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By R. A. Fitch, J. D. Griffith

A performance calculation method was used in conjunction with experimental studies to develop means of predicting and interpreting miscible floods and to explore possible methods. of improving their efficiency. The calculation method is based upon the division of reservoirs into multiple independent zones or strata. Comparison was made with some experimental floods and with a field project to obtain some measure of the applicability of the method. Two aspects of miscible flooding were considered: (I) the displacement of a miscible front through a reservoir, and (2) the distribution and utilization of the solvent volume injected to maintain miscibility. Calculations and experihental observations indicate that alternate gas-water injection behind a miscible front significantly improves miscible flood performance, both within a single stratum and in a multistrata reservoir. Calculations were made on the extent to which miscibiliry is maintained by a given solvent volume in a stratified reservoir. Two alternate criteria for determining the optimum volume of solvent for injection are discussed. The preinjection of a small volume of water ahead of the solvent is suggested as a method of obtaining more efficient utilization of solvent. Calculations and experiments were made to investigate the effects of water preinjection. INTRODUCTION Miscible fluid displacement as a possible means of recovering oil has been the subject of extensive research and numerous field tests over the past several years. This work has brought out both favorable and unfavorable features of the miscible recovery methods. Many tests have shown that a miscible fluid can displace all of the oil contacted, leaving no high residual oil saturation, as is characteristic of immiscible displacements. The miscible methods have proven dificult to control, however, as evidenced by early breakthrough of the displacing fluid and poor sweep efficiency in several field projects. It became apparent early in the investigation of miscible displacement that the development of improved techniques and better methods of control would be required to extend the range of applicability to any significant portion of our petroleum reservoirs. The purpose of this study was to consider the problem of designing miscible floods to obtain better performance. A performance calculation was used in conjunction with experimental studies to develop means of predicting and interpreting miscible floods and to explore possible methods of improving their efficiency. Two aspects of miscible floods were considered separately in this study and the results are presented in two parts. The first part concerns the manner in which the miscible front is displaced through the reservoir. In these calculations the condition of miscibility between the reservoir oil and the displacing fluid is assumed. In the second portion the distribution and utilization of the preinjected solvent in maintaining rniscibility is considered. This portion dealing with solvent utilization applies only to the enriched gas or LPG slug processes. CALCULATION METHOD AND EXPERIMENTAL STUDIES COMPUTATIONAL MODEL The calculations for expected reservoir performance are based upon the multi-strata concept of reservoir properties. The method assumes multiple, independent strata (no crossflow between strata) and explicitly includes variations in patterns, injectivity, areal sweep and displacement efficiency. Lateral variation in permeability within the strata (for example, directional permeability) may be considered in the calculations, provided the variations are similar in all strata. The calculations based on this model furnish the rates of injection and rates of production of both oil and the displacing fluid for the composite system of strata. To carry out calculations on the mathematical model described, information is required on the performance of the displacement process under consideration in a single stratum element of the pattern to be used. In particular, for a given pattern and displacement process, data are required relating injectivity and composition of the produced stream to the volume of fluid injected. Data on the variations in areal sweep must also be available if it is desired to track the areal sweeps in the multi-strata model. These data may be obtained from experimental work such as model studies or other suitable methods. This representation of reservoir properties is, of course, an approximation and may be inappropriate in some cases. But the representation is not an arbitrary one since most oil reservoirs are essentially successive layers of sediment with the net producing pay zone often comprising but a fraction of the gross formation thickness. The fact that permeabilities measured in the vertical direction are frequently but a fraction of the horizontal permeability adds some evidence to the validity of this model. This type cal-

Jan 1, 1965

By C. R. Kyle, R. L. Perrine

A transparent model of a reservoir has been used to study some characteristics of instability in miscible displacement. The linear model dimensions are 1/4 in. x 91/2 in. x 10 ft. The model is packed with spherical glass beads. Thee groups of experiments have been performed. The objectives were to measure, respectively, the rate of growth of the transition zone, flow velocity variations in the transition zone, and the effect of a graded viscosity zone on stability. All experiments were compared, where possible, with theory. The transition zone grew almost linearly with distance traveled, regardless of flow rate, where adverse viscosity ratios were used. At very adverse viscosity ratios and large distances traveled, some reduction below linear growth was noted. This could be attributed to the effects of mixing. General similarity in flow pattern was commonly shown in different tests, although exceptions occurred at the higher viscosity ratios. Injection of tracer spots permitted direct experimental measurement of velocity variations. Statistical methods were used to compare observed velocity variations with recently published theories. Surprisingly good agreement with some theoretical predictions was obtained. In the experiments using an initially graded viscosity zone, macroscopic stability was reached before predicted by theory. Under conditions theoretically considered to be slightly unstable, any fingering tendency was too slight to become observable within a 10-ft long system. The general correlation of all experiments with published theory was good, and suggests that theoretical predictions can be extended to reservoir problems. INTRODUCTION Early laboratory studies of miscible displacement demonstrated the high recovery efficiency possible with this method. Linear laboratory models showed that, under some circumstances, all in-place hydrocarbons could be recovered using as little solvent as 5 per cent of the pore volume. These results led to a series of pilot field projects. Under realistic conditions, however, other laboratory studies showed that a small solvent bank may not recover much more oil than a conventional gas drive. The cause of this lack of efficiency is unstable viscous fingering. The size of the solvent bank required to give optimum recovery is, therefore, a question of great economic significance. The object of the experiments described in this paper was the quantitative measurement of unstable flow parameters, the verification of present theories on the miscible displacement process, and correlation of these theories with ex peri mental observation. Of the theories which have been advanced, those by Dougherty, Koval and Perrine show promise of predicting reservoir performance with reasonable accuracy.l-7 The present experiments were correlated, where possible, with the theories of Koval and Perrine. Dougherty's theory was not used because of the additional computational difficulty it presented and the belief that no further information would result. EXPERIMENTAL EQUIPMENT A transparent reservoir model, consisting of a vertical reinforced plexiglass column, was used for the experiments. The column was packed with glass beads, which served as the porous medium. To induce a known velocity disturbance in the flow, a double cosine wave restriction in the transverse cross-section was placed at the top of the column. To mark the flow field and provide a means of measuring the local fluid velocity, a dye-spot injection system was provided. The column was 10 ft high by 1/2 in. wide by 1/4 in. deep. The cosine restriction was placed 16 in. from the top of the column. The glass beads were smooth and spherical and had a mean diameter of 0.0102 cm. Liquids entered the top of the column through a manifold allowing three points of entry (left, center, and right, or any combination of these). A positive-displacement pump with variable-speed drive was used to control liquid flow rates. The pump transferred viscous oil from a reservoir to an accumulator, which displaced the test liquid into

