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By R. J. Wygal

A method is presented by which homogeneous, isotropic, and reproducible aggregates of particles such as glass beads, sand, ground glass, etc., may be prepared simply and quickly by using a "particle distributor". Several applications of the packing method to the construction of model reservoirs are described. The flow characteristics of these packings me given. Some factors which limit the usefulness of unconsolidated packs for simulating reservoir rock are overcome through artificial cementation of the aggregates. INTRODUCTION Many laboratory studies of porous media are based on experiments using test packs of sand, glass beads and other granular materials. More confidence can be had in the results of such studies if the test packs are known to have uniform properties throughout, to be mechanically stable and to be accurately reproducible. This paper presents a method by which such packs of a variety of shapes and sizes may be constructed using a particle distributor. Some factors which limit the usefulness of unconsolidated packs as a means for simulating reservoir rock are described. A method of overcoming these limitations, which involves artificial cementation of the packs, is presented. DEVELOPMENT Particles packed by the tamping or vibrating techniques are usually either non-uniform or mechanically unstable. An invention by Currie and Gregoryl overcomes these difficulties to some extent. The invention is based on the use of a stream of falling particles impinging on and passing through a distributor matrix of several layers of closely spaced spheres. The particles are well dispersed by numerous collisions with the spheres. They become homogeneously distributed at some distance below the distributor matrix and at that position are collected in the sample container. This apparatus, however, was found to be ineffective when small particles were used since small particles accumulate on the top surfaces of the spheres. An improved distributor matrix was made, first in the form of a stack of five sieves, and then in the more adaptable form of spaced layers of wire screen. Fig. 1 shows a longitudinal view through a five-layered distributor of eight-mesh wire screen. This device gives excellent results.* Fine particles pass through the distributor with very little hold up. The fine structure of the wire matrix with its many deflecting surfaces ensures good particle distribution. There are no dead areas immediately below the screen as were sometimes observed to occur below a matrix of spheres. Using such a device, 20-30 mesh sands were packed to a porosity of 32.1 per cent at rates varying from 0.17 to 6 lb/rnin. The lowest porosity achieved by tamping small increments of similar sands into a container was 33 per cent. Motion pictures at 3,000 frarnes/sec of the surface of a growing pack of 2-3/4 mm glass beads have helped to show the mechanism by which packs of low porosity are obtained. The beads, although packed at the rate of 5 lb/min, were observed to hit the pack surface singly, for the most part, and at well spaced points of impact. Part of their energy is transferred to surface beads which are thereby

By J. N. Sicking, F. H. Brinkman

A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium-ratio data for reservoir studies of condensates and volatile crude-oil systems. The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and variom reservoir pressures. Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems. In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir. INTRODUCTION As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids—thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated. Unfortunately, because of the complex nature of hydrocarbon mixtures, accurate K-values are hard to obtain. The equilibrium ratios for a particular component will vary not only with the temperature and pressure, but also with over-all composition of the system. The importance of composition is quite critical at elevated pressures, but becomes negligible at pressures below about 300 psia. Therefore, because most phase behavior problems involve the high-pressure region, each fluid system becomes a special case. Experimental programs to determine characteristic K-values are quite difficult and time-consuming. Thus, it is often necessary to resort to approximations of the K-value data. Charts giving K-values for various mixtures and classes of mixtures are available in the literature. However, there are two major difficulties in using them: (1) the K-values of the "plus" component (that mixture of components heavier than the last one analyzed) must be obtained by extrapolation from the K-values of the other components; and (2) the K-values obtained must finally be adjusted by trial and error to agree with observed volumetric data. To eliminate these difficulties, a new method of determining equilibrium ratios was developed. Briefly, after the composition of the system as a whole has been analyzed, the method uses empirical correlations and the gross fluid properties of the system (relative vapor-liquid volumes and densities) to calculate K-values. Because the calculative procedure is long, it is best solved on a digital computer. About one hour of machine time on an IBM 650 computer is required to develop a K-chart for the fluid being examined. DEVELOPMENT OF THE METHOD OF OBTAINING K-VALUES Equilibrium ratios are defined as the ratio of the mole fraction of a component in the vapor phase to its mole fraction in the liquid phase. This statement is expressed in Eq. 1. A typical plot of equilibrium ratios for a particular system is shown in Fig. 1. It should be noted that, at pressures near the saturation pressure, the K-values appear to converge to a common point. This apparent convergence point is called the convergence pressure and is a characteristic of the system involved. Various empirical correlations of K-values have been noted. It has been observed that an isothermal plot of

