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By G. W. Nabor, H. J. Ramey

A blotter-type electrolytic model was utilized to prepare flow diagrams for a field test of the in-situ combustion process. It is pointed out that the areal sweep of a combustion pattern is similar to sweep patterns that would be developed at an infinite mobility ratio, which exists (approximately) across a combustion front because of the complete removal of liquids from the sand behind it. The precision of the blotter method was tested by comparison with results obtained by other techniques and was found to be satisfactory. The blotter-type model will not furnish as much information as more elaborate and expensive potentiometric models, but its speed of operation and ease of construction make it a highly satisfactory tool to determine areal sweep patterns. A tabulation of sweep efficiency and mobility ratio is furnished for various well geometries. INTRODUCTION In connection with the first field experiment with the in-situ combustion method of oil recovery," flow diagrams for the unique well geometry and boundary conditions involved in the subject test were developed. From these diagrams, information concerning the areal sweep and distribution of flow was obtained. A survev of the literature on potentiometric models, utilized to solve two-dimensional flow problems,1,2,3,4,5,6,8,9,10 indicated that the information desired could be obtained by means of a blotter-type model by making certain modifications in the technique. The following discussion describes the application of the modified blotter-type electrolytic model to the solution of the problem of the flow of gases in an oil reservoir for an engineering appraisal of the progress of the combustion front during the first field experiment. Considerable information has been published on the theoretical aspects of electrical model techniques. One author stated that:' "The models are based on the observation that since the velocity of an ion in an electrolytic system is proportional to the potential gradient, just as the velocity of a fluid particle in a porous medium is proportional to the pressure gradient, the paths of the ions in the electrolytic systems must be similar to those of the fluid particles in a porous medium with the same geometry and equivalent boundary conditions." This suggestion of a real analogy has been established repeatedly by comparisons of analytic derivations with model results. The analogy between the movement of a combustion front and the model results is not as apparent, since the combustion process differs from water flooding and gas cycling in that the velocity of the burning front is different from the velocity of the injected fluid at the front in combustion. Analogy between electric current flow and movement of the burning front exists because the local velocity of the burning front is proportional to the air (mass) velocity at this point (assuming frontal temperatures are at least as high as the ignition temperature of the fuel). Most model studies fall into one of two categories: (1) electron conduction, or (2) ionic conduction models. Examples of these are models which employ as flow media either a thin metal sheet, or a porous blotter saturated with an electrolyte, respectively. Of the two, the porous blotter model, an ionic conduction model, appears to be the most adaptable to the flow problem that results when using in-situ combustion. This problem requires that the mobility of the particles in the model be controlled analogous to the mobility of gas flowing through burned sand of high permeability to gas and then through oil sand of lower permeability to gas. Although the blotter model has heretofore been

Jan 1, 1955

By John B. Campbell, George G. Binder, Loren H. Jenks

Conventional methods of producing crude oil generally leave in the depleted reservoir 1 to 3 bbl of oil for every barrel brought to the surface. This paper describes a field test which explores the possibility of using gas-driven liquid propane to improve oil recovery efficiency. Laboratory theoretical and experimental studies leading to the field test indicated that low residual oil values could be obtained using limited amounts of propane driven by gas. The field test involved (I) repressuring the reservoir to the vapor pressure of liquid propane, (2) injecting the liquid propane, and (3) injecting dry natural gas to drive the propane and oil to the producing wells. Considerable preliminary work, including new drilling, work-overs, and a pressure survey was necessary. During the test, oil production rates have averaged about nine times the final primary rates. The field average GOR is still below the pre-test value. Oil recovery to date is 112,000 STB. About one-third of the 143,-000 bbl of propane injected has been produced to date. Results of the C-2 block test are encouraging and larger, more definitive field projects ore indicated. INTRODUCTION The cost of finding new crude oil reservoirs continues to increase. Today the oil industry is drilling more and deeper wells and making fewer big discoveries. Nevertheless, the demand for oil and oil products increases each year. It is natural that oil companies, faced with this situation, concentrate on recovering more of the oil existing in our known crude oil reservoirs. There is room for much improvement. For every barrel of oil brought to the surface by present day methods of producing crude oil, generally 1 to 3 bbl are left behind in the depleted reservoirs. The "unrecoverable" oil in petroleum reservoirs is largely "trapped" by capillarity. Since flushing with a solvent is exceedingly effective in combatting oil loss due to capillarity, much effort in this direction has been made in recent years1,2,3,4,5. Liquefied petroleum gas (LPG) has been suggested as a relatively inexpensive. abundant, easily recoverable solvent for crude. Some operators have observed striking responses in oil recovery at production wells offsetting input wells in LPG storage reservoirs6,7,8. In spite of the low unit cost of LPG, however, it is uneconomic in general to inject a volume of LPG into a reservoir to remove a like volume of oil. A modification of solvent flushing in which a limited quantity of liquid propane is gas driven through a reservoir appears capable of recovering much more than 1 bbl of oil per barrel of propane injected. Also, most of the propane injected should be recoverable for sale or re-use. Since such a process could well have widespread and profitable application, The Carter Oil Co. is making an extensive evaluation of the technique's possibilities. Laboratory development of the gas-driven propane recovery technique was sufficiently encouraging to justify testing in the field. Since 1952, the Production and Research Departments of The Carter Oil Co. have cooperated in a field test in the C-2 Block leases of the