Jan 1, 1966

By H. O. Jahns, R. A. Greenkorn, R. E. Haring, L. K. Shallenbarger

This paper is a study of the effects of heterogeneity on flow in an analog of porous media, the Hele-Shaw model. l-3 A set of experiments in heterogeneous Hele-Shaw models showed streamlines through and around heterogeneities of various sizes, shapes and levels. (A level, we define as the ratio between the transmissibility of the heterogeneity and that of the rest of the model.) The heterogeneities were restrictions or expansions of the flow stream analogous to variations in the transmissibility of porous media. The experimental data agreed well with numerical results and with an analytical solution, which we derived for a circular heterogeneity in an infinite field. This study considers the flow-stream distortion due to the shape, size and level of heterogeneities. Size and level are much more important than shape provided the heterogeneity is not long and narrow. Our analytical solution shows that a circular heterogeneity in a large field can be replaced by an equivalent circle of either zero or infinite permeability. The radius of the. equivalent circle is a simple function of size and level of the actual circle. INTRODUCTION With the availability of high-speed computers and numerical procedures to predict reservoir behavior, we are faced with an important question. How much information about the reservoir do we need to justify the cost of the computer in any given case? To answer this question, we have to know how various reservoir parameters affect flow behavior. Reservoir heterogeneity is one of these parameters. In this study, we used a simple, two-dimensional model of porous media, the hele-shaw model, to investigate the effect of heterogeneity on flow behavior. We restricted ourselves to linear, single-phase, steady-state flow in a rectangular field with a single heterogeneity at its center. The analogy between flow in Hele-Shaw models and in porous media is easily verified. Let us first consider a homogeneous Hele-Shaw model with constant plate separation h. (The Hele-Shaw model is constructed by placing two plates, usually glass, very close together and allowing liquid to flow between them. Streamlines are made visible by introducing colored fluid into the space between the plates at a number of points across the model.) We assume a cartesian coordinate system with its origin in the middle between the plates and the z axis directed perpendicular to the glass plates (Fig. 1). The fluid flow is always in a direction parallel to the glass plates and varies from a maximum value to zero in the very small distance from the middle (z = 0) to either plate (z = h/2). For slow motion of an incompressible fluid, neglecting inertia and body forces, we have the viscous flow equation: where p is the fluid pressure, p the viscosity, and v the velocity vector with components u, v and w in the x, y and z directions, respectively. In our rase. and the derivatives of 3 with respect to x and y are small as compared with the derivative in the z direction. Therefore, approximately, with Vp and v being two-dimensional vectors in the x-y plane. Two integrations with respect to z give

Jan 1, 1965

By D. J. Pye

Certain high molecular weight synthetic polymers in very dilute solutions decrease water mobility in porous media 5 to 20 times more than would be expected from the solution viscosity. This indicates that increasing water viscosity to reduce adverse mobility ratios in water floods is economically feasible in many situations. Laboratory results are consistent with accepted theory with respect to improved areal sweep, permeability distribution and displacement efficiencies as would be predicted from the solution mobility measured in the core. The laboratory results have been confirmed by field pilot floods which recovered 80 per cent and 100 per cent more oil than comparative water-flood pilots in fields containing 16 cp and 130 cp oil respectively. Economic analyses based on pilot data indicate the method to be profitable. INTRODUCTION The desirability of improving the water-oil mobility ratio in waterflood-ing operations has long been appreciated, especially for high viscosity crudes. Methods of reducing the oil viscosity by application of heat, gas resaturation and miscible drives have met with some success. Conversely, it has been generally conceded that increasing the water viscosity would also be effective, but the amount of thickening agent required to effect an appreciable increase in viscosity is discouragingly high. The use of such materials as glycerin, sugar, or glycols is completely out of the question economically, so that considerable attention has been given to the use of the much more efficient synthetic water-soluble polymers as viscosity improvers; but even these materials are not economically attractive. If increased water viscosity could be economically realized, marked improvements in areal sweep efficiency, as discussed by Caudle and Wittel and others, would be realized in field operations. Similarly, the improved mobility ratio would bring about increased recoveries by correcting permeability distribution problems as discussed by Stiles2 and Dykstra and Parsons,' and improvements in displacement efficiency would be obtained as recognized by Buckley and Leverett4 and Welge.5 LABORATORY STUDIES THE RESISTANCE EFFECT In the course of research to develop a more efficient water-soluble polymer viscosity builder, we discovered that a very few types of water-soluble polymers exhibited a most unusual and very interesting property not previously observed. Among the earliest materials showing such activity were polymers containing acry-lamide. Fig. 1 shows a typical plot of the solution viscosity vs concentration for one of these polymer solutions as determined in an Ostwald viscometer. As usual, such a plot is an approximate straight line on semi-logarithmic paper. Now, an inspection of Darcy's law, shows that a viscosity value can also be determined in a formation sample if the pressure, flow rate and permeability are known. If the core permeability is previously determined with wa- ter or brine, then the viscosity of another aqueous fluid may be determined from the equation. The viscosities so determined for glycerin (glycol or polyvinyl alcohol solutions, for example) agree with the viscometer determinations. However, in the case of the water-soluble polymer solutions in which we are interested, the viscosities measured in the formation sample depart very markedly from the viscometer values. A typical relationship for a polymer solution is also shown in Fig. 1. This unusual departure from the expected response is referred to as a resistance property of the polymer and is quantified as "resistance factor". Since the resistance factor R can best be determined in a core under study, the term has been defined on the basis of the ratio of the brine mobility to the polymer solution mobility at residual oil saturation so that:

