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By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By C. R. Dodson, D. Goodwill, E. H. Mayer

The paper summarizes the historical background of the pressure-volume-temperature analyses of reservoir fluids, the errors involved in both the sampling and testing of reservoir fluids, the type of information required of a PVT determination, and the field conditions that limit the application of any one analysis. Particular emphasis is placed on the necessity for approximating as closely as possible the liberation sequence occurring in the producing formation, flow string, and surface separators. A combined differential and flash or "composite" liberation is suggested as the best means of approximating this liberation sequence. HISTORICAL BACKGROUND Petroleum reservoir engineering commonly is considered to be one of the newest fields of petroleum science, yet much work of a theoretical and intuitive nature was done many years before the modern techniques of reservoir analyses were developed. The period 1910-1924 saw considerable work in the field of reservoir behavior done by the U. S. Bureau of Mines. This work:.' although entirely theoretical, pointed out the importance of gas in the recovery of oil from the reservoir. The statement by J. 0. Lewis that 20 per cent or less of the oil originally in place in a pool was recovered from the ground under uncurtailed production conditions caused some operators to re-examine and modify their production methods. However, though these works showed methods of production that have subsequently resulted in greater oil recoveries, they in general went unnoticed, even though there was a fear that the nation's petroleum resources were being exhausted. The period 1924-1933 saw the industry take considerably more interest in reservoir behavior because of an unfounded fear of its inability to replace oil reserves, the possibility of government regulation, and the energy of one man, Henry L. Doherty. Doherty aroused heated discussions in the industry concerning conservation. To prove or disprove his theories the first experimental work on the reservoir behavior of petroleum was undertaken. The papers of Dow and Calkin,' Beecher and Parkhurst," and Mills and Heitheckere are classics although their experimental procedures were crude. These papers proved that the properties of petroleum in the reservoir are quite dissimilar to the properties measured at the well head. Gas dissolved in the oil phase was recognized as having considerable importance as had been predicted by the earlier theorists. Slightly later Miller and his co-workers assembled the first text correlating all the known data on the reservoir behavior of petroleum and used, these data to show the economic value of conservation. Quantitative application of pressure-volume-temperature analyses of reservoir fluids was given in the paper of Coleman, Wilde, and Moore"; this work showed that with sufficient laboratory and production data prediction of reservoir behavior was possible. The refined sampling and labora-

Jan 1, 1953

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By E. H. Timmerman, A. F. van Everdingen, J. J. McMahon

The prevent paper contains a method which combines the material balance equation' with the water influx equation' to obtain reliable values for the active oil originally in place and a quantitative evaluation of the cumulative water influx. The method is illustrated by an application to a reservoir without original gas cap. In the absence of an original gas cap. results may be obtained using only field production and pressure data, PVT analyses. and a minimum of subsurface information. CHARACTERISTICS OF RESERVOIR AND RESERVOIR FLUIDS Production in the field under review is obtained from the top of the Wilcox formation of Eocene age, at a depth of approximately 8,100 ft subsea. The structural map, Fig. 1, shows that the accumulation, half elliptical in shape with the long axis in east-west direction, is trapped to the north and on the upthrown side of a normal fault. A number of east-west faults with additional minor faulting in random directions are found in the general area, and seismic information and production performance indicate in this particular case the existence of a second fault a short distance downdip, with a strike more or less parallel to the fault controlling the accumulation. It is estimated that 1,830 acres were originally underlain by oil and that the maximum thickness of the original oil column, about 37 ft, was only slightly greater than the maximum thickness of the oil-bearing sand. Maximum net sand thickness was estimated at approximately 26 ft. From logging and subsurface information the gross sand volume has been placed at 37.400 acre-ft. which reduces to about 27,500 acre-ft after probable non-productive intervals have been deducted. The following table presents laboratory analyse; data for the Wilcox sand cores. Average Average Samples Considered Permeability Porosity All Samples 236 md ..19.9percent Samples with k>l md 256 md 20.5 per cent Samples with k>8 md 275 md 20.9 per cent Interstitial water was estimated at 15 per cent. The initial gas-oil ratio was approximately 900 cu ft/bbl. and the initial shrinkage factor was determined by the laboratory to

