Search Documents

By F. W. Jessen, H. Kazemi

A washing technique has been developed to form a spherical cavity in massive salt. The technique is, basically, a process of controlling the fluid motion in the cavity, the concentration distribution of brine, the rate of dissolution at the walls of the cavity, and the particular settings of the wash pipe, or pipes (inlet and outlet pipe) employed. For a particular arrangement of tubing and casing, fresh water enters from the casing annulus at a position above the bottom of the tubing, and the dissolved material leaves the cavity through the tubing near the bottom of the projected hole. The initial configuration of the cavity is cylindrical, representing the drilled hole situated at the axis of the projected cavity. As washing progresses the original hole is enlarged radially (any direction perpendicular to the axis of the hole). An inert fluid (generally a hydrocarbon, natural gas, or air) which serves as a blanket is injected through the annular space between the original hole and the casing. The controlled downward motion of this blanket maintains the upper edge of the brine region that is expanding on the surface of the projected sphere. A large spherical glass container and a radial model were used to investigate the flow patterns and the concentration distribution of brine occurring during the progress of solution of the salt. Aluminum flakes and dye were injected and flow patterns were observed and recorded on motion picture film. Based on the results of these model studies and other work carried out in this laboratory, the controlled washing technique was formulated. INTRODUCTION Underground cavities leached in salt beds and salt domes have been used extensively for storing hydrocarbons. Little attention has been focused on the shape of the cavities as long as large volumes were obtained and the cavities were structurally stable. The general process involves circulating fresh water and removing brine. Two distinctly different circulating systems can be employed, each of which yields characteristically different shapes. By far the most generally accepted method of washing storage caverns in salt domes is the direct circulation system. Water is introduced through the innermost pipe of a concentric pipe system, and brine is withdrawn through the annulus. In the reverse-circulation method, water enters through the annulus and is discharged through the smallesc tubing string. The size of the operation, and hence the size of tubing and casing used, depends on such factors as cavity volume, length of hole, availability of water, disposal of brine and power requirements. Underground caverns are from 100 to 1,000 ft or more in length, and when completed vary from 40 to 100 ft in diameter, providing storage of 100,000 bbl or more. The volumes of water required per volume of salt removed vary from 6 to 7 for the reverse circulation method to 10 to 11 for the direct circulation method. Up to 80,000 BWPD are often circulated. In the direct circulation method, because water enters near the bottom of the projected cavity, solution of salt is greatest at this point, particularly in view of the fact that when the washing is begun turbulent flow undoubtedly exists in the immediate vicinity of the discharge of the inlet water. As the diameter of the hole increases, flow rates also are increased, so perhaps the condition of fluid turbulence is maintained for some time. During the later stages of leaching, when capacity of equipment may be the limiting factor in maintaining flow rates, there may still exist some turbulence adjacent to the point of influx; however, for the most part laminar flow conditions prevail. There appears, therefore, rather good evidence to indicate that the state of fluid motion is responsible for the typically shaped cavity which results from such washing — namely a cylindrical form, generally somewhat larger at the bottom than at the top. Depending on the number of so-called stages which might be employed, the walls or surfaces of the salt diminish rather uniformly from bottom to

Jan 1, 1965

By C. R. Johnson, R. A. Greenkorn, R. E. Haring

Three confined five-spot miscible displacements at unity, favorable, and unfavorable mobility ratios were conducted in a shallow, water-saturated sandstone of Pennsylvan-ian age near Chandler, Okla. These studies, plus associated laboratory experiments, were designed to measure miscible displacement performance in a controlled natural system, using known scaling criteria to develop an approach to modeling the heterogeneous field system. We have concluded from these studies that: (I) displacement efficiency in the field is a pronounced function of mobility ratio, indicating that miscible fingering observed in simple laboratory models occurs in the field: (2) field displacements can be quantitatively predicted by scaled laboratory models if the degree and location of field permeability variations are preserved in the models: and (3) arbitrary simplifications of heterogeneity will not necessarily predict observed displacement efficiency, and the simpler the model, the more optimistic the prediction. INTRODUCTION Many processes to achieve miscible displacement of reservoir oil by injected fluids have been conceived and field tested by the oil industry. Among the better known are high-pressure gas, enriched gas, and LPG banks. The simplest form of miscible displacement—one fluid miscibly displacing another fluid of different viscosity but the same density—has been studied extensively in homogeneous laboratory models. Observations of unstable fingering have been made which explain the significant decrease in displacement efficiency as the mobility ratio (ratio of displacing fluid mobility to displaced fluid mobility) increases. General industry experience with field tests of miscible displacement projects, mostly LPG banks, has been premature solvent breakthrough and lower than predicted production rate increases. These results have been attributed to either unstable fingering, unusual or unexpected permeability stratification, or both. Miscible displacement data in a controlled natural system have never been reported, however. Also, it has not been shown that properly designed and constructed laboratory models quantitatively predict field-scale behavior. The purpose of the combined field and laboratory ex- periments reported in this paper is twofold. The first was to measure miscible displacement performance at different mobility ratios in natural rock approaching field size under precise, controlled conditions. The second purpose was to utilize known scaling criteria plus several approaches to heterogeneity to model the field. Comparison of model and actual field results should then determine whether or not the laboratory phenomena (manifested by miscible displacement efficiency) are exhibited in large, natural rock systems. We carried out our program by first locating a shallow, water-saturated reservoir whose rock properties were representative of oil-bearing reservoirs. Detailed reservoir description by core analysis and interference testing showed the field site to be heterogeneous. A sequence of controlled, aqueous-phase miscible displacements was conducted at unity, favorable and unfavorable mobility ratios. A central, confined pattern was used to obtain the displacement data. A laboratory program using sand-packed models was conducted to determine the modeling criteria necessary to simulate field behavior of miscible displacement in a heterogeneous system. SCALING THEORY The detailed derivations and descriptions of the scaling laws that apply to laboratory models of reservoirs are adequately described elsewhere, so the following discussion will be restricted to facets of importance in this study. For a displacement in which one liquid miscibly displaces another, the following dimensionless groups are required to have the same numerical value in the model as in the field: The model also must be geometrically similar to the field, be spatially oriented the same as the field (same dip angle), and have the same initial and boundary conditions as the field (same initial fluid saturations and same injection-production well arrangement). When these conditions are satisfied, the theory predicts that at dny dimensionless time (pore volumes of produced fluids) the dimen-sionless flow potential and dimensionless fluid concentrations will be identical at all dimensionless spatial locations within the model and the field. If this prediction is correct, then the local dimensionless velocities must be identical, thus the instantaneous fraction of displaced fluid produced and the cumulative recovery expressed as fraction of original fluids in place must be identical at all dimensionless times. The theory outlined above has been obtained by either dimensional analysis or inspectional analysis of differential