Jan 1, 1965

By W. B. Gogarty

The reported decreases in water mobility do not seem unusual in view of non-Newtonian fluid properties. Shear stress vs shear rate diagrams have been reported for other solutions of water-soluble polymers. Some of these polymers are similar to the type mentioned by the author. Generally, the shear stress-shear rate is a non-linear function for these solutions. Data for plotting apparent viscosity vs shear rate can be obtained from this function. Apparent viscosity is defined as the ratio of shear stress to shear rate at a given shear rate. When plotted, the apparent viscosity decreases with increasing shear rate. This behavior is typical of a pseudoplastic fluid. For some water-soluble polymer solutions, the apparent viscosity decreases more than 50 times while the shear rate increases 1,000 times. Thus, viscosity of a pseudoplastic fluid only has meaning at a specified shear rate. Results of Fig. 1 could be explained in these terms. Viscosities measured in the Ostwald viscometer represent values at a given shear rate. Some average shear rate is affecting the polymer solutions while flowing through the core. This average value fixes the apparent viscosity as long as the flow rate remains constant. Viscosities measured by the two methods will be equal if shear rates are the same. The results indicate that shear rate in the core is lower (higher apparent viscosity) than in the viscometer. In the paper by Johnson, Bossler and Naumann, the relative permeability is independent of viscosity ratio. Thus, the relative permeability with respect to water flow at residual oil should be independent of the flowing phase viscosity. Polymer solutions will appear as Newtonian fluids The discussion emphasizes the nature of the "resistance factor effect" as discussed in the paper. Repeated anomalies arising in hundreds of experiments led us to the conclusion that non-Newtonian flow is not the only factor. Several of the key anomalies are as follows: 1. Measured viscosities over a range of shear rates from <1 sec-&apos; to 1,000 sec-&apos; do not account for but a minor fraction of the R observed in cores when compared in similar shear-rate ranges. 2. The slope of R vs flow rates in cores is always different from that expected from viscometer shear-rate measurements as shown in Fig. 2. in a core, the level of viscosity being fixed at a given flow rate. With these conditions, the definition of resistance factor R by Eq. 2 is simplified to Since , is constant with rate, R becomes a measure of the apparent viscosity in a core at a given flow rate. Variation in flow rate could easily account for the changes of R shown in Fig. 5. Also, this points to the fallacy of assuming R to be a unique parameter. The constant resistance factors at different flooding velocities appear to be in disagreement with the above discussion. The author furnishes Fig. 2 to support his arguments. As shown, the resistance factors remained substantially constant in the two cores over a considerable range of flooding velocities. However, in the 73-md core, the factor increases at lower rates. This behavior agrees with known characteristics of some pseudoplastic material. These materials act both as Newtonian and as non-Newtonian fluids in different regions of shear rate. Some exhibit first Newtonian, then non-Newtonian, finally, Newtonian character. Others are first non-Newtonian and then Newtonian. This latter type would explain the results with the 73-md core. The Fann-instrument results are not significant since shear rates in the core may be much different than with the viscometer. The higher resistance factor at high rates in the 150-md core is more difficult to explain. The greater resistance at increased flow rates could be attributed to what might be termed temporary bridging. As envisioned, changes in polymer configuration occur at the higher energy associated with the increased flow rate. These changes could cause less effective passage of polymer through the core. Correspondingly, increases in pressure drop will occur. These will be interpreted as higher resistance factors. 3. Most polymer solutions are non-Newtonian and many are more shear-rate sensitive than the polymers in question, yet only a very few polymers demonstrate useful R values. Gogarty&apos;s assumption that viscosities in cores and vis-cometers will be the same if measured at the same shear rate is only valid if non-Newtonian rheology is the only parameter. The experimental evidence does not validate this assumption. The anomalies observed in the equilibrium displacement experiment shown in Fig. 5 are not explained on the basis of varying flow rates since the rates were held constant. M

