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By Francis J. Quinn

The Natural Gas Act, of 1938, which put interstate pipelines under the jurisdiction of the Federal Power Commission, did not place a protective competitive shield around such companies - nor does any provision of the act guarantee them a profit. Natural-gas pipelines are competitive with each other and also with the coal and oil industries. Gas distributing companies must compete not only with the coal and oil industries, but also with the electric industry. Natural gas has captured markets from oil, which had taken them from coal. Oil men contend that gas prices have: been, held to an artifically low level by regulation. The electric industry is moving into the space-heating market, which pleases the coal people because the coal industry's largest customer since losing the railroads to dieselization has been the electric companies. The coal industry is attempting to monopolize the industrial and electric generating market through government intervention, and this is being done under the guise of concern for the national welfare through advocation of a "National Fuels Policy purporting to, further the cause of fuel conservation. Such a policy is contrary to American principles and would result in the individual's loss of freedom of choice and ultimately, in less reserves of preferred fuels because of diminished exploration efforts.

Jan 1, 1961

By Louis V. Bender

THIS paper gives a short review of the installation for and the use of gas, as a. fuel, at the Anaconda Reduction Works of the Anaconda Copper Mining Co. Before putting in gas tile fuels used were pulverized coal, lump coal, coke distillate and oil. These fuels are now almost entirely eliminated. For nearly fifty years bituminous coals from Wyoming and Montana fields had been used. These coals were of a good grade, analyzing 11,300 B.t.u. and having an ash content of 12 per cent. When hydro-electric power replaced steam-driven equipment, the coal requirements were reduced; and, on account of improvements in metallurgy and/ or in furnace design, the quantity was lessened. Later, oil and distillate were introduced and used in some of the operations. All of these things tended toward the lessening of the amount of coal used, and had it not been for the increase in the size of the plant, the tonnage used would have been small when the change was made to gas.

Jan 1, 1932

By E. R. MARBLE

THE introduction of a new fuel, such as natural gas, necessitates careful study where it has not been used previously. At the El Paso smelter natural gas required the installation of apparatus with which no one at the plant was familiar, either as to the type of equipment needed or as to the burning of the gas in it. Observation of existing installations of a similar character and assistance from gas engineers served as a basis to determine what was advisable to use. The gas line entering the plant goes to a metering station equipped with a duplicate system of pressure regulators, a temperature recorder and the gas company and smelter orifice meters in tandem. There are three distribution lines that can be inter-connected at a later date, if necessary, to assist in equalizing the plant load. All the larger lines are of heavy

Jan 1, 1930

By Don B. Carson, Donald L. Katz

NATURAL gases under pressure form crystal-line hydrates with water. Experimental data are reported on four-phase equilibrium for the methane-propane-water, methane-pentane-water, and methane-hexane-water systems. Temperatures and pressures for equilibrium between gas, water-rich liquid, hydrocarbonrich liquid, and hydrate were measured, as well as the percentages of methane and propane in the hydrate. The data indicate that natural gas hydrate behaves as a solid solution and that pentanes and heavier hydrocarbons do not enter into the solid phase. Vapor-solid equilibrium constants are presented that permit the approximation of the conditions for hydrate formation, from the composition of a gas. INTRODUCTION Natural gas hydrates have been the object of considerable research in recent years, because of the trouble they have caused in the natural-gas and natural gasoline industries. Natural gas hydrates are white crystalline compounds of water and gas, which, under pressure, exist at temperatures considerably above the freezing point of water. Because of the relatively high temperatures at which the hydrates exist, they become a nuisance in high-pressure gas operations where water is present, since their formation causes partial or complete plugging of valves and pipes. From a practical standpoint, the trouble incident to hydrate formation has been solved by dehydration of the gas before it enters the plant or pipe line, or by other remedial measures. Extensive work on gas hydrates in the latter part of the nineteenth century, by Villard1 and others, gave data on methane hydrate and on ethane hydrate. Schroeder summarized these theoretical studies.2 Hammerschmidt3 introduced the information on gas hydrates to the gas industry and Deaton and Frost4-6 gathered a considerable number of data on the behavior of natural gas hydrates. Recent papers7,8 have extended both the data and the theory of these hydrates. At present, data are available on temperatures and pressures of hydrate formation for pure methane, ethane, propane, n-butane, methane-ethane mixtures, methane-propane mixtures, methane-butane mixtures, and some 15 natural gases, all in the presence of excess water. However, up to the present time no method has been available for predicting the temperature at given pressures or the pressure at given temperatures at which natural gases will form hydrates if saturated with water. This paper pre¬sents data on the methane-propane-water, methane-pentane-water and methane-hexane water systems in four phases, one of which is the hydrate. The application of the phase rule to the methane-propane-water data proves that hydrates behave as solid solutions. The data of this paper and those in the literature were used to develop vapor-solid equilibrium constants,8 which permit prediction of conditions of hydrate formation from the analysis of a natural gas.