Jan 1, 1958

By J. G. Richardson, F. M. Perkins

Results and procedures are pre-cented covering a laboratory investigation of the effect of rate of water advance on the displacement of oil from clean water-wet sands. The experiments included water floods at atmospheric pressure with and without gas present over a range of flow rates from reservoir rates to rates ten thousand-fold higher. Water floods were also conducted at various rates at elevated pressure with no gas present. Other tests were made at elevated pressures by forming a free gas saturation by evolution of gas from solution in the oil before water flooding. Recovery of oil was found to be independent of the rate of water advance with or without gas present and independent of the pressure level of the water flood. A dimensionally-scaled model of a reservoir composed of a thick uniform sand was used to study the effect of rate on the tendency of water to underrun the oil because of the greater density of the water. Another model was used to study the effect of rate on the tendency of water to channel down the more permeable sand in a stratified reservoir composed of sands of diffierent per-meability in intimate contact. The effect of the presence of gas on the flooding conformance was studied with both models. The results obtained using these simple models provide a basis for predicting behavior in more complicated systems. INTRODUCTION In spite of the great amount of research on the flow of fluids in porous rocks, there still exists some disagreement as to the influence of the rate of water advance on the displacement of oil by water flooding. Various investigators have found that increasing the rate of water injection would decrease, increase, or have no effect on recovery of oil. One reason for this disagreement has been a lack of understanding of the effects of the capillary forces which influence the results obtained in the laboratory at low rates with short columns. Other causes of the disagreement have undoubtedly been inconstancy and uncertainty of the wetting properties of the porous media studied, inaccurate saturation determinations, and in some instances conclusions based on insufficient data. Capillary forces are involved in the displacement of oil by water in two ways. On the microscopic scale, the capillary forces control the dis- tribution of oil and water in the pore spaces of the sand. The magnitude of these forces is governed by the preference of the sand to be wet by water, the pore sizes and geometrical shapes, and the interfacial tension between the water and oil. On the macroscopic scale, differences in saturation at the flooding "front" when water displaces oil result in capillary pressure gradients. These gradients cause water to flow preferentially ahead of the front. In short laboratory columns at low rates, the front can span the entire column length. Also, at the outflow boundary the preference of sand to be wetted by water results in retention of water and a high water saturation in the region of the outflow face. This effect is commonly called the boundary effect.' The capillary pressure gradients which complicate the interpretation of flooding performance of short laboratory columns at low rates of water advance become negligibly small under certain conditions. The conditions where capillary pressure gradients are negligible are in long, homogeneous reservoir sands,' at high rates of water advance in short laboratory columns,3 and at any rate in laboratory columns as the residual oil saturation is approached. Thus, laboratory water floods, conducted

Jan 1, 1958

By T. M. Geffen, H. N. Hall

One-third to one-half of the original oil is left in most reservoirs even after thorough gas driving or waterflooding. In contrast, essentially all of the oil contacted con be recovered by flooding with a solvent (a fluid miscible with the reservoir oil). It is not economical to fill a reservoir with solvent since the value of the solvent would very likely exceed that of the oil. A practical method would be to inject a small bank of solvent to displace the oil. This solvent bank in turn could be driven through the rock by a less valuable scavenging fluid, such as natural gas which is also miscible with the solvent. Such a method of oil recovery was studied in the laboratory using long (up to 95 ft) core systems. It was found that, as the solvent moves through the reservoir, the front end of the solvent bank becomes mixed with the oil and forms a relatively short mixing zone between undiluted crude oil and pure solvent. An engineering correlation was obtained which can be used to predict the length of this zone. Displacement of the solvent by natural gas can be achieved with complete miscibility (above the critical pressure of the gas-solvent system at reservoir temperature) or with partial miscibility at lower pressures. Under conditions of complete miscibility, it was found that the length of the gas-solvent mixing zone could be predicted from the correlation developed for the solvent-oil mixing zone. With partial miscibility, two phases exist and the solvent is displaced by a modified gas drive in which vaporization and condensation occur. Equations are developed to predict the performance of this type of displacement. Two plans are suggested for application of miscible fluid displacement. one for miscible displacement of the solvent and the other applying to lower pressures where partial miscibility occurs during solvent displacement. Calculations based on the laboratory tests indicated that a bank of solvent with a volume of less than 10 per cent of the hydrocarbon volume under consideration will generally be adequate to obtain high oil recovery from the portion of the reservoir contacted in miscible fluid displacement. INTRODUCTION The conventional methods by which oil is displaced from reservoir rock—solution gas drive, conventional gas drive, and waterflooding—are all processes in which the oil is expelled from the rock by direct displacement with a fluid immiscible with the oil. Because of the immiscible type displacement, complete recovery of the reservoir oil is not achieved. In economically successful flooding operations, as much as 50 per cent of the original oil may be abandoned in the reservoir as unrecoverable. The use of a solvent (miscible with oil, such as LPG) as an injection fluid does not have the undesirable displacement features common to the use of gas or water (immiscible with oil). It can be readily appreciated, however, that it would not be economically feasible to displace the oil and entirely replace it with a solvent. A process was therefore devised for use in field operations in which only a small volume of solvent would be required to obtain essentially complete oil recovery in the portion of the reservoir contacted. In this process, the solvent acts as a buffer between the reservoir oil and injected gas, allowing the natural gas to displace indirectly the oil with much greater efficiency than if the gas displaced the oil directly. DESCRIPTION OF OIL RECOVERY PROCESS The solvent oil recovery process will be described in