Jan 1, 1965

By F. O. Jones

The capabilities of small proportions of divalent cations, such as calcium or magnesium, for controlling clay blocking are reported. Potentially sensitive formations can be exposed to fresh water if at least one-tenth of the salts dissolved in both the native water and invading fresh water are calcium and magnesium salts. Often, even less suffices. The behavior evidently depends upon the cation exchange properties of the clays, which favor adsorption of calcium and magnesium over sodium. Clays having sufficient adsorbed calcium and magnesium resist dispersion by water and consequent blocking of permeability. An allied phenomenon, the dependency of clay blocking on salinity contrast, is also reported. Abrupt change from highly saline to fresh water can cause blocking which may not occur if salinity is lowered slowly. A process related to osmosis is thought responsible for this behavior. Applications of findings to drilling, fracturing and water flooding are discussed. INTRODUCTION Many formations, when exposed to fresh water, can lose permeability through clay effects.&apos;,&apos; For example, drilling-mud filtrate can cause oil permeability decreases, which persist long enough to interfere with drill-stem testing and well completion.3 Ultimate productivity may suffer when clay damage is severe, especially if drawdown pressures are low.&apos; The injection pressures and the time required for water flooding can increase if clay blocking occurs. Earlier work indicates that clay blocking is caused by obstruction of flow channels by clays or other mineral fines dispersed by fresh water.&apos;!" It is well known that increasing salt concentrations in water tends to prevent clay blocking. Also it is well established, although perhaps not as widely known, that the nature of the dissolved solids is also important. If, for instance, formation clays are exposed to calcium chloride solution and then exposed to weaker solutions of calcium chloride or distilled water, considerably less permeability damage results than if the clays had been exposed instead to sodium chloride solutions. The reasons for this behavior are: (1) clays are cation-exchange, or base-exchange, materials similar in this respect to zeolites or exchange resins, and (2) clays in the calcium form do not disperse easily in fresh water, whereas clays in the sodium form do. The base-exchange form of a clay is easily altered by flowing a solution through it. For example, a sodium clay can be changed to a calcium clay simply by passing a calcium chloride solution through the clay bed. There is general agreement that the reason calcium and magnesium clays do not disperse easily in fresh water is because the calcium ions do not ionize easily from the clay surfaces.&apos; Sodium clays, however, are believed to allow the sodium ions to ionize from the clay particle surfaces. In fresh water, this allows the particle to accumulate a net negative electrical charge great enough for the particles to repel one another and, therefore, disperse more easily. The foregoing suggests that, even in the presence of a large excess of sodium, a relatively small ratio of divalent cation, such as calcium or magnesium, might serve to prevent clay dispersion. The divalent ion probably adsorbs to a disproportionately large extent, because of being adsorbed more tightly, with the result that the proportion of divalent cation on the exchange positions of the clay might then be great enough for the clays to resist dispersion. Consequently, an investigation was conducted to find how mixtures of salts in solution influence clay blocking. APPARATUS AND PROCEDURE Water permeability tests were conducted using conventional techniques. The equipment is illustrated schematically in Fig. 1. Flow rates of solutions driven through small core samples at known temperatures and pressures were measured. Regulated compressed air, usually at 10 to 15 psig, was used to drive the solutions. Core samples 0.75 in. in diameter and 1 in. long were used for the most part. Cores were saturated by evacuating and then admitting a de-aerated solution. Tight core samples were first saturated with carbon dioxide gas and then evacuated and saturated with the test solution. After saturation, 140 psig pressure was imposed for several hours. Cores were tested to insure absence of gas saturation by a Boyle&apos;s

Jan 1, 1965

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By J. J. Taber, W. K. Meyer

Experiments on consolidated sandstones have shown that a variety of conditions are responsible for the wide range of behavior observed when oil and water are displaced simultaneously by a solvent which is miscible with both. The type of displacement is influenced most strongly by the relation between the plait point of the ternary phase diagram and the composition path followed by the system as it achieves mis-cibility. Neglecting viscosity, the displacement becomes less efficient as the distance between the composition path and plait point is increased in either direction so that a very wide spectrum of displacements is possible with different alcohol, oil and brine systems. It is possible by choosing various composition paths as miscibility is achieved to exercise some control over the actual displacement mechanism. Control over the composition path is exercised by adding oil or water in specific amounts to the alcohol prior to its injection into the porous medium. This technique apparently makes it possible to obtain piston-like displacements with systems which are usually characterized by the efficient displacement of only one of the two phases i.e., either oil or water, while the other phase lags behind. However, the simultaneous displacement of oil and water is not as efficient as other miscible displacements at a similar mobility ratio. The evidence indicates that both oil and water "leak" into the alcohol "piston" in compensating amounts. With oils of low viscosities the displacement is inefficient because the low oil saturation in the stabilized bank causes oil to be trapped by water before miscibility is attained. INTRODUCTION The simultaneous displacement of oil and water by solvents such as alcohol has been investigated in the laboratory and in the field. The laboratorv workers investigating all-liquid miscible systems have recognized the great importance that the nature of the traingular phase diagram exerts on the efficiency of the miscible displacement. Gatlin and Slobod pointed out that displacement efficiency will be improved if miscibility can be retained for long periods and that this behavior tends to be followed if the applicable phase diagrams have very low binodal curves. In their unconsolidated sand tests the alcohol was considered an ideal miscible piston displacing both oil and water phases. Later workers have pointed out that an important feature of the phase diagram as far as oil recovery is concerned is the location of the plait point. This is particularly true in the case of consolidated Sandstone.3 Since the original discussion of this effect, the importance of plait-point location has been confirmed and discussed by other author The early workers394 recognized that the position of the plait point could be altered by changing the oil or the alcohol used in an experiment. In addition, recent work has demonstrated that the plait point can be shifted by altering the nature and concentration of dissolved salts in the aqueous phase. However, the entire scope of the relationship between displacement and plait point has not been discussed previously and a technique for changing the composition path as miscibility is achieved in a particular ternary system, i.e., oil, water and solvent, has not been demonstrated. * The importance of oil viscosity on the efficiency of oil displacement by alcohol has not previously been observed, probably because the range of viscosities used in earlier experiments was too restricted. It is the object of this paper to describe the relationships between the ternary phase diagram, fluid properties and the displacement achieved. A technique for controlling the nature of the displacement is also presented. THEORY AND DEFINITIONS PISTON-LIKE THEORY The theory of alcohol flooding has been discussed in some detail.2-4 The concept was advanced that