Jan 1, 1941

By J. E. Powers, T. D. Taylor, N. E. Wood

A computer program has been developed to simulate a gas transmission 1ine operating under transient conditions. The program was developed by application of the basic mass and momentum balance equations. The nonlinear equations thus obtained were transformed by the method of characteristics and finite-difference techniques to make them suitable for machine computation. Three tests of the computer program were made. In each of these, the initial condition was assumed to be steady-state flow, the inlet density was held constant at the initial condition, and the outlet mass flow rate was varied with time. One test was theoretical in nature, but the others were made for direct comparison with actual field data. Results of the tests are presented in graphical form. INTRODUCTION Theoretical investigations of the transient flow of gas in long pipelines have been limited in number. In 1951, Olds and Sage4 developed a gaphical method of solving the nonlinear flow equations describing transient gas flow in a long pipeline. Research in this field at the U. of Oklahoma was initiated by Nelson1 in 1956. Nelson utilized a computer to solve numerical equations involving a lengthy trial-and-error procedure, and his results have been reported in the literature? It does not seem likely that Nelson's method can be extended to the analysis of transient behavior of pipeline networks; therefore, the investigation to be discussed in this paper was undertaken to improve and extend the previous work. The following discussion presents, briefly: (1) the basic differential equations governing transient flow, (2) transformation of these equations into a form suitable for machine computation. (3) role of boundary conditions in the calculations, (4) a very brief description of the computer program which was developed to simulate the pipeline and (5) results of tests of the computer program.

By L. K. Nemeth, H. T. Kennedy

The investigation presented in this paper was performd to develop a relationship between the dewpoint pressure of a hydrocarbon reservoir fluid and its composition, temperature and characteristics of the heptanes-plus fraction. This is part of an over-all program to develop correlations for the essential properties of reservoir fluids with the composition, temperature and pressure. In all, 579 dewpoint pressures, determined experimentally on 480 different condensate systems along with their compositions and temperatures, were obtained from the literature and from previously unpublished sources. Compositions were expressed in terms of mol fractions of methane through heptanes-plus, nitrogen, carbon dioxide and hydrogen sulfide, and the molecular weight and specific gravity of the heptanes-plus fraction. Distribution of the samples assured a good representation of most of the major oil-producing areas in the world. A multiple regression analysis program written for the IBhl 7094 digital computer was used to compare numerous equations and to calculate their coefficients. The final equation containing 11 coefficients resulted in an average absolute deviation of 7.4 percent for all the samples. Segregation of data on the basis of one or more variables did not materially improve the results. The correlation developed is useful in predicting the dewpoint pressure of condensate reservoir fluids from variables normally measured in the laboratory. INTRODUCTION In any discussion of the dewpoint of hydrocarbon mixtures, it should be noted that there are two kinds of dewpoints which must be distinguished. The first type, or normal dewpoint, usually occurs at low pressures as dry gas is compressed to the point where liquid first forms. The second type, sometimes called the retrograde dewpoint, occurs when a gas mixture containing heavy hydrocarbons in solution is depressured until a liquid is formed. The first type, as applied to condensate mixtures, would normally be below atmospheric pressure and would be of no interest in reservoir performance. The second type is of great significance in interpreting reservoir behavior and is the property referred to throughout this paper. Laboratory measurement of dewpoints is laborious, expensive and subject to many errors, and it is desirable to find a reasonably accurate method to predict dewpoint pressures from the composition and other readily available properties normally measured on the fluids. A possible method of calculating dewpoint pressures would be to employ a set of equilibrium ratios (K-values). 1 However, the K-values themselves depend on composition as well as temperature and pressure; presently their use adds nothing to the accuracy of predicting dewpoints. If future correlations provide a significantly better method of estimating K-values for heavy hydrocarbons, they may be of greater use. REVIEW OF LITERATURE In 1944, Olds, Sage and Lacey 2 studied the behavior of fluids from the Paloma field. Properties of seven mixtures were studied at temperatures ranging from 100 to 250 F and at pressures up to 5,000 psia. From the information obtained, the influence of composition and temperature upon the dewpoint was determined. It was found that removal of the intermediate molecular weight components from the mixture resulted in considerable increases in the dewpoint pressures. Results indicated that the effect of changes in temperature was relatively minor when compared with the effect of modifying the mixture by removing the intermediate components. Thus, removal of propane and butanes resulted in an increase in dewpoint pressure more than 10 times greater than a change in temperature from 100 to 250 F. The authors stated that althouah