Jan 1, 1958

By John C. Calhoun, J. E. Warren

A study of waterflood efficiency, given in terms of oil recovery at water breakthrough and u1timate recovery, has been made on short, consolidated Pyrex glass cores rendered oil-wet by chemical treatment. Contact angle. interfacial tension, permeability and porosity were the variables considered. Oil and water viscosities, core length and velocity of flooding were held constant. The data permit interfacial tension, contact angle, porosity, and permeability to be grouped into a scaling coefficient along with viscosity, velocity of flooding and length of core. Correlation of the .scaling coefficient with recovery at water breeakthrough is found to follow prediction; correlations of ultimate recovery demand a scaling coefficient different from that which correlates breakthrough recovery. The work indicates that, with proper control, a group of similar natural cores, of permeability plug size, call he correlated 10 indicate basic flooding performance. INTRODUCTION The fraction of oil recovered from a porous medium is related to both reservoir conditions and production techniques. An investigation of all factors that enter into this relationship is necessary in order to arrive at the optimum method of exploitation for oil reservoirs. To define this relationship, laboratory studies have been made by a great many investigators. However. an important obstacle arises if the results of these experiments on water flooding are to be applied to practice. Ditferences in behavior are to be expected between reservoirs of the dimensions encountered underground and those used in laboratory work. Factors which play an important role under laboratory conditions may be of no consequence in reservoirs. Laboratory operating practices generally differ from field operating practices. Thus. a mere understanding of the mechanism of the displacement of oil by water is not enough. It is just as necessary that the process be analyzed dimensionally to give continuity and validity to the conversion from laboratory to field. The theory of oil displacement that has come to be accepted by the majority of those who are associated with reservoir mechanics had its beginning in the work of Leverett¹ and Buckley and Leverett2. The banking of oil, observed by many previous workers, was described by the "fractional flow" and the "frontal advance'' equations. The validity of the Buckley-Leverett theory was substantiated by the experimental and theoretical work of Terwilliger et al³; moroever, the theory was extended by the introduction of the idea of a "stabilized zone" to describe the banking of oil. Levine5 showed that the Buckley-Leverett equations gave reasonable agreement between calculated and experimental breakthrough recoveries only if the capillary pressure and gravity terms were included. Rapoport and Leas1 investigated the properties of linear floods and showed that both breakthrough and maximum recovery are related to a "scaling coefficient'' derived from the Buckley-Leverctt equations. Jones-Par-ra and Calhoun6 presented another scaling coefficient which included both viscous and capillary variables. Such scaling coefficients should suffice to predicl waterflood efficiency. However, some experimenters report data which does not appear consistent with the healing coefficient approach. For example, Engelberts and Klinkenberg7 conducted an extensive series of experiments on a dimensional model which contained a

Jan 1, 1956

By J. L. Fitch, B. G. Hurd

The presence of gypsum in samples subjected to standard core analysis introduces serious errors in the measurement of water saturation and porosity. The magnitude of these errors, depending upon the type of analysis procedure used, has been evaluated experimentally and theoretically. Water-saturated pore volumes determined by vacuum distillation or retort procedures may be too high by as much as 48 per cent of the volume of gypsum present. The maximum error in this value determined by Dean-Stark extraction with toluene is 36 per cent of the gypsum volume. If pore space is measured by a Boyle's law type porosimeter the maximum erorr due to gypsum is 38 per cent of the original gypsum volume present. The conscientious core analyst may eliminate the errors caused by gypsum by either of two methods. He may apply suitable corrections for the water of crystallization removed from gypsum, or take special precautions to prevent dehydration of gypsum during core cleaning and alzalysis procedures. These alternatives are discussed and methods for obtaining reliable core analysis data are proposed. Gypsum (CaSO4 . 2H2O) occurs as a common mineral in many of the world's sedimentary basins. In addition to its presence as primary bedded evaporitic deposits, it is often found as secondary replacement zones and pore-fillings in host rocks. That it may cause false indications in porosity, both on neutron logs and in standard core analysis, has been generally recognized. False porosity interpretations from neutron logs result because the chemically bound water in gypsum attenuates neutrons as effectively as free water. Errors in core analysis result when gypsum is dehydrated prior to or during the analysis. Vacuum retort procedures used by many laboratories to determine fluid saturation and porosity effect a complete removal of water of crystallization from gypsum. The crystal water, distilled and collected with free water from the sample, is counted as water-sat11rated pore space. Dehydration of gypsum results in a decrease in volume occupied by calcium sulfate and a corresponding increase in pore volume. Thus, if gypsum is dehydrated by sample cleaning and drying procedures, subsequent porosity measurements with gas expansion or compression instruments will be high. The qualitative effect of gypsum on porosity determinations by retort procedures was discussed in a recent article by Bynum and Koepl3. They concluded that since false porosity was interpreted as being water saturated, determinations of oil content were not affected. Others in the industry, however, have pointed out that porosity values are often used with values of water saturation determined independently, e.g., from electric resistivity logs in making reserve estimates. Values of water saturation calculated from the formation resistivity using the Archie equation, S4= are actually low if values of are high due to gypsum. In this case, false porosity values due to gypsum could cause serious errors in calculations of oil-in-place. This investigation was made to determine quantitatively the effect of gypsum on porosity values determined by different core analysis procedures. EXPERIMENTAL PROCEDURES Dehydration of Gypsum The extent and rate of removal of water of crystallization from gypsum under conditions encountered in core analysis procedures were studied. Taken for the experiments were three types of relatively pure, naturally occurring gypsum, viz. selenite, satin spar and massive gypsum. Although all samples probably contained trace chemical impurities, each type lost the theoretical amount of water upon complete dehydration. An automatic recording thermobalance, similar to one described by Mauer2, was used to obtain dehydration rate data for samples heated in dry air. Water