Jan 1, 1965

By B. B. Sandiford

It has been known for many years that the efficiency of a water flood can be improved by lowering the water-oil mobility ratio in the system. Such a change leads to better sweep efficiency and also to more efficient oil displacement in the swept zone. Data from our laboratory water-flood tests of both small cores and long sand packs are presented which show that water mobility can be reduced and oil recovery increased by the addition of certain polymer solutions to flood water. The reduction in mobility, in many cases, is greater than would be expected from conventional viscosity measurements. These solutions, however, do not cause significant reductions in oil mobility. The over-all effect of these mobility changes is increased waterflood oil recovery. Encouraged by results of our laboratory work, we expanded our study to include pilot field tests of floods with such solutions. One such test, made in the West Cat Canyon field, Santa Barbara County, Calif., is described in detail in this paper. Three other field tests are also discussed. INTRODUCTION Oil production from most reservoirs following primary depletion and/or water flooding is often less than 50 per cent of the original oil in place. Heavy oil reservoirs seldom yield over 15 per cent of their original oil. With new reservoirs becoming harder to find, the improvement of oil recovery efficiency is one of our very important problems. We describe here some of our attempts to increase the efficiency of oil displacement by adding a water-soluble polymer, partially hydrolyzed polyacrylamide, to flood water. This technique will be termed "polymer solution flooding". The concept of using high-viscosity water to increase the efficiency of water flooding is not new. In 1944 Detling (Shell Development Co.) obtained a patent covering the use of several additives for viscous water flooding.&apos; His objective was to improve water-oil mobility ratios by increasing the viscosity of the flood water. Other patents2-27 have been granted covering specific water-SO~LIble polymers or specific conditions of viscous water flooding. Barnes&apos;" described his laboratory model study of the injection of a viscous water slug into a reservoir which had been partially invaded by bottom water. He concluded that, for this type of reservoir, "the cost of viscous water should not exceed a few cents per barrel for viscous water slug injection to be economically feasible" Our studies have led us to a somewhat different conclusion in a number of cases where hydrolyzed polyacrylamide solutions have been injected into reservoir models or actual reservoirs. Possible reasons for this difference are discussed in this paper. Our studies have shown that polymer solutions may lead to an increase in oil recovery over that from an ordinary water flood by (1) improving sweep efficiency, (2) improving microscopic displacement efficiency, or (3) a combination of these mechanisms. In the work of Barnes, only the benefit of improved sweep efficiency was considered. Also, our work has shown that there are marked differences in the effectiveness of different water-soluble polymers as flood water additives. Partially hydrolyzed polyacrylamide is better than many other water-soluble polymers we have tested because, even in very low concentrations, it can lead to increased oil recovery. This is an important advantage when either a dilute polymer solution is injected continuously or a relatively concentrated slug is injected followed by water. In the latter case! portions of the slug become diluted and function in the formation as very dilute solutions. As dilution takes place the effective slug size will increase which, in turn, will reduce the cost per barrel of the effective flooding medium. The reason that partially hydrolyzed polyacrylamide solutions are more efficient at low concentrations than certain other polymer solutions of equivalent viscosity (when measured in conventional viscometers) is not fully understood. We do know that the shapes and sizes of macro-molecules dissolved or suspended in liquids influence the flow properties of their solutions or suspensions. Solutions of partially hydrolyzed polyacrylamide cause greater reductions in water mobility than would be expected from conventional viscosity measurements. LABORATORY STUDIES Laboratory water floods were run in linear and radial systems with different water-soluble polymers and under varying conditions of flow. including reservoir conditions of temperature, pressure and fluid composition. Some of these runs are considered in this section. OIL DISPLACEMENT IN LINEAR MODELS In this group of runs the sweep efficiency approached 100 per cent because the linear sand packs used were as nearly uniform as possible. Results reflect primarily the micro-scopic displacement efficiencies. The laboratory models were unconsolidat-ed sand packs the lengths of which varied from about 4 in, to 40 ft. Further information on the flow models used is listed in Table 1. Using conventional procedures, water floods were run on sand packs containing either refined or crude oil at restored state. Frequently, a repeat run, similar to the first, was made as a check. Then a third run was made on the restored-state model using either polymer solution or a combination of polymer solution (slug) and water. Details of these runs are also reported in Table 1. In Figs. 1 and 2 results of two different groups of runs are shown in which the oil used was a 62-cp refined oil and the flooding medium

