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By Frank Marotta, Louis B. Lesem, Frank Greytok, John J. McKetta

Although one of the primary variables in the calculation of the flowing bottom-hole pressure in gas wells from surface measurements is the temperature at any point and its distribution in the flow-string, only few experimental data are available in the literature and little attention has been given to analysis of the problem. Virtually all of the recently published methods of calculating flowing bottom-hole pressures depend on the assumption that either the temperature is constant at some average value or that the variation is linear with depth. The purposes of this work are to analyze the problem theoretically and to verify the analysis by comparison with experimental data so that practical problems in the analysis of the behavior of gas wells can be solved with greater accuracy, reliability, and ease. MATHEMATICAL OUTLINE OF PROBLEM Assuming that: 1. The mass velocity and chemical composition of the gas stream are constant and in normal gas well operations, the change in linear velocity in the entire flow-string is trivial, 2. The product of the density and heat capacity of the gas is constant, 3. No horizontal temperature gradient exists in the gas stream, 4. Net flow of heat by conduction within the formation and in the gas stream in the vertical direction is trivial in magnitude and can be neglected, 5. The regional vertical geothermal gradient is constant, and 6. The temperature of the gas entering the borehole is constant, and equal to that of the reservoir, a set of two simultaneous, linear partial differential equations with appropriate boundary conditions was derived to describe the temperature distribution in the gas stream and the surrounding formation. These equations were solved by operational techniques for the distribution of temperature in the gas stream. The resulting integrals were evaluated numerically on an IBM 604 at the Machine Accounting Div. of the Railroad Commission of Texas. DERIVATION OF FUNCTIONS FOR THE DISTRIBUTION OF TEMPERATURE The physical system is a circular hole of radius a in an infinite medium with thermal conductivity K, density p8, and heat capacity c,. Under shut-in conditions the well is in thermal equilibrium with the surroundings and the increment in temperature is given by - ?T3/L x. Gas of density pg and heat capacity c.. flows upwardly through this hole in the direction of increasing x with a linear velocity W. Writing a heat balance on an element of gas ?x in thickness, convective heat transfer + conductive heat transfer + energy required to lift a unit mass of fluid = change in energy content. pa2W po Co To - pa2Wpo Co To x+xx - 2apK?x ?T8/?r r=a - Wpa2 po?x/778 = CoPopa2?x?To/?t... Dividing by (copopa2?x) and taking the limit as ?x tends to zero, -W (?To/?x + 1/778Co) + 2 K/a Po Co ?T3/?r r=u = ?To/?t

Jan 1, 1958

By J. S. Aronofsky, R. Jenkins

A simple means of predicting the flowing well pressure history in a natural gas reservoir has been developed. The differential equation for unsteady radial flow of gases through porous media was solved by numerical methods using electronic punch card machines. The results obtained from these calculations are presented in a generalized form which is believed to be most convenient for engineering use. These results are compared with those presented in a paper by Bruce, et al4. An effective radius of drainage has been defined which permits the equation of steady state gas flow to be used easily to predict well pressures in gas reservoir depletion. An equivalent effective radius of drainage is defined for liquid flow systems and a comparison is made of the gas solution to the liquid solutions. INTRODUCTION This paper presents a numerical method for describing the transient flow of gases radially through a porous medium from which the production rate is specified. The results obtained from these calculations are presented in a generalized form which is believed to be the most convenient for engineering use. The principal application of these calculations should be to flow in natural gas reservoirs, in the interpretation of pressure drawdown tests, in the estimation of reserves, and in calculation of injection pressures required in gas injection and cycling operations. The evaluation of natural gas wells is based upon back-pressure tests in which measurements of production rate and flowing well pressure are made for periods of one, two, or more days. The flow is assumed to have stabilized at this time, and the observed values of pressure and production rate are used with standardized formulae to determine the well's allowable production rate. Furthermore, the results obtained from such a test of short time duration are extrapolated in such a manner to allow a prediction of what the well pressure will be at some future time for a specified (but possibly untested) flow rate. The manner of conducting such back-pressure tests suggests several questions as follows: 1. 'What is the definition of stabilized flow and what factors determine the length of time required for the flow to become stabilized? 2. How may the recorded values of pressure and rate be utilized? 3. As the well is produced and the reservoir pressure falls, how will the flowing well pressure change? Can this flowing well pressure be predicted from the back-pressure test? 4. Are the results obtainable from the test influenced by a particular procedure used in obtaining the results? 5. Is it possible to estimate the gross reservoir permeability from back-pressure data? It is not within the scope of this paper to provide solutions Or even to discuss adequately all the above questions. However. in considering such matters, the

Jan 1, 1955

By J. M. Campbell, T. S. Buxton

The most widely used methods of predicting the volumetric properties of gas are based on the principle of corresponding states, which asserts that the compressibility factor is a universal function of reduced temperature and pressure. Previous studies have shown that the acentric factor, as proposed by Pitzer, l is an important addition to reduced pressure and reduced temperature as factors affecting the compressibility factor. Results of this study indicate that, if the pseudocritical temperature and pressure used to determine the reduced conditions are adequately predicted, characterization of natural gas-carbon dioxide mixtures with the acentric factor will allow reliable determination of the compressibility factor. Comparisons of predicted and experimental compressibility factors have shown that the pseudo-critical constant rules of Stewart, Burkhardt and Voo 2 are satisfactory for hydrocarbon mixtures. However, these rules fail to predict the pseduo-critical constants for hydrocarbon-carbon dioxide mixtures. Based on graphically determined pseudocritical temperatures for binary hydrocarbon-carbon dioxide mixtures, a correlation which gives the required correction to the Stewart, Burkhardt and Voo rules was prepared and a compressibility factor prediction technique was proposed. To test the proposed technique, compressibility factors for live mixtures of methane, carbon dioxide and either ethne or propane were experimentally determined at 100, 130 and 160F and pressures up to 7,026 psia. The predicted and experimental compressibility factors for these live mixtures had an average absolute deviation of 0.55 percent. INTRODUCTION Two-parameter generalized correlations based on the principle of corresponding states (PCS) are presently available for reliably predicting the compressibility factor of lean natural gas, i.e., natural gas with low concentrations of hydrocarbons heavier than methane. When these same correlations are used for mixtures of natural gas and carbon dioxide, large deviations between actual and predicted compressibility factors are observed. This study was undertaken to provide a means for accurately predicting the compressibility factor for such mixtures. In the past, two avenues of approach have been employed to extend the applicability of the PCS. The first has been to introduce additional parameters. The second has been to develop combination rules for predicting pseudocritical constants which do not suffer from the limitations of the commonly used molal average constants. In this study, both of these approaches have been considered and employed to arrive at a method for predicting the compressibility factor of mixtures of hydrocarbons and carbon dioxide. SELECTION OF A THIRD PARAMETER Failure of the original PCS to predict the compressibility factor for all pure gases, regardless of their mass, shape or polar moment, has led to the introduction of additional parameters into the PCS. Parameters have been introduced to correct for quantum deviations,3-5 non-spherical or globular shapes6-9 and for polar moments.8-12 In addition to these parameters which are based on some microscopic property and intended to correct for some specific cause of deviation, more general parameters based on some bulk property have also been introduced.1913-16 To use additional parameters to correct for each of the possible causes of deviation among the individual constituents of a gas mixture would require a rather complex form of the PCS. To maintain the PCS in as simple a form as possible, it is more desirable to have a single third parameter which is based on some bulk property influenced by several of the factors causing deviations. The third parameter selected for use in this study is a factor originally proposed by Pitzer.9

