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By R. J. Reynik

A semiempirial small flunctation theory of diff- sion in liquids is presented, which employs a fluctuation energy assumed quadratic for a small atomic or molecular displacement and Einstein's random-iralh model. The resulting diffusion equation is given by In these equations. D is the diffusivity, is the average liquid shite coordination number (at interatomic distance d. cm. T is the absolute temperature, xu. em, is (the diffusive displacement. K, is the quadratic fluctuation energy force constant, and rg, cm, are the radii oj diffusing atoms A and B, respectively. The quantities Xn and K are calculated from the computer-filled values of the slope and intercept. respectively. The radius of self-diffusing atom or radii and of diffusing atoms A and B are eta United and compared with values reported in the literature.. The predicted linear variation of diffusivity with. It tempera lure htm been observed in approximately thirty-iire metallic liquid systems, and in over seventy-fiee other liquid systems, including the organic .alcohols, liquified inert gases, and the molten salts, ALTHOUGH the average density within a macroscopic volume element of liquid is constant for fixed total number of atoms. pressure. and temperature, there exist microscopic: density fluctuations within the respective volume element. As such the microscopic volume available to an atom and its Z first nearest neighbors at any instant of time fluctuates above and below the average volume available to these atoms. If one assumes that liquid state atoms vibrate as in a solid. and further postulates that the mean position of any atom in the liquid state is not stationary. but shifts during every .vibration a distance 0 5 j 5 xo. then every atom in the liquid state continuously undergoes diffusive displacements which vary in the range 0 5 j 5 ro. Mathematically. for a binary liquid system consisting of atcrms A and B. the maximum diffusive displacement. .YO, is defined by the equation: where d is the average liquid state interatomic distance at specified liquid state coordination number Z. and v~ \ and vg are the effective radii of diffusing atoms A and B: respectively. For self-diffusion. r^ equals rg , and Eq. [I.] reduces to: It is interesting to note that Eq. [l] or [2] can be used to compute the radii of the diffusing atoms, provided one had an experimental evaluation of xo. As such. the computed radii could be compared with metallic or crystallographic ionic radii to ascerlain the electronic character of the diffusing atoms. Thus it is proposed that in the liquid state the n~otion of an atom relative to its original equilibrium position of oscillation represents the thermal vibration of any atom and its Z first nearest neighbors. while the small and variable displacements. 0 5 1 5 xc,. of the centers of oscillation represent the complex diffusive motions of the atoms at constant temperature and pressure. This is consistent with data obtained from slow neutron scattering by liquids1 ' and resembles an itinerant oscillator model of the liquid state.'" It is further postulated that the atomic displacements characterizing the liquid state diffusion process are essentially a random-walk process. As such. it nlay be described by Einstein's equation:' where D is the diffusivity. sq cm sec-'. j2 is the mean square value of the diffusive displacement. and i> is the frequency of density fluctuations giving rise to diffusion. FORMULATION OF DIFFUSION EQUATION The effective spherical volume occupied by an atom, as a consequence of a microscopic density fluctuation which enlarges the volume available to any atom, exceeds its average liquid state atomic volume by an amount: where AV is the enlarged spherical volume, v is the radius of the diffusing atom. and j is the elementary displacement distance from the original center of oscillation of the vibrating atom to a new center of oscillation position. For small atomic displacements. where c is a constant whose value depends upon the assumed geometry of the enlarged volume. For a spherical increase in volume, c equals 4nr2. Following the treatment of Furthl' and ~walin." assuming the enlarged volu~nes AL7 for the diffusing atoms are distributed in a continuunl. the probability of finding a fluctuation in the size range 0 5 j 5 xo defined by Where c includes the geometric constant cl and Eij) is the fluctuation energy causing the volume change. But the proposed model assumes all the Z first nearest-neighbor atoms are centers of oscillation. and hence the probability that any of these atoms is adjacent to a fluctuation of magnitude 05j5xo is unity. Thus:

Jan 1, 1970

By Benjamin C. Craft

Oil and gas development in Louisiana during 1935 brought this state at the close of the year up to fourth place in the nation as a producing area. A review of development in North Louisiana centers around Rodessa, the most important reserve discovered in this area in many years. While the producing limits have not been defined, this discovery is one of the major developments of the year. New gas fields were discovered in Lincoln, De Soto and Bossier parishes. The Lincoln Parish discovery, completed flowing a highly saturated gas from the Glen Rose, further indicates the importance of deep-seated prospects in the interior salt-dome area. Minor extensions were made at Sligo and Pine Island. During the year, 126 oil wells and 103 gas wells were completed in North Louisiana as compared with 144 oil wells and 68 gas wells during 1934. The North Louisiana oil production was 9,617,405 bbl. as com-pared with 9,274,050 bbl. during 1934, an increase of 343,355 bbl., while the gas production increased 18 billion cu. ft. in 1935 over its 1934 figure. The Louisiana Department of Conservation gage of Nov. 1, 1935, shows an open-flow capacity of 4,563,725,000 cu. ft. per day from 941 wells in the Monroe field and 682,770,000 cu. ft. from 159 wells in the Rich-land field. A great deal of leasing continues in North Louisiana as a result of the Lincoln Parish discovery and development in the Rodessa field, especially in Bossier, De Soto, Winn, Lincoln, Bienville, Webster, Ouachita and Richland parishes. South Louisiana's position as an area of important reserves was further proved during the past year. Increased drilling resulted in the discovery of seven new fields: Lafitte, Garden Island Bay, Tepetate, Bunkie, St. Martinsville, Jeanerette and Big Lake. New sands or producing horizons proved productive in 15 of the proven fields. The total oil production for South Louisiana during 1935 was 40,731,-056 bbl. as compared with 23,255,437 bbl. during 1934. There were 222 oil and gas wells completed in South Louisiana during 1935 as compared with 214 oil wells during the previous period. Drilling during

Jan 1, 1936

By Benjamin C. Craft

Oil and gas development in Louisiana during 1935 brought this state at the close of the year up to fourth place in the nation as a producing area. A review of development in North Louisiana centers around Rodessa, the most important reserve discovered in this area in many years. While the producing limits have not been defined, this discovery is one of the major developments of the year. New gas fields were discovered in Lincoln, De Soto and Bossier parishes. The Lincoln Parish discovery, completed flowing a highly saturated gas from the Glen Rose, further indicates the importance of deep-seated prospects in the interior salt-dome area. Minor extensions were made at Sligo and Pine Island. During the year, 126 oil wells and 103 gas wells were completed in North Louisiana as compared with 144 oil wells and 68 gas wells during 1934. The North Louisiana oil production was 9,617,405 bbl. as com-pared with 9,274,050 bbl. during 1934, an increase of 343,355 bbl., while the gas production increased 18 billion cu. ft. in 1935 over its 1934 figure. The Louisiana Department of Conservation gage of Nov. 1, 1935, shows an open-flow capacity of 4,563,725,000 cu. ft. per day from 941 wells in the Monroe field and 682,770,000 cu. ft. from 159 wells in the Rich-land field. A great deal of leasing continues in North Louisiana as a result of the Lincoln Parish discovery and development in the Rodessa field, especially in Bossier, De Soto, Winn, Lincoln, Bienville, Webster, Ouachita and Richland parishes. South Louisiana's position as an area of important reserves was further proved during the past year. Increased drilling resulted in the discovery of seven new fields: Lafitte, Garden Island Bay, Tepetate, Bunkie, St. Martinsville, Jeanerette and Big Lake. New sands or producing horizons proved productive in 15 of the proven fields. The total oil production for South Louisiana during 1935 was 40,731,-056 bbl. as compared with 23,255,437 bbl. during 1934. There were 222 oil and gas wells completed in South Louisiana during 1935 as compared with 214 oil wells during the previous period. Drilling during