By D. G. Russell

Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary eflects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estitnates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. On the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. INTRODUCTION The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottom-hole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + ?t)/ ?t (where At is shut-in time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "afterproduction" or "fill-up" portion of the pressure build-up. During the period that the well fill-up effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the afterproduction period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the afterproduction period is a paper by Gladfelter, Tracy and Wilsey.1 In the approach of these authors it is necessary to measure the rate of influx into the well during the afterproduction period. This is done through sonic measurements or through measurement of tubing-head and casing-head pressures simultaneously with

Jan 1, 1967

By C. R. Knopp

Gas-oil relative permeability ratio is an important relationship in oil reservoir predictive calculations. A correlation has been developed from 107 gas-flood k/k tests on Venezuelan core samples. The correlating parameter is based on restored-state water saturation tests and' is applicable to both consolidated and poorly consolidated sandstone reservoirs. Data of the correlation show that there are no distinguishah1e differences between the mass-data groupings for the two c1assifications A procedure is recommended for running .sufficient relative. permeability analyses to compute a geometric mean of the sample group. The geometric mean is more representative of the total core, and probably the entire reservoir. For example, while only one in four of the k,,/k,., test curves agreed closely with the resultant correlation of this report, the geometric mean curves of the 16 suites (three samples or more). showed good agreetment ill three cases out of four. INTRODUCTION The gas-oil relative permeability ratio is an important, fundamental relationship in most oil reservoir predictive calculations. Predictive calculations are made to estimate future reservoir production characteristics and ultimate oil recovery. The k1,/k2, relationship is specifically needed to relate the surface gas-oil ratio to the reservoir oil and gas saturation, and to calculate the relative movement of these phases within the reservoir whenever some of the more complex driving mechanisms are present. Laboratory k1/k2, tests are not generally run as a routine analysis. Consequently, k1/k2 data often are not available when needed because the cost of laboratory work could not be justified or the need for such data had not been properly anticipated. When laboratory k1/k2, data are available, they are often very difficult to interpret. For example, wide divergence is sometimes shown in a family of k1,/k1, tests representative of the producing horizon in a single well. With these considerations in mind, a study was made to determine if a relationship might exist between the k1,/k2, curve and some other simple laboratory test criteria. The most probable k1/k2, curve correlation for Venezuela described in this paper is the result of the investigation. The presented correlation defines the most probable gas-flood k,,/k,, curve through the medium of air-water capillary displacement and centrifuge water saturation tests. The laboratory procedures of these tests are. relatively simple, and inexpensive; test data should be. widely available- from routine analysis. DATA AVAILABLE, LABORATORY METHODS The report correlation utilized 107 gas-Hood k1/k2, tests run on sandstone cores of Venezuelan reservoirs. Table 1 is a general tabulation of data pertinent to the tests, while Table 2 summarizes the data. Thetests include 96 from Western Venezuela and 11 from Eastern Venezuela. Eighty-two- of the 107 test samples were sandstones that varied from poorly consolidated to-unconsolidated; 25 were consolidated. The average sample porosity was 26.7 per cent and the average permeability was 1,121 md; these values typify the better sandstone reservoirs of' Venezuela. The Welge gas-flood technique,' based on fundamental Buckley-Leverett frontal displacement theory, was introduced in about 1952 and is widely accepted in the industry. The laboratory procedure is relatively simple, rapid, and can be performed on small core samples. While there have been some minor variations in sample preparation and laboratory procedure in the tests used for the correlation, these tests can be generally summarized as follows. The core sample was first sol vent-extracted and dried. Connate-water saturation was restored by the oil-flushing or evaporation-blow down methods. At the beginning of gas flood the hydrocarbon pore volume was completeiy saturated with the test oil phase. Unsteady-state gas-oil displacement then began with the injection of nitrogen or helium. while the displaced oil and gas phases were incrementally metered at the out-flow face. From the test data, the k,,/k,, curve was calculated by the Welge method.' The individual oil and gas relative permeabilities were also calculated." CORRELATING PROCEDURES In attempting to establish a basis of correlation, we found that broad mid-range sections of 105 of the 107 k,,/k,, test curves could be closely duplicated by a straight line. Only two curves did not show a degree of linearity in this region. Correlation-curve definition parameters were subsequently developed from this observation of consistent mid-range linearity. Possible correlating variables were limited to the physical properties measured on core samples that (1) were widely available as common test data and (2) could be easily and cheaply obtained through future laboratory work. The more obvious possibilities were porosity, permeability and