By F. W. Jessen, R. W. Durie

The development in the laboratory of mall salt cavities illustrated that the rate at which salt dissolved was affected by the rate at which fresh water was injected into the cavity. Experiments carried out with small salt cores indicated, however, that the rate of salt removal with forced convection was not significantly different from that with natural convection, provided the flow was in the laminar range. The rate of salt removal was apparently controlled by the water salinity, which was indirectly determined by the rate at which fresh water was injected. With turbulent flow at the salt surface, the rate of salt removal could be increased several-fold with the same salinity in the cavity. A quantitative evaluation of the rate of salt removal under natural convection was attempted by using techniques developed for the analogous heat convection system. The values of the rate of salt removal obtained experimentally were considerably greater than the calculated values due to surface irregularities. To determine the effect of these irregularities, the rate of salt removal was found for a smooth surface by experimentally determining the rate of salt removal as an irregular surface developed and then extrapolating this trend back to initial time. Excellent agreement between the experimental and calculated values then were obtained. INTRODUCTION Underground cavities leached from massive salt formations have been used extensively for many years for storing LPG products. The development techniques for storing methane gases in the liquid state at a low temperature leads to speculation that underground salt cavities of controlled geometry may be quite important in this field. In any case, the increasing number of salt cavities used for storage indicates an impending need for a better knowledge of the washing process to efficiently develop maximum storage volumes within specified regions. It is the purpose of this paper to discuss some aspects of -the mechanism of the dissolution of salt in the formation of cavities of controlled geometry. Although no attempt is made to resolve the problems that may be associated with the storage of methane in the liquid state in salt formations, the fact that salt cavities can be formed at reasonable cost would appear to justify investigation in this direction. Further, underground cavities have the advantage of allowing storage at higher pressures (and hence higher temperatures) than surface installations. Although the thermal conductivity of salt is somewhat higher than frozen earths, 0.017 cal/(sec) (cm)(c) for salt at 32F vs 0.005 cal/(sec) (cm) () for ice at this temperature, this disadvantage is offset by the higher storage temperature in underground cavities. For example, at atmospheric pressure, the temperature of liquid methane would be —258F. In a storage cavity at 2,000 ft, the pressure would be approximately 1,000 psia, which would allow a storage temperature of -9OF. The formation temperature would be roughly 110F at this depth, hence the total temperature differential would be 200F. Under surface storage conditions the corresponding temperature difference would be some 333 F (75 F + 258 F). The results of this difference can be compared more readily by substituting the appropriate values of thermal conductivity, temperature difference, heat capacity and density into the solution of the diffusion equation for the unsteady linear conduction of heat. For the underground salt storage, the heat flux is 15cal/(sec) (sq cm), where t is the time in seconds from the initiation of the cooling. For the surface system, and using the thermal properties of ice at the average temperature, the corresponding figure is 21cal/(sec) (sq cm). Hence, the heat losses through ice under surface conditions would be some 30 per cent higher than the underground salt storage. This ratio would vary, considerablv. Of course, for other conditions, but it indicates that an advantage over surface facilities may be obtained by storage in underground salt cavities.

Jan 1, 1965

By M. R. Tek, F. H. Poettmann, M. L. Grove

The general problem of single-phase natural gas flow through porous media has been considered both by mathematical analysis and field experiments. Theoretical studies on the fluid dynamics of natural gas wells resulted in derivations of expressions which permit a ber-ter understanding of the flow mechanism for conditions under which Darcy's law is no longer valid. In applying these results to natural gas production and testing technology, special emphasis war placed on the study of low permeability, slowly stabilizing formations. These applications resulted in a method of predicting the performance coefficients of tight natural gas wells. The calculation of the performance coefficient requires the determination of the "test-index", pkh/µ, the drain- age radius, R, and the effective wellbore radius, rw. Methods for estimating these parameters from field data were also developed. Field data from 15 wells were collected and analyzed. The measured values of the performance coefficients were compared with the predicted values. This statistical evaluation gave a bias of 7.14 per cent and a standard deviation of 11.6 per cent. INTRODUCTION The performance of a natural gas well is determined by the physical properties of the reservoir rock, the extent and the geometry of the drainage area, the properties of the flowing fluid, and the conditions of pressure distribution within the drainage matrix. The relation between the quantity of gas delivered and the pressure drop within the reservoir is characteristic of the behavior of each well and is often referred to as the back-pressure behavior of the well. It is well established that for normal, single-phase gas wells the relationship between the gas delivery rates and the bottom-hole pressure take, in general, the form, Q = c(P3 8 -P2 1)n. ,.......(1) where C is the performance coefficient, and n is the exponent corresponding to the slope of the straight-line relationship between Q and (P2 s, — P2 l) plotted on logarithmic coordinates. The determination of a well's performance by the back-pressure behavior not only permits the production engineers to analyze many operating problems, but also provides necessary information useful and essential to predict the future development of the field.' Important engineering and production problems such as calculation of gas deliverability into a pipeline at a predetermined line pressure, design and analysis of gas-gathering lines, determinations of spacing and number of wells to be drilled during field development to meet future market or contract obligations, etc., all depend, at least in part, on the availability and use of reliable back-pressure curves.' In the past the behavior of gas wells was evaluated

Jan 1, 1958

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By H. O. McLeod, J. M. Campbell

