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By D. R. Conlon, E. R. Brownscombe

Errors in measurement of reservoir pressure include: (I) gauge errors, and (a) interpretation errors. Gauge errors may be reduced by: (a) reading charts with a comparator microscope, (b) use of hard metal stylus points to give clear lines, (6) insuring temperature equilibrium, and (d) making multiple tests. Check calibrations are equally as important as check well tests. A statistical analysis of such check runs shows quantitatively the advantages of a standardized "zero pressure line'' and of the use of field calibrations made at bottom-hole temperature on the same chart run in the well. Interpretation errors include: (a) fluid heads, which should be corrected to the top of the perforations on the basis of well-fluid gravity and from the top of the perforation to the datum level on the basis of reservoir-fluid gravity, and (b) gradients around the well. Conventional shut-in periods may be entirely inadequate to overcome these, necessitating a reservoir study based on build-up curve data, reservoir history, core analysis and any other available information. Interest in engineering studies of the pressure changes in oil and gas reservoirs is increasing. This type of work yields important information and doubtless will be greatly extended in the future. One of the factors limiting the work, however, is the accuracy with which the reservoir pressures can be determined; for if the inaccuracies in the pressure measurements represent an appreciable percentage of the pressure changes, the engineer is seriously handicapped, and must delay the reservoir study until the reservoir pressure has changed a relatively large amount. This delay can greatly reduce the benefits of such studies, at least from the point of view of aiding the leasing, drilling and completion programs. Thus, from the point of view of reservoir analysis, it is frequently important to obtain the most accurate pressure data possible early in the history of any field—particularly for the gas-distillate fields now being developed. This paper deals with improvements in the measurement of bottom-hole pressures that permit pressures even as high as 4000 or 5000 lb. per sq. in. to be determined with gauge errors of only+ ±I to 2 lb. per sq. in. Since pressures out in the reservoir rather than in the bottom of the hole concern the reservoir analyst, differences between bottom-hole pressures and actual reservoir pressures are also considered. In general, errors in pressure measurement may be divided into: 1. Gauge errors: a. Errors due to inaccuracies in reading the pressure charts. b. Errors due to irreproducibility of the pressure element and recording system. c. Errors caused by failure to allow the gauge to reach temperature equilibrium. 2. Internretation errors: a. Errors caused by a fluid head between the gauge position in tubing and the pressure at the datum level in the reservoir. b. Pressure gradients in the reservoir.

Jan 1, 1946

By Rollin E. Hook, Attwell M. Adair

The yield and fracture behavior of recrystallized chromiztm have been studied in order to gain an understanding of the recrystallization embrittlement-rheotropic recovery phenomenon. The duc tile-brittle tensile transition temperature of recrystallized chromium was found to vary from 225 ° to -80°C as the ratio of specimen diameter/mean planar grain size decreased. The applicability of this observation to other bcc metals is briefly discussed. Brittle fracture in recrystallized chromium was found to be initiated predominately from intercrystalline rupture nuclei. Single crystals exhibit a high degree of ductility at 23 "C. The experimental data indicate that grain boundaries play a significant part in the yield and fracture behavim. Pres training significantly reduces the transition temperature, and high temperature aging does not result in re-embrittle-ment until complete recovery or re crystallization occurs. SEVERAL theories have been used to explain the recrystallization embrittlement-rheotropic recovery phenomenon in chromium. Wain, Henderson, and ohnstone' propose a Cottrell dislocation locking mechanism due to nitrogen, and Weaver and Gross and weaver 3 propose a strain-induced precipitation mechanism involving a chromium nitride precipitate. The researches of many investigators seem to leave little doubt that brittleness in chromium is promoted by interstitial impurities. Smith and seybolt4 have shown that the ductile-brittle transition temperature is lowered as the interstitial content is reduced. weaver3 provides evidence for a 150°C reduction in the tensile transition temperature as the nitrogen content is reduced from 20 to 5 ppm. Maykuth and affee' have suggested that the amount and orientation of grain boundary impurities may be responsible for the brittle nature of recrystallized chromium. This suggestion was based on their findings that wrought iodide chromium possessing a fiberous grain structure is ductile in tension at room temperature while a recrystallized grain structure is completely brittle. Previous investigations have not studied this phenomenon sufficiently to determine its cause. Perhaps this has been largely due to previous experimental findings that brittle fracture observed in chromium has been almost entirely transgranular.' In addition McNeil and imb,' who investigated coarse-grained as-cast chromium, describe the point of initiation of fracture as cleavage, close to the (100) plane, near or at grain bound-daries, or at included particles or voids. However, Hook, Adair, and ipsitt found that fracture in coarse-grained recrystallized chromium is initiated by intergranular rupture and then propagates nearly entirely by cleavage. This result, together with their finding that room temperature ductility in bending is observed for single crystals and coarse-grained polycrystalline specimens for which the number of grains through the specimen diameter is small, suggests that grain boundaries may play an important role in the brittle behavior of chromium. The recrystallization embrittlement problem can be resolved into two questions. These are, whether the controlling mechanism is predominately one of crack initiation or crack propagation, and whether brittle fracture is initiated predominately by slip or twin induced intergranular rupture or by cleavage. The following research was designed to study the role of grain boundaries on the brittle fracture of chromium in an effort to resolve these questions. EXPERIMENTAL PROCEDURES, RESULTS, AND DISCUSSION General Procedure. All tensile specimens (except 0.04 in. diam wires) were prepared from 1/4 in. diam swaged rod fabricated from one ingot. Details of fabrication are given elewhere. The results of impurity analysis for the swaged rod and for the