Jan 1, 1953

By J. C. Trantham, J. W. Marx

From 1955 to 1958 the Phillips Petroleum Co. conducted a series of small scale counterflow combustion field tests in a tar sand about 60-ft deep and 6 to 12-ft thick near Bellamy, Mo. A total of seven different well patterns, including conventional five-spots and seven-spots plus a 15-well line drive pattern and a 10-well radial pattern, were employed. Electric heaters, gas burners and wellbore fuel packs were tested as counterflow ignition devices. Direct drive ignition followed by reversal to counterflow operation was not possible in this case because of formation plugging by the semi-solid tar during the direct drive phase. Sustained counterflow burning was achieved with wellbore fuel packs under conirolled conditions which permitted close correlation of fire front velocity, air velocity, air-oil ratios and yields for a wide variation in process parameters. The tar in place was about 10' APl with a reservoir viscosity greater than 500,000 cp. The composite oil prodlcct was 26' API with a viscosity in the range of 5 to 15 cp. Vertical sweep efficiency in the line drive pattern was essentially 100 per cent, with no evidence of gravity segregation. Original tar in place ranged between 800 and 1,000 bbllacre-ft, specific rock permeability averaged about 800 md before burning and effective air pemeability with residual oil and water in place (at the time of ignition) averaged 250 md. The volume of oil recovered during stabilized line drive counterflow burning represented about 67 per cent of the volume of tar originally in place in the burned out zones. A minimum was found when air-oil ratios were plotted against formation air velocities, and a limiting air velocity existed below which the counterflow fire front reversed and burned back over its own trajectory, using the residual coke left behind. INTRODUCTION Early in 1955 the Phillips Petroleum Co. began preparations to field test counterflow underground combustion as a method for producing oil from high viscosity hydrocarbon deposits, such as bituminous (tar) sands. At that time all published information on the use of underground burning io increase oil recovery was based on the direct drive process, in which the fire front moved through the formatim in the same direction as the injected air stream. Such direct burning is not applicable to many heavy oil sands or to most tar sands because the heat-thinned native hydrocarbon congeals in the cold rock ahead of the fire front forming a gas permeability block which smothers the combustion. Laboratory experiments first demonstrated that this permeability blocking would not occur if the fire front and the air stream moved in opposite directions. In this counterflow (reverse) burning process the heated heavy oil or tar is driven back through the combustion zone. Here thermal cracking produces relatively light hydrocarbon products which pass through the heated rock behind the fire front (largely in the vapor phase) and are incapable of causing a gas permeability block.' Exploratory wring revealed that consolidated bituminous sandstones with a combination of tar saturation, permeability, thickness and depth favorable for experimental field testing existed at several points in western Missouri. By the fall of 1955, a test site for determining technical feasibility of the counterflow process under field conditions had been selected near Bellamy, Vernon County, Mo. — about fifty miles north of Joplin. The pay zone was too thin and too shallow to constitute a commercial prospect, but these same factors permitted controlled experimental operation with a small compressor installation and with a large number of monitor wells. These were needed for adequate observation of the underground phenomena at reasonable cost. RESERVOIR CHARACTERISTICS The reservoir chosen for the experimental field tests was a 124 thick section of tar sand extending from 49 to 61 ft subsurface, with shale and siltstone laminations sealing the top and bottom. This section was part of a larger 30-ft thick tar sand deposit which extended both above and below the test zone. Core analyses showed that the 12-ft sand was effectively subdivided into two approximately equal sections, with the lower zone being consistently more permeable than the upper zone. The most significant laboratory core data are summarized in Table 1. The line drive test which is the principal subject of this report utilized only the lower 6-ft thick zone, with the upper zone regarded as part of the 55-ft overburden. WELL PATTERNS The over-all field test program involved a total of seven different well patterns, including conventional five-spots and seven-spots plus a 15-well line drive pattern and a 10-well radial pattern. In some of the tests the full 12-ft zone was employed; in other cases only the more perme-

Jan 1, 1967

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965

By N. W. Ratliff, P. J. Closmann

Production of oil by expansion from a cylindrical reservoir composed of two concentric regions of different properties has been determined as a function of time for a reservoir producing at constant terminal pressure. The parameters involved are permeability, porosity, compressibility and oil viscosity. Results agree with those of a generally accepted method for uniform reservoirs when all parameters are taken as uniform. Cumulative production at any given time is reduced below that of the uniform reservoir when a region of considerably lower permeability adjoins the well; cumulative production increases when a high-permeability region adjoins the well. Curves are presented illustrating quantitative effects of these variations. INTRODUCTION Most petroleum reservoirs can be exploited by release of pressure and consequent expansion of underground fluid. During part of the production history of certain reservoirs by this mechanism, fluid compressibility can be considered small and constant. Cumulative fluid produced by this means as a function of time was calculated for a uniform reservoir by van Everdingen and Hurst.l For certain cases where a production well has been damaged or where an acid treatment has been used, a zone of properties different from those of the reservoir may be created around the production well. In such a case, expansion of the reservoir fluid takes place in a system composed of two concentric cylindrica1 regions of different reservoir properties. Such composite systems were studied in connection with heat flow by Jaeger2 who presented a solution for temperature distribution in a radial system with an infinitely large outer radius. Similar heat flow problems have been studied by other authors Oil production from composite reservoirs was studied for constant production rate by Hurst,4 Loucks and Guerrero,5 and Carter.6 THEORY This work considers constant terminal pressure. Cumulative flow is calculated for a composite bounded system in which no flow takes place across the outer boundary (Fig. 1). Since the flow is considered to be purely radial, the problem involves only one space dimension and time. It is convenient to define the following dimen-sionless pressure drops (Fig. 1).

By Jim Douglas, H. H. Rachford, D. W. Peaceman

The problem of unsteady-state gas flow through porous media has been solved numerically only for the case of linear or radially symmetric reservoirs. A recently introduced numerical method for solving the unsteady-state heat flow equation in two dimensions is applied to the calculation of the depletion of a square region containing a perfect gas. Solutions are presented in graphical form for various values of dimensionless parameters. The solutions are compared with published .solutions for radial reservoirs. I NTR ODUCTION The problem of unsteady-state flow of gas through porous media gives rise to a second-order non-linear partial differential equation for which no analytical solution has been found. Numerical approximations to solutions of the gas flow problem have been obtained by the stepwise solution of an associated difference equation1,2. However, the methods so far developed have required that the reservoir be either linear or radially symmetric. This restriction in shape has been necessary so that only two independent variables be considered, namely, one distance variable and time. In order to deal with reservoirs having more realistic shapes, it is necessary to develop numerical procedures for the solution of the gas flow problem involving two distance variables. A numerical procedure, denoted as the alternating-direction implicit method, for the solution of the heat-flow problem in two dimensions has recently been introduced" By the use of this procedure, approximate solutions have been obtained for heat-flow problems in a square8, and in regions having various non-rectangular boundariesa. Because of the similarity between the equation for heat conduction in solids and the equation for gas flow in porous media, it is reasonable to expect that the alternating-direction implicit method should also be useful for solving the gas flow problem in various two-dimensional regions. Solutions have been calculated for the simplest two-dimensional region, a square reservoir with a single well in the center. While reservoirs of such simple geometry seldom, if ever, exist, the solution of this problem is of some practical importance because it is also the solution of another problem, that of determining the depletion history about an individual well in an infinite uniform reservoir containing wells spaced throughout on a square lattice and producing equally from each well. Finally, it is of interest to compare solutions for a square reservoir with those for a circular reservoir and to determine the effect of the shape of the boundary for that particular case. METHOD OF CALCULATION Basic Differential Equation By combining the equation of continuity, the perfect gas law,