This paper presents the results of the data obtained in the first stage of a long-range study at high pressures of the system, vapor-hydrate-water rich liquid-hydrocarbon rich liquid. The data presented are for the three-phase systems in which no hydrocarbon liquid exists. Tests were performed on 10 gases at pressures from 1,000 to 10,000 psia. One of these was substantially pure methane, and the remainder were binary mixtures of methane with ethane, propane, iso-butane and normal butane. Several conclusions may be drawn from the data. 1. Contrary to previous extrapolations, the hydrocarbon mixtures tested form straight lines in the range of 6,000 to 10,000 psia which are parallel to the curves for pure methane, when the log of pressure is plotted vs hydrate formation temperature. 2. The hydrate formation temperature may be predicted accurately at pressures from 6,000 to 10,000 psia by using a modified form of the Clapeyron equation. The total hydrate curve may be predicted by using the vapor-solid equilibrium constants of Carson and Katz' to 4,000 psia and joining the two segments with a smooth continuous curve between 4,000 and 6,000 psia. 3. The use of gas specific gravity as a parameter in hydrate correlations is unsatisfactory at elevated pressures. 4. The hydrate crystal lattice is pressure sensitive at elevated pressures. INTRODUCTION Prior to 1950 many studies had been made of the hydrate forming conditions for typical natural gases to pressures of 4,000 psia.""'"'"" Most of these attempted to correlate the log of system pressure vs hydrate formation temperature, with gas specific gravity as a parameter. One of the more promising correlations was made by Katz, et al, which utilized vapor-solid equilibrium constants. The only published data above 4,000 psia are those of Kobayashi and Katz7 for pure methane to a pressure of 11,240 psia. In the intervening years, most published charts for the high-pressure range have represented nothing more than extrapolations of the low-pressure data, with the methane line serving as a general guide. The reliability of these charts has become increasingly doubtful (and critical) in our present technology as we handle more high-pressure systems. The portion of our high-pressure hydrate research program reported here was designed to: (1) investigate the reliability of existing charts; (2) obtain actual data on gas mixtures to 10,000 psia; and (3.) develop a simple hydrate correlation that was more reliable than those which simply used specific gravity as a parameter. Binary mixtures of methane and ethane, propane normal butane, or iso-butane were injected into a high-pressure visual cell containing an excess of distilled water. Hydrates were formed and then melted to observe the decomposition temperature of the hydrates at pressures from 1,000 to 10,000 psia. EQUIPMENT The equipment consisted of a Jerguson 10,000-lb high-pressure visual cell, a 10,000-1b high-pressure blind cell and a Ruska 25,000-1b pressure mercury pump. The visual cell was placed in a constant-temperature water bath controlled by a refrigeration unit and an electric filament heater. A Beckman GC-2 gas chromatograph was used in analyzing the gas mixtures after each run was completed. EXPERIMENTAL PROCEDURE After evacuating the gas system, the heavier hydrocarbon was injected into the high-pressure mixing cell to that pressure necessary to give the desired composition. This cell then was pressured to 1,100 to 1,200 psia by methane from a high-pressure cylinder. The mixing cell holding the gas contained a steel flapper plate and was shaken intermittently over a period of 15 minutes. After mixing, the valve to the high-pressure visual cell containing excess distilled water was opened, and the gas mixture was allowed to flow into the cell. The temperature in the water bath was lowered 10" to 15'F below the estimated hydrate decomposition point. As a first check, the temperature was increased at a rate of 1°F every six minutes to find the approximate point of decomposition. It was again lowered 1.5° to 5°F to form hydrates. The temperature was raised to within l° of the estimated decomposition point and then increased 0.2F every 10 to 15 minutes until the hydrates decomposed. This procedure was repeated at various pressures to obtain 7 to 13 points for each mixture between 1,000 and 10,000 psia. After completion of the hydrate decomposition tests, the gas mixture composition was analyzed with a calibrated gas chromatograph. These gas analyses have an estimated error of ± .1 per cent.

By A. Satter, J. M. Campbell

Reported herein are the results of a careful and detailed study of the non-ideal behavior of pure gases and their mixtures. Included are: (1) new data on five ternary systems composed of methane, ethane and H2 S; (2) a simple compressibility factor correlation that is inherently superior to present correlations, particularly for gases containing H2S and CO2; and(3) a detailed study of combination rules and the effect of system composition on the choice thereof. This study makes use of the rather large mass of data already available in the literature. A complete re-examination of the data and ideas presented in the last 25 years was considered desirable as a prelude to our basic concern — the effect of diluents on gas behavior. A consideration of both the macroscopic and microscopic properties of gases provides a better insight which, in turn, gives a firmer basis for improved correlation techniques. Such a study has shown that expressing the compressibility factor Z as a function of acentric factor w, as well as reduced temperature and pressure, yields a correlation that is broader in scope. The study of various combination rules has shown that better results are obtained by "tailoring" the rule used to the system composition. To do so improves the basic reality of results by overcoming some of the anomalies often found when using Kay's rule alone. Tentative recommendations are made regarding the most reliable combination rule for use with a given class of gas. The data presented are useful for estimating the direction and magnitude of the expected deviation when using a given rule. Although more work is needed, particularly around the critical region and with CO2 mixtures, the advantage of the classification scheme proposed is apparent. INTRODUCTION When one attempts to write a PVT equation to fit the data for actual gases, greater precision is obtained by the use of a multiple number of empirical constants. This has lead to multiple-constant equations such as Benedict-Webb-Rubin, Beattie-Bridgman, Keyes, etc., which are capable of yielding very precise results for pure gases in a range for which data to get the constants are available. As a matter of practicality, though, the use of such equations for gas mixtures is limited. Because of the infinite number of gas analyses available, any attempt to compile the constants needed requires a prohibitive amount of experimental data. This could be overcome by the use of a combination rule, but there is no real advantage in doing so because the end result offers no practical impovement over the Z factor correlation. The most widely used method of predicting the volumetric properties of pure gases is based upon the "theorem of corresponding states". According to this theorem, "all pure substances have corresponding molal volume at corresponding temperature and pressure if the reference point of correspondence is the critical point". Generalized compressibility charts for gases were prepared first by Cope and associates1 in 1931 and later by Brown and co-workers2 in 1932. However, the most commonly used charts are those of Dodge,3 Nelson and Obert,4 Hougen and atsson: and Standing and Katz.6 The work of Katz and co-workers has provided us with basic data for the hydrocarbons most widely used today. Their original chart6 was compared with a relatively large amount of multi-component data for gases consisting almost entirely of normal paraffin hydrocarbons. A deviation of only + 1.2 per cent was obtained.39 In the 20 years following publication of this work it has been found that the behavior of most mixtures of paraffin hydrocarbons could be predicted by this correlation within at least 5 per cent. Where difficulty has been encountered it has largely involved one or more of the following circumstances: pressures above 4,000 psig, mixtures containing large amounts of heavy ends and/or aromatics, systems in the critical region and mixtures containing polar compounds and/or CO2. The abnormal error sometimes found with such gases, not too unexpected for this method, is