Jan 1, 1936

By R. W. Harper, M. C. Fuerstenau, J. D. Miller

Data were obtained with hematite with octyl hydroxamate and oleate as collectors to determine the mechanism of collector adsorption and also to establish the roles that conditioning time and temperature assume in this system. The presence of hydroxy complexes of iron are apparently necessary for chemisorption of collector to occur, and it appears as if extended conditioning times and elevated temperature promote greater dissolution of the mineral and hence greater concentrations of hydroxy complexes. Data were also collected with two natural hematitic ores. With one ore that was ground to 70% - 15u, an addition of 0.4 lb per ton hydrox-amate resulted in a final concentrate recovery of 86% at a grade of 64% iron. Satisfactory concentrate grade could not be obtained with fatty acid under these conditions. The effect of conditioning time prior to the addition of collector was also examined with another ore. When the ore was conditioned for 3 min, 19% of the iron was recovered in the concentrate at a grade of 67% Fe. With a conditioning time of 7 min, 73% of the iron reported to the concentrate at a grade of 62% Fe. These products were obtained with an addition of 0.2 lb per ton hydroxamate. This ore also responded well to flotation with fatty acid. The use of potassium octyl hydroxamate as a collector for iron oxide has been the subject of an earlier study.1 From this initial study, it was suspected that hydrolysis of surface ferric iron was involved in collector adsorption. More recent work in other systems has shown that slight mineral dissolution, followed by hydrolysis of cations common to the mineral lattice, is apparently necessary, and that adsorption of these hydroxy com- plexes probably occurs prior to the adsorption of collector. In view of these facts, work has been continued on the hydroxamate-hematite and oleate-hematite systems to gain better insight into the mechanisms of collector adsorption on iron oxide. Microflotation experiments in conjunction with infrared analysis were used in this regard. In addition it was felt necessary to establish more clearly the responses that can be obtained from natural ores when hydroxamate is used as collector as compared to those obtained when fatty acid is used. Experimental Materials and Techniques Pure potassium oleate, potassium octyl hydroxamate, synthesized from hydroxylamine hydrochloride and methyl octanoate, and a distilled Tall Oil were employed as collectors. Conductivity water was used in the

Jan 1, 1971

By B. M. Larsen, K. Heindlhofer

Jan 1, 1945

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

By Hans Lundberg

AFTER the war years, great activity has been shown in geophysical exploration for ore. The appreciation by mining and government geologists of geophysical techniques and results is largely responsible for the popularity of these methods. In Canada, plans are being made to study, by geophysical methods, the structure of a portion of the Pre-Cambrian shield in the hope that such studies will not only give a clearer picture of the geology, but will be of direct aid to the mining companies when selecting areas for detailed prospecting. Although geophysics thus has become more popular, some engineers are still reluctant to employ the methods to their full extent. Allotted funds are often rather low, so that the least expensive