Jan 1, 1965

By F. F. Craig

Many full-scale waterflooding operations are preceded by pilot floods, one purpose of which is to provide an estimate of recoverable oil. A laboratory model study was made to determine the influence of the producing wells&apos; effective productivity on the oil recovery efficiency of single five-spot pilots, as well as single injection well pilot floods. The effective productivity is indicated by the value of Condition Ratio, defined as the actual well productivity to that of on undamaged and non-stimulated, normal-sized well in the same formation. The effects of initial gas satrcration and mubility ratio on recovery eficiency were also investigated in this model study. Model test results skowed that at favorable mobiliry ratios, a five-spot pilot flood can provide a direct quantitative estimate of the recoverable oil in the pilot area. If the pilot producer&apos;s Candition Ratio is 2.2 or more, upwards of 90 per cent of the recoverable oil in the pilot area is recovered from the inside producer, regqrdless of the mobility ratio or initial gas saturation. This Condition Ratio can be achieved with preyent fracturing techniques. Model studies also showed that over the range of imposed injection pressure differences and regional pressure gradients normally encountered in field operations, there was no effect on the recovery efficiency of a five-spot pilot waterflood. Model studies of single injection well pilot waterfloods showed that with no initial gas saturation, the total oil recovery at the offset producing wells can indicate the oil recovery possible by full-scale waterflooding. It is essential that the Condition Ratios of the offset wells be above 1.4. If an initial gas saturation exists prior to water injection, the recoverable oil cannot be directly evaluated by a single injection well pilot flood. However, the production per formance of such a flood can be used to provide information on volumetric sweep efficiency. INTRODUCTION Oil reservoirs are conlplex structures and cannot always be fully studied in the laboratory. Therefore, many operators consider it prudent to evaluate a waterflood prospect by means of a pilot flood. Pilot waterfloods generally involve one of two well arrangements: a single five-spot pilot waterflood, involving four injectors and an internal pilot producing well; and a single injection well pilot flood (sometimes called an inverted five-spot pilot) having one injector and four sur- rounding pilot producers. Some pilot floods are composed of multiple five-spot pilot patterns. To yield information applicable to field-wide performance, the pilot must be located in a representative portion of the reservoir. Pilot floods generally are conducted for one or more of the following reasons: (1) to determine whether water could be injected at desirably high rates, (2) to determine whether an oil bank or zone of increased oil saturation is formed by water injection, and (3) to estimate the oil recovery by waterflooding. Many of the early pilot water-floods were conducted for only the first two reasons. As soon as a buzz in oil production was obtained in the pilot, water injection was initiated throughout the entire lease or field. A number ot laboratory studies have been directed toward determining conditions under which a pilot flood could yield a quantitative estimate of the oil recovery possible by full-scale pattern flooding. One of the early studies of single five-spot pilot flooding&apos; showed that well damage to the inside pilot producer could reduce the total amount of oil recovered. In a study of the single injection well pilot flood pattern,&apos; the results indicated that if the model boundaries were no closer than a half-well spacing beyond the pilot pattern, the pilot performance in the laboratory is unaffected by these boundaries. In another study,? he effect of initial gas saturation and mobility ratio on the ratio of production to injection rate for various groupings of five-spot patterns was defined by mathematical and analog methods. In a study4 involving both potentiometric and flow model experiments at a mobiliry ratio of unity, four different pilot patterns were studied. These included a single five-spot, a single injection well pilot, a cluster of four single injection well pilots and six inverted five-spots. In this study the ratio of well diameter to the distance between injection and producing wells was held constant at 1:1000. The effect of the 7 ratio-—the ratio of the pressure drawdown at the producing wells to the pressure build-up at the injection wells on the pilot performance-was studied. The values of 7 ratio ranged from 0 to 0.34. Results showed that both the total oil recovery and the total fluid production from the pilot relative to the cumulative injection increased with increasing values of the 7 ratio. The effect of both the ratio of injection to producing rates and mobility ratio on the oil recovery performance of a liquid-saturated single five-spot pilot flood was studied in a series of flow model tests.5 Rate ratios ranged from one to four, and mobility rates ranged from 0.1 to 10. Resulls of these tests showed that at low rate ratios, the pilot producers may recover up to four times the recover-

Jan 1, 1966

By R. L. Dalton, L. A. Rapoport, C. W. Carpenter

Procedures have been developed to study the performance characteristics of unconfined pilot water floods using scaled laboratory models. The effects of operating conditions on pilot performance for variozrs well patterns have been investigated. The limitations of the laboratory model studies are outlined. Relationships between the oil recoveries of pilots and large-scale floods have been established. The applications of model studies to the prediction of large-scale waterflood performance and pilot flood design are discussed. INTRODUCTION Pilot water floods are undertaken to evaluate operational procedures and to gain advance information about the performance of an extensive water flood. In general, however, the performance of a pilot flood is not directly indicative of what can be expected from a large-scale pattern water flood. This difference stems from the fact that the over-all flow configurations are not the same for the two systems. A water flood normally consists of an array of identical well patterns. In such an array, the perimeters of the well patterns are axes of symmetry and act as impermeable boundaries. Thus, an extensive, pattern water flood can be visualized as a repetition of "confined" floods. In contrast, a pilot water flood involving only one or a few well patterns is "unconfined". Here the well patterns are not balanced by other flood units; hence, the perimeter of the pilot area does not act as an effective boundary. Accordingly, only a portion of the fluids injected (and also of those originally contained within the pilot area) is captured by the producers of the pilot. The rest escapes into the surrounding reservoir. This usually causes the amounts of oil and water produced in the pilot to be different from those recovered by a producer in an extensive water flood. Moreover, the recovery observed in the pilot can be expected to be greatly influenced by operating conditions, i.e., by the bottom-hole pressures at the injection and producing wells. The above considerations show that full utilization of pilot test results and reliable prediction of large- scale water floods require a knowledge of the relationship between the recovery performance of confined and unconfined well patterns. To date, only limited basic information is available on the behavior of pilot water floods. Craig, et al,&apos; have investigated the effects of initial gas saturation, oil-to-water mobility ratio, and well damage on the oil recovered from a single, "normal" five-spot pilot pattern (Fig. 1). Rosenbaum and Matthews2 studied the effect of initial gas saturation and mobility ratio on the ratio of production rate to injection rate for various groupings of five-spot patterns. Paulse113 investigated the effect of mobility ratio and distance from the pilot to the edge of the reservoir on the areal sweep in a single "inverted" five-spot (Fig. 1). However, none of these studies considered the effect of operating conditions on pilot flood behavior. Moreover, hardly any of the work to date dealt explicitly with the oil-recovery performance of the pilot floods. The purpose of this paper is to introduce the concept of interrelation between pilot flood behavior and operating conditions, to illustrate this interrelation by means of experimental data and to compare the recovery performances of dif-