By L. H. Wolfe, J. O. Thieme

The tensile and shear strengths of frozen soil and the compressive strengths of ice and frozen soil were measured These tests showed that the strength of ice and of frozen soil increased as the temperature was decreased. A method is presented for the measurement of thermal conductivity and specific heat of earth and ice. Using the parameters thermal conductivity, specific heat and density, the thermal diffusivity was calculated. Results of thermal property tests establish water as the major variable contributing to thermal property values. INTRODUCTION During the last few years, a considerable interest has developed in underground storage of cryogenic liquids such as liquid natural gas. Because of its economy and safety, underground storage is being used. Before underground caverns could be seriously considered, however, the strength and thermal characteristics of the soil had to be obtained. Methods are presented herein for measuring tensile, compressive and shear strengths, specific heats and thermal conductivities. The tests were performed on two soils at temperatures from ambient to -195C. Because it is difficult to find data in the literature that pertain to a particular soil, ice was used to evaluate some of the experimental procedures. Some of our ice data are compared to the published values. PHYSICAI, PROPERTIES SOIL SELECTION AND SAMPLE PREPARATIONS The physical and thermal tests were performed on recompacted samples of two typical soils that might be encountered in underground caverns: a gray, fire clay that had been pulverized and mixed with water into a pliable mud; and a brown, sandy silt that was dug from a dry river bank and subsequent1y mixed with tap water. The moisture content of the test specimens was 17 to 22 per cent (based on the wet weight of the soil). This amount of water nearly saturated the silt, but the clay was well below the saturation point. The soils are partially described by the sieve analyses (Fig. 1) which show the particle size distribution of the coarser than 44 micron portion of the soils. The curves also show that approximately 75 per cent of the clay and 20 per cent of the silt are finer than 44 microns. The particle size seems to affect some of the physical properties, and the finer than 44 micron portion is important in the thermal conductivity test. Physical specimens were cut with a bandsaw from frozen blocks of the soil. The specimens were then sanded and kept frozen until after they were tested. They were stored at the approximate test temperature for several hours. Then, to equilibrate the samples to the test temperature, they were stored at the temperature at least an hour before they were tested. TEST EQUIPMENT An Instron, which is a constant speed gear-driven instrument, applied force to the samples and drew stress-strain plots of the test. All of the samples were strained at 0.02 in./min. All of the physical tests were conducted in a temperature cabinet that controlled the temperature to 1C. TENSILE STRENGTH Briquette or "dog-bone" shaped tensile specimens were pulled with suitably shaped jaws. This shape of specimen, which is usually used for tensile tests of concrete, is satisfactory for testing frozen soils except that the samples tend to

Jan 1, 1965

By J. W. Wolfe

The Benedict-Webb-Rmbin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predrcted component K-vallles, mixture enthalpies and phase aensities within tile accuracy of available correlations for rune-component mixtures: significant deviations were noted when mixtures contained components heavier than heptune. INTRODUCTION Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas proccssing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently. the best equation of state for describing the behavior of pure, light hydrocarbons over single-and two-phase regions, both below and above critical pressure, is that of Benedict. Webb and Rubin.' The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the clevelopment of their equation as early as 1940.2 The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a serics of articles in 1951,' showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed,'-',"'-':' the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state." Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases. Consequent-

Jan 1, 1967

By David Cornell, D. L. Katz

Procedures for computing turbulent flow of gas in steady state near the well bore and a graphical method for predicting unsteady state laminar flow at distances from the well have been combined to compute pressure gradients in gas reservoirs. Methods are discussed for predicting single and multiple transients at constant flow rate in an infinite reservoir, predicting constant How rate. in a finite reservoir, reproducing and interpreting back pressure test data, and prediction of the behavior of a closed-in gas well. An example of the graphical method is given for a single transient and the results are compared to a published analytical solution. A typical calculation of the pressure gradient in a reservoir and the production of gas is made .starting with data from a hack pressure test. INTRODUCTION The calculation of pressure gradients throughouse a ga-reservoir at any point in its production history is a complex problem involving turbulent flow near the well bore and unsteady state flow of the gas from the reservoir. The problem is complicated further by the variety of boundary conditions that may be imposed upon the flow. Such boundary conditions include finite or infinite reservoirs. constant or variable rates of production, constant or varying bottom hole pressures, complex initial pressure distributions throughout the reservoir, and pressure maintenance through cycling. In addition to these problems there are the practical difficulties associated with natural gas reservoir analysis These might include: (1) variation. in the permeability and porosity throughout the formation. (2) variations in the thickness of the formation, (3) communication of the producing formation with other producing zones. (4) radial variations in permeability due to influx of drilling fluid. acidizing. or the buildup of liquid in the formation around the well, (5) partial penetration of the producing zone. (6) water flood, and many others. These problems will be considered eventually. In the mean- time, it is necessary to present methods of handling the case of radial flow through a homogeneous, regular, producing stratum to a single well uncomplicated by other factors. The idealized case of steady state, radial flow from a natural gas reservoir was studied by Elenbaas and Katz5 and by Mac-Koberts.' An analysis of the unsteady flow of gases through porous media has been made by Aronofsky and Jenkins' for the one dimensional laminar case with the boundary conditions of constant downstream pressure and uniform initial pressure. Solutions for the partial differential equation for unsteady state radial flow of liquids through porous media have been given by Van Everdingen and Hurst" for the constant bottom hole pressure and constant production rate cases for laminar flow in a reservoir initially at a constant pressure. The analogous heat transfer equation has been treated by Perry and Berggren9 for the case of quenching a cylindrical hole in an infinite medium to a constant temperature. The back pressure curve, which involves the variation of the bottom hole pressure as it is determined by the behavior of the reservoir as a whole. has been studied by Rawlins and Schellhardt,10 Binck-lev,' Baumel and Breitung,' and others. No complete. adequate treatment has been given for the unsteady state, radial flow of gases into a cylindrical hole from a porous medium with or without the presence of turbulent flow and for any set of boundary conditions. If one relies only on analytical solutions of the basic equations, a new solution must be obtained for each new boundary condition. Furthermore, the complexity of the mathematical expressions for boundary conditions other than the very simple cases limits the use of analytical solutions. Graphical methods exist, however. that are general in nature, accurate, and readily employed. The analysis of steady and unsteady, laminar and turbulent, radial flow for various boundary conditions with application to specific natural gas well problems by means of graphical procedures forms the content of this paper. STEADY STATE RADIAL FLOW EQUATION FOR LAMINAR AND TURBULENT FLOW A steady state radial flow equation for laminar and turbulent flow through unconsolidated sands has been given by Muskat as discussion of the work by Elenbaas and Katz.5 This equation is based on the properties of unconsolidated