Jan 1, 1963

By T. G. Lovering

Nonparametric statistical tests have practical application to many geological problems because, unlike the standard statistical tests, they do not require assumptions regarding the form of the population frequency distribution. Many of them do not even require that the variable be susceptible to numerical measurement. These tests are useful either 1) for geological data representing population distributions of unknown form, or otherwise not meeting the requirements for standard parametric tests; or 2) for sample attributes that cannot be measured but only ranked in order of relative magnitude. The application of two such tests will be illustrated. The Kolmogorov-Smimov test will be used to test for significant differences in copper distribution in samples of two rock types; the Spearman rank-correlation method will be used to determine whether there is a significant association between intensity of rock alteration and copper content of the rock. Nonparametric tests are, in general, quicker and easier to perform than the corresponding parametric tests, and they may be applied to a greater variety of data. They are not as powerful as the standard tests if used on data to which the latter are applicable, and computer programs utilizing them are not generally available. The use of standard or parametric statistical procedures for the interpretation of measured geological data is familiar to most mining engineers and explora- tion geologists. The computation of product moment correlation coefficients on sample assays for more-than one component is already standard procedure in some company operations, as is the use of Student's F test and Snedecor's F test for the comparison of means and variances of sample groups. The application of these three tests is limited by the prerequisites that the samples must be random, independent representatives of normally distributed populations and that the variables involved must be measurable. If such tests are applied to data which fall short of fulfilling these prerequisites, then the probability level attributed to the computed statistic is invalid and the conclusions based thereon may be erroneous. A number of nonparametric, or distribution free, statistical tests have been developed for use with data which are not amenable to standard parametric procedures. These tests have been widely used in the behavioral sciences such as psychology and sociology for some time, but their application to geologic problems is relatively new. Nonparametric tests may be grouped into two main categories: those which test for significant differences in a single variable by comparing either sample values with a standard value or representative values between two or more groups of samples; and those which test for significant association between pairs of variables in a single group of samples. The versatile chi square test, the Kolmogorov-Smirnov one and two sample tests, the Wilcox matched pairs signed ranks test, the median test, the Mann-Whitney U test and the Cochran Q test are examples of nonparametric tests with demonstrated or potential geological applications that belong in the first category. The contingency coefficient, Spearman rank correlation coefficient, Kendall rank correlation coefficient and the

Jan 1, 1963

By J. K. Kerver, J. S. Osoba, J. G. Richardson, P. M. Blair, J. A. Hafford

This paper presents the results of laboratory measurements of relative permeabilities to oil and gas on small core samples of reservoir rock by five methods, and describes the influences of such factors as boundary effect, hysteresis, and rate upon these measurements. The five methods used were the "Penn State," the "single core dynamic," the "gas drive," the "stationary liquid," and the "Hassler" techniques. In those methods in which the results are subject to error hecause of the boundary effect, the error may be minimized hy the use of high rates of flow. In order to avoid complexities introduced by hysteresis, it is necessary to approach each saturation unidirectionally. Observed deviations of relative permeabilities with rate can be explained as a manifestation of the boundary effect, and disappear as the boundary effect vanishes. The results indicate that all five methods yield essentially the same relative permeabilities to gas. Of the four methods applicable to the determination of relative permeability to oil, three, the Penn State, single core dynamic, and gas drive, gave relative permeabilities to oil which were in close agreement. The Hassler method gave relative permeabilities to oil which were consistently lower than the results obtained by the other methods. INTRODUCTION The relationship between the effective permeability of a reservoir rock to each of the fluids flowing through it and the corresponding fluid saturation is an important characteristic of the reservoir rock. Knowledge of this characteristic is and gas reservoirs and of the ultimate recovery to be expected extremely important in the prediction of the behavior of oil under various operating conditions. These effective permeabilities are usually expressed as the "relative permeability" to a fluid phase, defined as the ratio of the effective permeability to the permeability of the rock to a single phase at 100 per cent saturation. Relative permeability-saturation relations are not the same for all kinds of reservoir rock, but may vary from formation to formation, and within the different portions of a heterogeneous formation. In studying the performance of a specific reservoir, it is necessary, then, that the relative permeability characteristics of the individual portions of the reservoir be measured. These measurements may be made in the laboratory on small core samples from the reservoir. Various techniques have been proposed for the measurement in the laboratory of relative permeability-saturation relations. In varying degree, difficulties attend the use of all of the methods which have been proposed. It is the purpose of this paper to discuss the factors which influence the measurement of relative permeability, the difficulties encountered in several methods, and to present comparative results obtained by the use of various techniques. FACTORS WHICH INFLUENCE THE MEASUREMENT OF RELATIVE PERMEABILITY It is necessary that the relative permeability data measured in the laboratory yield the same relative permeability-saturation relationships that would govern the flow of fluids through the sample if it were to occupy its original position in the reservoir. Since the core sample upon which the laboratory measurements are made is not surrounded by similar core material as it was in the reservoir, an error in measuring the relative permeabilities may arise from the "boundary effect" which results from a discontinuity in capillary properties of the system at the effluent end of the core. Again, the rates of