Jan 1, 1956

By L. A. Schrider, J. A. Wasson

A method of predicting waterflood performance has been developed that combines certain facets of several previously published prediction techniques. The manner of combination has required the development and use of some new and some little-known relationships and has eliminated several of the weaker assumptions inherent in the original individual prediction methods. This approach, which was designed for computer solution, has removed the necessity of referring to plotted curves and permits the analytical prediction of water flood performance for a five-spot well pattern in either homogeneous or stratified reservoirs. The Predicted values are expressed in common oilfield units rather than in abstract or dimensionless terms. The calculation procedure has been programmed in FORTRAN IV and the entire program listing is available to potential users.* Introduction Prior to initiation of secondary recovery of oil by waterflooding, the possibilities of economic success or failure must be evaluated with the greatest practical accuracy. Although many prediction techniques are available, most, if not all, have serious limitations. In recent years, the Bureau of Mines has attempted to stimulate interest in the secondary recovery of oil from Appalachian pressure-depleted reservoirs. Waterflooding, because of its widespread acceptance and success, is the principal secondary-recovery method considered. During the life of the project, several performance prediction methods have been studied and applied. Because these methods, individually, have inherent assumptions and limi-tations, portions of some of them have been selected and combined in an effort to eliminate such shortcomings wherever possible. We believe that the resulting technique is as accurate as the necessary available data will permit and that it has several distinct advantages over previously published methods. Development of the Method The fractional flow equation developed by Buckley and Leverett' from Darcy's law is the fundamental mathematical statement describing immiscible fluid-fluid displacement in porous media. A generalized form of this relationship, whose derivation is readily available in the literature, is The formation dip, a, is usually very small in those petroleum reservoirs being considered for pattern waterflooding in the Appalachian area. Therefore. in many cases. a has an almist negligible value. In addition, Ap, the difference between the density of water and the density of oil, is relatively small. For these reasons the gravitational term may often be neglected. Capillary pressure is a function of saturation, which is in turn a function of distance from the upstream boundary of the system or the injection well. In this study it is assumed that the frontal zone of the waterflooding (or zone of capillarity) has negligible length and that only those saturations in the water-swept zone at breakthrough and later are of interest. As the distance in a waterflood pattern is comparatively large and the change in water saturation with distance is usually small, the change in capillary pressure with distance is negligible. The simplified form of the fractional flow equation is appropriate, therefore, in this application. Three variables must be considered in determining that fraction of the total fluid flow that consists of water: the viscosity ratio, saturation, and relative permeability ratio.

Jan 1, 1969

By N. H. Harrison, J. K. Rodgers, S. Regier

This paper presents comparisons of data obtained from a laboratory reservoir study and from a calculated behavior prediction with the actual production history of a condensate reservoir. A small non-commercial discovery was depleted under closely controlled conditions and the well fluids were sampled at frequent intervals. Data on the reservoir and production variables were accumulated on a fixed schedule. A laboratory reservoir study war made using the initial well fluid samples as charging stock. The production procedures and operating conditions were held constant throughout the study wherever possible and in general paralleled the field work. The well fluid compositions and the cumulative recoveries ar a function of the reservoir pressure were also calculated using conventional flash vaporization procedures and equilibrium constants. Comparisons based on the composition of the well fluid show good agreement, the laboratory study agreeing within experimental accuracy with the field work and the calculated data comparing equally well. The gas-oil ratios are also in good agreement, but with somewhat greater deviations at the higher pressures. In the overall picture, it is believed that a model st,~tiy can predict within experimental accuracy the production history of a condensate reservoir. Better equilibrium constants for the heavier hydrocarbons are needed in order to attain improved composition accuracy by calculation. INTRODUCTION In Aug., 1955, a gas condensate well was completed in San Juan County, Utah, that was initially thought capable of good commercial production. These conclusions were derived principally from core data and electric logs, which indicated good permeability, porosity and gas content. However, after the usual series of potential tests it was found that the reservoir pressure had declined some 22 per cent, and it was obvious that the zone tapped was but a small pocket or trap. It became apparent that, with a controlled depletion of a small reservoir, a unique opportunity was available to compare laboratory and calculated studies with an actual field depletion and to further the present knowledge of condensate reservoirs. FIELD WORK The Coalbed Canyon Well No. 1 was conventionally completed in the Paradox limestone formation to a total depth of 5,912 ft. The producing zone from 5,762 to 5,806 ft was perforated with four jet shots per ft. The wellhead and field equipment were also conventional, the major items consisting of a two-pass indirect fired line heater, a high- and a low-pressure separator with the necessary controls and accessories, gas meters, back-pressure regulators, flare stacks and condensate stock tanks. The initial testing of this well con-sisted of a series of flow potential and pressure build-up tests during which some 30 MMcf of gas was produced. The reservoir pressure declined from an estimated 2,300 to 1,782 psig during this period, from which it was concluded that the reservoir was very small. In order to approach steady-state conditions in the reservoir and so provide optimum conditions for making comparisons, the field depletion was programmed to approach, if possible, constant production conditions. Bi-hourly readings were taken of the tubing pressure, the pressure and temperature of the separators, oil and gas rates, and other pertinent operating data. The gas rate, as indicated by the orifice meter, was held constant by the adjustment of the choke in the line heater. The temperature of the first stage separator was held constant by adjustment of the line heater jacket temperature. Practical considerations of production made the maintenance oi a constant gas rate impossible. The test started with a gas rate of 4 MMcf/D and a separator pressure of 250 psig. This rate was maintained until the choke was fully opened. The gas rate then declined with the falling tubing pressure and production was continued until the rate was about 2