Jan 1, 1966

By G. T. Pruitt, T. L. Irby, P. B. Crawford, H. Ferrell

In water flooding peripheral, center-to-edge, line-drive or water-encroachment patterns the question has arisen, "when should a producing well be converted to a water-injection well?". It is realized that, if the producing well is shut in when water breakthrough occurs, some oil could be left in an unswept area. Yet, operation to high water-oil ratios may require processing much additional water. If a well is shut in, "where should the allowable be transferred?". A review of the literature indicates that very few data are available to the engineer to assist him in answering these questions. It is the purpose of this paper to present information which may be of value in selecting the flooding technique and the injection and producing wells and in scheduling injection and production rates. Certain phases of these problems can be studied in the laboratory. The Potentiometric model is well suited for studying many waterflooding problems. This model assumes that steady-state flow exists, that the mobility ratio is equal to one and that gravitational effects are neglected.'-' The three-phase sand model also has been recognized as an effective means for studying certain reservoir problems. Both models were used in making the study reported here. This paper discusses seven cases utilizing various waterflooding techniques. Data for the first five cases were obtained on the potentiometric model. Data for Cases VI and VII were obtained by constructing and flooding an unconsolidated sand pack (a three-fluid-phase system) and by determining the swept area and cumulative oil recovery for various types of operations. APPARATUS AND PROCEDURE The potentiometric model reservoir was 30 in. long X 10 in. wide by about 1/2 in. deep. Four wells were equally spaced in a line array along the lateral center line. (See Fig. 1.) Well No. 1 initially was an injection well for each of the patterns reported. The cases studied with the potentiometric model and sand model are described herein. The laboratory sand model reservoir was a 30- 10-in. rectangular Lucite vessel packed with sand to a depth of about 0.65 in. Four wells were equally spaced in a line array along the lateral center line. The reservoir material was an unconsolidated sand into which the reservoir fluids were mixed to yield fluid saturations of 55 per cent oil, 25 per cent water and 20 per cent gas. The water was added to the sand and the material mixed, after which the oil was added. Kerosene and water, the fluids used, gave a viscosity ratio of 1.64:1. In packing the reservoir, care was taken to assure constant fluid saturations and constant porosities. A new mixture was prepared for each run. During water flooding, a colored water was injected by a constant rate pump. The injection rate was 1.1 B/D/ft of sand thickness. For this series of tests, each of the producing wells was open to the atmosphere and, as in the potentiometric model study, Well No. 1 initially was an injection well for each of the patterns. KESULTS OF POTENTIOMETKIC MODEL STUDlES Two cases (Cases I and 11) involving equal pressure injections were studied, with the following results. Case Water injection was initiated at Well No. 1; the producing wells (Nos. 2, 3 and 4) were operated at constant and equal bottom-hole pressures. When water broke through at Well No. 2 and achieved the selected water-oil ratio, Well 2 was converted to a water injection well, resulting in two injection and two producing wells. The injection pressures at Wells 1 and 2 were maintained equal and constant; pressures at the producing wells were held equal, but they were lower than those at the injecting wells. A similar process was repeated when water broke through at Well No. 3. The flood was terminated when

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965

By D. M. Kehn

A method has been devloped for chromatographic analysis Of the vapor and liquid phases Of a a system containing methane to components having 20 or more carbon atoms. The method uses a windowed equilibrium cell in which volumetric phase behavior of the system can be observed accurately and from which small samples of gas or liquid can be withdrawn for analysis. Analyses are made using two chromatographs, one for the lighter and one for the heavier components in a sample. Combination of the two analyses yields a detailed analysis of the gas or liquid sample. The complexity of the condensate heavy ends is evident from the chromatograms of these fractions, and the predominance of the paraffin hydrocarborn serves as a useful marker in interpreting the chromatograms. The K-values obtained in this analytical method are presented for a high-pressure condensate system and predict closely the observed volumetric behavior of the system. INTRODUCTION Quantitative analysis of hydrocarbons from natural gas reservoirs is necessary for several reasons—to calculate the amount of sales gas produced, to calculate the amount of natural gasoline produced, to plan a liquid recovery system, or to calculate the potential economic value of a reservoir produced under one or more of several different conditions. Analysis of natural gas fluids produced to the surface consists of identifying and computing the mol fraction of each component of the mixture. Although methane is the predominant component, varying amounts of ethane, propane, butane, pentanes and heavier components are also present. Materials containing up to 30 carbon atoms occur in amounts which decrease with increasing molecular weight. However, the quantities of components in the 20 to 30 carbon atom range are usually so small that their importance is negligible, and they are undetect-able in natural gas by ordinary analytical methods. All the components up to those having 20 carbon atoms may sigsficantly affect phase behavior, however. Commonly, only the methane-through-pentane fraction is analyzed quantitatively for each component, while components heavier than Pentane are lumped and repored as "hexane- plus". Expensive, tedious techniques are required for analysis of this fraction. Consequently the detailed analyses needed for prediction of reservoir behavior are usually undertaken only when major gas fields are being developed. The need for complete analyses of condensate systems is apparent when it is recalled that most gas fields are produced by pressure depletion. As the pressure declines, some of the heavier hydrocarbons are lost as liquids which are in the reservoir. In many instances the amount of liquid in equilibrium with the gas phase at high pressure constitutes only 1 or 2 mol per cent of the total system. Flash calculations generally must predict the actual amount of liquid with an accuracy of a few per cent in order to be useful. This retrograde condensation has been understood for years, but accurate correlation methods to permit quantitative prediction of phase behavior in the retrograde region are not presently available. The increasing importance of natural gas has made accurate prediction of phase behavior and composition of produced natural gas streams an economic necessity. The work reported here was undertaken to provide a rapid, economical method for obtaining the vapor-liquid equilibrium information needed to predict accurately the composition of the fluids produced from a gas reservoir throughout its life. TO develop this method, a pressure cell equipped with windows was designed and built for observing the volumes of liquid and gas present at reservoir pressures and temperatures. Use was made of established chromatographic methods for rapid and detailed analysis of both phases. This paper describes the equipment and techniques developed for obtaining vapor-liquid equilibrium data, presents the results of analyses of a condensate system, and indicates the usefulness of these data in predicting hydrocarbon phase behavior. DESCRIPTION OF EQUIPMENT USED The equipment used in obtaining the required information on phase behavior and the complete analysis of hydrocarbon mixtures through C, will be described first, followed by a discussion of the operation of the equipment. It will be helpful, however, to consider first a brief outline of the technique used. A sample of separator gas and liquid is charged to the windowed cell (see Figs. 1 and 2) where volumetric equilibrium phase behavior at reservoir pressures and temperatures can be determined. Then samples of the coexisting phases are withdrawn. The methane-through-pentane fraction is analyzed with a chromatograph equipped with a hot-wire detector, and the pentane-plus fraction is analyzed with a second chromatograph equipped