Jan 1, 1966

By W. Hurst

What is entailed here is the extension of the sinzplified material balance formulas to encompass interference between oil fields. As previously reported, the ex-plicitness as so revealed for the cunzulative pressure drop as a function of all factors contributing to its change in the material balance equation, is now transcribed through the inter-conzmunicating aquifer to effect an increased pressure drop on an adjoining field by interference. Such is performed by mathematical analyses and the application of the Laplace transformations. What is accomplished is that the reiteration problems previously associated with interference studies are nullified, since volumetric changes for the fluids in situ are automatically adjusted by the explicitness so expressed, and what pertains to the superposition principle applies only to the impeded water drive upon a su.bject field, which is likewise incorporated in the over-all pressure drop that results. The mathematics treats with the rigorous solution of the problem, as well as with methods easily amenable to numerical interpretation by the practicing engineer. In all cases, however, what is deduced for areal extents, reveal interference between wells when time becomes large that further substantiate the analyses. Probably of equal significance, all variables and for/nation characteristics are accounted for. This applies to the differences in PVT analyses that occur from field to field and the physical parameters associated with the lithology of the reservoirs. The latter is deduced from a rigorous interpretation of the unsteady-state flow problem for sands of different permeabilities in series. Thus, what purports to be a trial-and-error calculation to include variations in sand conditions within the intercommunicating aquifer to define water drive has little importance compared to the designation of such paranzeters at the reservoir to constitute the essential criteria. INTRODUCTION In a recent publication, the reader has been introduced to the simplified material balance formulas,' It has been shown that the complexities formerly associated for identifying and determining reservoir pressure in the material balance relationship can be resolved by treating with the Laplace transformations, the inversion of which reveals pressure as an explicit function of all factors contributing to its change. For an under saturated oil reservoir, this constitutes an integrated effect from the inception of production; and for a saturated oil reservoir, such represents a survey traverse. However, what is most important, for the first time we are able to express the pressure change in a reservoir directly to the oil, gas and water produced, and to the physical parameters of the formation, in the same manner that reservoir pressure has served in the past to define well interference — which opens up this avenue of endeavor for investigating interference between oil fields. The occurrence of interference is by virtue of the juxtaposition of two or more oil reservoirs producing in the same aquifer. Thus, in any one field, the extended production so incurred creates a pressure lowering in the field, as well as in the aquifer, which can now be transcribed by these simplified material balance formulas to the adjoining reservoir to observe the increased pressure change so induced. These effects are retroactive from field to field, to reveal a pressure drop far in excess of normal depletion to evidence the interference pattern that can result. Such is the purpose for the present undertaking — to develop the mathematical physics treating with this phenomenon of interference between oil fields, employing the simplified material balance formulas. Since Ref. 1 often will be referred to in the text, it is identified as "The Simplification", in the same connotation that another paper has been referred to as the "Laplace Trans-formation. However, the amount of material to be covered in these passages is substantial; therefore, the total emphasis will be placed upon developing these fundamental ideas treating with interference rather than attempting to offer work curves, which always can be prepared. For the practical application of these simplified material balance formulas that form the framework of the present development, the reader will find a comprehensive treatment in the Appendix of Ref. 1, illustrating a factual field example. In essence, what is proposed by this presentation is to make available to the practicing engineer a simplified means to treat with interference between oil fields, independent of the complex machine computations that have attended such undertakings in the past. As the problem unfolds, a common pattern will be discernible, whereby the many reiteration processes that previously required computing devices are eliminated.