Jan 1, 1947

The following is an incomplete list of members and guests who called at Institute headquarters during the period Nov. 10, 1918 to Dec. 10, 1918. Arthur C. Adair, Camp Meade, Md. L. S. Mitchell, Montreal, Canada. Arthur K. Adams, Camp Humphreys, Va. T. E. Mitchell, San Francisco, Cal. Toner Antisell, Chevy Chase, Md. H. Mortimer-Lamb, Montreal, Canada. V. W. Aubel, New Castle, Pa. Edmund Newton, A. C. Black, El Paso, Tex. Paul T. Norton, Jr., Columbus Ohio. 0. F. Brinton, Baxter Spgs., Kans. Elmer W. Pehrson, San José, Cal. C. S. Corbett, Minneapolis, Minn. Joseph E. Pogue, Washington, D. C. W. M. Corse, Mansfield, Ohio. T. C. Roberts, E. Orange, N. J. G. C. Crossley, Toms River, N. J. D. R. Semmes, Richmond, Va. H. S. Emlaw, Grand Haven, Mich. H. L. Slosson, Jr., San Francisco, Cal. Rudolph Emmel, Boston, Mass. W. H. Staver, S. G. Garrett, U. S. N. R. F. A. L. Sweetser, Boston, Mass. Lt. Francis Geib, Denver, Colo. Lt. H. B. Taylor, Kansas City, Mo. Wm. E. Hubbard, Wichita Falls, Tex. Kirby Thomas, New York. Arthur Iddings, Wichita Falls, Tex. Benj. F. Tibby, Salt Lake City, U. Zay Jeffries, Cleveland, Ohio. J. L. Towne, Whitepine, Colo. S. J. Kidder, Mogollon, N. M. Chas. W. Tubby, St. Paul, Minn. Lt.-Col. W. H. Lanagan (Engrs.). A. G. Waite, Brookline, Mass. Major W. F. Lewis (Engrs.). Timothy D. Walsh, Denver, Colo. 0. M. Lewyn, Thomas Warner, Phoenix, Ariz. A. McClintock, DeKalb June., N. Y. J. P. B. Webster, London, England. Major Donald G. Miller, N. M. E. W. Westervelt, Los Angeles, Cal. C. E. LeN. Arnold, formerly with the Inspiration Cons. Copper Co. at Inspiration, Ariz., has accepted a position with the Consolidated Arizona Smelting Co. at Mayer, Ariz.

Jan 1, 1919

By R. V. Higgins, A. J. Leighton

A fast method is needed for calculating thoroughly the performance of two-phase flobr~ in reservoir rock with complex geotrietry. The authors present such a method and .slzow its accuracy by romparison with laboratory performrrnce of a five-spot pattern. In making the performance c.alculations, the octant of the five-spot pattern was divided into four channels. The computer tinle required for the culculation was one rllinrcte. This is rorighly about minute per channel. INTRODUCTION By using an electronic computer it is now possible to make reservoir performance calculations in which fewer assumptions and more significant variables are included than was possible with a desk calculator. These performance calculations include such variables as the properties of the reservoir rock and its contained fluids, properties of the rock-fluid system and even different well-spacing patterns. Usually, the more variables that are included the higher the computer cost—and time on the computer is expensive. As a result, a short procedure is needed so the many variables will be included and accurate performance calculations will result. If a reservoir is composed of alternate layers of permeable and impervioi~s rock, and if each conducting layer has a different relative permeability, the combined computer cost for calculating each layer by the present long computer programs (which includes different well-spacing patterns and other variables) would be expensive. The performances of complex spacing patterns in a field often are studied by a potentiometric model, but in these model studies the analogy is to the flow of only a single phase. This paper presents a procedure to calculate the performance of a five-spot pattern with two phases flowing using a potentiometric model as a guide for the dimensions of channels and other related data. The time required to calculate the complete performance is about one minute on the IBM 7090 or four minutes on the IBM 704. The procedure can be extended to calculate the performance of more complex well spacings or an entire field with little modification. The procedure has been tested on the performance of the laboratory water floods of a five-spot pattern reported by Douglas, et alThe range of viscosity ratios in the laboratory experiments is from 0.083 to 754, which is extensive. The accuracy of the performance calculations is excellent as shown by the plotted points in Fig. I. The recovery as influenced by the geometry of the five-spot, taking into account the deviation from true radial character, has been predicted by Aronofsky and Ramey." The authors used a potentiometric model to determine the sweep efficiency to breakthrough of the flooding agent. Dyes, Caudle and Erickson,' by means of a laboratory model, show the influence of mobility ratio on recovery after breakthrough of the injected material. Dyes, et ai, used the X-ray shadowgraph technique and miscible phases in their studies. Craig, Geffen and Morse from the analysis of the performance of their laboratory model correlate many variables, including average saturation of a flooding agent determined by permeability relationship. Craig, et al, used X-ray shadowgraphs to determine the sweep efficiencies in sandstone models. In this report the sweep efficiency is not needed, and the important effect of continuously changing saturation gradients before and after breakthrough