Jan 1, 1951

By H. K. Work

The Bessemer process is one of the most interesting methods of making steel. At one time it was by far the most important. In recent years, however, it has steadily lost ground to the open-hearth process. The forces working against this method of stccl-making are partly economic and partly metallurgical.1 In this paper, dealing as it does with the control of the process, the metallurgical factors alone will be considered, although it is obvious that economic factors must play a part in determining the ultimate status of the Bessemer process. This discussion has been limited in another respect—it deals primarily with the acid Bessemer process in bottom-blown converters, although much of the information is applicable to basic and side-blown converters. The fact that open-hearth steel has superseded Ressemer steel to a large extent has tended to create an impression that Bessemer steel is inferior. As a matter of fact, Bessemer steel is actually superior to open-hearth for many applications.2 There are, however, definite metallurgical limitations to the use of Bessemer steel, resulting largely from two factors: (1) the physical properties conferred by nitrogen and phosphorus, and (2) the variability from blow to blow. These, of course, are not entirely independent, since some of the variability covered in the second item is undoubtedly due to nitrogen. But the variability is also caused by other factors. One of these is the relatively small size of the Bessemer heats. Because of this, a given shipment of Bessemer steel is more likely than a shipment of open-hearth steel to contain the product of several heats, each with its own distinctive and slightly different characteristics. Added to this is the fact that the refining of Bessemer steel proceeds so rapidly that the timing of the end point is limited to a matter of seconds, whereas the finishing period in the open hearth extends over a period of one or two hours and the timing of the end point may vary by several minutes without seriously affecting the product. There is no doubt that this has contributed to the variability of Bessemer steel and has led to the use of open-hearth steel in many optional applications. That Bessemer steel may vary is not necessarily objectionable, and it may even prove an advantage, providing a precise control is available to secure the desired qualities for any specific application. With this in mind, a comprehensive research program was undertaken, one phase of which was directed toward securing more accurate control of the blow. The results have been encouraging, and it is the purpose of this paper to describe a method in which modern scientific instruments, based on photocells, are currently being employed to assist the blower. The Control Problem In this day of scientific control of technical processes, where the operating

Jan 1, 1941

By H. F. Perkins

CORROSION as an economic problem is growing rapidly in importance not only because it entails a replacement of corroded parts, but because it interrupts operation and causes hazards of damage and injury through failures of corroded equipment. Nearly all industries are interested in this subject. This paper, although concerned chiefly with corrosion in a complete refinery on the sea coast, discusses many of the various forms of chemical decomposition, most of which are found universally. The petroleum refining industry, in the writer's opinion, is seriously afflicted by the presence of sulfur in nearly all crude oils. The complete removal of sulfur from the crude as it enters the plant would cause such a relief from corrosion that this problem for research would seem to demand active attention. Next to sulfur the most troublesome corrosive agent is the saltmagnesium chloride, found in the water associated with crude oil, the last traces of which are so difficult to remove. This is much less serious, however, than the sulfur. Refinery corrosion can be tabulated as follows: Causes of Corrosion and Places of Attack in a Refinery CORROSIVE ELEMENTS MATERIAL ATTACKED Air: Pipe lines Moisture Tanks COQ Electric fixtures Sulfur gases Still towers Chlorine Condenser boxes Other acid-forming gases Ladders and stairs Smoke stacks Steel buildings All exposed metal Water: Alkali Fire lines and hydrants Acids Cooling water lines Air Condensers and coolers Other dissolved gases Boiler tubes Steam Steam pipes and valves Turbines Oil Sulfur compounds Tanks, pipes, valves, stills, towers MgCl2-Hydrochloric acid Condensers Air contamination

Jan 12, 1926

By Robert Maddin

THE application of electrolytic polishing of metals introduced a new technique for preparing surfaces, especially for single crystals. This procedure has generally been assumed to eliminate the strain introduced by mechanical polishing and to result in a more truly representative surface, particularly in the case of soft metallic materials. However, apparently little information is available concerning specific characteristics of a surface prepared electrolytically. The conventional method of mechanical polishing is known to produce a layer of distorted metal which is usually removed by a suitable chemical etchant. To what depth the strain introduced by mechanical polishing penetrates into the lattice is still obscure. The present investigation illustrates the apparently anomalous appearances of glide ellipses on electrolytically polished surfaces of aluminum single crystals. EXPERIMENTAL PROCEDURE AND RESULTS Aluminum single crystals, 99.975 pct pure, remaining from the investigation of Found,1 were polished electrolytically using a solution of fluoboric acid and a low current density. Laue back-reflection technique, interpreted after the manner of Greninger,2 was used to determine the orientation and the specimen axis rotation of the crystals. Three flat surfaces about 4 mm wide parallel to the specimen axis, one perpendicular to the theoretical slip direction and the other two 1200 apart, were polished mechanically and repolished electrolytically. A tensile load was applied using a Southwark-Emery tensile machine at a rate of about 40 lb per min. Elongation was measured by noting the initial and final gauge lengths. X ray diffraction was used to obtain the usual X and X values in order to calculate the elongation and shear by plotting stereographically the specimen axis rotation by means of the Schmid-Boas formula.3 In Table I may be found the value of the gauge diameter, measured elongation, calculated elongation and shear for the crystals investigated. Fig 1 shows the initial and final positions of the specimen axes of the crystals. [ ] At a low magnification the slip lines developed on specimen Al-I appeared straight and rather evenly spaced. However, at a high magnification, the slip lines were seen to be composed of small markings which were present throughout the length of the specimen (Fig 2). The distance between the markings was fairly constant and their directions all parallel to one another. Fig 3-5, photographed on different surfaces of the specimen, illustrate the interesting appearance of these lines. It may be noticed from Fig 4 that the markings, which present the appearance of