By J. H. Henderson, H. J. Ledbetter, N. B. Gove, J. D. Griffith

INTRODUCTION The results of a series of laboratory flood tests using liquid Iso-butane to displace refined oils from test cores are pre- ented and interpreted on an empirical bask. The study Revealed the similarity of the miscible liquid displacement to that of the immiscible-fluid displacement mechanism. The efficiency of the iso-butane flood decreased markedly as the oil Viscosity increased. but the effect of injection rate on the effectiveness of the primary production stage was negligible over the range investigated. The presence of free-gas saturation prior. to iso-butane breakthrough increased the volume of iso- Butane required to recover a given percentage of the oil present. Injection of liquid i.e.-butane prior to water follicle sculpted in a marked improvement in oil recovery by the water flood. INTRODUCTION The production of petroleum is often enhanced by the injec-1i1)n of extraneous fluids into the reservoir. It has been suggeited that the injection or cycling of a wet gas or a liquefied petroleum gas would he instrumental in increasing the effic.ienr!; of oil recover! to a greater degree than the commonly injected fluids. dry pas and water. Although instances of injection of light liquid hydrocarbons are not unknown, a systrmatic recording of the result is unavailable and superfi- cially, the practice gives the impression of being economicaIIy unsound. For specific types of displacement, analytic: solutions have been advanced which aid in understanding the physical mechanisms involved. However, there is no generalized theoretical concept which permits adequate prediction of displacement efficiency from a knowledge of readily measured reservoir rock and fluid properties. The Buckley-Leverett approach to oil displacement by an immiscible phase is an admirable analysiy of that type of mechanism. Dykstra and Parsons have introduced a useful concept in their evaluation of the role of the mobility ratio and its merit in rationalizing displacement phenomena. Everett, Gooch and Calhoun3 in their report on the effect of viscosity ratio and miscibility have pointed out the lack of a comprehensive theoretical approach and the desirability of investigating the mechanism of miscible-miscible displacement. In lieu of a well-developed theory concerning miscible-111isci1)le displacement and in view of the scarcity of engineering information on actual LPG injection trials, the limited program of laboratory experimentation described below was undertaken. OBJECTIVES The original broad objectives of the program, to study the oil recovery process using LPG as the displacing phase, defined the direction and scope of the laboratory tests. The specific objective. of the experimentation were to evaluate

Jan 1, 1953

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 Lee Hillard Meltzer, Ralph E. Davis