By Elmer W. Pehrson

OPINION seems widely divergent as to where we stand with respect to future mineral supply. From some quarters we hear that the United States is about to become a "have-not" nation and about to experience the evil consequences such a situation would entail. Others claim that we are still a treasure house of stored-up mineral wealth, the surface of which barely has been scratched. The data to be presented here support the conclusion that neither of these viewpoints is correct and that we are far from exhaustion of those mineral resources that are basic to our industrial economy. However, exhaustion is well advanced in a number of important subsidiary minerals so that we can no longer drift along with the easy-going philosophy that the earth will provide. The time has come when we must recognize the true situation and do something about it.

Jan 1, 1945

By J. Buchwald, R. W. Heckel

THE DeHoff method' of analysis of ellipsoids of constant shape provides a quantitative metallo-graphic technique whereby the actual size distribution of the ellipsoids may be determined from polished and etched random planar sections. This method provides a useful metallographic tool since it appears to be the only method available for determining the size distribution of nonequiaxed second-phase particles. This method, however, assumes that the type of particle being studied is known to be either oblate or prolate of a fixed minor to major axis ratio, q. This, in general, means that one assumes either oblate or prolate ellipsoids of a given q and checks the total volume and surface area of the second phase as determined from the particle size distribution to values of these quantities determined by other techniques. Suitable check methods may be point counting, lineal fraction, and areal fraction methods for obtaining the total volume and the Smith and Guttman2 method of intercepts for obtaining the total surface area. If the initial guess at particle shape and q were incorrect, i.c., the volume and surface information obtained from the particle size distribution data does not agree with those values obtained by other techniques, another assumption must be made and the particle size dist distribution must be recalculated. A current study in this laboratory has involved a large number of these calculations. To facilitate the handling of the calculations, the DeHoff method was programmed in the FORTRAN language for an IBM 1620 computer. The purpose of this note is to briefly describe this program. The complete program along with a list of variable names, a sample input, and a sample output may be obtained from the senior author. Basically, the program provides for the calculation of particle size distributions for a series of q values for both oblate and prolate ellipsoids for each set of input data. The total volume of second-phase particles per unit volume are calculated for each calculated particle size distribution. The output of the program is arranged to allow a rapid comparison of the calculated volume and surface values to data obtained by independent check measurements. A condensed flow chart of the program in the notation of DeHoff1 is given in Fig. 1 The calculation of the number of particles per unit volume in the jth size class, Ni, according to the DeHoff method' is: where k(q) is the shape-correction factor given by DeHoff as a function of q for both oblate and prolate ellipsoids, A is the size-class increment, k is the number of size classes, ni is the number of particles in the ith class on the planar measurement surface, and B(j,i) are the saltykov3 coefficients which correct for measurement surfaces which do not pass through the major and minor axes of the particles. The values of /3(j,i) are included as a two-dimensional array in the program. Particular values of k(q) are included in the program in increments of q of 0.05. The first calculation is carried out for q = 1 (spheres), the second for q = 0.95 oblate, the third for q = 0.95 prolate, and so forth. The number of q values chosen for the calculation is determined by a control card in the input for each set of data.