Jan 1, 1953

By A. B. Cook, C. J. Walker, G. B. Spencer

Although water will displace oil from a petroleum reservoir to a greater extent than gas will, there are some reservoirs in which gas rather than water should be used for pressure maintenance. This is indicated by the high-percentage oil recovery in the case history reports on the Pickton field1 in East Texas and the Raleigh field2 in Mississippi. In gas cycling, total oil recovery includes vaporized products from the immobile oil in addition to oil produced by displacement. If a large part of the immobile oil is vaporized, total oil recovery may be higher than that obtainable from pressure maintenance by water injection. However, the amount of immobile oil vaporized may range from almost 0 to 100 percent, and no simple and reliable method has been presented in the literature for calculating oil vaporization. Development of such a method was the purpose of this study. Several papers concerning the calculation of oil vaporization have been published,3 6 and each is based on the concept dealing with K values — equilibrium constants for the various components in reservoir oils. (K for a component in a system of vapor and liquid in equilibrium is the mole fraction in the vapor phase divided by the mole fraction in the liquid phase.) This appears to be the most logical approach. Yet, the problem is too great for a perfect solution, even with modem laboratories to analyze oils and high-speed digital computers to perform calculations; the number of components in reservoir oils is too large. Because of their complexity no two reservoir oils are exactly alike. Also, K values change not only with variations in pressure and temperature but also with composition of the reservoir oil. In addition, during gas cycling, the lighter hydrocarbons tend to vaporize first. Thus, the reservoir oil becomes more dense and less volatile as gas cycling continues. Furthermore, the greatest amount of oil vaporization occurs near the injection well. Therefore, a simplified method is required for calculating oil vaporization because a rigorous method is not practical. The present methods of calculating vaporization generally require knowledge of the reservoir oil composition in which the mole fractions of the lighter components through hexanes are given; the remaining oil is described as C, + (heptanes and others of greater molecular weights). Assigning one K value for the C,+ system provides the simplest solution, but this incorrectly assumes that K for C, + does not change as gas cycling continues. This assumption can cause large errors because the K value may become less than a thousandth of the original after a large amount of oil vaporization. Another way to solve the problem is to determine changing K values for C, + according to how much of the C, + has been vaporized. To determine these values a sample of the reservoir oil is injected into a pressure-volume cell, and dry gas is batched in and out of the cell. Appropriate measurements and tests are made to determine K

Jan 1, 1970

By C. E. Turner, J. R. Elenbaas, R. D. Grimm, J. A. Vary, D. L. Katz

A technique is presented by which well samples and core plugs of dolomite formations are classified by microscopic examination into seven different porosity grades. Quantitative values of porosity and permeability are determined for each grade by a statistical correlation of the core plug test data with the porosity grading system. These quantitative values are applied directly to the grades exhibited in the well samples for the purpose of estimating the reservoir void space for wells that were not cored. The procedure is described for estimating the gas reserves per unit area lor the South Hugoton gas field. but a reserve estimate for the field is not given. INTRODUCTION The miscroscopic examination of well sample; and the graphic recording of their lithologic qualities and other distinguishing characteristics of various geologic formations drilled is both a science and an art of long standing and wide application. Usually the primary objective of a geologist who "sits on the well" and examines the samples are: to identify the formation being drilled, determine the total depth, casing point. and completion interval. In most cases the porosity is described. if done at all, in general terms. such as: trace, scattered, fine, poor, fair, medium. good, excellent, or in some other relative terms. In fields where various geologists have examined samples and recorded observations on many wells considerable variations in lithologic terms and porosity descriptions occur unless there is primary effort to establish uniformity of logging observations and standards of recording observable porosity. When an estimate of the pore volume of a reservoir is made a geologic concept of the processes that control the magnitudes of porosity and permeability is developed by microscopic examination of well samples. The characeristics and appearances are then mentally related to rather general quantitative units of porosity based on physical core data from the same reservoir or on such data or experience in other reservoirs that have similar qualities. The reliability of such estimates depends largely on the variations of the lithology of the formations, the geometric properties of its void system. the extent of comparisons of sample appearances with porosity data, as well as the uniform recording of all relevant characteristics. This statement is particularly significant for dolo-mitized limestone formations of substantial thicknesses and heterogeneity such as the Permian Dolomites of the Hugoton gas field. Jn this field, as well as in most of the Permian Dolomite fields, the producing formations are of relatively great thicknesses in which the porosity and permeability of the reservoir varies substantially in all directions, depending on the crystalline structure. degree and kind of impurities, kind of fossils anti cementation thereof, degree of dissolution. and fracturing. The variations of the lithologic texture of the dolomites and post deposition alterations have resulted in porosities and permeabilities of such magnitudes that only a part of the gross thickness can be counted as "pay." At the time of this study insufficient gas production had been experienced to apply the pressure decline production method in the South Hugoton Field and the electric logs are not definitive enough. The problem of estimating gas reserves in the south part of the Hugoton Field is primarily one of determining the pay thickness and porosity from well samples and core data. The area studied embraced all that part of the field lying south of an east-west line through Guvmon, Okla., anti containing approximately 1.000,000 acres. This paper describes a technique of correlation of physical core data with well samples so that quantitative values of pay thickness, porosity. Permeability, and connate water may be assigned to well samples that are representative of a given interval, and thereby permitting the estimation of gas reserves lor a given unit area. The procedure was developed by a uniform microscopic qualitative porosity grading of the dolo. mite core plugs.. and relating these grades to the respective physical core data on a statistical basis The well sample-were also graded in a Similar manner in order that the quantitative values established lor the core plugs could be applied to the well Sample for wells that were not cored. GRADING OF DOLOMITE A group of experienced geologists was given the assignment of examining the samples on all wells in South Hugoton in order that they could log their observations in a uniform and standardized manner and grade the observed porosity so that it could be related quantitatively to the core data. The group initiated the study 011 chips from cores which bad been tested for porosity and permeability. This study continued until all of the geologists developed a common knowledge of lithologic terms and of the characteristic appearances of the samples and their relations to measured porosity. The characteristic appearances of the dolomite samples under twelve-power magnification as related to their qualitative porosities afforded a classification of the dolomite into :even grades of porosity, ranging from dolomite of no-visible porosity under twelve-power magnification to dolomite of excellent porosity. The assigned grade for a specific 10-ft interval is a weighted average of all visible grades of porosity exhibited by the cuttings representing that interval. The porosity characteristics were recorded by a color graph adjacent to the lithology column in conjunction with a numerical system for further definition of relative porosity as shown in Fig. 1. The three vertical lines to the right of the lithology column each represent 33 1/3 per cent. which lines were used to record the percentage of the samples, for any particular interval. that showed porosity under the microscope. The colors were used to denote actual pore size. i.e., orange. blue and I-ed for pore diameter of one-fourth or less. one-fourth to one-Ilalf. and greater than one-half millimeter, respectively. The area colored 1)). one or more colors represents the percentages of the samples exhibiting pores of the respective size or sizes. The numerals from one to six inclusive shown on the log in