Jan 1, 1948

By A. U. Seybolt, D. H. Haman

The rate of oxidation of the lowest nitride of chromium, Cr2N, was measured to be equal to the rate of oxidation of chromium metal. It was found that, while the presence of Cr2N in chromium does not affect the oxidation mechanism, a long exposure at high temperature affects the morphology of Cr2N in chromium, causing a massive internal nitriding along chromium pain boundaries. Marker expen' -ments showed that the rate of oxidation of Cr2N layers on chromium is determined by the rate of chromium diffusion through Cr,03. The rate of formation of Cr2N is determined by diffusion rate of nitrogen through Cr2N. This rate at 1000°C is around thirty times faster than the rate of oxiahtion. Evidence is presented which suggests that nitrogen from the air reaches the chromium through the Cr2O9 by migration through pores or cracks rather than by a diffusive process. IT has long been recognized that, when chromium or alloys containing substantial amounts of chromium are oxidized in air, some chromium nitride (Cr2N) is formed under the oxide scale. Although the presence of this nitride layer has often been described, there appears to have been no systematic study of the role played by the nitride during the oxidation process. Indeed, there have been conflicting re-ports'92 on the kinetics of oxidation of chromium and chromium alloys in air and in oxygen. However, it is now well-established'-5 that the rate-controlling process during the parabolic oxidation of chromium to Cr2O3 is chromium-ion diffusion through Cr2O3. Because of the importance of chromium-containing alloys as oxidation-resistant materials, it seemed desirable to investigate the behavior of chromium during oxidation with and without the presence of chromium nitride. Since a semicontinuous Cr2N layer forms relatively early during the oxidation of chromium in the air, chromium atoms must either pass out of or through the Cr2N layer to become incorporated in the growing Cr2O3 scale. Therefore, it seemed desirable to examine the oxidation behavior of the pure nitride. MATERIALS AND EXPERIMENTAL PROCEDURE The chromium used in this investigation consisted of slices of an ingot made from "five-nine" iodide chromium which had been argon-atmosphere melted in a Y2O 3-stabilized ZrO2 crucible in an induction furnace. The only impurity of any significance was 625 ppm of 0, which was usually reduced to a microscopically invisible amount by hydrogen annealing at 1400°C. However, one sample of chromium was used with the as-cast oxygen level as explained below. The samples were used after abrading through 600 Sic paper and then washing in toluene and alcohol. Both nitriding and oxidation experiments were performed in a vertical tube furnace connected to a glass vacuum system. 'This system was equipped with pressure measuring instruments for the range of 10 p to 1 atm, and a cartesian-diver pressure-control device was used in conjunction with a needle valve to allow control of pressure in the range of about 10 to 760 mm. The nitrogen or hydrogen gas was purified by passing through hot copper chips at 600°C, anhydrous calcium sulfate (Drierite), and liquid nitrogen. Oxygen gas was dried through the Drierite column and a dry-ice trap (-78°C). Changes in specimen weight were followed by a Pyrex helix used in conjunction with a cathetometer which could reproducibly be read to +0.001 cm, yielding an accuracy of about +0.2 mg. The spring was maintained in the cool upper part of the furnace tube where the temperature did not rise above about 35°C. The nitride in equilibrium with metallic chro-

Jan 1, 1964

By A. Gittens

In two recent papers stevens13,14 has compared the methods used by various investigators to calculate the contribution of grain boundary sliding to the total creep strain. In previous work Gittins15 has shown that the strain due to grain boundary sliding Egb may be estimated from the lateral, d, and vertical, v, displacements of a longitudinal marker line as it crosses a grain boundary. He obtained the formula, where nL is the number of grains per unit length measured on the specimens before creep, and \p and ?2 are, respectively, the angle between the grain boundary and the stress axis in the plane of the surface and normal to the surface (see Ref. 13, Fig. 1). The subscript L indicates that observations are made in a longitudinal direction parallel to the stress axis. It was generally found more convenient to measure the grain size of a specimen before creep; this was necessary to characterize the specimen. Stevens13,14 however prefers to define Egb in terms of NL, the number of grains per unit length after creep. Since nL - NL(l + €1) where cr is the total strain, Eq. 1 11 becomes The quantities d and ?, can be determined directly from the marker lines, while v and ?2 are found by sectioning normal to the surface. In the interior when symmetry considerations suggest that v = d and ?1 - ?2 the strain due to grain boundary sliding may be estimated from a suitable internal longitudinal marker line by the equation To determine cgb at the surface using either Eqs. |1| or [2] requires a large number of observations, particularly if many estimates of cgb are required, and also it is impossible to determine the variation of cgh with creep strain on the same specimen because the specimen must be sectioned to determine ?2. Gittins15 found that for a number of materials the sliding vectors d and v were related to each other so that provided one was measured the other could be estimated. Also during creep, grain boundaries tend to migrate to meet the surface at angles close to 90 deg,16 so that the term nL(v/tan?2)L was comparatively small when 4,- 90 deg. By determining the frequency distributions of ?2 on control specimens this term can be estimated without sectioning the creep specimen. In this way an empirical equation based on Eqs. |1| and |2| enables cgb to be determined with reasonable accuracy with fewer observations of the angles and sliding components. For B brass, the relationship between the sliding vectors indicated that ceb = 0.85nLVL . In Table I of Stevens paper this equation is stated to be incorrectly derived. However it should be pointed out that this is an empirical equation derived from Eq. |1|, based on a knowledge of the relationship between d and v and on the frequency distributions of ?1 and ?2 for a particular material under given experimental conditions. It was used only when these relationships were known, to reduce the number of observations required to estimate cb. Therefore the comment "derivation incorrect does not apply. Gittins did in fact make use of Eqs. |1| and 131. Author's Reply I must apologize to Dr. Gittins for the inadvertent misrepresentation of his work. Other slight errors in Table I have been pointed out to me. Langdon (No. 12 Table I), Gifkins (No. 7, Table I), and possibly other workers did not measure the number of boundaries per unit length after creep (A') but the corresponding quantity bejove creep (n). As Dr. Gittins points out, a completely analogous set of equations to those given in the paper can be derived by the same method: using the number of boundaries per unit length before instead of after creep. The basic equations corresponding to Eqs. [2] and 171 of the paper, from which all the others can be derived, are