By H. C. Johnson, J. K. Elliott

One of the primary requirements for successful operation of an enriched gas-drive project is to control the composition of injection gas. This can become a serious and difficult problem, particularly in cases where the enrichment material is being furnished from a number of field -produced gas streams. It is possible to effect control of the injection gas composition through frequent or continuous sampling; however, this can be extremely costly and, in many cases, impractical due to laboratory requirements of time. Another alternative would be to provide a calculation technique which would be flexible and sufficiently accurate to predict composition of the liquid and gas streams of interest at any point in the system. The purpose of this paper is to discuss a technique that was used successfully on an operating enriched gas-drive project for developing information which could be used for controlling composition of the injected gas. FIELD OPERATIONS The particular field (hereafter called Example field) in the example operation being discussed is composed of four oil reservoirs (A. B, C and E) and one gas condensate reservoir (D). Casinghead gas from the oil reservoirs and gas from the gas condensate reservoir are gathered through a field gathering system as shown in Fig. I for injection into Reservoir C. The gas mixture which is recovered from the five reservoirs for injection purposes is composed of gases liberated in 19 individual separators, each operating at a separate temperature and pressure. PROPOSED CALCULATION TECHNIQUE It is well known that vapor-liquid equilibrium calculations in general use throughout the petroleum industry can be used to predict reliably the phase behavior of hydrocarbon mixtures, particularly at pressures less than 1,000 psig. It is then a simple matter to account for the material on a ComPonent basis by m''ing flash and material balance calculations at each separation point in a hydrocarbon system. Accordingly, it was proposed to use vapor-liquid equilibrium and material balance cal- culations with a medium-sized electronic digital computer as a basis for developing a control procedure for use in controlling injection gas composition in the enriched gas-drive project. Although the approach is a simple one, the numerous vapor-liquid equilibrium calculations involved make the problem laborious; in this particular case, it would have been impractical to make sutficiently complete analysis without the aid of digital computing equipment. SAMPLING AND VERIFICATION OF CALCULATION PROCEDURE To obtain representative gas and liquid stream samples and to provide a quantitative measure of overall system Performance for comDarative purpLses, a thorough test of the field and plant system was conducted in the summer of 1957. Oil production at each battery was sta-

By Bruce F. Grant, Stefan F. Szasz

During 1947, a Sinclair research team was assigned to investigate thermal methods of oil recovery. The assignment was recommended by a survey of possible research approaches to increase the amount of oil that ultimately can be recovered from oil producing reservoirs. The use of heat to stimulate oil production rates by the melting of paraffin deposited in well bores can be traced back to within one or two decades of the drilling of the Drake well. The application of heat on a larger scale has been discussed by generations of oil producers. Shortly after the turn of the century, one intrepid operator is reported to have injected steam into a Pennsylvania property. After a few weeks, he apparently became discouraged and terminated his experiment. Subsequently, the literature contains references to several well-developed techniques for supplying heat to a producing well bore to melt paraffin or to reduce the viscosity of oil contained in the formation immediately around the well bore.1.?.3.4 Some early references discuss procedures to furnish heat to the reservoir,5,6 with the injection well as the heat source, thus obligating the process to maintain the entire rock mass at a temperature above that at which the desired improvement in oil recovery would occur. Another approach to reservoir heating was reported by a group of Russian technologists in 1935.7,8,9 They definitely demonstrated that combustion can occur within the porous structure of an oil-bearing sandstone. Their field experiments, however, relied less on combustion within the rock than on heat furnished by combustion of oil supplied to the injection well bore. Ignition of the air-oil mixtures in the well bore was found very difficult, and the field tests were carried on for only short periods of time. Publication of the Russian work spurred at least one independent operator in this country to try firing an air-gas injection well, on for only short periods of time. Publication of the Russian work spurred at least one independent operator in this country to try firing an air-gas injection well. The Brundred Oil Corp. reportedly obtained combustion in the sand immediately around the injection well bore, but the experiment was abandoned because of interference with normal production schedules. Injection capacity of the experimental well was greatly reduced by firing. The well was reshot and pieces of sand showing partial fusing of the quartz matrix were recovered. To the authors' knowledge no other field experiments utilizing combustion techniques for formation heating were undertaken prior to 1948, although the patent literature evidences continued interest in formation heating."'," CONCEPT OF COMBUSTION-SUPPORTED HEAT WAVE The references cited were in agreement that heat applied to a reservoir would increase recovery, but there