By J. Jones-Parra, R. S. Reytor

The porosities of fractured limestone reservoirs can be divided into two broad types in accordance with their effects on fluid distribution and fluid flow. In the coarse porosity, gravity segregation lakes place freely and the resistance to fluid flow is very small. In the fine porosity there is no segregation and a high resistance to flow, and it has relative permeability characteristics similar to tight sandstones. By analyzing the affect of the two porosities it is concluded that in some cases to recover the maximum amount of oil it is necessary to remove large quantities of gas from the reservoir by producing at high gas-oil ratios. In this manner the fine porosity is drained of its oil and the gas-oil contact drops slowly permitting higher production rates from the oil leg. Since this conclusion is contrary to widely accepted principles of conservation, a mathematical model (Fig. I) was constructed to duplicate the conditions desired. The behavior of the model indicates that under certain conditions it is possible to recover more oil by producing at high gas-oil ratios than by production at low gas-oil ratios, and that the rate of production is affected more by gas shut-offs than by the decrease in pressure (Figs. 2, 3, 4 and 5). INTRODUCTION It has been noted that certain limestone reservoirs behave in such a way as to indicate that there are two distinct types of porous spaces available for fluid storage and fluid flow. Regardless of the nature of these porous spaces the distinguishing characteristic is that in one type of porous space there is definite gravity segregation between the oil and the gas; while in the other, the gas evolved tends to remain distributed equally throughout the reservoir. For the sake of simplicity the porosity in which gravity segregation takes place at a fast enough rate to affect the behavior will be called "coarse po- rosity", while that in which this is not so will be termed "fine porosity". The behavior of a reservoir of this type would be different than that of a sandstone reservoir, especially if most of the oil is in the fine porosity. It has been observed that fluid flow to the wells takes place mostly through the coarse porosity. The large fractures which

By F. W. Jessen, G. F. Sears

Cavities in massive salt for the purpose of storage of liquid hydrocarbons have assumed a prominent position in recent years. This paper describes a program to facilitate leaching operations for the formation of specifically shaped storage cavities. Various forms and sizes of cavities may be possible through use of the techniques developed. INTRODUCTION The creation of large under ground storage facilities for natural gas and liquified petroleum gases has been practiced for many years. Use of cavities obtained through solution of salt for this purpose is a fairly new and novel approach, but has gained increasing importance due mainly to the economics of this type of mining operation opposed to hard rock mining or surface and pit storage.1 The idea of controlling the shape of any cavity dissolved from massive salt has not been a prime consideration of companies engaged in the formation of storage space. This has been due mainly to an insufficient knowledge of the mechanics of the leaching process and a dearth of published information dealing with both the desirability and ease of control possible for this type of operation. Two distinct advantages are readily ascertainable. From a stability standpoint (i.e., the ability of the completed cavity to withstand stress imposed by overburden pressure and lateral tectonic stresses) a controlled cavity may be generated which will yield the most favorable attitude to these external forces and remain in operable use for longer periods of time.2 A second advantage is that for a given volume, a sphere (which is one controlIed shape possible) represents the minimum surface area exposed. This may become more important in the future when dealing with refrigeration and product losses in underground cavities. The basic solution mining process, without regard for controlling the final shape, is quite simple in that the equipment and materials required to dissolve a cavity in a salt dome or layered salt section are a source of fresh water, a circulating pump, several strings of tubing and a means of disposal of the return brine. To add control measures involves the use of an inert blanket material above the position at which solution proceeds. Initially the annulus of the largest wash pipe is filled with this blanket down to the top of the proposed cavity. The bottom of the proposed cavity is determined by the depth of the original drilled hole or a blanking plug. The blanket material is added incrementally in stages and displaces the water in the enlarging cavity downward. Where the blanket material has displaced the water, no further solution takes place. The rate at which to add this controlling blanket material so as to be able to form specifically shaped cavities of any particular size is of considerable importance. THE PROBLEM It is desirable to have as much information as possible as to the behavior of the mining operation since visual observation obviously is impossible. It would be advantageous, for example, to have a step-by-step program showing how much salt is to be removed, at what rate and the time required. This type of program would facilitate procurement of surface equipment and provide for proper management of manpower requirements, as well as yield a host of intangible benefits. As mentioned earlier, only rule-of-thumb estimates were available until recently and made this type of pre-planned operation haphazardous at best. Recent work3-' has done much to clear up the ambiguities and inaccuracies attendant to solution mining of salt and has helped to place the operation on a more scientific basis. This study attempts to correlate much of the information thus far developed into a complete mining program; to extend the idea of controlled solution mining to include not only spheres, but solid conic sections of the ellipsoidal variety; and to refine the computation of the rate of removal of salt during the various stages of mining. Dommers3 and IIemson4 made extensive laboratory