Jan 1, 1965

By V. S. Gupt, W. H. Somerton

Rock may undergo great changes in physical properties when heated to high temperatures and then cooled, The temperature and intensity of reactions causing rock alterntiorl.s can he controlled by introducing certain chemicals during heat treament. Three typical outcrop sandsone samples were saturuted with common salt solutions, then heated to several maximum temperatures. After cooling, it was found that per-rrreuhilities had increased much more for salt-saturated samples than for samples not saturated with salt but heated to the same temperatures. This was only true, however. for samples heated above the melting points of the particrrlar salts. Potassium chloritle was particularly effective with Bandera sandstone. Samples saturated with potassium chlorirlr. solution and heated to 900C showed an 11-fold increa.se in perrrieahility. Samples without potasrirdrn chloritle but heated to the .same temperature. showed only a 2.7-jold incresre in permecahility. In application, it seems possible that injecting chemicalc into the formations from a wellbore followed by applying intensive borehole heating might promote reactions which would greatly improve permeability of the formalions. INTRODUCTION Great changes in the physical properties of rocks which have been heated to temperatures in the range of 600 to 800C have been reported earlier. Permeability increases of 50 per cent, and equivalent decreases in sonic velocity and breaking strength have been observed. Although there might be some suppression of certain reactions responsiblc for these changes when rock samples are heated under simulated reservoir pressure conditions. recent work has shown that these are more than offset by the increased importance of other reactions at high pressures. The reactions considered responsible for alteration of rock properties by heating include differential thermal expansion. dehydration, phase changes and dissociation of mineral constituents. Ceramists have long known that temperatures at which reactions occur can be raised or lowered by the presence of certain impurities in the sys. tcnl. Thus the possibility exists that by saturating rocks with appropriate solutions. desired reactions might be accelerated and unwanted reactions might be suppressec! when the rock is heated. Purpose of the present work was to investigate the effects of several common salts on the thermal alteration of sandstones. Types of reactions which might occur are reviewed and the findings of a number of thernlochemical alteration tests are presented. THEKMOCHEMICAL ALTERATION OF SANDSTONE MINERALS The most abundant constituent of most sandstones is quartz. Quartz can exist in at least eight different forms, but in the temperature range of immediate interest (to 900C) only two forms are of importance—alpha quartz below 573C and beta quartz above this temperature. Although the alpha-beta inversion of quartz is very important in thermal alteration of rocks. it is not particularly important here because the inversion temperature cannot be changed significantly by the presence of impurities or by the application of pressure. The transition temperature of quartz to tridynlite is 867C. but the transition is very sluggish. Tridymite is considered to be a metastable transition phase between two stable phases: quartz?cristobalite. However. the transition temperature for tridymite to cristobalite is 1,470C.4 The quartz-tridymite-cristobalite transition can be accelerated substantially by the presence of fluxing agents. Finely divided calcium, magnesium and titanium oxides accelerate the conversion while A12O may retard it. A Mixture of NaCl and CsCl reduces the temperature for cristobalite formation by as much as 420°C. Feldspars constitute the second most important mineral in sandstones. The melting points of feldspars range between 1,000 and 1,700°C depending upon the variety. No information available indicated any important role of fluxing agents in the thermal alteration of this group of minerals. Carbonate minerals are subject to dissociation at temperatures within the range of the present investigation. The dissociation of magnesite can start at a temperature of 373°C, but the reaction is sluggish and might not occur untll a temperature of 500°C or ,higher is reached. Dolomite dissociates in two stages at 500°C and 890°C, whereas calcite dissociation temperature is about 885C. Because CO2 is released in the dissociation of carbonates, ail such reactions are somewhat dependent upon CO2 partial pressure. In the absence of CO: in the surrounding atmosphere, the dissociation of calcite starts at 500°C.However. when 1 atm of CO surrounds the sample, the dissociation does not start until 900C. The other carbonates are apparently much less sensitive to a change in partial pressure of CO2. The aragonite calcite transformation can occur an!. where within the temperature range of 357 to 488°C. depending upon the presence of impurities such as barium. strontium. lead and perhaps zinc. The differential thermal analysis (DTA) curves of both magnesitc and dolomite vary with the presence of 'impuritics. The presence of iron in particular seems to affect the magnesitc DTA curve

Jan 1, 1966

By N. Mungan

Laboratory water floods were performed in oil-wet and waterwet alundum and Torpedo cores, displacing a refined oil with n-hexylamine or Triton X-100 solution. Also, some floods were performed in which a sucrose solution was displaced with n-butyl alcohol. The Purpose ot the tests was to see if the oil recotlery could be increased and to examine what role the inter-facial tension reduction and wettability change play in the recovery mechanism. it was found that the chromatographic transport of amine was influenced by core wettability. In oil-wet cores, the rate of advance of the amine band could be predicted from equilibrium chromato-graphy, while in water-wet cores the amine band moved faster than predicted, indicating a non-equilibrium process. By reducing the interfacial tension to 1.1 dyne/ cm, oil recovery was increased. More oil was recovered from Dri-filmed cores than from water-wet cores. Reversing the wettability of the porous media from oil-wet condition also resulted in some additional oil recovery. Neutral wettability floods did not increase oil recovery. INTRODUCTION Interfacial forces in petroleum reservoirs are responsible for retention of large quantities of residual oil. Increasing exploration costs have created an incentive to attempt recovery of this residual oil by new and novel processes. One novel process involves changing the interfacial forces by introducing a chemical into the reservoir during water flooding. Recently, several investigators have carried out laboratory displacement tests using amines. lt3.4 The amines adsorbed onto initially water-wet core surfaces, changing them to oil wet. Additional oil was recovered when the cores were flooded in a manner reversing the. wettability from oil-wet conditions. In all these studies, the wettability reversal was considered responsible for increased oil recoveries although it was noted that amines also reduced oil-water interfacial tension. In the present study, displacement experiments were performed in water-wet and Dri-filmed cores. The purpose was to separate the effects of lowering the interfacial tension from changing the wettability. LABORATORY STUDY All experimental data given in this paper have been obtained at a temperature of 70F + 1 and prevailing atmospheric pressure. FLUIDS AND MATERIALS The oil used in these experiments* was washed with H2S04 and passed through two 100-200 mesh silica-gel beds to remove unsaturates and surface active impurities. Normal hexylamine** of practical purity was used, and the alundum cores*** were composed of nearly pure A1203. Fused quartz (SiOi) and Lucalox (A12 )t plates were used in the contact angle measurements. DISPLACEMENT TESTS Displacement tests were performed in alundum and Torpedo cores. Before displacement runs, cores were acidized with 0.1 normal HCI, flushed with distilled water and fired at 1,200F to make them water wet. This procedure also reduced water sensitivity of the Torpedo cores. Oil-wet cores were prepared from water-wet cores by flowing several pore volumes of 1 per cent by weight Dri-film SC-87 solution in heptane through the cores, flushing the cores with nitrogen, evacuating, and finally heating the cores at 300F for 4 or 5 hours. Between floods, cores were cleaned by conventional procedures and treated again as above.