Jan 1, 1952

By A. F. Bertuzzi, M. R. Tek, F. H. Poettmann

A method is presented for predicting pressure drop for two-phase fluid flow in horizontal pipes. A set of 267 experimental measurements randomly sampled from approximately 1,000 measurements from various literature sources was used. Pressure gradients calculated by the procedure developed and compared with the experimental values showed a bias of +0.82 per cent and a standard deviation of 20.8 per cent. The advantatges of this method over other available methods of predicting two-phase flow pressure drop are (a) its comparative simplicity of application, (b) its relative independence of flow patterns, (c) its accuracy, which on the basis of a statistical evaluation predicts pressure drop closer than other available methods, and, (d) its ability to satisfactorily correlate laboratory data from various sources while the correlations from these sources do not appear to agree with one another. The method has been reduced to a simplified graphical procedure, suitable for field use. A two-phase f factor is defined and correlated with parameters involving the flowing gas-liquid mass ratio, a Reynolds number for the gas phase, and a Reynolds number for the liquid phase. The choice of parameters allows the correlation to reduce to the usual f factor plot for the limiting conditions of (111 gas or all liquid. INTRODUCTION The mechanics and characteristics of two-phase flow systems have been of interest throughout the industry for some time. In numerous engineering installations such as pipe lines, chemical reactors, and heat exchangers, two-phase flow conditions are of every day occurrence. In oil production operations it has been desirable, in some cases, to consider transporting gas and oil together in a common pipe from oil field to process plant. The trend toward centrally located stock tank batteries in oil fields has resulted in longer gathering pipelines in which more than one fluid phase is flowing. The increase in the producing capacity of oil wells due to new production tech- niques has created the need for review and re-design of many surface gathering lines for properly handling the increased production. Optimum pipe size for the situations described above has become an important factor. The problem which is of interest here involves the ability to predict the relationship between pressure drop, fluid properties, fluid rates, pipe diameter, and pipe length. Although the literature1,5,10,13,18,19 contains various articles dealing with specific cases of the problem, Lock-hart and Martinelli17 proposed the most general solution. Their method has been later modified by Baker:1 Alves2 demonstrated that different flow patterns are possible for a flow mechanism defined by Martinelli such as gas turbulent, liquid turbulent. Baker explained deviations experienced with Martinelli's correlations on the basis that different flow patterns could exist for the same flow mechanism. Using Martinelli's method of correlatioil, Baker correlated data for each flow pattern for the turbulent-turbulent flow mechanism. Bergelin and Gazley6,7 presented a correlation for predicting gas phase

Jan 1, 1957

By L. Cichowicz, K. K. Millheim

The constant-rate drawdown test performance for a low-permeability, verticany fractured gas well was investigated. A series of gar wells were tested by flowing each well at constant rate until the data could be analyzed using con-ventional radial flow theory. Each well was then shut in to build up. After a sufficient buildup was obtained, another flow Iest commenced but at a higher flow rate than Ihe first test. Again, the well was shut in when radial fiow was obtained. his procedure was repeated for three to four different flow rates. Two wells in the San Juan basin were tested using this procedure. Both wellere fractured after completion, cleaned up and then shut in until flow testing commenced. Test designs of both wells permitted investigation of the most realistic values of egective permeability, wellbore radius and turbulence factor. Also, being able to determine the eflective fracture flow area and vertical fraclure efficiency was inherent with this testing approach. It was observed that fractures in both wells influenced the Pressure behavior for approximately Is to 40 hours (depending on the flow rate) before radial flow was evident. After this time, drawdown data were analyzed using radial pow theory. When a low-permeability gas well has vertitally oriented, induced fractures, the early flow geometry ic. essentially linear. It will be shown how to determine when a flow test has been conducted long enough so lha' the most representative values of effective permeahiiity. wellbore radius and turbulence factw can be calculated. From the linear pressure data, valuable information about The fracture treatment, such as the effective flow area and vertical fracture efficiency, can be determined for vertically froctured wells. Introduction During tests on gas wells in the Sari Juan basin7 initial transient behavior lasted for many days because of the low permeability of some porous media. As a result, stabilized flow performance could not be obtained. If these wells received some type of stimulation treatment, early pressure behavior deviated from conventional theoretical radial Row. When conventional radial flow theory was used to analyze these low-permeability fractured gas wells, larger values of flow capacity and absolute open flow potentials (AOF) sometimes resulted. Wells were assigned open flow poten- tials that proved to be 3 to 10 times higher than the well would sustain over a longer period of production. In some cases where the wells had flowed for longer periods of time during a constant-rate drawdown test, it was noticed that the effective flow capacity appeared to be decreasing with time until a certain value was reached. The early nonradial pressure behavior can be explained If linear flow is assumed. Rusell and Truitt mathematic. ally investigated the vertically fractured well in a bounded area. They showed that early flow behavior was essentially linear and, for x,/x. approximately less than 0.10 radial flow was obtained after short periods of time. Then realistic values of effective permeability and skin could be determined. Scotta experimentaliy studied the vertically fractured well with a heat flow analog. He showed that earb flow was linear, Both studies indicate that, for small values of x,/x,, linear flow approaches radial flow if the well is tested long enough, To help prove this concept of early linear flow caused by induced vertical fractures, two low-permeability gas wells were tested. Both wells received large fracture treatments prior to testing. A vertical fracture was indicated from the analysis of fracture treatments, As anticipated, tests of both wells indicated early linear flow that was later followed by a period of radial flow, Data collected from each well were analyzed. From the well tests, plus other information on each well, the effective permeability, wellbore radius and turbulence factor were calculated. Effective fracture flow areas calculated from test analyses for each well proved to be approximately one-fourth the created area calculated from classic hydraulic fracturing theory: other fractured wells that were tested but not presented in this paper also indicated that the effective fracture flow area was one-fourth to one-third the created area predicted from hydraulic fracturing theory. The vertical fracturing efficiency was estimated from the calculated values of effective wellbore radius and fracture flow area. For the two wells tested, calculated fracture lengths x, were 112 and 105 ft, and the vertical fracturing efficiencies E, were 122 and 183 percent. Development of Flow Model Agnew' showed that most induced fractures below 1,500 ft are vertical. Anderson and Stah15 indicated that most of the fractures they studied were vertical. Thc model proposed for early flow in most vertically fractured gas wells is shown by Fig. 1. This model should approximate early flow behavior until radial flow is reached, at which time a radial model with an effective wellbore radius of 0.5 they will

