Search Documents

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

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

By K. H. Coats

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

By J. D. Rice, P. L. Wearden, W. L. Hensou

Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Scbiltbuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co. 's Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir perlormance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method. INTRODUCTION The numerical approach to the unsteady-state partial water-drive reservoir performance problem heretofore has been limited in that solutions have been resolved only for certain fixed parameters. Also, prior to the advent of high-speed electronic digital computers in the last few years, calculations were so tedious and time-consuming that they ordinarily were neglected, or some other means of obtaining the solutions were used. The analogue approach had been used for obtaining solutions to the transmission-of-heat problem and, consequently, means were developed for applying the electrical analogue to the unsteady-state reservoir performance problem. Bruce submitted a paper for AIME publication in Sept. 1942, in which he described an electronic device (now called the Bruce Analyzer) for analyzing the water-drive performance of any reservoir, based on either steady or unsteady-state flow characteristics. 1 Sun Oil Co. adopted the analogue approach in 1949 and now has two special-purpose high-speed electronic reservoir analyzers in use.2,3 Two main features of Sun's analyzers are (1) the high repetitive rate of reproducing the entire history of reservoir performance cyclically a number of times per second, and (2) the elimination of the necessity of knowing the properties of the associated aquifer. Since the advent of larger and faster digital computers, the possibility of incorporating this second feature into a numerical approach appeared feasible. Previous work has been done and material published covering the application of numerical methods to the behavior of the pressure with respect to time at any point in an associated aquifer? However, the aquifer parameters must be known from some source. The material presented in Ref. 4 has been used to a great degree in developing the numerical method described herein. DIFFERENTIAL EQUATION AND BOUNDARY CONDITIONS The problem of simulating the performance of a reservoir and the associated aquifer is to determine the characteristics of the aquifer such that the

By H. L. Stone, A. O. Garder

A numerical method of solving the partial differential equations which describe the one-dimensional displacement of oil by gas has been presented. Possible extension of the method to treat multidimensional flow is discussed, and the limitations of this extension are indicated. Using this method, it is possible to allow for the existence of a gas cap, the presence of any number of gas-injection or oil-production wells and the evolution of dissolved gas from the oil. It is also possible to allow for variation in the cross-sectional area, elevation, porosity and permeability of the reservoir. The influence of relative permeability and the force of gravity in the direction of flow upon the displacement is considered. The influence of capillary pressure upon the flow and the effect of gravity in the direction perpendicular to flow are neglected. The physical properties 01 the fluids are considered to be Junctions of pressure only, and equilibrium between contiguous phases is assumed. The numerical calculations can be readily carried out by the use of a digital computer. Several example analyses have been performed using the IBM 704 computer, and about one-third of an hour of computing time was required per case. Reservoir behavior predicted by use of this numerical method was compared to data obtained by other methods for three cases — complete pressure maintenance, dissolved-gas drive and gas-cap drive. The independent solutions to these problems were obtained by analytical solution, laboratory experiment and field data, respectively. Agreement of the numerical solution with data from these sources was good; this agreement establishes the convergence and accuracy of the numerical method. INTRODUCTION Most petroleum reservoirs can be produced by any one of several alternative programs. When a reservoir is produced by primary methods, production economics can be influenced by controlling the number and location of wells and the flow rate of each well. An even greater influence may be achieved by augmenting the recovery of oil obtainable by primary methods. This can be accomplished by injection of fluids such as water, natural or enriched gas or a bank of light liquid hydrocarbons. Selection of the most desirable operation requires a means of predicting the reservoir behavior which will result from each of the several alternative programs. The purpose of this paper is to present a mathematical method for predicting the behavior of reservoirs produced by gas-cap drive, dissolved-gas drive or pressure maintenance by gas injection. The method described herein takes cognizance of phase changes caused by a decline or an increase (due to gas injection) in reservoir pressure, of the presence of a gas cap and of the effect of gravity on the flow of gas and oil. Relative permeability relationships are used to define the flow properties of the rock. Allowance is made for variation in cross-sectional area, elevation, permeability and porosity of the reservoir. Both the influence of capillary pressure upon the flow and pressure gradients in the gas cap are neglected. Whenever a liquid phase and a gas phase are in contact, they are assumed to be in equilibrium. The physical properties of the fluids are considered to be functions of pressure only. Therefore, if the method is to be used to predict the effects of a gas-injection program, mixtures of the injected gas and formation crude should-have the same physical properties as mixtures of formation gas and crude. The equations to be presented in this paper apply only to a one-dimensional case; therefore, they neglect the influence of gravity in the direction transverse to the flow. As is well known, this gravitational influence may lead to overriding of oil by gas. Consequently, this procedure as presented is most applicable to long, thin reservoirs for which gravity overriding is not important. On the other hand, the equations presented can be generalized to treat multidimensional flow and, hence, to consider gravity overriding, if desired. A word of caution on two points is advisable here, however. First, the authors have not demonstrated the accuracy of the numerical technique for multidimensional flow. Second, and more important, capillary pressure will often be of importance in multidimensional problems. Obviously, in such cases a generalization of the