Jan 1, 1955

By J. D. Lindner, Gene E. Roark

Waterflooding operations in the Langston-Kleiner field. Young County, Tex., are described. Widespread application of formation fracturing has been practiced in both producing and injection wells. Field performance data arc cited which indicate than no detrimental effect on sweep efficiencies and that probable benefits in imectivily have resulted from the fracture treatments. I N T R O D U C I O N This paper is a report on a waterflood operation which is being carried out in the Lanpston-Kleiner field located in Young County, Tex. The oil reservoir aflected by this flood operation occurs in a Strawn sand member at an approximate depth of 3.550 ft subsurl'ace. The operators of' the project are Kleiner Estate. Turncr. Fiske. and West who are hereinafter collectively referred to as the Operators. Although the operation is unusual in several respects, the distinctive feature of this flood has been the widespread application of hydraulic formation fracturing treatments as a means to improve productivity and injectivity of the wells. It shall he the purpose of this paper to present basic information regarding the reservoir characteristics. op- craling practices, and waterflood behavior so that conclusions may be drawn concerning the effects which the fracture treatments have had on the performance of this water flood to datc. DEVELOP MENT Development of the 3,550 ft Strawn sand reservoir occurred during 1951 and 1952. The early development occurred on the Langston and Davis leases which arc in the northern region of the Operators' holdings and the wells were drilled on 20-acre proration units according to the field rules. However, studies of the economics of this program. coupled with the decision to proceed with pressure maintenance by water injection. resulted in the adoption of wider spacing in the later stages of development. This variation in spacing is apparent upon inspection of Fig. I upon which only the 3,550-ft Strawn sand producing and injection wells have been located on the Operators' properties. The development to the north of the operators leases is Ihe Garvey Strawn field and that to the south is the Taylor Strawn field. It wits determined that unitization of the leases to he involved in the waterflood program was not feasihle. Consequently. a system of offset injection wells, or lease line injection wells, was adopted from place to place as required to protect correlative rights in the program. This resulted in a dispersed array of injection and producing wells with relatively close proximity of wells along lease line areas and wider spacing toward

Jan 1, 1956

By A. B. Dyes, P. H. Braun, B. E. Cole

This paper presents a reservoir engineering analysis of the performance data for a waterflooding project in the Johnson Lease, South Ward field. This type of engineering analysis adds to the knowledge of the mechanics of water flooding. This study reveals that in general (a) high ultimate areal sweep-out efficiencies (95 to 100 per cent) can be expected, and (b) cross-flow among strata of different permeabilities during the fill-up phase can have an important influence on the behavior and should be dealt with in studying reservoirs for water flooding. The analysis further showed that the recovery predictions based on what was considered a consistent interpretation of core data and logs were low because little contribution was assumed from the low permeability, oil-bearing sand sections which have apparently yielded considerable waterflood oil. This project has yielded in excess of 2 1/2 times as much oil by water flooding as by primary depletion. These very favorable results were achieved without the use of any special injection well completion techniques. However, all of the low permeability material war included in the section open to injection despite its poor estimated primary yield. LEASE PERFORMANCE HISTORY The South Ward field lies in the southeast corner of Ward County near the southern tip of the tremendous Yates trend. Deposition of sand bodies along the seashore reefs during the latter part of the Permian period established what have turned out to be ideal conditions to form a great number of independent productive sands. Probably, these reservoirs in Ward and Winkler counties are providing operators with some of the nation's richest sources of secondary oil reserves through the use of waterflooding techniques. In South Ward field water has been very successfully used to flood oil from the Bennett sand occurring at a depth of about 2,300 to 2,400 ft. About 150 ft above the Bennett sand reservoir, the Grand Falls sand produced gas from a large cap extending over most of the field. The Atlantic Refining Co.'s 320-acre W. D. Johnson lease (Fig. 1) is on the northwest edge of the structure with only gas cap apparently present in the Grand Falls sand. The Bennett sand under this lease is oil productive, however, having a gross sand thickness averaging about 80 ft with a net of 18 ft of fairly clean, highly permeable sand, and about 36 ft of oil-bearing sand with low permeability and high water saturation. The lower permeability sand is interbedded with numerous layers of lime, shale, and anhydrite. Radioactivity logs from 12 wells and cores from two, examples of which are shown in Fig. 2, reveal that the total Bennett sand pore volume is about 71,000 bbl/acre. The estimated initial water saturation averages 41 per cent in the 54 ft of sand considered to contain oil; thus, also considering an estimated 18 per cent oil shrinkage, the lease originally contained about 34,000 bbl of oil per acre. Original pressure was probably about 1,400 psig. PVT correlations indicate that the reservoir fluid was originally saturated with gas. After discovery of the field in 1930, Atlantic completed the first well on the Johnson lease in March,