Jan 1, 1965

By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By R. L. Slobod, C. Gatlin

This .study defines the basic mechanism of the mis-cible displacerrzent of oil and writer from porous Medici by various water-driven alcohol .slugs. Three distinct alcohol slug processes were .studied. Considerable data concerning the quanity of alcohol required for oil recovery were also obtained. All data were obtained in a 1-in. diameter, 100-ft long, unconsolidated core. The porosity of this system was 35 per cent. and the permeability was approxitrlately 4 darcies. Total core pore volume wax 5,716 cc. All displacements were conducted at a constant injection rate of 5 to 6 cc//min, which corresponds to a frontal advance of 5 ro 6 ft/hr. The first portion of this paper is concerned with 111 use of one alcohol—isopropyl—a\. the slug material. Isopropyl alcohol (IPA) is completely miscible with both oil rind water; however, miscibility of the threc-component systems, oil-water-IPA, requires a relutively. high concentration of IPA. Hence, the displocement is not of the misoible type unless the IPA concentration is maintained above some critical value. A slug of IPA equal to only 13.5 per cent of the pore volume was jound to be sufficient to obtain complete recover?, of residua1 naphtha. In later studies two distinct process variations were developed. The firsr of these utilized methyl alcohol (MA) and IPA as slug materials. It was shown that methyl alcohol may he substituted for IPA at the front and rear of the slug with no loss of oil recovery. A .slug of 4 per cent MA-4 per cent IPA-4 per cent MA was sufficient for complere oil recovery. Because MA is considerably cheaper than IPA, this represents an important step toward economic application. A .second process variation used normal butyl alcohol (nBA) and MA as the composite slug, the nBA segnzent being injected first. This technique requires the smallest total slug size (approximately 10 per cent) of all processes studied. The high cost of nBA, however, precludes commercial application. It is possible that this basic process, subject to changes of alcohol type, may lead to a commrercicil process. INTRODUCTION Within the last 10 years, considerable study has been devoted to the general mechanics of miscible phase dis- placements in porous media. These studies have. in general, dealt with two-component displacernent. All reported field trials to date have been modified gas drives of one type or another. These utilize either lean gas at high pressure, rich gas at lower pressure or an LPG slug. The irreducible water content of the reservoir remains immobile during these processes. Although these techniques hold great promise. certain drawbacks do exist. Poor areal sweep efficiency, inherent in any displacement having a highly unfavorable mobility ratio, is one disadvantage. Furthermore, the miscibility of all processes which use gas is dependent on pressure. These pressure limitations may prohibit application to shallow reservoirs. There are also many areas where large quantities of LPG and natural gas are not readily available. These factors emphasize the need for improved techniques. The alcohol slug process is also a miscible-phase displacement process. It differs from the previously mentioned two-component techniques, however, in that both the reservoir oil and water are displaced by the slug. This behavior is a consequence of the miscibility of certain oil-water-alcohol systems. In the simplest case, a relatively small volume (slug) of an alcohol (such as isopropyl) is injected into the system. Water is then used to drive the slug through the medium. Thus. three components—-alcohol. oil and connate water-—exist at the front side of the slug. Miscibility is obtained at some alcohol concentration, this being dependent on the solubility of the particular system. Miscibility is maintained within the slug until the alcohol concentration falls below that value required to maintain miscibility. When miscibility is lost, the process reverts to a water flood. Certain inherent benefits of this technique are apparent. High pressures are not necessary to obtain miscibility in these liquid systems. Furthermore, water is a more desirable driving agent than gas because of the improved mobility ratio and the attendant improvement in areal sweep efficiency. The main disadvantage is, of course, the relatively high cost of alcohols. The use of an alcohol slug to recover reservoir oil is not a new idea." ' However, this process has received only limited study, presumably due to the lack of industrial interest caused by the seemingly prohibitive cost of alcohols. The main purpose of this study was to investigate the mechanism of the displacement of oil and water by various alcohol slugs and to develop process modifications aimed toward possible commercial application.