By H. N. Hall

Various factors must be considered in an engineering evaluation of gravity-drainage reservoirs. Among these are: (1) the effect of producing rate on total oil recovery; (2) the effect upon well productivity and ultimate recovery of the pressure level maintained during the producing life of the reservoir; (3) the economic advantage of full or partial pressure maintenance; and (4) estimate of the rate of gas production and injection and the possible purchase of gas under conditions of full pressure maintenance to ascertain compressor facilities needed. All of these factors can be evaluated only when a reliable method is employed for determining reservoir performance in gravity-drainage reservoirs. The purpose of this paper is to present a general method for calculating the performance of a gravity-drainage reservoir. This method is applicable for conditions of complete pressure maintenance, partial pressure maintenance and normal pressure depletion. Provisions are made to take into account variations throughout the reservoir of reservoir configuration, changes in permeability and fluid composition. Based on the method presented in this paper, an IBM 650 computer program has been developed. The past performance of an actual gravity-drainage reservoir producing under conditions of declining pressure and no gas injection was duplicated using this program. INTRODUCTION In tilted reservoirs the production of oil is influenced by drainage of oil from upstructure to downstructure locations. When this downstructure drainage of oil is sufficient to cause effective segregation of the gas and oil in a reservoir, the reservoir is usually classified as a segregation drive or gravity-drainage reservoir. (Discussion will be restricted to gravity-drainage reservoirs which have no encroachment of edge water.) The important feature in gravity-drainage reservoirs is the density difference between reservoir oil and gas. These phases tend to segregate in the reservoir with the result that in the gas cap the oil saturation is maintained at a higher level by drainage of oil from the gas-cap area. Oil can be produced from the oil zone at a low gas-oil ratio and reservoir energy is thereby conserved. The standard material balance in not adequate for predicting gravity-dramage reservoir performance because it does not take into account the difference in saturation above and below the gas-oil contact. Several authors'.' have presented methods for calculating the performance of gravity-drainage reservoirs in which reservoir pressure is maintained constant by gas injection into the gas cap. Using some simplifying assumptions, these methods can be employed with a desk calculator to give acceptable results. The problem of predicting the performance of gravity-drainage reservoirs under the conditions of declining reservoir pressure is many time more complex than that of constant pressure. fierefore, attempis to develop a method suitable for desk calculation have required excessively simplified assumptions. In the past several years, highspeed digital computers have become more widely available for reservoir engineering problems. These corn puters are well suited to problems such as the prediction of the performance of gravity-drainage reservoirs with pressure decline. Many of the simplifying assumptions necessary for hand computation can be eliminated so that a realistic approach to the gravity-drainage process can be made. CONCEPTUAL PICTURE OF OIL MOVEMENT IN GRAVITY-DRAINAGE RESERVOIRS Before attempting to develop an analytical treatment for conditions occuring in a gravity-drainage reservoir, a concept should be formed concerning the movement of fluids in the reservoir as oil is produced. A review of the literature'.' shows that it is customary to classify gravity-drainage operations into two categories—(1) with complete pressure maintenance, and (2) with declining pressure. The same line of reasoning will be followed in presenting the concept of the movement of fluids in the reservoir because it is easier to visualize the movement of fluids under conditions of complete pressure maintenance. After discussing complete pressure maintenance, an analogy will be made between that and the case of declining pressure. It should be kept in mind throughout that the final aim for the problem of solving gravity-drainage performance with digital computers will be to develop a general program for any kind of gravity-drainage reservoir. COMPLETE PRESSURE MAINTENANCE One feature which is generally common in gravity-drainage reservoirs is a gas cap located at the top of the structure. This is shown in Fig. 1(a). Fig. l(b) shows oil saturations that might occur through the reservoir. In the gas cap, oil saturation is lower than