Jan 1, 1958

By P. E. Schauer

During the initial nine-year deple-tion of the McKamie-Patton pool gas-condensate reservoir, the pressure behavior and fluid analyses indicated pressure maintenance by gas injection would be attractive relative to continued pressure depletion. As a result, a gas cycling program was inaugurated in Aug., 1949, which has since maintained reservoir pressure. In order to evaluate the benefits of this program, the recoveries for natural depletion and for cycling followed by blowdown were determined by calculating the fractional balance of the molar quantities of vapor and liquid remaining in the reservoir and produced at the surface for various stages of depletion. The results of the investigation show theoretical ultimate recovery due to the cycling program will be 42 per cent greater than would be realized under pressure depletion type operation. INTRODUCTION The benefits of gas injection pressure maintenance programs in condensate reservoirs have been recognized and qualitatively described in several papers1-8 during the past 15 years. Some of these papers also describe methods for calculating the increased recovery realized from cycling; however, as a rule, hypothetical reservoirs were used as examples".'.. This paper presents an evaluation of the pressure maintenance program for the McKamie-Patton condensate reservoir and includes a description of the fractional balance method employed to determine the benefits. Reservoir Development and Characteristics The McKamie-Patton pool, Lafayette County, Ark., was opened in June, 1940, with production obtained from the oolitic Smackover lime at a depth of approximately 9,300 ft. The structure is an anticline 8 miles long by 1 to 2 miles wide, and is one of many productive Smackover structures in Southern Arkansas. Of predominant importance is the condensate-bearing gas cap portion of the reservoir, which covers approximately 4,000 acres, attains a maximum thickness of some 200 ft, and has an average thickness of 90 ft. Development of the cap was accomplished with 21 wells drilled on 160 acre spacing. An isopach map of the cap is shown in Fig. 1. In addition, an oil rim is present along most of the periphery of the pool. Production practice includes field separation of black oil, and a high pressure gathering system which carries total well stream from gas cap wells to a plant where condensate is separated and the gas is processed for recovery of natural gasoline, butane, and propane. Since the gas contains appreciable hydrogen sulfide, it is removed by amine contact, after which free sulfur is produced by the Claus process. Core analyses from 1,767 gas cap formation samples averaged 14.2 per cent porosity and 379 md dry air permeability. Connate water was restored on seven samples of gas cap rock by air-brine capillary techniques, from which the interpreted water saturation averaged 28.17 per cent. During the early life of the field, it was believed the recovery mechanism, based on several of the other regional Smackover reservoirs, might be a natural water drive. However, subsequent production and pressure history revealed that the gas cap would not be produced by water drive, but would behave as a closed reservoir. In this respect, during the nine-year period of natural depletion from initial production to Aug., 1949, the cap production of 84.3 billion

Jan 1, 1958

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-

By H. A. Koch, R. L. Slobod

This paper discusses a new oil recovery process called the "miscible slug process." This process involves the injection of propane or LPG into the reservoir prior to gas injection. The operating conditions are maintained so that the slug is miscible with both the reservoir oil and the injected gas phase. Thus, a miscible phase displacement is achieved, and high recoveries are obtained from the area of the reservoir contacted. The most striking discovery of the laboratory study which included displacements from cores up to 123 ft in length was that relatively small slugs of LPG are effective over reservoir distances in the miscible displacement of oil. This makes possible the commercial application of the process. The important factors controlling the size of the slug are: (I) reservoir length, (2) reservoir fluid composition, and (3) reservoir pressure at the displacement front. Of lesser importance are the effects of injection rate and porous medium type. Questions which have not been completely answered deal with the effects of gravity and reservoir inhomogeneities on the process. INTRODUCTION One of the major problems facing the oil industry today is recovery of the large fraction of the discovered oil which will remain unrecovered unless some new processes are found. Water flooding has been one successful method used to increase recovery over natural depletion. But even successful water floods may leave 25 to 40 per cent of the pore space filled with residual oil. Recently a process which involves the use of thermal energy has been reported1,'*' which may prove useful in increasing recovery from shallow reservoirs containing highly viscous crudes. This paper deals with a new oil recovery process involving use of miscible phases to displace the oil from the reservoir. Miscible phase displacement oil has been an intriguing idea because the elimination of capillary effects in the reservoir leads to 100 per cent recovery in the areas contacted by the miscible displacing phase. The big deterrent in the past to the practice of miscible phase displacement has been the high cost involved in using large volumes of solvent in the process. The use of high pressure gas to achieve a miscible phase displacement of reservoir oil has been reported4,5 as one economically feasible method. However, this process calls for the maintenance of pressures above 3,000 psi at the dis-placement front. The process described in this paper is not restricted to high reservoir pressures; the only qualification being that the slug of material which is injected into the reservoir must be miscible with both the displaced oil 2nd the displacing phase. Two such cases are the use of an alcohol slug followed by water to achieve a mis-cable water flood, and the use of a low boiling hydrocarbon slug such as propane followed by gas to achieve a miscible gas drive. This paper will deal specifically with the propane dug process. This process will obtain a miscible phase displacement at pressures as low as about 1,200 psi at a reservoir temperature 01 150°F. The process is very simple. The propane displaces oil completely at one front because it is miscible with the oil, and gas displaces the propane completely at a second or trailing front because it is miscible with the propane. A small band of propane should thus remain wedged between the gas and oil phases. This idea has been called the "miscible slug process."6 Unfortunately, the propane slug will become diluted as it flows through the reservoir. This results from a mixing action since the fluids flow through a complex reservoir porous medium rather than simple capillaries. Fig. 1 diagrams a miscible slug displacement. The effects of some of

Jan 1, 1958

By J. S. Aronofsky, H. J. Ramey

Potentiometric model studies of the five-spot water flood to determine the influence of mobility ratio upon injection or production histories are described. The results suggest a method for the correlation of data from field pilot tests for the estimation of an effective mobility ratio and its effect upon field water floods. The effect of the well spacing-to-well radius ratio upon production histories is presented. A method of accounting for this factor is suggested. The influence of injection (or production) rates and injection and production well pressures upon production histories is shown. The five-spot well pattern was investigated for water-to-oil mobility ratios of 0.1 to infinity. INTRODUCTION It has been well established that mobility ratio has an important effect upon flood patterns.1,2,3,4,5 It should be equally apparent that injection and production histories must also be influenced by mobility ratio. However, none of the articles referred to above mention the importance of being able to predict the effect of well pressures (or injection rates) during the entire time history of a waterflood operation. A complete description of production histories (the terms "injection" and "production" are synonymous for the steady-state model under consideration) would provide values for well pressures and interface positions at any time for a specified injection rate. conversely, if the waterflood problem is specified in terms of a constant injection well pressure, then it would be desirable to know the injection rate and interface positions at any time. This paper describes the results of potentiometric model studies which were used to analyze the influence of mobility ratio on injection or production histories. A method is presented for calculating production histories over a range of ratios of well spacing-to-well radius. The basic method described in this paper to evaluate production histories is to: (1) determine interface position as given in Ref. 1, and (2) measure electrical current and voltage drop for each interface position. It should be mentioned that the current state of knowledge on flood patterns as affected by mobility ratio shows that significant discrepancies exist between the results of various investigators2,3,4,5. It is beyond the scope of this paper to discuss the reasons for such discrepancies. However, the method of determining production histories presented in this paper could be applied to any of the swept-area patterns presented in the literature. All results given in this paper are based on a set of swept areas obtained by the potentiometric method. Potentiometric analyzer technique is adequately described in the literature, but the basic assumptions involved in work of this nature bear repetition. It is assumed that: 1. A distinct oil-water interface exists in the reservoir; only water is mobile in the region behind the interface (water zone) and only oil is mobile in the region ahead of the interface (oil zone). 2. There is a fixed mobility value, (k/µ) w associated

