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 shadow graph technique using miscible oil phases of different viscosities in porous plate models 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:nearly complete (95 to 100 per cent) sweepout pattern efficiencies at abandonment conditions,production after breakthrough being responsible for as much as one-third of the total recovery at the lower mobility ratios, anda twofold variation in the operating life of the reservoir.
Published in Petroleum Transactions, AIME, Vol. 213, 1958, pages 281–283.Paper presented at 32nd Annual Fall Meeting of Society of Petroleum Engineers in Dallas, Tex., Oct. 6–9, 1957. ABSTRACT Miscible displacement recovers all oil in the area contacted by the injected fluid, whereas water or immiscible gas drives usually leave substantial amounts of oil as residual. However, the poor mobility ratios associated with a gas-driven miscible displacement cause the sweep pattern efficiency to be much lower than that obtained with water flooding. One way in which the sweep efficiency in a miscible displacement process can be increased is by decreasing the mobility behind the flooding front. This can be achieved by injecting water along with the gas which drives the miscible slug. This water reduces the relative permeability to gas in this area and thus lowers the total mobility. The main operating conditions for the simultaneous injection process are that a zone of gas exists between the miscible slug and the leading edge of the water and that a sufficient amount of gas be injected with the water to form the gas volume which is being left in the water zone. Laboratory model studies have shown that the ultimate sweep pattern efficiency can be as high as 90 per cent for a five-spot flooding system. If gas alone is used as the driving medium an ultimate sweep-out efficiency of about 60 per cent would be obtained in the same system. INTRODUCTION The miscible displacement processes are a step towards total oil recovery. Conventional gas or water drives usually leave 25 to 50 per cent of the oil as residual in the swept portion of the reservoir. This residual can be eliminated if the oil is driven by a fluid with which it is miscible. At some reservoir conditions natural gas will become miscible with the oil. This is the" high pressure gas process". More often, the oil does not contain enough light hydrocarbons to cause the gas to become miscible with the oil at reasonable pressures. In these cases a small band of fluid which is miscible both with the oil and gas must be kept between them. Less than 2 per cent of the reservoir volume of the slug material is needed to keep the displacement miscible.
An earlier publication has discussed three methods for obtaining relativepermeability data on small core samples and the apparatus and technique for thecapillary pressure displacement method. This paper describes the apparatus andtechnique for the solution gas and the dynamic displacement methods andpresents a routine procedure for obtaining oil-gas and water-oil relativepermeability data. Theoretical and experimental considerations are presented to show that theend effect commonly associated with the dynamic flow mechanism is extremelysmall where constant rates are employed in the flowing phase. An effect of flowrate on relative permeabilities obtained by the dynamic system is found onlywhen gas is one of the flowing phases and this effect is ascribed to a form ofchanneling in the capillary system. The apparatus and procedures used to obtain relative permeability data withthree phases flowing are described and some preliminary results of the use ofthis method are shown. Introduction In a previous publication from this laboratory there appeared a briefdiscussion of the concepts behind three basic methods for obtaining relativepermeability data. These three methods were called the capillary pressuredisplacement method, the solution gas displacement method, and the dynamicdisplacement method - the names being suggestive of the type of process usedfor obtaining the desired saturation prior to making the permeabilitymeasurements. In the same publication, the apparatus and technique for thecapillary pressure displacement method were described and some typical resultsobtained by this method were presented. This paper will present:The routine procedure used to obtain permeability data on small coresamples flowing;The experimental techniques for the solution gas and dynamic displacementmethods for obtaining relative permeability data;The results of some studies on the mechanism of fluid flow throughconsolidated porous media; and,The preliminary results on the determination of relative permeability for asystem in which three phases are flowing. T.P. 3056
A mathematical model particularly suitable for secondary recovery predictions is described. The model is based upon the flow lines generated by the superposition of line sources and sink solutions and is easily adaptable to arbitrary well patterns and fluid displacement mechanisms. Nonunity mobility ratios and reservoir stratification may be modeled. The model may be used with relatively small digital computing equipment. Previous models of this type have used the generated flow lines to outline "flow bundles", thus requiring a prior knowledge of the geometric shape of each of these bundles so that the flow through each could be computed. The modeling method described does not require any such prior knowledge of these flow lines since the volumetric flow in a stream bundle is computed as each chosen streamline is generated. This feature makes the model particularly adaptable to arbitrary well patterns. patterns. Examples are given to show the application of this model to both single and multiphase flow. Introduction Streamline models of secondary recovery projects result from the use of line source and sink solutions to the diffusivity equation to represent injection and production wells. Muskat described these solutions and their application to simplified problems. He used semi-analytic techniques to problems. He used semi-analytic techniques to obtain breakthrough sweep efficiencies for regular, dispersed injection patterns at a mobility ratio of 1. Collins described a finite-difference approximation for determining streamlines for unit mobility ratios in arbitrary well patterns. Both Muskat and Collins described image-well techniques for mathematically bounding the area being studied. Collins' finite-difference method is particularly adaptable to the use of a high-speed computer for obtaining streamlines and travel times along streamlines. Higgins and Leightons have described a technique for approximating the waterflood recovery of oil using streamlines generated by single-fluid how models (such as the method described by Collins). Their technique uses these streamlines to divide the total flow area into "stream channels", which flow in parallel between injection and production wells. Each stream channel is divided into a number of recovery rectilinear flow cells, in series, which closely approximate the shape of the stream channel. Through the use of shape factors determined for each flow cell, a Buckley and Leverett type of frontal displacement in each stream channel is computed. Combining the results from all stream channels gives the waterflood production history by this method. Once the stream channels, the flow cells, and the shape factors have been determined, a single computer program is used to obtain the production history. production history. Hauber has also described a method using stream channels formed by single-fluid streamlines. In this method, the cross-sectional area of each stream channel, as a function of length along a center streamline, is determined mathematically from the stream function, and an integration technique is used to determine the flow through each stream channel. Hauber applied this method to piston-like displacement in a five-spot injection piston-like displacement in a five-spot injection pattern. pattern. The stream-channel concept has been used and elaborated upon in subsequent publications dealing with the displacement of oil by fluids of unequal mobilities. This use of stream channels requires a prior knowledge of the single-fluid streamlines for the well spacing to be studied, so that flow cells and their shape factors, or the area functions of the channels, may be determined. The purpose of this paper is to describe a method which produces equivalent results but requires no prior knowledge of the streamlines or stream channels to be used. It is not necessary to know the eventual destinations of the "stream channels" in order to obtain production histories for arbitrary well patterns and either of the types of displacement patterns and either of the types of displacement mechanism mentioned above. SPEJ P. 7
In predicting the performance of a pattern injection operation, the engineer needs to know both the amount of oil to be recovered and the rate at which the recovery will take place. This paper describes fluid flow model studies on the effect of mobility ratio on the rate of oil recovery in a five-spot. The results show the change in fluid conductivity (total flow rate/ pres~~re drop) as the sweep-out pattern increases for mobllzty ratios between 0.1 and 10. These data, when combined with a knowledge of reservoir permeabilities and sweepout pattern efficiencies, can be used to predict the cumulative oil production as a function of time for homogeneous five-spot injection systems.
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