Jan 1, 1967

By L. A. Wilson, P. J. Root

The relative costs of heating a reservoir by steam injection and by combustion have been examined. The comparison was based on a model similar to that proposed by Chu.' The cost of boiler feed water, the price of fuel, pressure and plant capacity were parameters in determin-ing the costs of air compression and steam generation. The analyses compare the cost of heating to the same radius by the two methods. Results suggest that the two primary factors for comparison are the price of fuel and the amount of crude burned during underground combustion. The cost of fuel has a greater effect on the cost of heat from steam than it does on its cost by combustion. As a result, analyses indicate that when the price of fuel is low, steam may be unequivocally cheaper than air. The influence of heat loss is such, however, that as the heated radius increases combustion becomes relatively more competitive depending upon the amount of crude burned. This implies that steam may be cheaper for small stimulation jobs (huff and puff) but combustion may be more economically attractive for heating large areas (flooding). INTRODUCTION Use of thermal methods of recovery is an accepted fact today. After an induction period of several years, processes are being widely used that involve reservoir heating to augment recovery. Of the several techniques, steam injection and forward combustion appear to be destined to dominate the field. Although the objectives of both are the same, the basic differences between generating heat in situ and injecting heat after surface generation influence the cost in different ways. This study compares the cost of heating a reservoir either by steam injection or by forward combustion. There has been no consideration of recovery. Presumably, recovery from the swept region would be high in either case. The sole consideration was the cost of heating to the same radial distance by either process. PROCEDURE THE MODEL The basis for comparison was a mathematical model similar to that used by Chu' for combustion. The model simulates a radial heat wave in two-dimensional cylindricaI coordinates. It includes heat generation, conduction and convection within the reservoir and conduction in the bounding formations. Thus, heat losses from the formation are considered. Three significant modifications were made. 1. Equal logarithmic increments rather than equal increments were used for the mesh spacing in the r direction. By this technique large distances were simulated with relatively few mesh spaces. 2. A backward difference approximation to the convection term was used to avoid troublesome oscillations which result from a central difference approximation when the convection term is large. 3. The radial increments of the combustion zone motion were not necessarily uniquely related to the mesh configuration. The cumbersome step function introduced by the heat of vaporization of steam was circumvented by assuming the enthalpy of the steam to be a linear function of temperature between reservoir temperature and steam temperature. This is equivalent to assuming an average heat capacity numerically equal to the difference between the enthalpy of saturated steam and the enthalpy of water at reservoir temperature divided by the difference between the two temperatures. Heat losses obtained by this model are in essential agreement with those obtained by the analytical solution of Rubenshtein.' A detailed description of the model is presented in the Appendix. Using the model, the times required to heat to particular radial distances were obtained as a function of injection rate and other physical parameters. For the steam case, injected fluid was assumed to be saturated steam at pressures of either 500, 1,000 or 1,500 psia. The corresponding temperatures are 467, 544 and 596F, respectively. Thickness ranged from 10 to 50 ft and injection rate ranged from 100,000 to 1 million Ib/D. Reservoir and overburden temperatures at the injection well were assumed to be that of saturated steam at the injection pressure. The effect of maintaining the overburden temperature at the well at a different temperature (initial reservoir temperature) was examined with no significant change in behavior. The influence of wellbore heat losses for the steam case was determined in the following manner. The rates of heat loss as a function of time were estimated using an approach similar to that suggested by Ramey." he data were based on injection through 2%-in. tubing in 7-in. casing. Integration of these data over the entire iniection period yielded the total heat loss. Total heat losses were then corrected to their equivalents in steam (this number resulted from dividing the total heat loss by the latent heat). This was considered additional steam required to accomplish the reservoir heating and the total cost was increased accordingly.

Jan 1, 1967

By R. H. Adams, A. M. Khan

The Huntington Beach oil field is on the Pacific Coast, southeast of the City of Los Angeles (Fig. 1). It lies both onshore and offshore. Most of the onshore section is operated by Standard Oil Co. of California, WOI. The Tar reservoir is of upper Pliocene age, about 200 ft thick, and consists principally of fine-grained, unconsolidated, somewhat shaly sand, with thin inter-bedded shale stringers throughout (Fig. 2). The reservoir is a broad, highly faulted, elongated anticline, with an areal extent of about 370 acres. Most of the faults bisecting the structure are normal, trend north-south, and are the main cause of reservoir discontinuity (Figs. 3 and 4). From 1964 to Dec., 1967, 259 steam stimulations were performed on a total of 125 Tar sand wells. Eighty-six new wells were drilled and steam stimulated. Of the total, 96 have been stimulated twice, 34 three times and 3 four times. During this same period, a two-injector steam drive pilot has been in progress. The response obtained from this project has been compared with the response to cyclic stimulation. This paper presents an analysis of the field observations for the two methods of thermal recovery. History of Development Drilling to the Tar pool commenced in 1924 with an initial well production of 40 to 50 B/D of 12o API gravity oil. Complete primary development of the pool has been spread over several years. Approxi- mately 40 wells were drilled during the first phase of development, which was completed in 1945. The subsequent primary development started in 1960 with initial well productions of 30 to 40 B/D oil. Thirty-seven wells were completed in the Tar pool during this phase. For the most part, slotted, gravel flow packed liners have been used in the wells in this pool. A cyclic steam stimulation pilot was initiated in March, 1964. Based on the very successful stimulation in the pilot area, the cyclic stimulation project was expanded to include all of the Tar pool wells producing at the end of 1965 (Fig. 5). Also, a development drilling program was begun at this time. To date, 86 new wells have been drilled under this program. The number of wells drilled each year in this secondary phase of development is also shown in Fig. 5. New Well Completion Practices Most of the new wells have been completed to produce from both the Upper and Lower Tar zones. Generally, a casing stub is cemented from the top of Lower Tar to the base of clean Upper Tar sands to exclude intermediate water-bearing sands. The water string is then cemented from the top of Upper Tar to about 1,500 ft with neat cement and 30 percent silica flour. The annulus from 1,500 ft to surface is then filled with a petroleum-based gel through a high-temperature port collar. Once again, a history of sand-free production dictated the use of 60-mesh gravel flow packed liners. The Upper and Lower Tar