Jan 1, 1968

By P. M. Blair, D. W. Peaceman

The shape and position of the gas-oil transition zone during downdip displacement of oil by gas has been calculated using flow equations which include the effects of gravity, relative permeability, capillary pressure and compressibility of the fluids. The calculations treat the problem in two space dimensions, and results are compared with data from a laboratory model tilted at 30° and 60° from the horizontal on displacements near and above the maximum rate at which gravity segregation prevents channeling of the gas along the top of the stratum. The good agreement between calculated and experimental results demonstrates the validity of the tecbnique as well as that of the flow equations. INTRODUCTION Knowledge of the fluid distribution and movement in an oil reservoir is important in producing operations and estimation of reserves. The history of the oil industry has included steady progress in improving the accuracy of calculations which provide the required knowledge. The earliest method of calculating reservoir performance consisted of material-balance equations based on the assumption that all properties were uniform throughout a reservoir.l For many reservoirs such a simple formulation is still the most useful. However, when large pressure and saturation gradients exist in a reservoir, the assumption of uniform values throughout may lead to significant error. To reduce these errors, Buckley and Leverett2 introduced a displacement eqation which considers pressure and saturation gradients. Methods available at that time permitted solutions to the Buckley-Leverett equation in one space dimension; these solutions have been very useful in solving many problems related to the production of oil. However, the one-dimensional methods are not adequate for systems in which saturations vary in directions other than the direction of flow. An example of such a system is the case of gas displacing oil down a dipping stratum in which the gas-oil contact becomes significantly tilted. Of course, the Buckley-Leverett displacement method cannot predict the tilt of the gas-oil contact. Recent improvements3,4 of the one-dimensional Buckley-Leverett method achieve some success in predicting the tilt of the gas-oil contact at sufficiently low flow rates. However, at rates high enough that the viscous pressye gradient nearly equals or exceeds the gravity gradient, even these improved one-dimen,sional methods incorrectly predict the shape and velocity of the contact. Further progress in estimating such fluid movements in a reservoir appears to require consideration of the problem in more than one space dimension. The recent two-dimensional method of Douglas, Peaceman and Rachford5 appears adaptable to calculate changes with time of the saturation distribution in a vertical cross-section of a reservoir. The movement of saturation contours should represent the moving fluid contacts and include the effects of crossflow due to gravity, as well as variations in the rock and fluid properties. The nonlinear nature of the equations used in the method has prevented proof of the validity of the solutions. Douglas, Peaceman and Rachford made some comparisons with experiment but did not include cases in which gravity was important nor cases involving displacement by the nonwetting phase.For these reasons, a test of the two-dimensional method for a case in which these factors are included would be very desirable. The test selected was a comparison of calculated results with those from a carefully controlled laboratory experiment on a model with measured physical properties. The model selected was one in which gas displaced oil down a tilted, rectangular sand pack. The model can be thought of as representing a vertical cross-section taken parallel to the dip of a reservoir. The displacement thus simulates gas displacing oil downdip that might result from gas-cap expansion or gas injection. This report outlines the calculation method used

By H. Bernstein

Grain coarsening tests were carried out on AI-4.5 pct Cu and AI-4.5 pct Si alloys. The effects of three variables, melt composition, pour temperature, and mold temperature, were determined. It was found that the macrostructure generally coarsened with increased pour and mold temperatures. Coarsening was extreme in the unrefined alloys but was retarded by the active grain refiners like titanium and columbium. The effect of boron was spectacular in suppressing coarsening tendencies. The results of the investigation support the carbide theory of nucleation as opposed to the peritectic theory. A REVIEW of prior work on the subject of grain refinement in the light metals indicated that, for the most part, it had been concerned with the positive effects of addition agents upon structure. This work produced various theories of refinement. Prominent among them were the peritectic theory and the transition element carbide theory. Certain inadequacies in the former theory appeared to be explained satisfactorily by the transition element carbide theory. In order to appraise these theories further, a study was undertaken of the permanence of grain refinement effects when subjected to thermal or chemical variations. It was considered that a study of this kind would be of practical value, since the light metals are exposed to thermal and chemical variations in the normal course of foundry operations. Accordingly, two alloys of commercial importance were selected for this investigation, the A1-Cu and A1-Si alloys. Experimental Procedure and Results Raw Materials: The base alloys, A1-Cu and A1-Si, were prepared from virgin aluminum and hardeners, induction melted, and pigged for remelting. The grain refiners, including titanium, columbium, zirconium, and boron, were added as master alloys. Analyses of the raw materials and base alloys are listed in Table I. Melting and Casting Practice: The metals were melted in clay-graphite crucibles in a Hevi-Duty pit-type resistance furnace, equipped with a Leeds and Northrup Micromax Recorder and Controller. After melt down of the base alloys, the additions were made. For each casting, approximately 80 grams of metal were poured into a preheated graphite mold held in a transite flask. The mold (Fig. 1) weighed 320 grams. To determine the effect of superheat upon structure, a set of melts was heated successively to four temperature levels, 705°, 775°, 845°, and 915°C, and test specimens were cast at each level. Prior to each pour, the furnace temperature was held constant for 20 min. Next, a set of melts was put through a superheat cycle and test specimens were cast at melt temperatures of 705" and 915°C successively. The crucibles then were cooled in air to 705°C as deter-mined by immersion thermocouple and additional test specimens were poured. The cooling interval was approximately 1 min. Another set of melts was furnace cooled with the cover slightly ajar and test specimens cast as before. The interval in this case was 15 to 20 min, varying with the superheat temperature. The mold temperature for all these tests was 400°C. To determine the effect of cooling rate without superheat upon structure, a set of melts was heated to 705°C, and castings were poured at mold temperatures of 205", 400°, and 540°C. An interval of 15 min elapsed between each pour. Mold temperatures were measured by a direct reading millivolt-meter, using a chromel-alumel thermocouple located at midwall thickness of the mold. To demonstrate the phenomenon of chemical coarsening, agents such as chromium and beryllium, which had acted as coarseners in a previous investigation,' were added to the A1-Cu alloy. Test speci-