By W. D. Kruger

Methods for analyzing flooding or cycling projects by means of two-dimensional flow calculations are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The accuracy of such analyses depends on the basic reservoir data employed, especially the absolute permeability distribution in the reservoir; however, absolute permeability data normally are determined from well flow tests and/or core measurements and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. A calculation procedure is presented for determining the areal permeability distribution in the reservoir. Use of the procedure allows verification of the basic reservoir data through the matching of past reservoir conditions, thereby providing proper data for reliable predictions of future operations. The calculation procedure is a numerical technique based on a mathematical model of the reservoir and is designed for solution by means of an electronic digital computer. Results from field application of this procedure are presented. Permeability distributions from measured data are compared to those calculated to indicate the need for the analysis. Comparisons of field-measured and calculated pressure distributions are given to establish the validity of the calculation procedure. The conclusions of this paper are (I) use of the calculation provides data that allow a match of past reservoir conditions and thus reliable prediction of future operations; and (2) the procedure should, where applicable, be used to provide adequate reservoir data for use in two-dimensional flow calculations and related reservoir analyses. INTRODUCTION One means of providing more precise engineering control over reservoir operations during all stages of depletion is to develop some type of model to simulate the reservoir, using information developed from the behavior of the prototype to predict the performance of the actual reservoir. The use of mathematical rather than physical models for this purpose has been gaining in importance recently because of the application and availability of electronic computers. Mathematical models avoid instrumentation difficulties and allow easier handling of large-scale problems. At present, analyses employing two-dimensional models are common, and thought is being given to the use of models in three dimensions. The use of multi-dimensional models is necessary to show not only what is occurring in the reservoir, but also where in the reservoir the phenomena of interest are taking place. Methods for analyzing flooding or cycling projects by means of two-dimensional numerical models are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The applicability of numerical models and the results of using such analyses have been presented through field examples. The references indicated here discuss fully the data necessary to build the mathematical reservoir model and the way the model is used to study or predict the future performance of the reservoir. The accuracy of the analysis of such projects depends on the basic reservoir data employed in the construction of. the model. In order to be sure the model represents the reservoir, it must be used to match some known set of reservoir conditions, i.e., to match past reservoir performance. The accuracy of the model is directly dependent upon the absolute permeability distribution in the reservoir; however, absolute permeability data are normally determined from well flow tests and/or core measurements, and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. There is always the need for better data and for verification of existing data. The purpose of this paper is to show the use of the mathematical model to match past performance in flooding or cycling projects, the use of numerical techniques to adjust the basic absolute permeability data if necessary so that a match is obtained, and in this way to generate the effective areal permeability distribution of the reservoir. A review of the basic concepts of the numerical model will be given, followed by a discussion of the data-adjusting technique for matching past performance. TWO field examples will be cited to show

