature at which the transformation occurs by rapid cooling . . . is a phenomenon of undercooling or lag. It is in part explained by the fact that the transformation itself is a time-consuming reaction which, setting in during a rapid fall of temperature. is naturally protracted till the temperature has sunk far below that at which it is due. He does discuss, quite fully, the iron-carbon equilibrium diagram, as known at that time, introducing it by stating: As he is a reasonable man who is not deterred from using a hand truck for moving his trunk by the consideration that he has thus to move a trunk plus a truck, so am I reasonable in putting into your hands this useful, indeed indispensable, tool for mastering the ABC of iron metallurgy. Somewhat later, in introducing a discussion of the phase rule, which "it would be hardly proper to pass . . . by without an attempt to outline its meaning," for "a clear exposition of its applicability or jurisdiction is needed to restrain the half-initiated from misusing it and the uninitiated from being misled by these misuses," he writes-and I quote his statement because we cannot properly discuss the influence of time on a process until we know the state of equilibrium which would ultimately be reached by the system under consideration It is a most remarkable and valuable generalization, its conceptions help greatly toward getting a broad outlook on metallography, but its misconception has brought out a flood of obscuring writings. It tells us about the constitution towards which alloys tend, that which they reach when equilibrium is complete, when all tendencies have corrected themselves and have been complied with completely. Its application, in absence of true equilibrium, is like determining density with a telescope or even with a tuning fork; it is like the mad tea party at which the butter put into the works "f the watch was the best butter. If the reader learns no more than to beware of attempts to decipher the conditions of inequilibrium by a law which touches only the conditions of exact

Jan 1, 1942

By John Johnston

When I was honored by being invited to give the Howe Memorial Lecture, I decided to read Howe's book, "The Metallography of Steel and Cast Iron," published in I9I6—that is, about 25 years ago—in search of a text. I found the book written in fine, clear, attractive, yet precise style, as I expected, knowing that his father— Dr. Samuel Gridley Howe, his mother— Julia Ward Howe, and all of his four brothers and sisters had lived in a New England literary atmosphere and had written books. This leads me to suggest that many authors of metallurgical papers and books could well study Howe's writings with a view to the improvement of their own. I failed to find a specific text, but did find a subject, for in reading his book I was struck by the few instances in which time is considered explicitly as a factor in the phenomena examined, and by the fact that many of the hottest arguments would have been settled had time been taken properly into account. Indeed, Howe hardly mentions time except in a rather incidental way, as in a few references to lag; for instance: The lowering of temperature at which the transformation occurs by rapid cooling . . . is a phenomenon of undercooling or lag. It is in part explained by the fact that the transformation itself is a time-consuming reaction which, setting in during a rapid fall of temperature, is naturally protracted till the temperature has sunk far below that at which it is due. He does discuss, quite fully, the iron-clrbon equilibrium diagram, as known at that time, introducing it by stating: As he is a reasonable man who is not deterred from using a hand truck for moving his trunk by the consideration that he has thus to move a trunk plus a truck, so am I reasonable in putting into your hands this useful, indeed indispensable. tool for mastering the ABC of iron metallurgy. Somewhat later, in introducing a discussion of the phase rule, which "it would be hardly proper to pass ... by without an attempt to outline its meaning," for "a clear exposition of its applicability or jurisdiction is needed to restrain the half-initiated from misusing it and the uninitiated from being misled by these misuses," he writes—and I quote his statement because we cannot properly discuss the influence of time on a process until we know the state of equilibrium which would ultimately be reached by the system under consideration: It is a most remarkable and valuable generalization, its conceptions help greatly toward getting a broad outlook on metallography, but its misconception has brought out a flood of obscuring writings. it tells us about the constitution towards which alloys tend, that which they reach when equilibrium is complete, when all tendencies have corrected themselves and have been complied with completely. Its application, in absence of true equilibrium, is like determining density with a telescope or even with a tuning fork; it is like the mad tea party at which the butter put into the works of the watch was the best butter. If the reader learns no more than to beware of attempts to dccipher the conditions of inequilibrium by a law which touches only the conditions of exact

Jan 1, 1942

By C. C. Miller, C. A. Hutchinson, A. B. Dyes

This paper presents a simple and practical method for the estimation of effective permeability and reservoir pressures from the rise in bottom hole pressure when a well is shut in. The equations on which the method is based consider a stabilized well producing from a uniform formation when flow is shut off at the sand face followed by the unsteady state flow of a compressible liquid from regions far from a well to points closer in during the build-up period. An approximation for extending the method for two-phase flow in the reservoir is also presented. In order to compare the effects of extremes in the conditions existing at the external boundary of the reservoir, two general equations defining the build-up characteristics of the reservoir are shown: first, for a reservoir with constant pressure maintained at the radius of drainage, and second, for a reservoir with no influx over the radius of drainage. These equations define the build-up characteristics for the shut-in well as functions of time, the permeability and porosity of the drainage area, the viscosity and compressibility of the fluid flowing, the production rate prior to shut-in, and the radius of drainage of the well. When a well is shut in at the surface, rather than at the sand face, flow will continue into the well bore after shut-in due to the compressibility of the fluids in the bore. The effect upon the build-up characteristics of this flow into the well after shut-in has been studied by means of the electrical analyzer. From the basic relationships and consideration of the limitations due to continued flow after shut-in, methods have been developed for the estimation of the effective permeability of an area from the plot of the build-up characteristics of the well producing that area. Likewise, equations are presented for the estimation of the reservoir pressure from an early portion of the build-up curve. By means of the electrical analyzer, studies have been made concerning the variations in the build-up characteristics resulting from damaged or improved permeability in the immediate vicinity of the well bore. These studies show that the permeability estimated from the build-up curves represents the average effective permeability of the majority of the drainage area and that the permeability in the immediate vicinity of the well does not affect this estimate. Since the major portion of the drawdown is in the immediate vicinity of the well, variations in the permeability of this area greatly affect the productivity of the well as expressed by the productivity index. From pressure build-up and productivity index tests the ratio of the permeability of some arbitrarily specified area immediately surrounding the well and the effective permeability in the majority of the drainage area can be computed. This ratio is a measure of any damage to the well incurred in drilling or reworking and likewise any benefits as a result of remedial measures. In build-up tests and many other tests that are made on a producing well it is at least desirable, if not absolutely necessary, that the well be stabilized prior to testing. A method is presented here for relating the time required to stabilize a well and the reservoir and fluid properties. An equation is also presented for approximation of the length of shut-in time required to obtain sufficient build-up data for the estimation of permeability and reservoir pressure.

Jan 1, 1950