Jan 1, 1970

By J. B. Campbell, V. V. Valleroy, B. T. Willman, L. W. Powers

A steam drive of heavy oil was field tested in a shallow, low oil-saturation formation near Deerfield, Mo. The pilot was conducted in the Warner formation, a sandstone containing an 18' API oil having 1,000-cp viscosity at the 60F origind reservoir temperature. The formation war at a depth of 160 ft. Steam was injected into nine input wells arranged in an array of inverted five-spot patterns. In the completely confined center pattern, 14 temperature observation wells were installed to obtain thermal data and observe test progress. Late in the test, slugs of ammonia were injected to trace the flow paths of injected fluids. From the test area about 7,000 bbl of oil were produced. Data were obtained on areal and vertical temperature distribution, steam front advance, reservoir fluid movement and terminal saturations. This field test of a steam drive (I) demonstrated the feasibility of the method, (2) confirmed that the low residual oil saturations observed in the laboratory are obtained in the steam-swept region in the field and (3) provided recovery and conformance data for one set of field conditions. INTRODUCTION The Deerfield steam drive pilot test was conducted in a shallow sandstone containing 1,000-cp oil. The venture was undertaken cooperatively by the research and production departments of Carter Oil Co., which organizations have since been consolidated into Esso Production Research Co. and Humble Oil & Refining Co.. respectively. The production department was interested in steam injection at Deerfield because it appeared to be the most promising method of commercially producing this heavy oil deposit. The research department was interested in applying the new recovery method and in evaluating its performance in the field. At the time the test was begun, the initial oil saturation was not well known. Subsequent air coring and early pilot results confirmed that there was too little oil in place for profitable commercial exploitation by steam. Pilot termination at that time, however, would have been premature for evaluating field performance of the process, and the tert was continued to obtain additional data on steam injection as a recovery method. The test was located in Vernon County, Mo., about 10 miles north of the town of Deerfield and only a few miles from the Kansas border. The pilot site was selected as typical of the area. The location represented neither the highest nor the lowest oil saturation region in the acreage under lease in 1954. The steam drive was conducted in the Warner sandstone of Lower Pennsylvanian age. At the test site the top of the Warner occurs at about 160 ft subsurface and the formation is a fine- to medium-grained micaceous sandstone that dips gently to the northwest at the rate of 12 to 15 ft/ mile. A cross-section and permeability profile of the test location are shown in Fig. 1. At the pilot location the average total thickness of the Warner formation is about 43 ft, but the effective thickness for steam drive is 26 ft. Two distinct types of hydrocarbon saturation are apparent. The lower portion of the total sand, averaging about 17 ft thick, contains a very heavy asphaltic material that will not flow under the influence of a steam drive. This bottom interval, referred to as a dead oil residue, was not considered as part of the net sand undergoing steam exploitation. The initial formation and fluid properties of the upper 26 ft in the test area are summarized in Table 1, and variation of oil viscosity with temperature is shown in Fig. 2. Imbibition tests on preserved core samples taken at the end of the pilot test showed that the Warner sandstone was then neutral or slightly water-wet. Initially, the reservoir may have been strongly water-wet as indicated by low relative permeability to water during both water injection testing and early steam injection. PRIOR HISTORY Initial production tests of wells at the pilot site produced water with only a faint show of oil. No gas was produced except at Well 7-W in the pilot area and at another well about 1/3 mile northeast of the pilot. Prior to the start of the steam drive, a two-well water injection test and a two-well air injection test were conducted. No oil was produced by either. Water was pumped into Well I-W in the northeast corner of the pilot area with simultaneous production from Well 1 (Fig. 3). The air-injection tat was run at input Well 9-W and its offset, Well 2, in the southwest corner. Air and water injectivities were about the same when corrected for viscosity and pressure differences.

By R. A. Morse, C. R. Stewart, F. F. Craig

This paper preFents the results of a series of model flow test on a number of large limestone cores, having different pore configurations. For limestone cores having substantially sandstone type porosity, the production characteristics for solution and external gas drives are similar. For cores whose pore spaces were microscopically heterogeneous (i.e., consisted of combinations of solution cavities, matrix. and fissures), the production characteristics lor solution and external gas drives vary widely. The degree of divergence between gas-oil relative permeability relationships calculated from solution or external gas drive tests is an indication of heterogeneity of rock pore structure. The results of water floods on cores depleted by solution gas drive for each of these two general types of limestone porosity are also shown. Generalizations are made on the water flood recovery that could be expected from each of these two types of limestone porosity. The similarity between solution drive field performance and model solution drive performance on cores from the same formation is shown for several cases. This indicate? the feasibility of predetermining limestone field performance from such large core tests. Photomicrographs of plastic-impregnated rock thin sections of the samples tested are presented as an aid in understanding the flow test performances. INTRODUCTION During the past 15 years. reservoir engineers and research workers have developed methods of testing rock and fluid samples and applying the results, through calculation, to allow reasonably satisfactory predictions of oil recoveries and performances to be expected in sandstone oil recervoirs. It has been determined that representative fluid flow data can be obtained on rock samples as small as three-fourths in. in diameter by one in. long in most sandstones. However, little has been accomplished toward the laboratory determination of fluid flow characteristics in limestones. There has been a great deal of speculation as to the influence of variations in pore size, shape, and degree of interconnection upon oil recovery processes, and a great deal of thought has been given to the interpretation of limestone field perfomance. It has been generally recognized that predictions of reservoir performance based on oil displacement tests on small limestone core samples the size of those used for sandstone tests can often be misleading because of the improbability of obtaining a representative sample in such a small core. Obviously, if there are present in the rock, pore openings of the magnitude of 1/16 in., or fractures or solution channels up to one in. or more in length, it will be impossible to cut any sample less than one in. in any dimension which would represent the flow geometry of the gross rock system. In some formations, the individual openings in the rock are of such size that it would be impossible to obtain a good sample of the flow system even in the total core available from conventional-sized well cores. However, by increasing to the maximum the size of the sample used, it should be possible to obtain representative flow data from the majority of limestone reservoir materials which can be used for prediction of future primary production performance or response to be expected from secondary recovery measures. The only alternatives to obtaining good laboratory test data to serve these purposes are extrapolation of primary performance data obtained by partial depletion of a field, or obtaining information from pilot tests. It has been shown previously, and will be demonstrated further by the work reported in this paper, that extrapolation of solution gas drive performance for an estimate of gas injection response can be very misleading in reservoirs of heterogeneous type porosity. Although it cannot be expected that laboratory information can ever eliminate the necessity of small-scale pilot operations, it is expected, as is now the situation with sandstone reservoirs, that laboratory tests should provide reliable information for screening of