Jan 1, 1965

By J. R. Kyte, V. O. Naumann, C. C. Mattax

Imbibition and waterflooding tests at reservoir conditions show that conventional tests at room conditions sometimes lead to recovery estimates that are too low. Core samples which are of intermediate wettability at normal test conditions may be strongly water-wet at reservoir conditions. This was found to be true for samples from two of three reservoirs investigated. For the other reservoir, less difference was observed between the wettability of samples at normal test conditions and at reservoir conditions. Samples which became more water-wet at reservoir temperature and pressure also water flooded more efficiently at reservoir conditions. These results show that core analysis tests on intermediate wettability samples should be performed at reservoir conditions to obtain representative data. INTRODUCTION Throughout the oil industry, core analysis tests normally are performed using refined oils and at room temperature and pressure. This procedure has always been subject to question because the possibility is generally recognized that the reservoir environment may influence displacement behavior. Burkhardt, et al,' have performed waterflood tests at reservoir conditions on East Texas cores. They found little difference between results obtained at reservoir conditions and results of conventional flooding tests at room conditions. As they pointed out, however, this situation might not be general since they obtained data on only one rock and crude-oil system. This paper presents data which demonstrate that it is sometimes necessary to perform core analysis tests in a simulated reservoir environment to properly represent the reservoir wettability and displacement characteristics. The work is specifically concerned with reservoirs which were thought to be of intermediate wettability on the basis of conventional test results at room conditions, i.e., core samples imbibed only small amounts of either oil or water and exhibited no decided preferential wettability characteristics. Tests were performed on cores from three such reservoirs to determine their behavior in the reservoir environment. lmbibition and waterflood tests were used to demonstrate the effect of reservoir environment on reservoir rock wettability and displacement characteristics. Results of tests performed at reservoir conditions were compared with results from conventional tests. Imbibition tests were performed on samples from all three reservoirs. Waterflood tests were performed on samples from only one reservoir. Fluid properties for the three reservoirs studied are shown in Table 1. Tests at reservoir conditions were performed using bottom-hole crude oil at reservoir temperature and pressure. The aqueous phase used in these tests was a synthetic brine approximating the reservoir brine composition. Conventional tests were performed at room conditions with refined oils and synthetic reservoir brine. The oil-to-water viscosity ratios were adjusted to the reservoir values. The cores used in all the tests were taken from the reservoirs using either brine alone or a bentonite-car-boxymethylcellulose mud without additives as coring fluids. Previous tests show that these fluids have no significant effect on the wettability of reservoir rock samples.1 The cores were preserved in brine at the wellsite to prevent wettability changes during shipment and storage. Wellsite imbibition tests have been performed on fresh samples from several reservoirs (including Reservoir A) and compared with later laboratory imbibition tests on samples preserved in brine. The comparison showed that the wettability of the preserved cores was the same as that of fresh, surfaced cores at the wellsite.2 IMBIBITION TESTS Conventional imbibition tests were performed on preserved cores using the apparatus and procedures described by Bobek, et al.2 A sketch of the apparatus for imbibition tests at reservoir conditions is shown in Fig. 1. The preserved samples were first centrifuged to expel excess water and then placed in a stainless-steel container which served

By JOHN D. SUMMER

THE Premium Price Plan for copper, lead, and represent, the approach of the Office of Price Administration to the urgent of wartime problem of securing increased output of nonferrous metals. Some of the problems encountered in too operation of the Plan and the considerations which led to it?s adopt it will here he reviewed. The Plan provides for extra payment by the Metals Reserve Co., to mine operators who exceed established quotas of production. Producers are thus directly, compensated for the higher costs of working ores that are not commercial at the ceiling price, although the metal obtained from these ores is directed into regular channels of distribution at the established prices for copper, lead, and zinc. Higher-cost metal is thus available to fabricators and to the government agencies at the regular ceiling price and the dual objective of increased production and table pries is achieved.

Jan 1, 1943

By T. A. Pollard, C. R. Sandberg, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By C. R. Sandberg, T. A. Pollard, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18