Jan 1, 1955

By W. R. Purcell, C. S. Brooks

The internal surfaces of rocks which are in contact with interstitial fluids are known to influence in some degree the recovery of hydrocarbons from pay zones. Despite the admitted importance of the influence of solid surfaces on hydrocarbon recovery, little information is available concerning the extent of surface of reservoir rocks. In this paper a description is given of the apparatus and procedure employed in the determination of the surface areas of sedimentary rocks, and values are reported for a variety of sandstone and limestone cores. In addition, consideration is given to the Kozeny equation, which relates surface area to porosity and permeability. A colliparison is made between the surface areas as calculated from this equation and the geometrical areas of a series of packs of spherical glass beads. Also, for a group of sandstone cores. Kozeny areas are compared with surface areas as determined by the gas adsorption method employed in this investigation. INTRODUCTION It has long been recognized that many processes which are of importance to hydrocarbon production are controlled in some degree by the extent of the surface of the reservoir rock through which the hydrocarbons move. For example, the recovery efficiency that is obtained in a given reservoir is certainly determined in part by the action of interfacial forces between the reservoir fluids and rock, and this action is influenced in turn by the extent of solid surface. Despite the admitted importance of surface effects to problems of petroleum recovery, little information is available concerning the extent of surface of reservoir rocks." It is the purpose of this paper to describe an apparatus which has been employed for the measurement of the surface areas of rock samples and to present the values which have been obtained for a variety of sandstone and limestone cores. In addition, the relationship of surface area to permeability and porosity, as given by the Kozeny equation, will be discussed. METHOD OF MEASURING SURFACE AREA The method of determining surface areas as employed in this work has previously found wide use in studies of porous solids such as catalysts. The method involves the measurement of the amount of physical adsorption of an inert gas, such as nitrogen or argon, on the bare surface of the solid at reduced pressure and constant temperature near the normal liquefaction temperature of the gas. With the aid of the theory of isothermal adsorption as developed by Brunauer, Emmett, and Teller,' it is possible to ascertain the amount of gas (and hence the number of molecules) which is required to cover the solid surface with a single layer of molecules. From a knowledge of the covering area per molecule the total surface ares of the solid can be computed. Since the Brunauer. Emmett, Teller (BET) theory has been adequately discussed elsewhere: it will suffice here merely to present their final equation as ordinarily employed for surface-area calculations. This equation relates the volume of gas, V, which is adsorbed at pressure, P, to the liquefaction pressure, Po, of the gas, and to the volume of gas, V.,, that is required to form a monomolecular layer: In this equation C is a quantity which is related to the heats of adsorption and liquefaction of the gas; for a particular solid-gas system at Constant temperature, C is considered to have a constant value. The basic adsorption data can be presented in the form of Equation (1) by plotting the quantity P/V(Po- P) as a func-

Jan 1, 1952

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute'.' for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.' Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956

By H. H. Kaveler

Education is for the purpose of developing citizenship, and, if it is pursued for the additional purpose of preparing for a professional career, such as engineering, it is also directed to developing a knowledge of essential science, aptitude for the application of science to practical situations, and a knowledge of the industrial art in which the engineer will be engaged. The process of education required for engineering must of necessity extend beyond the classroom into industry. For that reason, the education of engineers should be divided as between the university and industry. Specialization in engineering should logically come as a result of experience in an industry. The student cannot take the time in a university, and, the university cannot teach the skills required to develop a specialist without sacrifice to the more essential broad purposes of formal education. In addition to talent in science, aptitude in the application of scientific fact, and knowledge of the industrial art, the engineer should possess certain personal qualities which are helpful in the pursuit of a professional career. Those personal qualities are: the ability to work as a partner in an enterprise, the ability to do jobs in a way whereby job performance is a means of gaining experience and increased responsibility, the capacity to write and speak in an understandable manner, and, a Proper regard for the "significance of answers." These pcrsOnal qualities may be of almost equal importance to acabemic accomplishments in the field of science. Development of such personal qualities are an essential part of the student's training in the university and in industry. They can be developed effectively through the leadership of instructors. Compulsory Education Nature played a mean trick On the human race when the evolutionary Process failed to develop in the individual a capacity to inherit knowledge. Were knowledge transmissible in a cumulative manner from generation to generation, mankind would be by inheritance wise beyond measure within a few generations. Then there would be little if any need for a "system of education." As matters stand, however, all must suffer the burden of starting life at the "zero " level of learning from which station each rises depending upon individual capacity to assimilate knowledge left of record by our predecessors and the individual effort exerted to compensate for Nature's failure to endow the offspring with intelligence. In the United States some degree of education is generally regarded as essential and necessary. Therefore, all citizens are subjected by law to an educational process covering the primary school age from six to sixteen years. Beyond the schooling required by law, many attend secondary schools, and beyond that, schools of higher learning. Our standard of living is at a level that permits an increasingly large fraction of the population the opportunity to go through all of the formal educational process. As a result, education in the colleges and universities has almost reached a mass production level. In spite of the high