INTRODUCTION During the past few years emphasis has been placed upon methods of estimating the future expectancy of gas production from natural gas fields. Before technical methods were applied, the production expectancy over future years was based upon the knowledge of gas well behavior, learned through long experience and embedded in the "know-how" of men long in the gas producing business. It is doubtful that a technical study of future expectancy of a gas field or a group of fields was ever prepared for the preliminary planning of a natural gas pipe line system built prior to about five years ago. The decline in well production capacity was naturally recognized by all familiar with the business since its earliest beginnings more than 75 years ago. In 1953, the Bureau of Mines published Monograph Number 7, "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices," which gave to the industry the first technical analysis of the decline in production of individual gas wells. This method affords a means of estimating the future production in relation to decline in reservoir pressure. The demand for technical determination of expectancy of future gas productivity from fields or a group of fields led technical men to the application of the knowledge of well behavior to the problems. The decline in a well's ability to produce as pressures declined could be estimated by the use of the curve known as the "back-pressure potential curve" as developed by the Bureau of Mines. A field containing few, or even numerous, wells could be analyzed on the basis of the sum of potentials of all wells. In most studies of this nature, the problem is to estimate the rate of production that can be expected, not only from present wells but also, from wells that will in the future have to be drilled into the reservoir being studied. The "back-pressure potential" method requires that the following data be known or estimated: (1) Proved gas reserves. (2) Current shut-in pressures and rate at which shut-in pressures change with production. (3) Back pressure potential data on wells in the source of supply. (4) Ultimate number of wells which will supply gas, and their potential. (5) Limitations on productivity such as line pressures against which the wells will produce, friction drop in the producing string, and so forth. It is evident that the resulting estimate of gas available in each year for a future of say, 20 years, contains many uncertainties. While the method may have considerable merit for a field that is fully developed, it cannot be completely dependable in fields that are only partially developed. In such cases, some of the data upon which it is based can only be estimated or assumed. In the study of this problem during the past few years, a method has been developed which we believe has great merit, especially when applied to fields subject to substantial future drilling, and when applied to the study of fields which, on the average, appear to have characteristics similar, in general, to the average of the fields used in the development of the "yardstick" outlined herein. From an analysis of the production history of 49 reservoirs which are depleted, or nearly depleted, a curve has been constructed which shows the average performance of the reservoirs during the declining stages of production. When properly applied, this "average performance curve" can be used to determine the stage of depletion at which a reservoir or group of reservoirs will no longer be able to yield a given percentage of the original reserves. "AVAILABILITY" AND "AVAILABILITY STUDIES" The rate at which. a reservoir will yield its gas depends basically upon physical factors, such as the thickness and permeability of the sand, the effect of water drive, if any, and other conditions, and upon economic factors, such as the number of wells drilled. Within the ranges set by the physical conditions, a rate of delivery tends finally to become established. The rate (or range of rates) represents a balance between the interests of the operator, who desires the maximum return from his property and of the pipe line owner, who desires to maintain a firm supply for his market. This balance, which is influenced by the terms of the contract, determines the capacity which will be developed by the operator, and the time and rate at which the decline in production is permitted to occur. Thus the "availability" of gas

Jan 1, 1953

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 K. H. Coats

This paper describes an approximate technique for handling the problem of percolation of evolved gas upwards through the oil column in computer simulation of natural depletion. This technique has been incorporated into a general model for simulating three-phase flow in one, two or three dimensions. The mathematical model for perfonning these calculations is described in detail in a separate article. 1 While vertical gas percolation occurs during natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle reel or bioherm. The reel may have an areal extent less than one section with a thickness of up to 800 It. The upward percolation of evolved gas often limits the time step in calculations as little as one day. Using this small time step, computer expense for a single 30- to 40-year simulation on even a one-dimensional basis has exceeded 92,000. The method described here for handling the percolation allows time steps of 60 days or more (depending on reservoir size and production rate), resulting in a considerable reduction in computing expense. The method also allows calculations in which secondary gas caps build up in tight zones of the oil column below the main gas cap. The validity of the method is indicated in connection with an example pinnacle reef field. Calculated results using a 2-day time step (where the method in question is not needed and not invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results from one- and two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was also performed and the required computing time is given. INTRODUCTION A general analysis for simulating three-dimensional, three-phase flow in reservoirs has been developed. 1 In applying this model to reservoirs undergoing natural depletion, a time-step restriction was encountered due to the flow of evolved gas upwards through the oil column and toward the gas cap. A remedy for this problem has been incorporated in the analysis and is described here. The time-step restriction is encountered only in calculations which include flow in the vertical or near vertical direction. The restriction occurs to some extent in reservoirs of any geometrical configuration, but it is especially pronounced in the pinnacle reef or bioherm where the ratio of thickness to areal extent is unusually large. This paper describes the problem, a method of handling it, incorporation of the method in the three-dimensional, three-phase model, and, finally, a test of the method's validity in an application to an example pinnacle reef reservoir. THE PROBLEM During the early stages of reservoir depletion, pressure falls below bubble point in progressively lower regions of the oil column. Continuing production results in evolution of dissoived gas throughout the oil column. This gas then percolates upwards toward the top of the reservoir. If the gas encounters a sufficiently low permeability zone in its travel upward, then it can accumulate and form a secondary gas cap. If no zones are encountered which are tight enough to hold gas against the gravity forces, then the gas travels on until it reaches the top of the sand or the main gas cap. Numerical simulation of multiphase flow in reservoirs is generally performed with time steps such that the flow of a fluid into or out of a block in one time step is a fraction (considerably less than one) of the total amount of that fluid present in the block. Use of a time step where the time step's