By J. W. Lacey, F. H. Brinkman, J. E. Faris

This paper presents an analysis of the high-pressure, gas-driven LPG-slug process, based on fluid flow tests in areal models. Two types of tests were made. One series was made in low-pressure models which permitted observation of fluid movement. Three completely misci-ble analog fluids were used. A second series of tests was made in high-pressure models using methane, propane and a light refined oil saturated with methane at room temperature and 1,550 psig. Under the test conditions of room temperature and a pressure level of 1,550 psig, the phase diagram for the fluids used is similar to those for many of the field systems where the process is considered for use. A method for using these laboratory data to calculate field performance of the process is outlined. As a result of this work, it is concluded that small banks of LPG (5 per cent HV or less) are not effective in increasing oil recovery in horizontal reservoirs. Znstead, where small banks are used, the driving gas quickly penetrates the LPG bank because of fingering and channeling; and from this point on, the process behaves essentially as an immiscible gas-injection project. The validity of this conclusion was substantiated by: (1) laboratory studies of the effect of rate, model size and mobility ratio on miscible displacement in areal models; and (2) calculation of field recovery, which compared closely with actual field recovery. INTRODUCTION Field applications and pilot tests of the gas-driven, LPG-bank, oil-recovery process are on the increase. Most of these tests are employing small banks (2% to 5 per cent hydrocarbon volume) of LPG, which is miscible with both the driving gas and the oil in place, in an effort to attain an effective yet economical miscible displacement of oil by gas. The expectation of miscible displacement with small banks is based on the concepts that: (1) lengths of solvent-oil mixed zones, measured during miscible displacements in long slim cores, are representative of those that will occur in the field; and (2) areal sweep efficiencies5 measured in electrolytic model studies are applicable to miscible displacement in reservoirs. Our experimental evidence indicates that the mixed-zone lengths and sweep efficiencies mentioned are not applicable to miscible displacement in reservoirs. In this paper we present an evaluation of the gas-driven, LPG-bank oil-recovery process based on fluid flow experiments in areal models. These results are used to predict the performance of a field pilot test of this process, and the results are compared with the actual test results. THE EFFECTIVENESS OF LPG BANKS The effectiveness of LPG banks of various sizes in accomplishing miscible displacement of oil by gas was determined by displacement tests in a model representing one-quarter of a confined five-spot pattern. The model, 12 X 12 X 1/4 in. in size, was packed uniformly with glass beads. It was operated at a pressure of 1,550 psig and at room temperature; the fluids used were methane, propane and refined oil saturated with methane at 1,550 psig. The saturated oil had a viscosity of 1.2 cp at room temperature. The results of these tests are shown in Fig. 1, where recovery is plotted as a function of the volume of fluid injected for: (1) an immiscible-gas drive with an oil-to-gas viscosity ratio of 85; (2) three sizes of LPG banks; and (3) two completely miscible displacements with mobility ratios of 85:1 and 10:1. (The miscible displacement data plotted are the averages of several tests.) The results show that a 2½ per cent bank of LPG does not increase oil recovery over that obtained by immiscible-gas drive. The 7 and 17 per cent banks are, respectively, about 30 and 50 per cent effective (with reference to the M = 85 miscible-displacement curve) in increasing oil recovery at the point where 2½ hydrocarbon volumes (HV) of fluid have been injected. The percentage effectiveness of the banks at a given volume of fluid injected is defined as Recovery by Bank — Recovery by Gas Drive Recovery by Miscible Recovery by Flooding Gas Drive We conclude from these results that banks of LPG smaller than about 5 per cent HV in an individual stratum will cause from little to no increase in oil recovery. This finding was substantiated by work in low-pressure models, which permitted visual observation of fluid movements. In these tests, three completely miscible fluids having the same viscosity ratios as those used in

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By T. L. Loucks, E. T. Guerrero

Pressure drop characteristics in a system composed of two adjacent concentric regions of different permeability were studied. The differential equations for continuity of mass flow in the two regions were solved using the Laplace transformation and the necessary boundary conditions to give the pressure distribution in the composite reservoir, the resulting equation for pressure drop at the inner boundary was evaluated for a variety of composite reservoirs and compared with the results for a uniform reservoir. From this study it was found that under certain conditions the permeability in both zones, as well as the size of the inner zone, can be determined from the pressure drop curve. INTRODUCTION The theory for the pressure distribution and pressure build-up behavior of a well producing a single, slightly compressible fluid from infinite and finite homogeneous reservoirs was presented by Hornerl and Miller, Dyes and Hutchinson.2 Extensions on this original work to provide improved and extended interpretations and better agreement between theory and observed results have been made by Matthews, et a1,3 van Everdingen,4 Gladfelter, et al5 Stegemeierand Matthews,6 Hurst and Guerrero,7 and Perrine.8 More recently Lefkovits, et al,9 studied pressure build-up behavior in bounded reservoirs composed of stratified layers. Houpeurtl0 has suggested various approaches to the general problem of variable permeability and porosity but presented no analytic solutions for particular permeability variations. Albert, Jaisson and Marionll studied the finite composite reservoir and presented numerical solutions to the unsteady-state case and an analytical solution valid only for large times. They also studied the so-called pseudo-steady state for several examples of radial permeability variations. Very similar examples have been treated in the unsteady state with application to pressure build-up by Loucks in an unpublished manuscript. More recently Hurst12 has presented the complete point-sink solution (valid for all times) for the infinite composite reservoir. He applied these solutions to interference between oil fields along with an even more elegant application of his explicit solution to the material-balance equation including water influx. Mortada 13 approaches the same application by avoiding the point-source limitation but gives the solution for the aquifer region which is valid only for large times. Hopkinson, Natanson and Temple14 have treated both the finite and infinite composite reservoir obtaining the pressure distribution for the inner zone valid for large times. This paper presents a theoretical study of the pressure distribution in an infinite composite reservoir composed of two adjacent concentric regions of different permeability. The object was to determine the manner in which pressure drop at the inner boundary of a composite reservoir depends upon time, the permeability of each zone and the size of the inner zone. Expressions for the pressure distribution in both zones are developed which take into account the radius of the sink and are valid for small times as well as large times. It was felt that an understanding of the pressure drop behavior in various composite reservoirs would be of assistance in the interpretation of some pressure build-up curves which do not behave according to the theory derived for uniform systems. Often the region surrounding the wellbore is either more permeable or less permeable than the reservoir because of the various drilling and completion practices. The effects of reduced permeability due to drilling-fluid invasion and of increased permeability due to fracturing or acidizing need to be more carefully defined. Therefore, an equation for the pressure drop in a composite reservoir was developed, and the effects of both the permeability in each zone and the size of the inner zone were studied. STATEMENT AND SOLUTION OF PROBLEM BOUNDARY CONDITIONS AND ASSUMPTIONS The physical system studied was a composite