By R. Wiesenthal

A method is developed for improving the low recovery efficiency which results when viscous oils are flooded by water. Viscous oil has been diluted with a lighter liquid miscible in it in any ratio which produces a mixture possessing a reduced viscosity and which is then displaced by water. Light gasoline was used in these tests to reduce the viscosity of the oil in place. Oils possessing viscosities in the range of 1.28 to 324 cp at the test temperature of 30C were displaced from a cylindrical unconsolidated sand core, with a length of 2 m (6.6 ft) and a diameter of 10 cm (3.9 in.) at a flood of 6.27 cc/sq cm/hr. In two test series up to I PV of light gasoline was injected into the core before water flooding. In the first series the recovery of a low-viscosity oil (1.28 cp) increased as the volume of light gasoline was increased. However, only the oil which could not be recovered by water flooding alone could be replaced by the light gasoline. In the other series, the recovery of a more viscous oil (13.5 cp) was not increased even if large quantities of light gasoline were injected. An oil bank built up ahead of the water front so that the flood water met with equivalent saturation conditions, as would be the case in flooding solely with water. However, the recovery of more viscous oils could be increased substantially when the core was first flooded with water, followed by a slug of light gasoline, and then flooded with water again. Furthermore, an oil bank ,built up ahead of the second water front. The formation of this oil bank is particularly favorable for the displacement process; the greater part of the light gasoline injected was pushed out of the core ahead of the oil and recovered. Using a light oil of low viscosity, it was possible to replace only the residual oil that could not be recovered by water flooding by the light gasoline. As the basic study had shown that highly viscous oils could be recovered by flooding first with water, then with light gasoline, followed by a second injection of water, the study was extended by tests made with reservoir fluids and cores taken from the low-gravity oil reservoir of the Wietze field, Germany. A great increase in recovery over flooding with water alone was obtained in these tests. The results may show a way to recover high-viscosity oils by a comparatively simple flooding procedure. INTRODUCTION In fields where oil recovery has not benefited from natural water drive, increased recovery may be obtained by the injection of water into the reservoir, especially in the case of fields which produce high-gravity, low-viscosity oil. There is a rather close relation between the viscosity of the reservoir fluid and the recovery that can be obtained by water flooding. As the viscosity increases the oil recovery decreases proportionately, so that an oil viscosity about 30 times that of water is generally considered to be the upper limit for an economically successful water flood.' This limitation has been recognized theoretically by Buckley and Leverett,' and has been verified by numerous laboratory flooding tests, such as by Croes and Schwarz,V n the viscosity ratio range of oil to water from 1 to 500. The reason for the inferior recovery of viscous oils by water flooding can best be understood by considering the mechanism of flood tests. In such tests water is introduced into one end of a sand-packed tube which is saturated with oil of the viscosity to be tested, and oil is produced from, the other end. Oil, with a viscosity lower than that of water, is pushed ahead of the advancing water with considerable uniformity, and irregularities in the displacement process tend to be eliminated as the oil saturation decreases and the water saturation increases. However, oil recovery is not complete, for the water forms interfaces with the oil and traps residual oil droplets in certain of the pore spaces. These residual oil droplets are distributed rather uniformly through the sand, and they are not susceptible to recovery regardless of the amount of water passed through the test cylinder. In the case of an oil possessing a viscosity greater than that of water, the injected water tends to move irregularly through the sand in the test cylinder. At the place in the sand where initial water movement takes place, resistance to the movement of water is lowered and the water finger so formed will grow perceptibly; it will extend to the outlet end of the test cylinder so that a breakthrough of water takes place long before much of the oil-saturated volume of the sand has come in contact with water. Once the breakthrough of water takes place, the water-oil ratio is gradually approaching the economic limit, even though much of the oil in the test cylinder remains unaffected by water. Disconnected drops of oil are trapped in the portion of the sand that has been invaded by water, just as when an oil of low viscosity is flooded. The poor recovery of the more viscous oils, therefore, is due to the irregularity of water movement through the test cylinder, and the rate of water movement through restricted sections of the oil-saturated sand increases with the more viscous oils. There are three ways whereby the recovery of viscous oils by water flooding can be improved:' (1) adding materials which will increase the vis-

Jan 1, 1965

By W. E. Howlett, R. L. Slobod

Jan 1, 1965

By B. Habermann

Artificially consolidated sand models, representing one-quarter of a five-spot, have been developed and used to study factors aflecting misciblt. displacrmenr. Sweep efficiency at breakthrough, size of the mixing zone between two miscible liquids and per cent area contacted by drive after breakthrough were determined tor the high mobility ratios encountered in actual resvrvoirs. Quantitative relationships between the degree of viscous fingering and mobility ratio were obtained by measuring the length of the fluid interface. Scaled miscible-slug experiments, supported by field evidence reported in the literature, have shown that when the slug is followed by dry gas the process is less efficient than expected. In addition to low areal sweep efficiencies encountered for high mobility ratio displacements, the effectiveness of a miscible slug is greatly reduced. This is caused by an accelerated growth of the mixing zone between the driving and the displacing fluids. INTRODUCTION Considerable interest in miscible displacement as a secondary recovery process has been shown by the oil industry in recent years. In addition to extensive laboratory investigations, numerous field operations have been initiated so that 39 miscible displacement projects had been reported' in the United States by early 1959. By far the most popular approach in these projects is the use of an LPG slug followed by dry gas. Laboratory tests have indicated that with a small miscible slug, amounting to several per cent of the hydrocarbon pore volume, practically 100 per cent recovery of the oil in place can be achieved and that all of the slug material can be recovered by a subsequellt gas drive. However, these experiments were conducted on small-diameter long cores that can be considered as essentially uni-dimensional reservoirs that do not represent actual field conditions. It soon became apparent that the inherently adverse mobility ratios existing in the reservoir cannot be ignored in any miscible displacement field project. When a less viscous fiuid such as an LPG slug drives a more viscous reservoir oil, fingers develop that reduce the areal sweep efficiency. The slze of the miscible slug to be used is a subject of some controversy. It has been proposed that the size of siug needed be calculated by setting lengths of the mixing zone proportional to the square root of the distance traveled. This proposal is based on experimental evidence' and theoretical considerations"' in which fingering was not a factor. A prerequisite for successful application of the miscible displacement process to field operations is a better understanding of the following factors. L What is the effect of mobility ratio on the rate of deterioration of a miscible slug? 2. How large a slug should be used for given reservoir conditions? 3. What is the sweep efficiency? The purpose of this investigation was to provide some additional laboratory data that should help to answer these questions. More specifically, it was intended to study more quantitatively the effect of viscous fiinger-ing, mobility ratio and slug size on the efficiency of this relatively new secondary recovery process by means of experiments on thin, horizontal, porous medium models.