By F. F. Skiba, J. E. Warren

An idealized miscible displacement process in a three-dimensional, heterogeneous porous medium has been studied via experimental computation based on a "Monte Carlo"&apos; model. The macroscopic dispersion which results solely from variations in the permeability of the porous system is related to the scale of the heterogeneity as well as the distribution function for the permeabilities. The interpretation of laboratory data is often subjective and may bt? misleading since ambiguities are not always recognized. Furthermore, an experiment performed on a conventional oil-field core does not yield a valid measure of Macroscopic dispersion for reservoir engineering purposes since the scale of heterogeneity that is significant in the laboratory is not significant in the reservoir. The analysis of field-performance data is discussed and it is shown that a unique characterization of the reservoir can not be obtained from this information alone. A possible method based on a minimum of data, for estimating the spatial distribution of permeabilities in a reservoir is postulated INTRODUCTION Many studies concerned with diffusion and dispersion in porous media have been undertaken because of the potential importance of miscible displacement processes for increasing the recovery of oil. The results from a large number of these studies have been published; in a recent paper Perkins and Johnstonl presented a comprehensive survey of the pertinent literature and excellent appraisal of the "state of the art". In this investigation, dispersion resulting from macroscopic variations in the properties of the porous medium is of primary interest. Dispersion, in this sense, is caused by fluctuations in the velocities of the individual fluid elements as they move through the porous system. This phenomenon is the result of inhomogeneities in the permeability and/or porosity, but it can be amplified by differences in the characteristics of the fluids involved. The objectives of this study are the following: (1) to determine the qualitative manner in which macroscopic rock properties affect the observed dispersion coefficient; (2) to evaluate the possible influence of macroscopic dispersion on laboratory experiments; and (3) to appraise the significance of macroscopic dispersion with regard to reservoir performance. Investigations of this type are essential since many miscible displacement processes, while seemingly understood from a mechanistic point of view, do not behave in a predictable manner under field conditions. Although a plausible explanation is that the process is dominated by the environment, little serious effort has been devoted either to describing the reservoir itself or to determining the probable effect of the reservoir properties on the process. This study is intended to be exploratory in nature; however, it is hoped that it will provide additional insight into the physical problem and that it will suggest areas suitable for further investigation. EXPERIMENTAL COMPUTATION MODEL To limit the observed dispersion to that which results solely from variations in the properties of the porous medium, an idealized process in which one incompressible fluid displaces another identical fluid is simulated. This simulation is achieved by means of a modified Monte Carlo method — by tracking a number of mathematical particles (tracer) through the system according to the steady-state, single-phase velocity distribution. Then the system is characterized by the distribution of the residence times of the particles. Since any number of particles can be injected simultaneously (a true delta-function distribution) and only pressure conditions are imposed on the boundaries, the model is completely determinate. Furthermore molecular diffusion, microscopic dispersion, adsorption and/or reaction are automatically precluded from the model. The heterogeneous medium is represented by a rectangular, three-dimensional array of uniform, homogeneous porous blocks which are randomly arranged; it is assumed that any two opposing faces of the system are held at fixed potentials

Jan 1, 1965

By M. A. Torcaso, P. Raimondi

To study mass transport in systems simulating oil recovery processes, different porous media were saturated with a mobile (carrier phase) and a stationary phase. Slugs of carrier phase containing a small amount of solute were displaced with pure carrier phase. By analogy to the chromato-graphic processes, the velocity of the solute can be predicted from a knowledge of the partition coefficient and the saturation provided that equilibrium between the two phases exists. Equilibrium was found to exist for different porous media, solutes and rates. The conditions were varied over the range normally encountered in the laboratory and in the field. The longitudinal dispersion of a solute undergoing interphase mass transfer was also investigated. INTRODUCTION The production of hydrocarbons by gas cycling, enriched gas drive and C02 or alcohol displacement involves, among other factors, relative motion between two phases and compounds, hereafter called solute, which are soluble in both phases. The solute is carried forward by the faster flowing phase at a lower velocity than the average velocity of that phase. Retardation of the solute is caused by chromatographic absorption and desorption in the slower flowing phase and by the degree of departure from equilibrium. At equilibrium the concentration of solute in the two phases can be related by the equation* CSw = K Cso ,............(1) where C, and C are the concentration of solute in the aqueous and oleic phases respectively and K is the equilibrium ratio, or partition coefficient. Displacement theories must contain an explicit assumption with regard to equilibrium, i.e., whether the compositions can be related by Eq. 1. The existance of equilibrium depends, in general, on the relative velocity between the phases. Unfortunately, other factors such as gravity segregation and viscous fingering, also depend on velocity. For this reason, whenever effects of rate on displacement were observed,2-4 it was practically impossible to discern what caused them — lack of equilibrium or the factors mentioned above. Equilibrium between phases has been the subject of extensive studies in fields such as extraction or chroma to graphy. It has received only small attention in flow through the type of porous media encountered in oil production.5 For this reason a method was developed which makes it possible to study the movement of a solute as it is affected by rate, type of porous media, partition coefficient and carrier phase, but in the absence of segregation or fingering. The information obtained enables one to determine when the assumption of equilibrium can be made. Briefly, the method consists of (1) saturating the core with a mobile and an immobile phase, (2) injecting a slug made up of the same fluid as the mobile phase and a small concentration of mutually soluble solute, (3) measuring the lag and the peak height of the slug at arrival and (4) correlating these variables with fluid properties such as partition coefficient and mixing constants of the medium. PROPOSED MECHANISM The principles of chromatography are combined with the equation of longitudinal mixing to predict the velocity of a solute slug compared to the bulk velocity and the peak height of a slug.6-9 The equation so obtained is valid under equilibrium conditions only. Therefore, a comparison between experimental and predicted results will give a measure of departure from equilibrium. This work was done with either the oleic or the aqueous phase being immobile. For simplicity, the following development is based on the case where the oleic phase is immobile. However, the treatment is the same in either case.