Jan 1, 1957

By B. H. Caudle, A. B. Dyes, R. A. Erickson

The study of the influence of fluid mobilities on the sweepout pattern resulting from the injection of gas or water has been extended to cover the production period which follows breakthrough of the injected material. Mobility ratios over the range common in field operations (0.1 to 17) were studied for several pattern floods (five-spot, staggered, and direct line drive). The experimental data required for these studies were obtained by the use of the x-ray shadowgraph technique using miscible oil phases of different viscosities in porous plate mode1s of a reservoir element. From the shadowgraph pictures obtained before and after breakthrough of the injected fluid, flowing ratios at the producing well and cumulative volumes injected were calculated. The method for applying such data in predicting field behavior is illustrated for a water flood of a five-spot. For this case a range of mobility ratios of 0.5 to 5.0 results in: (I) nearly complete (95 to 100 per cent) sweepout pattern efficiencies at abandonment conditions, (2) production after breakthrough being responsible for as much as one-third of the total recovery at the lower mobility ratios, and (3) a twofold variation in the operating life of the reservoir. In determining the merits of a secondary recovery operation, the fraction of the reservoir which is ultimately to be swept by the injected fluid is of major importance. Because of its significance a large amount of research has been applied to the study of areal sweepout efficiency. Muskat, Wyckoff and Botset1,2 have presented the classic analysis of the pattern efficiency at breakthrough for several injection patterns in which the mobility of the fluids ahead of the injected phase front was equal to the mobility of the fluids behind the front. Aronofsky3 as extended this analysis of recovery at breakthrough through numerical computations and by the stepwise use of the potentiometric model to include the effect of different fluid mobilities ahead of and behind the invasion front on the line drive performance. Fay and Prats' have also employed numerical computations to show the influence of one other condition of fluid mobilities on the five spot flood. In a previous paper' a new method of attack on this problem which employed x-ray and porous plates was described. At that time experimental results were also presented which described the effect of fluid mobilities on the reservoir area contacted by the injected fluid at breakthrough for the five spot and direct line drive patterns. Most of the literature pertaining to sweepout pattern efficiency has emphasized the pattern which is obtained at breakthrough of the injected phase. The increase in the sweepout pattern which occurs after breakthrough

Jan 1, 1955

By F. F. Craig

A series of both welter and gas puttern Hoods was made in the laboratory to study the oil recovery performances of .such operations. These tests were contlrrctt~tl on consolidated sandstone models, using oil. water, and gas. The model floods were scaled to reprotlrrce field performance under gas arid water five-spot injection. X-ray shadowgraphs permitted observation of the gross fluid movement within the models. A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The area1 sweep efficiency. tit breakthrough for dispersed gas drives is much higher than previorsly expected, Iying in the range of 50 to 100 per cent. A method is presented for predictitig the water-oil ratio performance of five-spot pattern water flood., in uniform sands. This method is verified experimentally for the cotidition of 120 free gas initially present and for va1ues of gas saturation normally encountered in fields following depletion operations. Prodrrction perfort?zut~cc for pattern gas injection is also predictable by this method. INTRODUCTION In field pattern hater flooding or dispersed gas injection operations, the displacing fluid (water or gas) is injected and oil is produced through wells which are, area-wise. small openings in a large container or rescrwir of oil. As a result, not all of the area between the injection and producing wells is necessarily contacted by the injected fluid by the time it first reaches the producing wells. The question arises in predicting oil recovery. as to what traction of the pattern area involved is contacted by either the injected water or gas due to the relative position of the injection and producing wells. This is the areal sweep efficiency. It is also desirable to know how well arrangement affects the oil production performance. A solution to this problem has been attempted by many means. Mathematical analysis¹,²,³, and electrolytic models', have been used to establish a breakthrough areal sweep efficiency of 73 per cent for a five-spot pattern in which the ability of the oil to flow ahead of the invading fluid is equal to the ability of the invading fluid to flow in the invaded zone. All of these studies simulate only one of many field conditions. Improved studies of areal sweep efficiency at breakthrough were made using the fluid mapper5, poten-tiometric models" and X-ray shadowgraph techniques. In these it was possible to study the effect of variations in mobility of the injected and displaced fluids, and so to cover a wide range of field conditions. The limitation of these studies is that, with these models, it was not possible to simulate the saturation gradient behind the flood front when oil is displaced by gas or water. In the most recent published technical paperS on the subject, a method was presented for predicting the oil recovery performance after breakthrough in a five-spot pattern water flood. The method involved correlations which were obtained experimentally using miscible fluids. One limitation of this work was that a saturation gradient, usually found in immiscible fluid displacement, was absent in these studies. Also the laboratory studies did not cover the situation of a water flood following oil recovery by depletion drive. as is the situation in most field water floods. The tests reported in this paper were made using oil. water, and gas, thus eliminating the simplifications of former studies. Also reported are laboratory studies on