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt' studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger' discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and

By G. W. Tracy, R. D. Carter

Numerical calculations were made to determine the behavior of reservoirs with high-pressure drawdown and wide well spacing where the initial productivity is low and the wells are completed by hydraulic fracturing. The two-phase flow equations were solved for the flow into a single well. This well was assumed to be producing from a reservoir with hydraulically created horizontal fractures (four different systems with fractures were studied). For comparison purposes, additional two-phase flow calculations were made assuming a reservoir with uniform rock properties. The two-phase flow results were also compared with the conventional calculation methods, which do not include the effect of saturation gradients resulting from a simultaneous flow of oil and gas which are normal to this type reservoir. It was found that the conventional methods predict (1) a high and too optimistic value of ultimate recovery, (2) a high producing rate and a high reservoir pressure at a given oil recovery and (3) a low trend of gas-oil ratio with oil recovery. Included in the two-phase flow calculations were provisions to control the oil production rate by an allowable rate and, also, by a gas-oil ratio penalty rule. For the systems with hydraulic fractures, the producing rate was controlled by the gas-oil ratio penalty rule for most of the life. This is in contrast to the system with uniform rock properties which went "on decline" almost immediately. An unexpected characteristic of the systems which included fractures was the early rise in producing gas-oil ratio from 730 cu ft/bbl to approximately 1,200 cu ft/bbl, followed by a "leveling off" before the normally expected gas-oil ratio rise began. Additional features which are a result of hydraulic fracturing are (I) greater ultimate recovery, (2) higher average producing rates and (3) a lower average reservoir pressure at a given oil recovery. INTRODUCTION Some oil fields discovered during the past few years are producing from certain volumetric ally controlled reservoirs (often referred to as solution or internal gas- drive reservoirs) which are characterized by high-pressure drawdown at the wells. Since the available pressure drawdown at a well is limited by the static reservoir pressure and the producing rate is controlled by the available drawdown, wells completed in this type of reservoir usually produce at a rate less than the allowable from the time of completion. Because of this, this type of reservoir is referred to as a low productivity reservoir. Economic considerations require the use of wide well spacing and well stimulation by hydraulic fracturing to make commercial wells in this type of reservoir. Performance predictions for volumetrically controlled reservoirs have been made using a combination of two standard equations. 1. The "Schilthuis" or "Muskat" type material balance equation is used to relate the average reservoir pressure and the cumulative oil recovery. 2. The results from the material balance equation and the productivity factor as described by Pirson' are used to relate the cumulative recovery with producing rate and time. The material balance equation assumed uniform pressure and liquid saturation conditions throughout a reservoir. The steady-state radial flow formula allows for a pressure gradient toward a well but assumes uniform liquid saturation. These calculation methods are adequate for application to reservoirs wherein the drawdown at the well to realize satisfactory producing rates is small compared to the total pressure. In low productivity, volumetrically controlled reservoirs, the pressure drawdown at the well is large cornpared to the total pressure. Although a precise number cannot be given for the magnitude of a large pressure drawdown, values in excess of 1,000 psi would definitely be included. For practical considerations, this usually occurs when the formation flow capacity is less than about 100 md-ft. However, this limit of formation flow capacity will vary with the well producing rate. The low pressure in the neighborhood of the well which results from a high drawdown causes evolution of large volumes of gas. This causes the gas saturation to be higher near the well than at a greater distance—-hence, a non-uniform gas saturation. Also, the relationship between the relative permeability to oil (K/K) and gas saturation is nonlinear but decreases approximately in an exponential way with increases in gas saturation. Because of this, the following chain reaction is established.