Jan 1, 1969

By R. E. Holmes, T. W. Leland

The solution to the unsteady-state mass- and heat-transfer equations describing the adsorption of a dilute component from a gas stream flowing through a packed bed is readily applicable to the design of hydrocarbon recovery units. The solution to these equations depends on the assumption of a linear equilibrium equation to relate concentrations on the surface to concentrations in the gas. This assumption is shown to be justifiable for components which are very dilute in the gas stream. This approach permits the prediction of the effects of bed shape and size, cycle time, and gas mass velocity on the recovery of each component. It also allows the time and gas flow rate needed for regeneration to be determined. The equations involve a constant for each component and another constant characterized by the type of adsorbent. These constants must be evaluated from operating data. Values of these constants determined for silica gel are presented. This paper points out the type of experitrrental data needed for a thorough design of hydrocarbon adsorption units. INTRODUCTION The growing importance of adsorption processes to recover hydrocarbons from natural-gas streams has created an urgent need for better methods to design and predict the performance of these processes. Since the original use of solid adsorbents in natural-gas processing was for dehydration, most of the current design methods for hydrocarbon recovery re extensions of those developed earlier for dehydration. These methods are based on an adsorptivity or bed loading factor defined as the amount of a particular component adsorbed per unit weight or per unit volume of the packed bed. The recovery of a given component is then expressed as an empirical function of its adsorptivity on a given adsorbent. In spite of the simplicity and initial utility of these methods, they are not completely satisfactory in that they do not predict the effect of the dimensions of the bed in relation to flow rate and cycle time, and do not predict the distribution of various components along the length of the bed. It is possible, however, to make a considerable improvement in the design of these processes by applying the basic equations of mass and heat transfer applicable to gases containing small concentrations of adsorbing components flowing through granular beds. These equations have been developed and solved by Anzelius,' Furnas,% nd Hougen and Marshall." where G = mass velocity of the inert constituents (assumed to be methane), lb/hr-sq ft, y = weight of an adsorbing component in the gas per unit weight of inert, lb of a given constituent per lb of methane, x = bed length, ft, p, = packed bed density, lb/cu ft, P, = gas density, Ib/cu ft, f = void fraction in the bed, t = time, hours, and w = weight of a given component adsorbed per unit weight of adsorbate free solid, Ib/lb pure adsorbent. The term on the left side of Eq. 1 represents the flow rate per unit bed volume of a component entering less the flow rate per unit bed volume of that component leaving the differential bed length. The terms on the right side represent, respectively, the accumulation rates per unit bed volume on the solid and in the gas phase within the differential bed section. The last term is negligible for this application since pgfv is quite small in comparison with p, and G. The partial differential is determined by the mass-transfer rate between gas and solid in the differential section.

By R. F. Hinds

A pressurizing system was designed and built to apply a radial pressure of 5.000 psi to rock samples. Samples of the Bradford, Weir and Kirkwood sandstones were subjected to radial pressures parallel and perpendicular to the bedding in the system and the changes in conductivity, porosity and permeability were deter-mined. Asymptotic decreases in conductivity, porosity and Klinkenberg permeability were observed over the 0- to 3,500-psi range. From these data, the increase of formation factor over the same range was calculated. The cementation exponent expressed in the Archie equation was found to increase with pressu,re. The rate of change varied from formation to formation. Only small differences were observed for samples taken parallel to the bedding as comnared to those taken perpendicular to it except for the Bradford sand. Above 3,500 psi the data are not good enough to tell if the properties continue to fall-off asymptotically or in a different manner. A possible explanation for the probable litnit of the asymptotic rate around 3,500 to 4,500 psi is that this represents the maximum pressure which the formations have unrdergone during their geological life as a result of burial. INTRODUCTION For many years measurements have been made in the laboratory of the properties of oil-bearing sandstones with little consideration being given to whether these properties had been changed when the samples were moved from their original position in the ground to the laboratory. Relatively little has been reported in the literature on the effect of pressure on the properties of sandstones. The changes in permeability for eight typical consolidated oil-bearing sandstone samples with overburden pressure (0- to 15,000-psi range) was presented by Fatt and Davis' in graphical form. In 1953 Fatt' also reported the relationship between porosity and overburden pressure for four typical consolidated oil-bearing sandstone samples (0- to 5,000-psi range). Fatt later described the changes of formation factor and porosity of 20 typical oil-bearing sandstone samples with overburden pressure changes (0- to 5,000-psi range) giving the values of the coefficients and exponents in the Archie' equation, and the more general Winsauer equation', where C, k and m are empirical constants, F is the formation factor, and + is the porosity. During the experiments of this investigation the core was contained in a neoprene rubber sleeve as shown in Fig. 1. It was held between two steel end members which were mounted in a steel cylinder. The unassembled pressure cylinder with its component parts is shown in Fig. 2. The core was insulated from the two steel end members by a Teflon sleeve with a small hole in the