By M. M. Mebta, G. W. Dean, W. H. Somerton

With the advent of underground heating operations, interest has developed in the alteration of rock properties by high-temperature treatment. In the present work a number of sandstones were heated to temperatures in the range of 400°C to 800°C under both atmospheric and simulated reservoir pressures. Pertneabilities increased by at least 50 per cent and sonic velocities and breaking strerlgths decreased by an equivalent amount. Differential thermal expansion and other reactions of constituent min-era1 grains are the causes of these alterations. INTRODUCTION In the underground combustion of petroleum reservoirs, temperatures of the order of 600C are reported to have been reached in the combustion zone.' At this temperature rocks are subject to extensive thermal alteration. Temperatures of this magnitude and higher may also occur in subsurface formations when subjected to bottom-hole heating, thermal drilling operations, and underground nuclear explosions. Temperatures of this magnitude might also be generated by conventional rock drilling methods at points of bit-tooth contact. In earlier work, the permanent deformation of rocks resulting from heating was reported. Major structural damage of rocks occurs due to differential thermal expansion of mineral constituents. A number of mineral alterations including crystal inversions, loss of water of crystallization and dissociation, may also contribute to changes in physical structure and properties of rock. In the present work, samples of three typical sandstones were heated to several temperatures up to a maximum of 800C and then allowed to cool to room temperature. Heating was done under both atmospheric pressure and simulated reservoir pressure conditions. Physical properties of the samples were measured before and after heating and comparisons made. Measured properties included permeability, sonic velocity, breaking strength and fracture index. Changes in physical properties were compared to changes in mineralogical characteristics as determined by thin-section. X-ray diffraction and chemical tests. EQUIPMENT AND PROCEDURE Two outcrop sandstones (Bandera and Berea) and one sub-surface sandstone (St. Peter) were selected for the tests. These samples have a wide ranee in composition and physical properties as shown in Table 1. The first series of tests was made on 2-in. diameter by 5-in. long test specimens. Test specimens used in all later work were 3/4-in. diameter by 1 1/8-in. long, this being the specimen size required for heating at simulated reservoir pressures. After careful washing, the cores were oven dried at 100 ± 5C for a minimum of 24 hours before the tests were run. Test specimens were heated in an electric furnace at a constant rate of temperature increase of 3C per minute. When maximum temperature of the run was reached, the sample was allowed to soak for one hour. The furnace was then cooled to room temperature at the same rate of 3C per minute. The entire heating operation was designed for reproducibility without subjecting the test specimens to excessive thermal shock. For samples heated under simulated reservoir pressures, a pressure cell designed by Dean was used (Fig. 1).3 The core sample was inserted into a thin-walled (0.006 to 0.01-in.) copper cup which was then mounted in a high-pressure cell. Provisions were made for the application of internal pore pressure as well as confining pressure. Tests showed that the thin-walled copper cup closed tightly around the core and satisfactorily transmitted confining pressure to the core. The core was heated by placing the entire cell into the electric furnace. The heating program was the same as that used in the atmospheric pressure runs: tempera-ture rise of 3C per minute to maximum temperature of the test, soaking at maximum temperature for one hour, and cooling at a rate of approximately 3C per minute. The cell was designed to withstand 5,000 psi at 1,000C. However, since it was considered likely that repeated heating and cooling would in time weaken the steel, 2,000 psi at 850C was set as a working limit. In the present series of tests, the pore pressure was held constant at 750 psi and the confining pressure at 1.500 psi. The pressure source was a high-pressure nitrogen tank. The two pressures were controlled manually but are accurate well within ± 50 psi.

Jan 1, 1966

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By S. J. Prison, C. R. Smith

The effect of fluid injection to control water coning in oil and gas wells was investigated. Analytical and model techniques were employed. The factors investigated were the position and length of the completion interval, the point of fluid injection, the viscosity of the injected fluid and the relative thickness of the oil and water sections. The resulting influence of these factors on the net producing water-oil ratio was determined. Several important conclusions can be drawn from the study. In general, it was found that the net producing water-oil ratio can be reduced by fluid injection. The magnitude of this reduction depended on the factors listed above. An important practical consideration is that the injection fluid may be either oil or water. If the injected fluid is less dense than the connate water of the reservoir, the fluid will not be lost. This fact is reassuring when valuable oil is being injected. Efforts to suppress water production were more successful when the injection fluid was more viscous than the reservoir oil, or when a zone of reduced permeability existed in the vicinity of the point of fluid injection. Under test conditions, little benefit was derived through the use of impermeable barriers or cement "pancakes". INTRODUCTION The occurrence of water coning has been known for at least 60 years. In thin oil or gas pay sections, the presence of an oil-water or gas-water contact hinders production and often causes early abandonment of the afflicted well if a completion is even attempted. Even when relatively thick pay sections are found, the encroachment of water when a water drive is present will eventually pose serious water coning problems. This water is often corrosive, expensive to separate from the oil or gas and is costly to dispose of. The theory of water coning has been discussed by a number of authors. 1,2,3,4 Briefly, water coning to the producing interval in a well is due to pressure gradients resulting from the production of fluid from the reservoir. These pressure gradients will cause a water cone to rise toward the bottom of the producing interval if a water-oil or water-gas contact exists. The tendency of the water to cone is offset or partially offset by gravity forces since the water has a higher specific gravity than the oil. A balance then exists between two forces, gravitational forces arising from the difference in specific gravities of the oil and water, and the pressure gradients causing the flow of fluids to the wellbore. If the pressure gradient exceeds the gravitational force, water coning to the wellbore occurs and water production results. Through the years considerable thought has been given to the water coning problem. More than 50 U. S. Patents have been granted to inventors on the subject. A relatively complete literature review of the water coning problem has been made. 5 A number of these patents hold considerable promise for the solution or the partial solution of the water and/or the coning problem. Very little has been written describing field tests of techniques for the suppression of water coning. A notable exception is the paperby West. 6 He reports success in reducing gas coning by a combination of gravel packing and oil injection above the oil-producing interval. He also describes a comparable method to prevent water coning, but provides no field examples. This study experimentally and analytically verifies the benefits of oil injection as a means of partially or completely suppressing the water cone. While the gas coning problem was not treated, it is anticipated that results comparable to those obtained in water suppression could be obtained with reduced oil injection since the viscosity contrast between oil and gas exceeds that between oil and water. For the purpose of this study, the conventional potential flow theory was applied to the water-coning problem. The experimental verification centered on both a radial and a linear model. The model study permitted the investigation of complex flow configurations and the use of fluids of differing densities and viscosities. No analytic expressions are available to permit a solution of the problem as stated (see Fig. 1).

By D. C. Lindley, D. H. Gaucher

The displacement of oil by water in a waterflood project is accomplished by the action of transient viscous, gravitational and capillary forces which drive fluid through interconnecting pore spaces toward production wells. The relative importance of each of these forces to the effectiveness of the displacement and the production history depends on properties of the reservoir itself and the manner in which it is operated. There has been considerable discussion'-3 concerning the importance of these factors and the extent to which they control the performance of individual waterflood projects. No data have been presented, however, to demonstrate the effect on waterflood behavior of variations in rock permeability, water-injection rates and mobility ratios in three-dimensional reservoir systems in which viscous, gravitational and capillary forces are allowed to assume the proper relative influence on fluid flow. Much information relevant to water flooding has been gained from the study of field case histories. But, the complexity of the systems involved, the difficulty of defining geometry and obtaining sufficient data, and the fact that the same reservoir is never flooded twice with the same initial conditions, all obscure the role of process variables such as rate. Further, mathematical calculations of waterflood behavior are restricted at this time by available mathematical techniques to highly simplified situations. Scaled models, however, do offer an approach at the present time to evaluation of the effects of the pertinent variables. Several investigators have predicted prototype reservoir behavior from observations of model waterflood performance under a variety of conditions. Two-dimensional aspects of waterflood pattern efficiency have been investigated by Muskat, Aronofsky, Dyes, et al, raig, et al,' and Rapoport, et al. he effects of gravity segregation, viscous fingering and permeability stratification have also been studied in two-dimensional models. Craig, et al," studied the importance of gravitational forces on frontal displacement in three-dimensional models with wells on a five-spot pattern. This work in- vestigates the tendency for water to segregate in homogeneous reservoirs because of gravity and to under-run the oil for a range of water-inject ion rates. The effects of permeability stratifications were investigated by these authors using miscible fluids to simulate water-channeling through permeable strata in systems of negligible capillary force. In this investigation, a three-dimensional model of a five-spot pattern flood was designed to represent typical prototype conditions, and the sand and liquid properties were selected so that capillary, gravitational and viscous pressure gradients were scaled. It was not, however, possible to achieve exact similitude regarding viscous fingering when the more viscous oil was used. The effects of rock stratification on waterflood behavior were studied by changing both the permeability ratio and the position of the more permeable sand stratum in a two-layered, horizontal model. For each type of stratification, constant-rate floods were performed and the rates were varied, in separate experiments, over a tenfold range. To observe the effect of mobility ratio on flood performance, two series of constant-injection-rate floods were performed on the most highly stratified reservoir at a water-oil viscosity ratio of one.