By L. G. Jones, A. S. Odeh

A theoretical developtment is presented which provides a straightforward method of handling the drawdown analysis for both oil and gas wells flowing at variable rates. In the past our inability to analyze variable-rate drawdowns has been a major obstacle in using them for formation evaluation. This method should permit wider use of these tests in the future. INTRODUCTION Pressure build-up analyses are widely used to obtain reservoir data such as the effective flow capacity of the formation. On the other hand. although pressure drawdowns have been run for a long time, they have not been used extensively to evaluate reservoirs because they are difficult to analyze. One of the difficulties in analyzing pressure drawdowns has been that the theory developed until now has required the test to be run at a constant rate. For both oil and gas wells this is a difficult requirement to satisfy. especially during the early period of a well's life when drawdown tests are usually run. In spite of this limitation, drawdown tests are often run with build-ups as a check. In this paper a theory, which handles the drawdown analysis for variable rates, is presented for both oil and gas wells. Thus, one of the biggest deterrents to running drawdowns is removed, and they should become a much more useful engineering tool in the future. THEORETICAL CONSIDERATIONS 011, RESERVOIRS The general equation used for describing the unsteady-state radial flow of slightly compressible fluids in homogeneous porous media can be written in cylindrical coordinates as where r is the radial distance in cm, t is the time in seconds, p is the pressure at r and t in atmospheres, + is the fractional porosity, p is the viscosity in cp, c is the compressibility in vol/vol/atm, and k is the permeability in darcies. There are a number of solutions of Eq. 1 for various boundary conditions. One of these is the so-called "point-source" solution, which approximates the case of an infinite oil reservoir with a well located at r = 0 and produced at a constant rate. The point-source solution of Eq. 1 is

Jan 1, 1966

By M. A. Jones

Performance of a pilot flood in eastern Kansas indicates improved recovery and accelerated production resulting from mobility ratio control obtained by adding a high moleculur weight polymer to injected water. Ultimate pilot flood recovery of the 75-cp reservoir oil is anticipated to he 350 bbllacre-ft during the six-year flood life. Cumulative recovery to date totals 242 bbl/acre-ft after 30 months of injection. Reservoir parameters and flood performance are disc~rssed in detail to provide a case history relating to the feasibility of polymer flooding. INTRODUCTION The Vernon Polymer flood of the Brazos Oil & Gas Co., located in Sec. 2, 24 S., 16 E., Woodson County, Kans., was begun in late Oct., 1963. Injection of a 500 ppm solution of Pusher* polymer was initiated in a 15-acre pilot to determine feasibility of improving oil recovery by mobility ratio control. Performance to date and the anticipated recovery of 115,000 bbl from the 329 acre-ft pilot indicate efficient displacement of the viscous reservoir oil. Dependence of flood recovery on the displacing fluid-displaced oil mobility ratio has long been recognized. Displacement efficiency of the reservoir oil decreases with increasing mobility ratio. Therefore, economic reduction of this parameter is an attractive approach to improving oil recovery. particularly from viscous oil reservoirs where mobility ratios are often quite high. Waterflood mobility ratios can be controlled by dilute solutions of certain polymers'; which provide a displacing fluid with considerably reduced mobility. Reservoir parameters and flood performance are emphasized in this paper to provide data relating to polymer flood applicability. THEORY The polymer used in the Vernon pilot exhibits the property of unusually high resistance to flow through porous media.'.' A small concentration in injected water effects a mobility reduction considerably beyond that predicted from increases in bulk viscosity as measured in a capillary or rotating cup viscosimeter. Water mobility in the subject flood is reduced by a factor of 7.55 with the addition of 500 ppm Pusher chemical to injected water while the bulk viscosity is increased from 1.03 to only 1.40 cp at 75F. The exact flow mechanism causing resistance to flow has not been established; however, it is observed only in tortuous flow systems and appears to be influenced by brine properties, rock properties and oil saturation. Consequently, mobility reduction is estimated from flow studies for a given sample of reservoir rock and is expressed in terms of a "resistance factor".' This parameter is defined as the ratio of brine mobility to polymer solution mobility measured at residual oil saturation: RF= ?m/?p= (km/µm)/(kp/µp)M.......(1) where RF = resistance factor (dimensionless) k*. and A, = mobility of water and polymer solution, respectively k,,, and k,, = water and polymer permeability, respectively (darcies) µie and µp = viscosity of water and polymer, respectively (poise). Eq. 1 is similar to the expression commonly used to relate the relative mobility of the water bank at residual oil saturation to oil-bank mobility at irreducible water saturation: where M =mobility ratio of water to oil (dimension-less) A, = mobility of oil k, = permeability to oil (darcies) )i* = oil viscosity (poise). From Eqs. 1 and 2 it is apparent that the polymer-solution-to-oil-mobility ratio can be approximated by dividing the brine-to-oil ratio by the resistance factor RF: Mpn=M10/RF...........(3) where M,-, = mobility ratio of polymer solution to oil (dimensionless). This simplified presentation assumes no dilution of the polymer solution by connate water. Also, the presence of a connate water bank separating the polymer solution from the displaced oil is not considered. Displacement of oil by waterflooding is increasingly dominated by viscous forces as the viscosity of the oil displaced increases. When the oil mobility is less than that of the injected water, the oil-water interface is not a piston-like front.3,' Instead, instabilities occur at the flood front in the form of viscous fingers which tend to penetrate the less mobile oil bank. The magnitude of these protrusions, or the degree of channeling, increases