By G. J. Heuer, J. N. Dew, G. C. Clark

The effect on well behavior of partial permeability barriers, changes in producing rates and well spacings have been calculated through use of a radial, unsteady-state, two-phase-flow mathematical model. This model allows for variations in permeabilities and porosities with distance from the wellbore. The numerical methods necessary to solve the problem require use of a highspeed digital computer, in this case an IBM 704. In each instance, pressure and saturation gradients, gas-oil ratios and recoveries around a well producing by solution-gas drive have been calculated as a function of time and distance from the wellbore. Comparisons are made to show the effect of changes in producing rate and of varying permeability near the wellbore and out in the formation on the production and pressure history of the well. The effect of different well spacings on producing rate and ultimate recovery is considered. Although the mathematical description of the reservoir is simplified in comparison to an actual reservoir, the results do give some insight into the difficult problem of spacing and proration in a heterogeneous solution-gas-drive reservoir. Results show that for the cases considered spacing has little effect on ultimate recovery and that permeability barriers removed from the well decrease producing rate for a period of time but have only a small effect on ultimate production. INTRODUCTION The effect of spacing and producing rate on the production characteristics and ultimate recovery of a well producing by the solution-gas-drive mechanism have been topics of interest to the oil industry for many years and the subject of many hearings before state regulatory bodies. The problem is very complicated because of the difficulty of simulating in the laboratory a reservoir producing by the solution-gas-drive mechanism under anything like normal field conditions. This paper gives the initial results of a study aimed at determining the effect of these factors on production from reservoirs simulated by a mathematical model. Two-phase, unsteady-state equations are used to calculate pressures, saturations, and rates of oil and gas flow as a function of time and distance from the wellbore. The model is radial, and reservoir properties may be varied with distance from the wellbore. A decrease in permeability at a given distance results in a low-permeability ring concentric with the wellbore through which all the fluids from more distant portions of the reservoir must flow. The current mathematical model allows for variation of permeability, porosity and saturations as a function of distance from the well. Any desired drainage radius for the well may be selected. Drainage radii of 745 and 1,053 ft, which correspond to 40- and 80-acre spacing, were chosen for the calculations which follow. A large amount of the input data has been held constant. No investigation was made into the effect of changes in fluid properties and relative permeability characteristics on oil and gas production behavior. Fluid properties and relative permeabilities are essentially those of the White Mesa portion of the Greater Aneth area in southeastern Utah. A recently concluded hearing before the Utah Oil and Gas Conservation Commission to determine spacing for the field aroused interest in the possible effect of permeability constrictions located some distance from the well on production and recovery. This interest stimulated the present study. In this paper, no attempt has been made to simulate any field production characteristics exactly. Only the solution-gas-drive mechanism has been investigated, and production by liquid expansion has not been considered. This investigation is exploratory in nature but does give some insight into the problems of spacing and proration in a solution-gas-drive field having permeability variations. THE MATHEMATICAL MODEL The mathematical model is similar to that proposed by West, Garvin and Sheldon.' Approximately the same techniques have been used in arriving at a solution. The equations are nonlinear, partial differential equations which have been known for some time. The particular equations used for this study neglect the effects of capillary pressure and gravitational forces. The advent of modern digital computing equipment has made their solution practical. Basically, the method solves for pressure, saturations, and oil and gas flow rates as a function of distance and time. In our model, distance to the