By K. H. Coats

This paper presents the development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertical direction due to router flow are taken into account. A vertical permeability equal to a fraction of the horizontal permeability is also included in the model. The solution is given in the form of a dimensionless pressure-drop quantity tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservoir pressure from a known water-influx rate, to predict water-influx rate (or cumulative amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. The model is applied in example problems to gas-storage reservoirs, and the difference between reservoir performances predicted by the thick sand model of this paper and the horizontal, radial-flow model is shown to be appreciable. INTRODUCTION The calculation of aquifer water movement into or out of oil and gas reservoirs situated on aquifers is important in pressure maintenance studies, material-balance and well-flooding calculations. In gas storage operations, a knowledge of the water movemenr is especially important in predicting pressure and pore-volume behavior. Throughout this paper the term "pore volume" denotes volume occupied by the reservoir fluid, while the term "flow model" refers to the idealized or mathematical representation of water flow in the reservoir-aquifer system. The prediction of water movement requires selection of a flow model for the reservoir-aquifer system. A physically reasonable flow model treated in detail to date is the radial-flow model considered by van Everdingen and Hurst.1 In many cases the reservoir is situated on top of the aquifer with a continuous horizontal interface between reservoir fluid and aquifer water and with a significant depth of aquifer underlying the reservoir. In these cases, bottom-water drive will occur, and a three-dimensional model accounting for the pressure gradient and water flow in the vertical direction should be employed. This paper treats such a model in detail — from the description of the model through formulation of the governing partial differential equation to solution of the equation and preparation of tables giving dimensionless pressure drop as a function of dimensionless time. The model rigorously accounts for the practical case of a vertical permeability equal to some fraction of the horizontal permeability. The pressure-drop values can be used in given equations to predict reservoir pressure from a known water-influx rate or to predict water-influx rate (or cumulative amount) when the reservoir pressure is known. The inclusion of gravity in this analysis is actually trivial since gravity has virtually no efFect on the flow of a homogeneous, slightly compressible fluid in a fixed-boundary system subject to the boundary conditions imposed in this study. Thus, if the acceleration of gravity is set equal to zero in the following equations, the final result is unchanged. The pressure distribution is altered by inclusion of gravity in the analysis, but only by the time-constant hydrostatic head. The equations developed are applied in an example case study to predict the pressure and pore-volume behavior of a gas storage reservoir. The prediction of reservoir performance based on the bottom-water-drive model is shown to differ significantly from that based on van Everdingen and Hurst's horizontal-flow model. DESCRIPTION OF FLOW MODEL The edge-water-drive flow model treated by van Everdingen and Hurst1 is shown in Fig. la. The aquifer thickness b is small in relation to reservoir radius rb. water invades or recedes from the field at the latter's edges, and only horizontal radial flow is considered as shown in Fig. 1b. The bottom-water-drive reservoir-aquifer system treated herein is sketched in Fig. 2a and 2b. Here the aquifer

By J. P. Heller, H. B. Bradley, A. S. Odeh

A potentiometric model technique is presented for determining the areal sweep efficiency of a five-spot well pattern, at and beyond breakthrough. A sharp interface between displaced and displacing fluids is assumed. Although the prototype svstem is referred to as a waterflood operation, obvious changes in the notation and computations will adapt the results to other displacement processes. The results of the study include the following. 1. Areal sweep efficiencies for a five-spot well pattern, at and beyond breakthrough, for mobility ratios (displacing to displaced fluid) of 4:1, 2:1, 1:1 and 1:4. 2. Extension of potentiometric analysis to the investigation of the areal sweep efficiency beyond breakthrough in a five-spot pattern by the application of conformal mapping and conductive-solid models. 3. The use of layers of conductive fabric in representing mobility ratio changes in potentiometric models. 4. The development of a probe mechanism for probing conductive solids. The results obtained by conductive-cloth models agree with earlier areal sweep efficiencies at breakthrough obtained by Aronofsky and Ramey 1 on the potentiometric analyzer using electrolytic-tank models. Results beyond breakthrough differ from those obtained by the X-Ray Shadowgraph technique. Data from this study show that, for mobility ratios greater than one, water cut rises rapidly as fluid is produced after breakthrough. However, for mobility ratios smaller than one, a large increase in area swept resulted with only a small increase in water cut. INTRODUCTION In calculating reservoir performance of waterflood-ing operations and other fluid-injection programs, it is necesssary to estimate the areal sweep efficiency * before and after injected-fluid breakthrough into production wells. Influence of mobility ratio on oil-production history, before and after breakthrough for a five-spot well pattern, has been studied by X-Ray Shadowgraph techniques 2-5 and by gelatin models.6 In none of these investigations was the transition zone controlled experimentally. Steady-state anaiog techniques assume that a vertical and discrete interface exists between the displacing and displaced phase. Thus, when using a potentiometric analysis, it is assumed that no transition zone exists. To determine the areal sweep efficiency beyond breakthrough for a five-spot well pattern using the potentiometric analyzer, four principal problems had to be resolved. These were the following. 1. The laborious method of representing changes in mobility ratio in electrolytic tanks by means of contoured wooden blocks. 2. Vapcrization of the electrolyte solution during the study causing concentration changes and, thereby, variable conductivity. 3. The scale-limitation problem 7 that is accentuated by abrupt eiectrolyte depth changes. 4. A wellbore geometry problem. EXPERIhlENTAL EQUIPMENT AND PROCEDURES CONDUCTIVE-SOLID MODEL The theory, equipment and procedural techniques of the electrolytic-tank potentiometric model have been treaced excellently by Lee8 and by Muskat.9 By the use of a conductive solid to represent the fluid conductivity of the porous media, the need for contouring wooden blocks to represent mobility ratio was eliminated. It was found that a carbon-black coated fabric, Uskon D-16,** could be employed as a fairly uniform conductive media. This material, when stacked in appropriate layers and pressed together, can be used to represent changes in mo-