Jan 1, 1967

By R. J. Wagner, F. F. Craig, H. G. Riley, J. D. Griffith

Peripheral water injection has been underway in the Sholem Alechem Fault Block "A" Unit, Stephens County, Okla., since 1955. In the engineering planning of the flood, it was recognized that maintenance of pressure in the large, dry gas caps was vitally necessary to prevent the loss of an estimated 27 million bbl of oil through saturation of the gas caps by the oil banks moving updip on the peripheral flood pattern. The development of an abundant, low-cost water supply and the rising cost of makeup-gas purchases indicated that gas-cap control by water injection was desirable from an economic standpoint, provided an eflective water barrier could be placed without premature water breakthrough into downdip oil producers. A laboratory model scaled to the existing reservoir conditions was comtructed to evaluate the feasibility of gas-cap water injection. Model studies indicated that (I) water injected at the edge of the gar-oil contact would form a continuous barrier between the oil and gas zones, and (2) water would advance uniformly downdip without segregation due to gravity effects provided a specified, minimum water-injection rate was maintained. The model test results also indicated that it was not necessary to fill the gas cap completely with water. Water injection at the edge of one of the gas caps was initiated in March, 1958, to field test gas-cap water injection. Water breakthrough occurred at a downstruc-ture producing well in April, 1959, after approximately 2.5 million bbl of water had been injected into the gas cap. This was the volume calculated to be required to form the barrier between the oil zone and gas cap. This performance indicates that prevention of oil encroachment into dry gas caps in a peripheral water flood by water injection at the gas-oil contact appears practical and that the model studies provided a valid prediction of field performance. INTRODUCTION The Sholem Alechem Fault Block "A" Sims Sand Unit was one of the fist major waterflood projects in Oklahoma to utilize a peripheral injection pattern. Design of control measures to minimize oil encroachment into the large crestal gas caps was one of the greatest single problems during engineering planning of this flood. Engineering studies indicated that saturation of the gas caps with oil displaced by the peripheral water flood could result in a loss of about 27 million bbl of oil, or over one-half the estimated waterflood recovery. This estimate was based on a residual oil saturation after water flooding of 35 per cent pore volume, compared to the negligible oil saturation initially in the gas caps. The Sholem Alechem Springer field, located in Stephens County, Okla., is an elongated anticline with structural dips varying from 400 to 1,000 ft/mile. The structure contains numerous faults, some of which are sealing. The portion of the field considered in this paper is Fault Block "A", which is the largest of the five major fault segments in the field. A map of the unit is shown on Fig. 1. The unit is bounded on the east and west by major sealing faults, on the north by a water-oil contact and to the south by a deterioration of sand development. Two domes, each having gas caps, exist in the unit and are separated by a north-south fault as shown in Fig. 1. The sands being flooded are the Sims sand members of the Springer series of early Pennsylvanian age. The Sims sands average over 100 ft in thickness in Fault Block "A" and have a porosity of approximately 19 per cent. Core permeabilities average 160 md, with interstitial water saturation of about 23 per cent pore volume. Three different zones can be correlated over most of the area. However, they are commingled in most of the producing wells. The two upper zones, designated as First and Second Sims, are the most important. Both the First and Second Sims have gas caps in the east dome, while only the First Sims has a gas cap in the west dome. These gas caps, whose limits are also shown on Fig. 1, initially occupied nearly 11 per cent of the total reservoir volume. The major concern of this paper is the control of the two gas caps in the First Sims sand. Fig. 2 is a cross section, to scale, across the east dome of this formation. Notable features are the relatively shallow dip, the deterioration of the First Sims sand on the south side of the gas cap and the water-oil contact on the northern edge. The formation dip at the gas-oil contact in this cross section is approximately 5".