Jan 1, 1949

By Frederick V. Lawrence

Broadly speaking, fluxes are substances which promote wetting and spreading or enhance the fluidity and manipulative properties of materials in joining, fusion, and smelting operations. The term most strictly applies to substances used to facilitate soldering and brazing; but in the discussion which follows, the definition will be broadened to include materials used to promote fusion in arc welding and which aid in the smelting of metals. In each of the mentioned applications, the role of flux and its composition differs considerably; consequently in the discussion which follows, fluxes for soldering, brazing, arc welding, and smelting applications will be considered separately. Soldering and Brazing Fluxes Soldering and brazing are metallurgical joining processes in which a joint is formed using a filler metal of composition dissimilar to that of the joined pieces (base metal). The filler metal, solder or braze, is always of lower melting point than the base metal. Consequently with these processes there is no melting of the base metal. The successful creation of the joint depends upon the wetting and spreading of the solder or braze around or throughout the joint. The obstacles to successful soldering and brazing are contaminants and tenacious oxide films on the metal surfaces. In soldering and brazing applications, fluxes act to remove and exclude oxides and other impurities from the joint. There is no fundamental difference between soldering and brazing. The distinction between them is made on the basis of temperature. Join¬ing operations carried out at temperatures above 500° C are termed brazing. The higher temperatures used in brazing enable higher melting point filler metals to be used which generally provide stronger joints. The higher temperatures of brazing processes also require fluxes which are substantially different from those used in soldering and which will remain effective at high temperatures. Consequently the distinction between soldering and brazing can also be made on the basis of the fluxes used. Soldering Fluxes Even thoroughly cleaned and degreased, metal surfaces still possess tenacious oxide films which inhibit the soldering of the joint. The reactions which form these films increase with increasing temperature. The rate of oxide formation and the tenacity of the film varies with each base metal. Aluminum, magnesium, stainless and high alloy steels, aluminum and silicon bronzes when exposed to air form hard, adherent oxide films. These metals require highly active and corrosive fluxes to remove and prevent the reformation of oxide films during soldering. Metals such as copper and silver, on the contrary, form less tenacious films at a lower rate, so that mild fluxes are sufficient. Soldering fluxes must dissolve or remove oxides and promote rapid wetting and spreading of the solder. The flux removes the oxide film by loosening and floating it off into the main body of the flux. The oxide removal is often aided by the alloying of the solder with the base metal, undermining small areas of the oxide and detaching them (Anon., 1959). The flux coagulates and suspends the oxide particles which have been loosened. The flux forms a protective cover preventing the reformation of the oxides, permitting the spreading of the solder and the formation of a metallic bond between the solder and the base metal. Constituents of Soldering Fluxes: Soldering fluxes are commonly grouped into three categories: highly corrosive, intermediate, and noncorrosive. One normally would choose to use the least corrosive flux which will give satisfactory performance.

Jan 1, 1983

By R. A. Morse, C. R. Holmgren

The production of oil by water flooding can be substantially increased by the maintenance of free gas saturation in the reservoir during the flooding operation. This effect is accomplished by the alteration of oil relative permeability characteristics and the occupation by gas of pore space that would otherwise be filled with residual oil. The amount of reduction In residual oil can be calculated from appropriate water-oil relative permeability characteristics. This paper presents experimental data in support of the foregoing conclusions and an example of the calculations. The microscopic pore saturation concepts of the mechanism are discussed. A method of practical application to field floods is presented together with discussion of certain limitations. INTRODUCTION The presence of free gas has been reported by a number of investigators to significantly affect the oil recovery which can be obtained from sandstone flow systems by water flooding.1,2,3,4,5 The effect of gas, noted in every instance, has been to cause lower residual oil saturations than could be obtained by water flooding the same systems in the absence of free gas. The degree of improvement in recovery has been observed to vary widely, depending on the systems used and the conditions of the tests. The increased oil recovery obtained because of the presence of gas during a water flood has been variously attributed to changes in physical characteristics of the oil, selective plugging action of the gas, inclusion of oil mist in the free gas phase, and the additional sweeping or driving action of the free gas. All but the first of these suggestions imply changes in the displacement mechanism. The change in viscosity and inter-facial tension of the oil phase, within the pressure range used for all the experimental work, is certainly not sufficient to account for the differences in residual oil saturation noted dess there is a drastic change in the displacement process. One other effect which logically seems capable of causing differences in residual oil saturation of the magnitude noted in the experimental work is that of simple replacement. In a water-wet system containing oil, water, and gas, it is to be expected that the gas will exist inside the oil. This is the position of minimum free surface energy, since the gas-oil interfacial tension will be less than the gas-water interfacial tension. There is no apparent reason to expect that the existence of free gas within the oil phase should alter the saturation at which the non-wetting phase (now oil and gas) should become discontinuous and hence trapped so as to be unrecoverable by direct displacement by water. If this is the situation, then trapping of a certain percentage of gas saturation during water flood should result, at infinite water-oil ratio, in a like reduction of oil saturation below that attainable by flooding in the absence of free gas. It is visualized that the gas will exist as bubbles inside the discontinuous residual oil as illustrated in Fig. 1, with the size of the oil bubbles being substantially unchanged due to the presence of the gas. As a practical matter, it can be anticipated that the presence of a free gas saturation inside the oil phase will reduce the relative permeability to oil which will exist at any particular water saturation. This reduction will be caused by two factors — -the addition of the gas-oil interface, and the reduction of area available for oil flow in the pores containing gas. This reduction in oil permeability at any particular water saturation will result in water breakthrough at a lower water satu-

Jan 1, 1951

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By J. P. Hammond, C. J. McHargue, S. E. Adair