By A. L. Lee, M. H. Gonzalez, R. F. Bukacek

Experimental viscosity data for methane are presented for temperatures from 100 to 340F and pressures from 200 to 8,000 psia. A summary is given of the available data for methane, and a comparison is presented for that data common to the experimental range reported in this paper. Correlation of the data is presented, and predicted values are given for temperatures up to 460F and pressures up to 10,000 psia. INTRODUCTION The increasing ranges of temperature and pressure at which fluids are produced, transferred and processed in the petroleum and chemical industries stress the need for accurate information on physical properties, both for engineering calculation and for improving the methods used to estimate physical properties. A survey of the literature reveals that disagreements between published data on the viscosity of methane are common and that most investigations have been conducted over restricted temperature and pressure ranges. This situation made it desirable to undertake an investigation with a scope common to most of the literature data available. APPARATUS AND MATERIALS The apparatus used in this investigation was the capillary tube viscometer'described by Dolan,10 with modifications introduced in the general design and operation of the instrument. It has an effective pressure range from 14.7 to 10,000 psia and a temperature range from room temperature to 400F. The design of the viscometer is based on the establishment of a manometric head between two vessels containing the test fluid and a volume of mercury. The reservoirs are connected by a capillary tube through which the test fluid flows and a tube through which mercury flows. A pressure gradient is established by elevating one of the vessels above the other, the resulting flow of mercury displacing the test fluid through the capillary. The schematic diagram of the system (Fig. 1) shows the arrangement of the equipment auxiliary to the viscometer. The density cells assembly (E, Fig. 1) was not used in this investigation since reliable data are available on methane. 23 The assembly consists of a bank of eight 316 stainless steel pycnometers. Experimental values of the density of a natural gas19 and i-butane14 samples have been obtained for pressures up to 8,000 psia and temperatures up to 340F. The methane used was obtained from the Southern California Gas Co. Mass spectrometric analysis showed a composition of 99.8 percent CH4, 0.1 percent C2H6 and 0.1 percent C3H8. EXPERIMENTAL VALUES AND ACCURACY OF DATA Determinations were carried out at several temperatures. With the temperature in the cabinet controlled at a given level, a series of runs were made at various pressures. To establish pressures lower than that obtained from the methane cylinder, it was necessary to vent the gas slowly to the atmosphere until the desired pressure was reached. The consistency of the test run time for a particular condition can be used as a criterion for the accuracy of the data. A further check is obtained by comparison of the viscosity values obtained using different driving heads. To establish the instrument's reproducibility, a large number of runs were made at three completely different conditions of temperature and pressure. Data obtained were analyzed statistically to determine the most reliable value for the variance of the experimental data. It was found that the variances of the data taken at different experimental conditions were not statistically equivalent, but they were small. The largest variance was found at 8,000 psia and 100F, where the standard deviation was 0.385 micropoise. Therefore, 99.9 percent of the data can be expected to fall within 1.15 micropoises of the population mean, except for the intervention of systematic errors in operation.

By D. B. Robinson, C. A. Macrygeorgos, G. W. Govier

Experimental data have been obtained on the volurrletric behavior of ternary mixtures of methane, hydrogen sulfide and carbon dioxide at temperalures of 40°, 100" and 160°F up to pressures of 3,000 psia. The results indicate that the compressibility factors for this system do not agree with compressibility factors for sweet natural gases at the same pseudo-reduced conditions. The deviation increases as the temperature and methane content decrease. Discrepancies of up to 35 per cent were observed. A careful analysis has been made of the existing pUrblished data on compressibility factors for binary systems containing light hydrocnrbons and hydrogen sulfide or carbon dioxide. It has been found that the deviation of actual from predicted compressibility factors for methane-acid gas mixtures is a function of the methane content and the pseudo-critical properties,.v of the mixture. The ratio between actual compressibility factors for methane-acid gas mixtures and compressibility factors for sweet natrlral gases at the same pseudo-reduced conditions has been currelated over a range of pP,, from 0 to at least 7 arid a range of pT, from about 1.15 to at 1east 2 0 with an error not exceeding 3 per cent and over most of the range within I per cent. The validity of the correlation for mixtures containing appreciable hearvier hydrocorbons has not been fully established, but it is shown to be preferable than the use of a corretation based only on hydrocarbons. INTRODUCTION Although a relatively accurate method for predicting compressibility factors of pure materials is provided by charts based on reduced properties and the assumption that the compressibility factor is a unique function of T P and z the determination of the correct values of compressibility factors for gas mixtures is somewhat difficult. Two general methods of dealing with gaseous mixtures have been proposed. The first assumes a direct or modified additivity of certain properties of the mixture in terms of the properties of the individual components. Examples of this method are based on the familiar laws of Dalton and Amagat. The second method averages the constants of an equation of state applicable to the pure components. Both of these methods are of limited value in engineering calculations because the first usually provides reliable answers only over narrow ranges of pressure and temperature and the second is cumbersome to handle. In petroleum engineering practice accurate estimations of the volumetric behavior of natural gases arc frequently required. To fulfill this need, several generalized compressibility charts have been developed.' ' Of these, the one prepared by Standing, el al is widely used at present. In the construction of charts of this type a third method for dealing with mixtures has been followed. It is based on correlation of pseudo-critical properties as outlined by Kay and calculated from the critical properties of the individual components in a mixture. Although these charts provide relatively accurate information on the compressibility of dry or wet sweet natural gases, they are less reliable when used for gases containing high concentrations of hydrogen sulfide or carbon dioxide or both. Thus, an experimental program, although time consuming, is the best means now available for the determination of the volumetric behavior of sour or acid gas mixtures. An increased interest in the behavior of these gas mixtures, particularly in connection with some of the fields in Western Canada where the acid gas concentration of the reservoirs may be as high as 55 per cent and where hydrogen sulfide alone may be as high as 36 per cent, provided the incentive for this study. It was the purpose of the investigation to determine the volumetric behavior of selected mixtures of methane, hydrogen sulfide and carbon dioxide over a range of temperature from 40" to 160°F and at pressures up to 3,000 psi. EXPERIMENTAL METHOD The apparatus used in this investigation was basically the same as that described by Lorenzo.'" The amount of each pure component used in preparing the gas mixtures was measured over mercury in a glass-windowed pressure vessel. The pure components were then transferred individually in the desired amounts to a second glass-windowed pressure vessel where the volumetric behavior of the mixture was determined. Volume was varied by mercury injection or withdrawal. The capacity of the cell was about 125 cc. Temperatures in the cells were measured with copper-constantan thermocouples and a Leeds Northrup semi-

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.'," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".'"', '" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"' have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.' The final expression presented by Starling and Ellingto'n is: i'. (micropoise) -- /t,, exp rX(7') p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) ' ' ' X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay's method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967