By D. H. Henley, F. F. Craig, W. W. Owens

The oil recovery performance of systems producing entirely by bottom-water encroachment has been experimentally determined in a series of scaled laboratory-model tests. The effects of well spacing, fluid mobilities, rate of production, capillary and gravity forces, well penetration and well completion techniques on the oil recovery performance have been investigated. The laboratory tests were performed using two uniform, un-consolidated sand-pack models. The models have ratios of the interwell distance to the formation thickness of 12 and 2, respectively. Tests at constant total fluid production rate were performed simulating a range of uniform reservoir characteristics and operating conditions encountered in field operations. The performance was determined by material balance and by observation of the encroachment of dyed fluids into the models. The results of the model tests agreed with those obtained mathematically when the conditions previously considered in theoretical studies were simulated, that is, when the oil and water are of equal density and no capillary forces exist. The model study of bottom-water drive indicated that certain variables can aoect the oil recovery performance to a greater degree than can be predicted by present analytical methods. In one comparison, the oil recovery at a water-oil ratio of 20 (obtained at a wide well spacing) varied as much as threefold, depending upon the system's properties and the production rate. Lesser effect of mobility ratio and no eflect of capillary forces over the range studied were observed. The test 'results also showed that the deeper the well penetration into the oil column, the greater the total water production to a producing WOR of 20. However, the ultimate sweep efficiency, and so the oil recovery to this level of WOR, did not vary significantly with well penetration. Horizontal fractures at the top of the formation did not significantly change the sweep characteristics of the reservoir models when values of radius and fracture capacity encountered in actual reservoirs were used. Impermeable pancakes at the bottom of the well moderately increased the oil recovery efficiency both at water breakthrough and at high water-oil ratios. A method is outlined by which the oil recovery performance of other uniform bottom-water drive systems can be estimated from the information obtained in these model tests. INTRODUCTION When oil is produced from a well which partially penetrates an oil zone completely underlain by water, the water rises directly beneath the well in a symmetrical cone when the system is uniform. Two different flow mechanisms can cause the water cone to form—coning and bottom-water drive. In coning, the aquifer is relatively inactive and the cone is formed beneath the well by the pressure gradients associated with the oil flow to the well. The oil can be produced by a solution-gas drive, an edge-water drive or other driving forces in the interwell area. In a bottom-water drive, the driving force for oil production comes from an upward encroachment of the underlying active aquifer. Two papers have analyzed the theoretical performance characteristics of bottom-water drive reservoirs. In the initial mathematical investigation, Muskat' established the equations which determine the pressure distribution in this type of reservoir and solved these equations for certain conditions. Specifically, it was assumed that the water and oil had equal mobilities and equal densities, there were no capillary forces, the pressure throughout the oil zone remained above the bubble-point pressure, a constant pressure existed at the initial water-oil contact and the oil was completely displaced by the encroaching water. These assumptions were used in obtaining analytical solutions. In general, Muskat found that the sweep efficiency to initial water breakthrough to the well was larger for the thicker oil zones, the closer well spacings, the lower ratios of vertical to horizontal permeabilities, the smaller the penetration of the well into the oil zone and the smaller the bore size of the well. The production history after water breakthrough was expressed as a volumetric sweep efficiency at a given producing water-oil ratio. The results indicated that cumulative oil production at producing water-oil ratios of 10 is less affected by the well spacing than is the water-free production history. Muskat studied well spacing which today would be regarded as close. The maximum value of his dimensionless well spacing (ratio of interwell distance to formation thickness) was 4.3. This would require the development of a 50-ft-thick oil sand on less than 10-acre spacing if the vertical and horizontal permeabilities were equal, with

By C. D. Stahl, E. E. Templeton, R. F. Nielsen

It has been customary, in predicting saturation changes, to use the Leverett fractional flow formula", obtained by eliminating the unknown pressure gradient from the generalized Darcy equations for the separate phases. The formula presents difficulties in the case of counterflow, since the "fractional" flow may be negative, greater than unity, or, in the case of a closed system, infinite. Recently, it has been shown by several authors that the corresponding equations (with capillary pressure and gravity terms) for actual flow of the phase may be used just as well. These equations are in agreement with Pirson's1 statement that, if the two mobilities differ considerably from each other in a closed system, the flow is largely governed by the lower value. The present study was undertaken because of an apparent lack of experimental data on gravity counter-/low with which to test the theory. A 4-ft sand-packed tube in a vertical position was employed. Electrodes for determining saturations by resistivity were spaced along the tube, one phase being always an aqueous salt solution. Air, heptane, naphtha, or Bradford crude oil was used for the other phase. A reasonably uniform initial saturation was set up by pumping the phases through the system, alter which the tube was shut in and saturation profiles obtained at definite intervals. Cumulative flows over certain horizontal levels were obtained by integration of the distributions; hence, differentiation of the cumulative flows with respect to time gave instantaneous flow rates. To compare experimental and theoretical flow values, capillary pressures were assumed given by the final saturation-distribution curve. The upper part corresponds to the "drainage" region and the lower part to the "imbibition" region, where trapping of the nonwetting phase occurred. While calculations indicated that the capillary pressure saturation function and, probably, the relative permeability saturation functions changed during the segregation, the relation of the measured rates to saturation distributions are in general accord with the frontal-advance equation. It appears that the Darcy equations, as modified for the separate phases, are generally valid for counterflow due to density differences. The usual method of predicting saturation changes, which involves a continuity equation and the elimination of the unknown pressure gradient from the flow equations, should therefore be applicable. However, the need for advance knowledge of drainage and and imbibition "capillary pressures" and relative permeabilities during various stages presents difficulties. INTRODUCTION The present study was undertaken because of a seeming lack of experimental data relating to vertical counterflow of fluids of different densities in porous media. In particular, it was desired to determine whether data obtained from these laboratory tests were in accordance with certain mathematical treatments of counterflow which have been proposed. The gravity "correction" has been incorporated into the flow equations (and, hence, into displacement theory) nearly as long as both have been used. field4 and laboratory5 data have generally borne out the validity of the theory as applied, for instance, to downward displacement by gas, with all fluids moving downward. However, the modifications for counterflow have only recently been pointed out. 2-3 It has been customary to use fractional flow rates instead of actual flow rates in displacement calcuIations. In the case of counterflow, this results in negative values, values greater than unity and, when rates are equal and opposite, in infinite values. As pointed out by Sheldon, et a1,3 and by Fayers and sheldon,2 actual flow rates may be used just as well. The fact that these may be of opposite signs for the two fluids does not present any difficulty.