Jan 1, 1969

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the 'drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By R. G. Turner, M. G. Hubbard, A. E. Dukler

Gas phase hydrocarbons produced from underground reservoirs will, in many instances, have liquid phase material associated with them, the presence of which can affect the flowing characteristics of the well. Liquids can come from condensation of hydrocarbon gas (condensate) or from interstitial water in the reservoir matrix. In either case, the higher density liquid phase, being essentially discontinuous, must be transported to the surface by the gas. In the event the gas phase does not provide sufficient transport energy to lift the liquids out of the well, the liquids will accumulate in the wellbore. The accumulation of the liquid will impose an additional back pressure on the formation that can significantly affect the production capacity of the well. In low pressure wells the liquid may completely kill the well; and in the higher pressure wells there can occur a variable degree of slugging or churning of the liquids, which can affect calculations used in routine well tests. Specifically, the calculated bottom-hole pressures used in multirate backpressure tests will be erroneous if the well is not removing liquids on a continuous basis, and gas:liquid ratios observed during such a test may not be correct. Several authors1,3,8,14 have suggested methods to determine if the flow rate of a well is sufficient to remove liquid phase material. Vitter14 and Duggan' proposed that wellhead velocities observed in the field would be adequate for keeping wells unloaded. Jones8 and Dukler3 presented analytical treatments resulting in equations for calculating, from physical properties, the minimum necessary flow rate. An analysis of these studies indicates the existence of two proposed physical models for the removal of gas well liquids: (1) liquid film movement along the walls of the pipe and (2) liquid droplets entrained in the high velocity gas core. Although there probably is a continuous exchange of liquid between the gas core and the film, they will be treated separately for the purposes of this study. The development and comparison of these separate models with experimental data will permit the determination of which, if either, is the controlling mechanism for the removal of liquids from gas wells. The Continuous Film Model Liquid phase accumulation on the walls of a conduit during two-phase gas/liquid flow is inevitable due to the impingement of entrained liquid drops and the condensation of vapors. The movement of the liquid on the wall is therefore of interest in the analysis of liquid removal from gas wells. If the annular liquid film must be moved upward along the walls in order to keep a gas well from loading up, then the minimum gas flow rate necessary to accomplish this is of primary interest. The analysis technique used follows Dukler2 and Hewitt5 and involves describing the profile of the velocity of a liquid film moving upward on the inside of a tube. The minimum rate of gas flow required to move the film upward is then calculated.