By R. F. Nielsen, R. G. Bentsen

Jan 1, 1966

By R. W. Heins, N. Street

An investigation was made of the Rehbinder-Kuznetsov pendulum as an instrument to aid in the study of rock drillability and of the effect of surface active agents on rock drillability. The "critical weight", i.e., the pendulum weight at greatest sensitivity, was determined for several solids and it was shown that a change in surface environment changed the maximum value of the apparent hardness but not the critical weight, and the critical weight increased with increase of hardness of the solid used. Using silver halides as the solid material, and solutions of either silver nitrate or the appropriate alkali halide, it was shown that there is a hardness maximum at the zero point of charge of the particular silver halide. INTRODUCTION The development of relative hardness measurement by the method of damped oscillations, or what has been called the pendulum sclerometer, is due largely to the Russian workers P. A. Rehbinder and V. D. Kuznetsov and their co-workers.1,2 The apparent simplicity of the method has led to its use in a number of fields, particularly those where relative hardness has to be determined on a brittle solid. As will be shown, the simplicity of the method belies its complexities. THEORY OF THE PENDULUM SCLEROMETER The operation of the pendulum is quite simple. Make a sharp point such as a diamond, hardened steel or tungsten carbide, as the fulcrum of a pendulum, with the center of gravity of the system below the point of support. The attenuation of this pendulum is a function only of air friction, provided no fragmentation, breakage or other work is performed by the point. However, when the solid surface breaks or disintegrates under the point, and the latter penetrates the solid, part of the energy of oscillation is absorbed in the work of creating new surface, and the rate of attenuation increases. In the case of brittle solids, the point of the pendulum produces fragmentary particles, whereas the point produces plastic deformation in a plastic solid; but in both cases damping occurs. This pendulum damping is a function of the hardness or strength of the solid. Whereas a pendulum oscillating on a hard material attenuates primarily by air friction, in the case of a soft material, the points penetrate the surface of the solid, producing new surface, and the pendulum damps much faster. Thus the attenuation rate is a function of the hardness or strength of a material in both plastic and brittle substances. Russian workers initially used a single support for the pendulum, but this created many problems because of oscillation of the pendulum in more than one plane. A revised version used two points, or sometimes a prism as support, successfully confining oscillation to one plane. The version using two points was constructed and used throughout this investigation, making the recording of the attenuation as a function of time relatively easy. That both points should be in contact with the solid during the damping is implied. Rehbinder (c.f. Kuznetsov2) proposed that the hardness H as measured by this method could be expressed by a quantity which is inversely proportional to the relative initial rate of attenuation of amplitude. where H = hardness parameter (arbitrary units) a, = initial amplitude da/dt = rate of attenuation of amplitude with time. In the simplest case of damping with a constant logarithmic decrement, H can be regarded as a constant for the duration of the whole damped oscillation process. That is

Jan 1, 1966

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

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

Jan 1, 1965

By D. M. Kehn

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

Jan 1, 1965

By R. Wiesenthal

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

Jan 1, 1965

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

Jan 1, 1965

By B. Habermann

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

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

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