Jan 1, 1956

By L. D. Wooddy, W D. Moore

Water drives may be natural or artificial. For the case of a natural water-drive reservoir, the volume of water influx corresponding to reservoir pressuve-production history may be calculated by means of the material bal-ance-unsteady state equation. For the artificial water drive or pattern injection water flood, the material balance equation is sufficient to determine the reservoir pressure-production, injection history. However, for both cases to reliably predict reservoir performance, it is necessary to calculate the saturation distribution of the reservoir fluids at different stages of depletion. This paper consolidates the various equations used to determine the performance of water-drive reservoirs into one approach that is applicable to any reservoir that has a natural water drive or is to be produced by water injection. The numerical procedure has been simplified considerably, and the solution is adaptable to either hand calculations or digital computer operation. INTRODUCTION A water-drive reservoir is one in which the predominant source of energy for production of oil results from the encroachment of water into the oil zone. The water drive may be either natural or artificial. Water invasion takes place by expansion of water in the aquifer as a result of the pressure decline transmitted from the oil reservoir. Because water is practically incompressible, a natural water drive requires an extensive aquifer containing a volume of water many times the volume of oil in the reservoir. Provided the permeability of the formation is reasonably high, a moderate decline of reservoir pressure usually causes adequate water influx. If the reservoir pressure decline becomes excessive because of low permeability or a high rate of production, part of the oil production may result from the liberation of dissolved gas which may cause excessive quantities of free gas to be produced along with the oil. In extreme cases, reservoir pressure may decline so rapidly as to cause the oil to be produced predominantly by dissolved gas drive, leading to abandonment of the reservoir before the advancing water has had a chance to flush the entire reservoir. In reservoirs that are not connected to extensive aquifers, an artificial water drive may be created by injecting water into or around the lower edges of a reservoir. Sometimes water is injected within the reservoir through wells interspersed among the producing wells. When injection is carried out in such fashion, the reservoir is in effect subdivided into a number of separate producing segments, in each of which the displacement of oil is simultaneously taking place, and the shapes of which are fixed by the well patterns employed. Because of the natural tendency of oil and water to segregate according to their relative densities, water will tend to migrate downdip regardless of where injected. Accordingly, the injected fluids can be retained within the intended reservoir segments only when conditions are unfavorable to their migration under the force of gravity. Pattern injections are usually confined, therefore, to reservoirs having low structural relief, or low permeability, or when production and injection rates are such that fluid movements in the reservoir are dominated by the pressure gradients rather than by the force of gravity. In the case of natural water-drive reservoirs and artificial water-drive reservoirs in which the water is in-

Jan 1, 1958

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By C. S. Matthews, W. R. Strickler, M. Prats

To gain an insight into the deviations from normal behavior caused by dip. a mathematical study has been made of single-fluid five-spot floods in dipping reservoirs for flooding techniques likely to be employed in such cases. Streamline patterns and sweep eficiencies are computed for a number of different cases, and the results, where possible, are presented in graphical form. An increase in sweep efficiency can be obtained by moving the central injection well updip, and the opti~num position is found for several cases. The applicnhility of the results is discussed. INTRODUCTION Because of the growing importance of water flooding in California and in other locations where large angles of dip are quite common, it is important to know at least some of the effects of dip on the performance characteristics of water floods in such instances. In the past, only reservoirs having relatively mild dips have been wateflooded. Consequently, little is known today as to the effect of dip on the performance characteristics of a flooding operation from the point of view of field experience; and because of the complexity of the problem, little, if anything, has been done on the problem from the point of view of theory. There are two distinct aspects of the role played by gravity in a flooding operation. The first is that of the preferential segregation of the reservoir fluids at the time when the flood is to commence. The second is the role that it may play in affecting the performance of the reservoir during the course of the flooding operation. In this paper the reservoir is assumed to be filled with only one fluid, so that there is no preferential segregation of reservoir fluids at the commencement of the flood. Moreover, the injected and in-place fluids are assumed to have the same characteristics, so that in effect we consider only a single-fluid problem. Single-fluid results have been used as a guide in the past for predicting and interpreting the behavior of regular five-spot floods in horizontal reservoirs. It is thought that single-fluid results might likewise be used for five-spot patterns in dipping reservoirs as a norm to which the effects of the multifluid problems might he referred.* In confining our attention to the single-fluid case, we therefore do not consider the preferential segregation of injected water in the oil bank, or of the oil bank in the unflooded zone. Instead we consider the deviation from the behavior of a horizontal five-spot which is caused by use of flooding techniques (i.e., the flow potential pattern at injection and production wells) likely to be employed during flooding operations in dipping reservoirs. In other words, we consider effects which are caused by the pattern of injection and production well pressures which we choose to apply. Performance characteristics are given for the five-spot spacing pattern as a function of two parameters; one is the ratio of gravity head to potential difference bctwccn the high updip injection well and the low downdip producer of the same five-spot, denoted by Rg; the second is the orientation of the five-spot pat-

Jan 1, 1956