Jan 1, 1970

By R. Al-Hussainy, H. J. Ramey

Previous gas well test analyses have been based mainly upon linearizations of ideal gas flow results, although a method for drawdown analysis based upon real gas flow results has been proposed. Linearizations based upon ideal gas flow require estimation of gas physical properties at Tome sort of average pressure, and implicitly involve the assumption that pressure gradients are small everywhere in the reservoir. A new real gas flow equation has been developed by means of a substitution which couples presTure, viscosity and gas law deviation factor. This sub-stitution has been called the real gas pseudo-pressure. Use of the real gas pseudo-pressure leads to simple equations describing real gas flow which do not contain pressure-dependent gas properties, and which do not require the assumption of small pressure gradients everywhere in the flow system. Equations required to determine flow capacity, well condition and static formation pressure from pressure drawdown and build-up tests with the real gas pseudo-pressure concept are presented. Also shown are applications of the real gas pseudo-pressure to back-pressure testing, the gas materials balance and rigorous determination of average gas properties for previous gas flow equations. Included are sample calculations for well test analyses. INTRODUCTION A recent study' of the flow of the transient flow of real gases in ideal radial systems showed that it is possible to consider gas physical property dependence upon pressure by means of a substitution called the real gas pseudo-pressure. The substitution has the advantage that it enables engineering solutions for steady and transient flow of real gases that are more accurate and general than those previously available. The solutions are particularly important for the case of gas flow in tight, high-pressure formations under large drawdowns. Even for more ideal flow conditions, the real gas pseudo-pressure concept leads to important rules for finding average gas physical properties pertinent for older well test analyses. Ref. I provides a detailed study of the theory behind the real gas flow correlations to be used in this paper. The purpose of this paper is to provide necessary engineering forms for use of the real gas flow results, and to illustrate applications. The following considers flow of real gases in an ideal radial flow system. It is assumed that: (1) formation thickness, porosity, water saturation, absolute permeability, temperature and gas composition are constant; (2) gas compressibility and density are functions of pressure as described by the gas law pv = znRT; (3) gas viscosrty is a function of pressure; (4) effective permeability to gas may be a function of pressure to account for liquid condensation; (5) condensate is immobile; and (6) the formation has no dip.

Jan 1, 1967

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967

By W. Hurst, R. E. Leeser, W. C. Goodson

Three aspects of gas deliverability are presented in this paper. The first treats with the gas deliverability or availability of a normal depletion-type dry gas field. Such encompasses not only the period of stabilized constant rate, but more so, the "tailings" when a fixed abandonment pressure is reached and the rate by necessity must decline. A comprehensive work plot is offered, developed from mathematics herein included, that removes the triai-and-errnr computations that attended such undertakings in the past. The second part treats with the discount factor of the open flow potential constant from what is observed initially in testing a gas well to what is evidenced when stabilization is reached. This prevails in tight formations, such as the Kansas Hugoton field which is offered as the example. The means of establishing this factor are pressure build-up curves which, as sustained by analytical deductions, reproduce this entire period of transient flow under conditions of a constant rate influx. Finally, what is offered in this paper is the deliverability performance of an exceedingly rich gas condensate field producing from a tight formation. The example shown is the Knox Bromide field in Oklahoma, producing from the Bromide formations. The results are ominous, showing early reduction in permeability to gas pow, due to the retrograde condensate forming in the pore space, with the attending early logging-up of these wells. The analytics of lowered permeability are incorporated in the gas deliverability formula along with the PVT data that gives the increased condensate liquid saturation as the gas flows to the well bore. This paper would not be complete without a critique oflered at the end. With the many gas wells now in production and those that have completed their life, there has been no factual information collected by any source as to what constitutes that permeability range where a gas well would be unimpaired in its gas deliverability by the presence of rich condensate content, and the lowered range where such would be harmful. This question confronts all producers. INTRODUCTION Various aspects of gas deliverability are presented in this paper that includes depletion-type reservoirs, deteriora- tion factor of the gas deliverability constant, and the performance of a rich gas condensate reservoir producing from a tight sand. With respect to the presentation of gas deliverability and its tailings for depletion-type gas reservoirs, one notes that this is essentially the information offered by every gas transmission company and producer appearing before the Federal Power Commission for Letters of Conveyance in the dedication of reserves. In the ordinary procedure, as many engage upon this study, trial-and-error calculations are included, particularly as apply to the tailings. For many years one of the writers has employed mathematical analyses to perform this step and avoid the complexities so associated. In the preparation of this paper these analyses have been amplified to include any slope n for the open flow potential relationship for which the tailings can be determined from Fig. 1. With reference to the deterioration or discount factor of the open flow potential constant as such occurs in the gas deliverability formula, this for the most part has been an unexplored subject. Although the issue first appeared in the Kansas Hugoton field, where such was surmised but only recently resolved, this situation of a deterioration of the gas deliverability constant can occur wherever dry gas production from a tight sand is encountered. The first concerted attacks upon this problem were the presentations of Hurst' and Goodson' before the Kansas Corporation Commission to show that transient fluid flow and unsteady-state flow formulas prevailed. This was amplified later before the Federal Power Commission3 to show that this deterioration factor could be identified from pressure build-up curves. This has been reported by McMahon.4 Its importance to the industry merits the review of these essential features in completing the program on the aspects of gas deliverability. Finally, as illustrated here, for a low permeability formation such as the Knox Bromide field where the gas is rich, representing some 165 bbl of condensate per MMcf of effluent gas, the gas deliverability can be of limited extent in the life of the field, leaving substantial amounts of condensate and gas unrecovered. In cases such as this, gas cycling is mandatory. This is particularly revealed by the fluid mechanics introduced here, employing factual field as well as laboratory data, to show this-restriction upon gas deliverability. PRESSURE DEPLETION What will now be offered is the study of gas deliver-