Cold-rolled sheet textures have been determined for binary solid solutions of aluminum, columbium, tantalum, and zirconium in titanium. An alloy containing 3.8 pct Al had a (0002) [10101 texture, whereas alloys with the other elements had rotated (0002) [10101 textures similar to that of iodide titanium. THERE have been relatively few studies of the effect of alloying on deformation textures. A second element may be present in the base metal in solid solution and/or as a second phase. The literature offers no satisfactory explanation for the effects of solid solution alloying on textures noted thus far. For example, there is no satisfactory explanation of the difference in the textures of copper and a brass. The most complete study of the effects of solid solution alloying on deformation textures has been that of Brick, Martin, and Angier.¹ These investigators reported that the copper texture was retained by alloys of copper with up to 30 pct Ni, less than 5 pct Zn, less than 2 pct A1 or Co up to the limit of solubility. Copper containing more than 5 pct Zn, more than 2 pct Al, or the maximum soluble concentration of tin, silicon, or manganese showed the deformation texture of a brass. Bakarian² reported that additions of 0.20 pct Ca to 99.98 pct Mg or 2.0 pct Mn plus 0.15 pct Ca to magnesium resulted in entirely different textures than for the pure magnesium. The texture obtained for high-purity magnesium sheet showed the basal plane to be concentrated parallel to the rolling plane. The texture obtained for the alloy containing 0.20 pct Ca had the basal planes concentrated in elliptical areas whose centers were tilted 15" from the center of the pole figure toward the rolling direction. This split basal orientation was even more pronounced in the alloy containing 2.0 pct Mn and 0.15 pct Ca. Fuller and Edmunds" studied the rolled sheet textures in a zinc alloy containing 1 pct Cu and 0.01 pct Mn. The basal pole figure of this alloy contained a region of strong concentration not found in the pole figure for pure zinc.' In the above cases, results were discussed in terms of possible changes in slip and/or twinning systems and critical shear stresses. However, there were no experimental data to relate these speculations with the observed textures. It has been suggested that the deformation textures of titanium, zirconium, and beryllium could be directly ascribed to their low c/a ratios. The complex deformation mechanisms of titanium" also have been suggested to be characteristic of hexagonal close-packed metals with low c/a ratios. The purpose of this investigation was to study the cold-rolled sheet textures in binary titanium-base a alloys in which the c/a ratios were greater than, less than, and about the same as the c/a for iodide titanium. The annealed textures of these alloys will be reported in a subsequent article. Materials and Methods The chemical analyses of the metals used in this investigation are given in Table I. The alloys were prepared as 15 g buttons on a water-cooled copper block in a vacuum arc-furnace. The furnace was evacuated to pressures of the order of 10.' mm Hg, flushed with 99.98 pct pure argon, and melting was carried out in 0.2 atm pressure argon. Each button was remelted until radiographs and chemical analyses indicated complete solution of the solute elements. All buttons were forged and homogenized 72 hr at 500°C. The buttons to be rolled were ground and etched to sizes and shapes suitable for the rolling

Jan 1, 1954

By L. D. Jaffe

From the limited experimental data in the literature, preliminary values were derived for the thermal diffusivity of titanium alloys and for the quenching severity of various mediums used in heat treating them. The thermal diffusivity, under quenching conditions, was found to be approximately 0.006 sq in. per sec. The quenching severity H for brine is approximately 8, for water 4, for oil 0.9, for air 0.08, and for argon 0.02 in. -' The quenching severity of the Jominy-Boegehold end quench water jet against titanium alloys appeared effectively infinite. Using these results, graphs were prepared showing ideal round sizes and Jominy positions having cooled conditions equivalent to those at the center and surface of titanium alloy rounds, plates, and sheets quenched in various media. THE importance of proper quenching of steel parts has long been recognized, and much quantitative work has been done on the subject. Recently, it has become evident that for titanium alloys, too, the rate of cooling from high temperature is important in obtaining high strength and hardness. Maximum hardness and strength may not be attained in the as-quenched condition but rather after a subsequent tempering or aging treatment. Nevertheless, if cooling from temperatures near the ß transus is too slow, for the hardenability of the alloy used, a soft a-ß structure will be produced which will not harden on subsequent aging.'-" The quenching of parts of practical interest can usually be approximated by simple shapes, such as cylinders (rounds) and plates (or sheets) of various thickness and combinations of these. A standard that has been used extensively for comparison purposes is the center of an ideal round: a cylinder quenched in a medium that instantly cools its surface to room temperature." For steel, considerable practical use has been made of the Jominy-Boegehold end quench hardenability specimen,".' and its value for titanium alloys is becoming evident. It therefore appeared worthwhile to attempt comparison of cooling conditions in titanium alloy rounds and plates of various sizes quenched in various media with cooling conditions in ideal round and Jominy quenches. These comparisons are based upon measurements reported in the literature. Quenching Severity of Jominy Water Jet and of Brine As one starting point, there were available the data of Phillips and Tobin8 for positions on a Jominy specimen having the same hardness as the centers of round bars of various size quenched in 5 pct NaOH brine, shown in Table I. The Jominy speci- men is a round bar, normally 1 in. diam and 4 in. long, quenched by a water jet at one end and air cooled on the other surfaces.' After quenching, hardness is measured vs distance from the quenched end on longitudinal flats ground 0.015 to 0.10 in. deep. The data of Table I were based on a subsized specimen of 3/4 in. diam. Since the positions tested are close to the jet quenched end, cooling there may be taken as due solely to the jet, and air cooling can be neglected. These positions are then equivalent to various locations near one surface of an 8 in. plate jet quenched on both sides. Assuming that the thermal diffusivity is constant and that Newton's law of cooling holds, temperature vs time curves at corresponding positions in Jominy specimen and round bar then may be calculated for various assumed quenching severities of the water jet and of the brine. Cooling curves are generally taken to be metallurgically equivalent when they show the same time to reach a temperature halfway between the initial (heat treating) temperature and the final (quenching medium) temperature.5 On this basis, using Russell's tables,9 upplemented by heat flow tables derived in similar fashion by the author for positions near the surface of severely quenched plates, it was found that the experimentally observed equivalence, Table I, was best matched if the quenching severity H of the Jominy water jet was taken as infinite (H = co). This means that the jet quenched surface should be considered as instantly cooled to the temperature of the water

Jan 1, 1956

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965