Jan 1, 1966

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

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 J. F. Wilson

An experimental investigation has been made of gas-driven slug displacements in a system of high gas saturation to evaluate the process for use in a California reservoir. Fluid compositions, temperature, pressure and core permeability duplicated reservoir conditions as closely as possible. The temperature was above the critical of the slug materials. The slug composition required for 100 per cent oil recovery in the linear flow systems was found to agree with that determined from equilibrium phase studies. A qualitative theory for the slug displacement of two-phase systems is proposed and found to be in general agreement with the observed flow behavior. The theory predicts that the length of the reservoir fluid-slug transition Zone will increase with increased initial gas saturation and decrease with increased oil swelling accompanying the composition change from reservoir oil to the critical composition. The precipitation of small amounts of an asphaltic phase during the formation of the transition zone had no adverse effects on the flow behavior of otherwise miscible systems. INTRODUCTION Despite the large number of recent publications relating to oil recovery by miscible displacement, little information is available concerning the behavior of crude oil-natural gas systems at conditions likely to be encountered in field application. The laboratory data reported here were obtained during an investigation of the possibility of using a gas-driven LPG slug in a partially depleted California reservoir. Seven gas-driven slug displacements employing slugs of different compositions and sizes were made in 26- to 27-ft long sandstone cores. The equilibrium phase behavior of the systems was also determined. The features of primary interest in this study are the following. 1. Data were obtained on the displacement of reservoir fluids at reservoir conditions. 2. A high gas saturation existed in the long cores at the start of the displacements. 3. The temperature of the studies was above the critical of the slug materials. 4. A comparison between the flow behavior and equilibrium phase behavior, as illustrated by a pseudo-ternary phase diagram, is afforded for a system of considerable complexity. THEORY Phase Behavior The use of the pseudo-ternary phase diagram to illustrate the phase behavior in miscible displacements has been discussed by Clark, Schultz and Shearin. Sie-vert, Dew and Conley and Arnold, Stone and Luffel&apos; have presented both phase equilibrium and flow data for true ternary systems. For the true ternary, the application of the theory is straight-forward; for a reservoir system represented as a ternary, the theory undoubtedly gives a qualitatively correct picture. One purpose of this investigation was to see if the pseudo-ternary phase diagram could be used to predict with reasonable accuracy the conditions necessary for miscible displacements with actual reservoir systems. MiscIBLE Displacement of Two-Phase System A large number of papers "I3 have treated the miscible displacement of a single-phase fluid from both an experimental and a theoretical viewpoint. However, the normal field application of the process will be in a partially depleted reservoir. Often the state of the system will be such that the mobility of the gas phase is greater

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.&apos;-&apos; 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 B. H. Caudle, R. E. Watson, I. H. Silberberg

The production history of an inverted nine-spot injection pattern was studied with a porous plate model similar to Habermann&apos;s. Colored fluids were used so the boundary movements could be photographed. By varying the production rates of the side and corner producing wells, the optimum pattern sweep efficiency can be obtained. Results of the laboratory tests indicate that interpolation of the pattern sweep and conductivity ratio data will permit application of the data to predicting fluid injection operations with mobility ratios between 0.1 and 10 and production rate ratios between I and the optimum values. INTRODUCTION The inverted nine-spot injection pattern in Fig. 1 has some unique advantages over other regular injection patterns (five spot, line drive, etc.) used in secondary recovery operations. It has three producing wells for each injection well, while the five-spot and line-drive patterns require an equal number of injectors and producers. Futher-more, of the eight producing wells surrounding each injection well, four are of the "side well" type which lie nearer the injection well than the remaining four "corner wells". This allows the production rates of these two types of wells to be adjusted independently of each other to obtain better pattern sweep efficiency. This latter advantage may well be the reason why the nine-spot patterns have not been studied as extensively as the patterns containing only one type of injection or producing well. The pattern sweep efficiency of the inverted nine spot is affected almost as much by operating with different producing rates of the comer and side wells as by differing mobility ratios. Possibly because of this added operating parameter, published studies of nine-spot systems have been limited in their coverage of the pertinent variables.&apos;-&apos; The model studies reported here covered the mobility-ratio range normally found in waterflood operations, as well as the variation in well production rates necessary to achieve optimum pattern sweep efficiency. Conductivity ratios — a measure of the change in total flow at constant pressure difference — were obtained during each model run. A porous-plate model with miscible fluids representing the in-place and injected fluids was used in this study. This model technique is the same as that used in both X-ray shadowgraph" and visual techniques4 described in the literature. Using miscible fluids eliminates residual oil in the model, and the permeability to the injected fluid is the same as to the in-place fluid. Thus the mobility ratio in the model is given by the ratio of the viscosity of the displaced fluid to the viscosity of the injected fluid. Because of the non-linear nature of the viscosity vs composition curve for two miscible liquids, the mobility change across the boundary between the two fluids is reasonably sharp. This technique thus represents the displacement of a region of one fluid mobility by a region of possibly different mobility in an isotropic system under steady-state flow conditions. Table 1 shows the dimensionless similarity groups used to scale the model conditions and results to

Jan 1, 1965

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