Jan 1, 1923

By James A. Lewis

It is the purpose of this paper to show the importance of sand characteristics, when combined with other physical data, in evaluating production obtained by secondary recovery operations, and to indicate the benefits to be gained from the application of these principles to primary production. Introduction During the past 10 years there has been a growing interest within the industry regarding the movement of fluids through oil reservoirs. A number of research projects have been directed toward the development of the physical laws governing this movement. In the period 1933 to the present, correlations between laboratory analysis of cores, reservoir fluids and well performance have been established and have been applied to successful secondary water-flooding recovery operations; and to the completion, production, reconditioning and evaluation of wells in new fields. The application of these data to water-flooding, either natural or artificial, is comparatively new, but the principlcs involved were set forth in 1880 by John F. Carll,1 who said: The flooding of an oil district is generally viewed as a great calamity, yet it may be questioned whether a larger amount of oil cannot be drawn from the rocks in that way than by any other, for it is certain that all the oil can-not be drawn from the reservoir without admission of something to take its place. If one company owned all of the wells drawing upon a pool, and had accurate records of the depth and characteristics of the oil producing stratum in each well, it is quite possible that some system might be devised by which water could be let down through certain shafts, and thus the rocks be completely voided of oil and left full of water. As it is, however, no systematized plan of action can be adopted. The careless handling of one well. by which water is let down to the oil rock, may spoil several others belonging to different parties. A clashing of interests at once arises and is likely to result in disaster to the whole district. In judging of the probable effects of the intro-duction of water into any particular oil district several things are to be considered. (1st) The time of flooding—whether early in the progress of development, while yet a large percentage of oil remains unexhausted or at a later period after the supply has suffered from long continued depletion. (2nd) The structure of the rock—whether regular and homogeneous throughout, or composed of fine sand inter. bedding connected and irregular layers of gravel, sometimes lying near the top and at others near the bottom. (3rd) The shape of the area being flooded. (4th) The position of the point at which water is admitted. in relation to the location of the surrounding wells still pumping oil. (5th) The height (which governs the pressure) of the column of water obtaining admittance. (6th) The duration of the water supply. Although we may take exception to part of Carll's reasoning, particularly " and thus the rocks be completely voided of oil and left full of water," we must give him credit for pointing out the increased effectiveness of water encroachment in displacing oil from a sand and for his recording six of the present seven considerations necessary for evaluation of production of oil by water

Jan 1, 1942

By James A. Lewis

It is the purpose of this paper to show the importance of sand characteristics, when combined with other physical data, in evaluating production obtained by secondary recovery operations, and to indicate the benefits to be gained from the application of these principles to primary production. Introduction During the past 10 years there has been a growing interest within the industry regarding the movement of fluids through oil reservoirs. A number of research projects have been directed toward the development of the physical laws governing this movement. In the period 1933 to the present, correlations between laboratory analysis of cores, reservoir fluids and well performance have been established and have been applied to successful secondary water-flooding recovery operations; and to the completion, production, reconditioning and evaluation of wells in new fields. The application of these data to water-flooding, either natural or artificial, is comparatively new, but the principlcs involved were set forth in 1880 by John F. Carll,1 who said: The flooding of an oil district is generally viewed as a great calamity, yet it may be questioned whether a larger amount of oil cannot be drawn from the rocks in that way than by any other, for it is certain that all the oil can-not be drawn from the reservoir without admission of something to take its place. If one company owned all of the wells drawing upon a pool, and had accurate records of the depth and characteristics of the oil producing stratum in each well, it is quite possible that some system might be devised by which water could be let down through certain shafts, and thus the rocks be completely voided of oil and left full of water. As it is, however, no systematized plan of action can be adopted. The careless handling of one well. by which water is let down to the oil rock, may spoil several others belonging to different parties. A clashing of interests at once arises and is likely to result in disaster to the whole district. In judging of the probable effects of the intro-duction of water into any particular oil district several things are to be considered. (1st) The time of flooding—whether early in the progress of development, while yet a large percentage of oil remains unexhausted or at a later period after the supply has suffered from long continued depletion. (2nd) The structure of the rock—whether regular and homogeneous throughout, or composed of fine sand inter. bedding connected and irregular layers of gravel, sometimes lying near the top and at others near the bottom. (3rd) The shape of the area being flooded. (4th) The position of the point at which water is admitted. in relation to the location of the surrounding wells still pumping oil. (5th) The height (which governs the pressure) of the column of water obtaining admittance. (6th) The duration of the water supply. Although we may take exception to part of Carll's reasoning, particularly " and thus the rocks be completely voided of oil and left full of water," we must give him credit for pointing out the increased effectiveness of water encroachment in displacing oil from a sand and for his recording six of the present seven considerations necessary for evaluation of production of oil by water