During development mining, ventilation capacity may decrease and the ventilation requirements may depart from initially planned values depending on the mining rate, increases in the methane emission rate, and changes in ventilation airway leakages. Insufficient ventilation air quantities and the occurrences of high methane liberation rates can overwhelm the existing quantity of ventilation air and result in elevated levels of methane gas during development mining. This condition can both limit the development of that section and increase the risk for an ignition that may lead to an explosion. Thus, the prediction of ventilation air requirements prior to mining can enhance worker safety by reducing the likelihood that explosive methane-air mixtures form. This study presents an approach for prediction of methane inflow rates using coalbed methane reservoir modeling. For this purpose, a two-phase coalbed reservoir model of a three-entry type roadway is developed. In the model, grids are dynamically controlled to simulate development of entries. Examples are given for methane inflow and ventilation air requirements as a function of mining rate, development section length, mining height, and the existence of degasification boreholes. This technology can be used to limit the methane concentrations occurring as a result of the influences of various coalbed and operational parameters.

Jan 1, 2008

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By W. Tempelaar Lietz

The Ten Section oil field is located in the San Joaquin Valley in Kern County, California. about 12 miles southwest of Bakersfield in Township 30 South, Ranges 25 and 26 East. The accumulation is in a low relief anticlinal dome and has a productive area of approximately 2,200 acres. Discovered in 1936 as a result of seismic work, it was the first field on the floor of the Valley to obtain production. It had a small primary gas cap, and since its inception has been produced by depletion with controlled withdrawal from the gas cap to minimize blowthrough. STRUCTURE AND STRATIGRAPHY The Ten Section structure is an elongated anticlinal dome with flank dips of only about 7 degrees. A map of the field, now fully developed, and a composite log are shown in Figs. 1 and 2. Contours shown on the map are on the top of the first zone, or Marker XA as indicated on the composite log. As shown, the field has a productive closure of only some 350 feet, and there apparently is no faulting in the reservoir. The productive measures in Ten Section are of Upper Miocene age and are known as the Stevens sand. They contain thin, irregular shale or siltstone streaks which vary considerably in stratigraphic position and thickness and apparently are rather discontinuous. As a result, individual sands and shales cannot be correlated over any appreciable area, which makes it difficult to subdivide the sand body into separate zones which are distinct throughout the field. However, there are two fairly persistent siltstone bodies that at the time of development were considered to divide the productive measures into three - zones. The first, or uppermost zone is productive over the entire field and has an average thickness of 180 feet, of which some 65 per cent is sand. It had a primary. gas cap in the crestal area with an areal extent of 930 acres. The second zone has a productive area somewhat smaller than the first zone, but it did not have any original gas cap. It has an average thickness of about 360 feet, of which 55 per cent is sand. The third zone has a very limited areal extent and a maximum productive thickness of 100 feet, of which 80 per cent is sand. Recently, a deeper oil accumulation, termed the "53" sand, was discovered, but it is not discussed in this analysis. In the first and second zones the water table was at 7,980 feet subsea, while in the third zone it was at 8,080 feet subsea. RESERVOIR CHARACTERISTICS Sand Characteristics The Stevens sand in Ten Section is hard and well consolidated, and numerous wells were cored for core analysis. Core data on four representative wells are shown, plotted beside the electric logs in Figs. 3 to 6. The average porosity is 20 per cent, with porosities ranging from 15 to 30 per cent. It is estimated, from cores taken with oil base muds, that the interstitial water content is about 40 per cent. The average weighted permeability is approximately 140, with measured permeabilities ranging from 10 to 3,000 md. As might be expected with practically no correlation of individual sand