By A. J. Garnier, N. H. van Lingen

Rock downhole is known to be lesc. drillable than when brought to the surface. This must be ascribed mainly to the presence under downhole conditions of a pressure differential across already made chips, which hinders their being lifted. The pressure differential has partly a static and partly a dynamic origin. Balling-up of bits is another consequence of this pressure differerztial. Reduction in penetration rate owing to an increase in the strength of the rock is governed by the difference between the mud pressure and the pressure of the for/nation pore liquid. Rotationally symmetric geostatic stresses have 170 effect on drillability. Fracture of rock when drilling will be brille in most cases. The above is supported by laboratory drilling experiments with drag bill and roller bits an elevated mud, pore, and confining pressures On rocks differing in strength and permeability. INTRODUCTION In oil well drilling drillability of rock is found to decrease with increasing depth of the hole. Naturally deep rock will be more compacted and, therefore, harder to drill than shallow rock of the same type. However, apart from this the drillability of a sample of deep and compacted rock brought to the surface is generally much higher than in its original location downhole. In view of the economic implications of this reduction in drillability, it seems worthwhile to analyze its causes. The origin clearly has to be sought in the difference of environment. The only conceivable factors would seem to be the presence of mud under pressure, the pressure of the formation pore liquid, and the overburden of the rock. Down the borehole the rock is compressed triaxially by mud pressure and overburden. It is well known that the strength of rock is increased when confined by external pressure1. Various authors have, therefore, ascribed the difference in drillability mainly to the strengthening of rock by triaxial compression. Another factor, mentioned by Bobo and Hoch5, is that forces. including "pressure differential forces", tend to hold a dislodged particle in place. However, the conditions determining their magnitude are not clarified nor is their effect on drilling rate assessed. In the laboratory, drilling experiments on pressurized samples of rock yielded evidence that pressure differential forces holding the chips down are the major factor in reducing rate at depth. This paper describes the experiments and shows how the results enable both a qualitative and a quantitative interpretation of the factors determining the effect of chip hold-down on drilling rate. The implication with respect to balling-up and jet action is also discussed. The greatcr part of the experiments were performed in the pressure vessel shown in Fig. 1. The spacc between the sample of rock and the vesscl is divided by "0" rings into three separate chambers. The rock sample is confined laterally by pressurized oil in thc middle chamber. Penetration of oil into the sample is prevented by partly jacketing it with brass foil. Thc pressure of the drilling fluid in the hole can be adjusted via the upper chamber. Permeable rock specimens arc water saturated before being drilled. With a properly plastering mud as drilling fluid the pressure of the pore water can be adjusted independently via the lower chamber.

By J. G. Richardson, K. H. Coats

During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and high rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leuerett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas. INTRODUCTION In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of the gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating — for given aquifer characteristics and fluid properties — the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formula1 and Buckley-Leverett2 method have some applicability to the problem; Woods and comer3 reported one-dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer.4 Douglas, Peaceman and Rachford5 presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek,6 Blair and peaceman7 and Goddin.8 Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here. One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques might reasonably be applied. However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability, porosity, reservoir thickness and dip angle.

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