Jan 1, 1942

By F. W. Schremp, J. W. Chittum, T. S. Arczynski

This paper describes a laboratory study of causes of external casing corrosion and the test work that led to the use of oxygen scavengers to prevent this attack. External casing failures are classified as water-line, casing-casing, collar and body failures. A corrosion mechanism based on principles of differential oxygen availability is developed that is consistent with facts known about each kind of failure. The field use of oxygen scavengers is depicted as a direct result of the laboratory study. A part of the paper is devoted to reporting on the field use of hydra-zine to control external casing corrosion. Results of field measurements made over a period of several years are presented as evidence of the efectiveness of the hydrazine treatment. The first conclusion reached is that the use of hydrazine materially reduces the cathodic protection requirements for treated wells. This result is interpreted to mean that a reduction is taking place in the amount of corrosion on the casing. Results indicate also that hydrazine shows its greatest usefulness within the first 12 to 18 months after a well is completed when pitting corrosion is likely to be most active. INTRODUCTION According to surveys sponsored by the National Association of Corrosion Engineers,' the cost of repairing casing leaks caused by external corrosion may exceed $4 million per year. In addition, well damage and lost production resulting from casing leaks probably costs the petroleum industry an additional $5 to $6 million per year. Concern about the cost of external casing corrosion led to an extensive laboratory study of factors causing this external corrosion and to the development of a new approach to its prevention. This paper presents a discussion of various causes of external casing corrosion, details of laboratory studies and the results of the field use of an oxygen scavenger in well cementing fluids to prevent the external corrosion of oil-string casing. Measurements on test wells over a period of several years show that cathodic-protection current requirements are greatly reduced when hydrazine is used in cementing mud. Reduction of current requirements can be interpreted to mean that removal of oxygen by hydrazine has greatly suppressed corrosion cells on the external surface of the casing and thereby, has reduced corrosion. To date, hydrazine has been used by the Standard Oil Co. of California in more than 200 well completions. KINDS OF CASING FAILURES A survey of a large number of casing leaks disclosed four types of external casing failures — water-line, casing-casing, collar and body failures. These types are identified largely by their location on the casing. Water-line failures are found just below the surface of water or mud in the casing annulus. Casing-casing failures occur on the oil string just below the shoe of the surface string. Collar failures are found in the threaded ends of casing joints where they are screwed into casing collars. Body failures may occur at any point on the body of a casing joint. Ex- amples of each kind of failure have some of the general characteristics that are shown in Fig. 1. Water-line failures usually result in the circumferential severance of an oil-string casing. The corrosive action causing a water-line failure usually is sharply defined and is limited to a short length of the casing. Casing-casing failures usually are accompanied by pitting corrosion distributed around the oil-string casing for distances up to 100-ft below the shoe of the surface string. Casing-casing failures may also sever the casing. Collar failures seem to start on the first thread at the bottom of recesses between collar and casing joint. Corrosion proceeds across the threads by what appears to be a normal pitting mechanism. Both casing and collar are severely attacked. Body failures are the result of highly localized pitting at any point on a casing wall. Besides the pit that perforates a casing, a large number of other pits usually are found along one side of the casing joint. The pits occasionally are filled with corrosion products consisting largely of oxides and sulfides.' Frequently, the mill scale is largely intact on the rest of the casing. Examination of a casing failure does not always reveal the cause of the failure. Frequently, the necessary details are destroyed when the failure occurs. For example, formation water flowing through a perforation at high velocity may enlarge the hole and destroy any remaining evidence of the cause of the failure. One way to obtain undistorted information about a failure is to study the nature of other pits on the casing in the vicinity of the failure. A study of such pits frequently suggests that they are characteristic of an attack resulting from the differential availability of molecular oxygen.

By Paul A. Beck, John Towers, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350' to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.' Fig I shows a log D vs. log t plot of French's data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French's data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.' Walker's specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker's data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949