Jan 1, 1953

By H. J. de Haan, J. van Lookeren

In view of their size and favorable characteristics, Shell's heavy-oil fields on the eastern coast of Lake Maracaibo, Venezuela — known as the "Bolivar Coast" — are obvious candidates for the application of thermal recovery methods. During the last decade various methods have been tested, such as steam drive,', steam soak and in-situ combustion.3 Steam soak was discovered as a promising production method rather accidentally in 1969, during early steam drive testing in the Mene Grande Tar Sands1 When steam erupted at the surface due to breakdown of the overburden, the injection wells were back-flowed to relieve the reservoir pressure. This resulted in high oil production rates, all the more impressive because the reservoir is unproducible by primary means. It was concluded that injection of limited amounts of steam might be a very effective method for stimulation of heavy-oil wells. To obtain information that would be more widely applicable, testing of the process was continued in the eastern part of the Tia Juana field (Fig. 1). Here even more favorable results were obtained than in Mene Grande. This created sufficient confidence to prompt a large-scale project, which was considered essential for an adequate evaluation of ultimate recovery, steam requirements, mechanical problems and economic prospects. To obtain an early answer on the ultimate recovery a fairly depleted area was selected in the western part of the same field ("A" in Fig. 1). The first steam was injected in March, 1964. This paper describes the performance until the end of 1966. The production mechanism and well inflow performance are discussed in some detail. In view of the favorable results obtained so far, steam soak operations have expanded considerably since the start of this project. Presently, five other projects are under way, of which two are about the same size as the one under discussion, with further extensions being programmed. Description of the Project Reservoir Data Shell's part of the Main Tia Juana reservoir has a proven area of 8,800 acres and an average net oil sand thickness of 130 ft. It contained an initial quantity of 2,750 million bbl of stock tank oil (STOIIP), with an API gravity ranging from 10 to 15 API and a viscosity of 100 to 10,000 cp (at 122F). As a geological unit it is known locally as the Lower Lagun-illas member of the Lagunillas formation, which is early Miocene in age. The sand bodies are believed to be distributary channel sands deposited in a lower coastal plain. Most of the channel sands have lateral and some vertical communication. The field was developed mainly in the period from 1936 to 1950. The ultimate primary recovery is estimated at 18.1 percent of STOIIP, of which 12.5 percent STOIIP had been produced by the end of 1963 from some 540 wells. By then the average pressure had decreased from an initial value of 960 to 550

Jan 1, 1970

By M. C. Miller, M. R. Tek, D. L. Katz

Previous studies have shown the influence of geometric variations on the drawdown and buildup behavior of a well completed in a homogeneous, porous medium containing a single-phase fluid. Other papers have shown the influence of leakage across caprocks on drawdown tests on water wells and aquifers. This paper presents two additional cases: the influence of an adjacent, expansible source of fluid, and the effect of caprock leakage on the measured in situ permeability and compressibility. Methods are developed for evaluating the influence of these two deviations from a uniform aquifer upon the in situ permeability and compre.ssibility indicated by pump tests. INTRODUCTION In relatively uniform porous media, saturated with a single-phase fluid, the effective reservoir permeability and compressibility of the water porous bed system may be obtained from drawdown and build-up data on wells, such as the initial wells drilled in aquifer storage reservoirs (Homers and Katz et al.7). In considering the drawdown and build-up behavior of wells adjacent to storage reservoirs, or of wells in an aquifer adjacent to an unknown gas field, questions arise as to the quantitative effect of the presence of compressible fluid on the measured permeability and compressibility of the formation. The solution to this problem is presented, using a constant pressure line source at some distance from two wells, one of which is pumped and the other used as the pressure observation well. The solution is presented in terms of the geometry of the wells and their relationship to the constant pressure line. It is known that caprock leakage can interfere with the determination of an aquifer in situ permeability and compressibility (Mantush4, Hantush and Jacob3 and Witherspoon and Muellerll). This paper presents an added case of the effect of leakage through a caprock of known thickness and permeability on well tests starting with a reservoir of constant pressure above the caprock and contributing to the aquifer as a result of the pump test. Again, both a pumping well and an observation well are postulated. These two cases are presented together since both a compressible fluid nearby and. caprock leakage show similar deviations from expected in situ permeability and compressibility results, and the solutions are similar in form. EFFECT OF A NEIGHBORING CONSTANT PRESSURE SOURCE ON IN SITU MEASUREMENTS Bixel, Larkin and van Poollenl presented a paper showing the influence of a discontinuity of the properties of a fluid formation system on drawdown and build-up performance. Their case is related to the present study but may be distinguished from it in that their numerical work and resulting graphs relate only to the performance of the pumping well itself. Incorrect values for in situ reservoir properties may be obtained from pump test data if the skin effect of the well and after-flow are not considered. Analysis of this problem by the authors indicated that the more reliable method of evaluating the influence of an adjacent gas field or expansible source was to use one well for pumping and another well at some distance from it for observing the aquifer pressure performance. An expansible source of hydrocarbon near a pumping well may be approximated by a line of constant pressure for a pump test. Fig. 1 illustrates a pumping well and an observation well near a line of constant pressure. Pressure behavior of an observation well during a drawdown pump test near a line of constant pressure is given by the diffusivity equation:

Jan 1, 1967

By T. K. Perkins, L. R. Kern, R. E. Wyant

Many factors influence the results of hydraulic fracturing to stimulate well productivity. Most of these factors have been studied and their effects discussed in the literature. However, the movement of sand through the crack during fracturing has received little consideration. Exactly where the sand goes in the fracture, how it gets there, and how this might influence results have not been studied, judging from published reports. To get an answer to some of these questions we have studied sand movement through a simulated crack segment in the laboratory. Although the work is preliminary, we have answered some questions about sand movement in a semiquantitative sense. We are reporting our results at this time in the hope of stimulating interest and further study in this important aspect of fracturing. LABORATORY EXPERIMENTS Fig. 1 is a schematic diagram of equipment used in this study. A segment of a vertical crack 0.25-in. wide was formed between two Plexiglas plates, and movement of sand in fluid through the crack was observed under various conditions. Sand and fluid were injected into the crack at constant rates. The top and bottom of the crack were closed so that the fluid flowed horizontally. Because of gravity most of the sand settled to the bottom before moving very far through the crack. If the fluid velocity exceeded a certain critical value, then all the sand injected was washed on through the crack even though it had settled to the bottom. When the fluid velocity was less than this value when sand injection was started, most of the sand which settled in the crack remained in place until enough of the area open to fluid flow was blocked by the settled sand to increase the fluid velocity to the critical value.. At this point all injected sand moved on through the crack even though it settled to the lower portion of the moving fluid section. All sand previously settled remained in place. When fluid velocity was increased at this paint by increasing fluid injection rate (without also increasing sand injection rate), some of the previously settled sand was washed out until enough area was open to flow that the velocity dropped to the critical value. Conversely, when the fluid velocity was decreased by decreasing the fluid injection rate (without changing the rate of sand injection), additional sand would settle until the critical velocity was again attained. In short, the critical velocity is an equilibrium value which the system will automatically seek, if possible. The equilibrium (or critical) velocity was measured under several conditions. The results of these measurements are shown in Pig. 2 where the equilibrium velocity is shown as a function of the amount of sand injected per minute. The points falling in the shaded band shown in Fig. 2 were obtained with water. The higher viscosities were obtained by adding CMC (carboxymethylcellu-lose). Data indicate that the equilibrium velocity is not very sensitive to sand size or transport fluid viscosity, or to sand injection rate (except at very low rates). Points connected by the solid CUrve in Fig. 2 were obtained with water and 20- to 40-mesh steel shot. The equilibrium velocity is apparently fairly sensitive to difference in density between particle and fluid. Only one run was made with a gelled fluid and that was gelled water at zero sand injection rate as shown in Fig. 2. (Measurements of equilibrium velocity at zero sand injection rate were made by filling the crack

By H. T. Kennedy, S. G. Dardaganian, J. L. Clanton

This paper presents equilibrium ratios measured on oil and gas samples taken from the Kelly-Snyder field at the reservoir temperature of 128°F. From these data smoothed curves were constructed for the reservoir fluid up to the bubble-point, 1,874 psia. A material balance calculation, based on the use of equilibrium ratios instead of the usual solubility and shrinkage meayr~rements is made on the field and compared to the con\.entional method. DETERMINATION OF EQUILIBRIUM RATIOS The equilibrium ratios, or K values were obtained by recombining separator samples of oil and gas taken when the reservoir was above its bubble point, and thus represented the reservoir fluid before any change had occurred due to the evolution of gas. The well sampled had a gas-oil ratio of 617 cu ft of high pressure sepalator gas per barrel of separator oil. and a bottom-hole temperature of 128°F. Samples were brought to equilibrium by agitating for 24 hours in a thermostat, maintained at the proper temperature within 0.2ºF, mercury being added when necessary to maintain the pressure constant. Samples of oil and gas were then taken by constant pressure displacement, and analyzed by low temperature frac-tionation. Equilibrium ratios were determined at 128°F and 500, 800, 1,000 and 1,400 psig. At the latter pressure, there were indications that the gas samples were contaminated with small quantities of oil, and only data taken at the first three pressures were included in Fig. I. This figure has been extended to higher and lower pressures by the use of the Fluor charts for 3,000 psi convergence pressure, on which the experimental points fit well. MATERIAL BALANCE EQUATIONS The possible errors involved in conventional material balance equations have been analyzed by Muskat1. Where the errors occur in field measurements, or in obtaining effective averages from variables such as gas-oil ratio and pressure, they will evidently be involved in any attempt to estimate the content of the reservoir. On the other hand, substantial errors may be introduced in conventional material balance calculations by: (1) the neglect of the amount of oil dissolved in gas at high pressures and temperatures in the reservoir, but which condenses under separator conditions; (2) the assumption that the separation of oil and gas in the reservoir may be duplicated by a differential liberation in the