Jan 1, 1949

By W. Tempelaar Lietz

The Ten Section oil field is located in the San Joaquin Valley in Kern County, California. about 12 miles southwest of Bakersfield in Township 30 South, Ranges 25 and 26 East. The accumulation is in a low relief anticlinal dome and has a productive area of approximately 2,200 acres. Discovered in 1936 as a result of seismic work, it was the first field on the floor of the Valley to obtain production. It had a small primary gas cap, and since its inception has been produced by depletion with controlled withdrawal from the gas cap to minimize blowthrough. STRUCTURE AND STRATIGRAPHY The Ten Section structure is an elongated anticlinal dome with flank dips of only about 7 degrees. A map of the field, now fully developed, and a composite log are shown in Figs. 1 and 2. Contours shown on the map are on the top of the first zone, or Marker XA as indicated on the composite log. As shown, the field has a productive closure of only some 350 feet, and there apparently is no faulting in the reservoir. The productive measures in Ten Section are of Upper Miocene age and are known as the Stevens sand. They contain thin, irregular shale or siltstone streaks which vary considerably in stratigraphic position and thickness and apparently are rather discontinuous. As a result, individual sands and shales cannot be correlated over any appreciable area, which makes it difficult to subdivide the sand body into separate zones which are distinct throughout the field. However, there are two fairly persistent siltstone bodies that at the time of development were considered to divide the productive measures into three - zones. The first, or uppermost zone is productive over the entire field and has an average thickness of 180 feet, of which some 65 per cent is sand. It had a primary. gas cap in the crestal area with an areal extent of 930 acres. The second zone has a productive area somewhat smaller than the first zone, but it did not have any original gas cap. It has an average thickness of about 360 feet, of which 55 per cent is sand. The third zone has a very limited areal extent and a maximum productive thickness of 100 feet, of which 80 per cent is sand. Recently, a deeper oil accumulation, termed the "53" sand, was discovered, but it is not discussed in this analysis. In the first and second zones the water table was at 7,980 feet subsea, while in the third zone it was at 8,080 feet subsea. RESERVOIR CHARACTERISTICS Sand Characteristics The Stevens sand in Ten Section is hard and well consolidated, and numerous wells were cored for core analysis. Core data on four representative wells are shown, plotted beside the electric logs in Figs. 3 to 6. The average porosity is 20 per cent, with porosities ranging from 15 to 30 per cent. It is estimated, from cores taken with oil base muds, that the interstitial water content is about 40 per cent. The average weighted permeability is approximately 140, with measured permeabilities ranging from 10 to 3,000 md. As might be expected with practically no correlation of individual sand

Jan 1, 1949

By W. G. Frailing, W. P. Sims

The Lakeview Pool of Kern County, California, was discovered in 1910 with the drilling of Lakeview No. 1 which blew out and produced an estimated 8,250,000 bbl of oil in 544 days of uncontrolled flow. The well has since been known as the Lakeview Gusher. Full exploitation of the pool did not take place until about 25 years later. A total of 112 producing wells were completed in the Lakeview sand through April 30, 1949. As of that date, about 30 per cent of the total wells drilled were still producing, with an average pool production rate of approximately 2000 bbl per day. The cumulative oil production was about 41 million bbl of oil, or 55.3 per cent of the tank oil originally in place. The pool is bordered on its down-structure side by a body of inactive edgewater and water production where present has been principally the result of coning. Since the depletion of the greater portion of the gas energy by the Lake-view Gusher, the pool has operated under gravity drive. Relatively high angle dips, good permeabilities and favorable fluid characteristics have made gravity drainage particularly effective. Since January, 1942, the oil recovery -has been relatively constant at about 53,000 bbl per ft drop in fluid level. Correlations between the volume of reservoir space drained and the cumulative oil produced indicate that an ultimate recovery of 63.3 per cent of the tank oil originally in place is attainable. INTRODUCTION The Lakeview Pool is an outstanding example of gravity drainage. It is one of many productive reservoirs of the Midway-Sunset Field, and is located in Kern County, approximately five miles southeast of Taft and two miles north of Maricopa, California. Its position rel- ative to surrounding pools and to the Thirty-Five anticline is shown on Fig. 1. The northern portion of the pool lies in sections 32 and 33, Township 32 South, Range 24 East, Mt. Diablo Base and Meridian, while the southern portion lies in sections 25, 26, 35 and 36, Township 12 North, Range 24 West, San Bernardino Base and Meridian. As no two sections bear the same number, they will hereafter be referred to by section number alone. The purpose of this paper is to review the performance of the Lakeview Pool in an effort to evaluate the effectiveness of gravity drive as a recovery mechanism. REGIONAL STRATIGRAPHY AND STRUCTURE The oustanding structural feature is this area is the Thirty-Five anticline, the axis of which plunges South 75" East through the center of Section 35. As shown on Fig. 2, the following zones are oil and gas bearing in the Thirty-Five anticline area: Pleistocene Basal Tulare Tar Sands Pliocene San Joaquin Mya Sands Top Oil or Scalez Zone Etchegoin Kinsey Sand Wilhelm Zone Gusher Sand Calitroleum Sand Miocene Reef Ridge Lakeview Sand Sub-Lakeview Miocene Sands Monarch Sands or fractured shale equivalent Maricopa Webster Sand or fractured shale equivalent Fractured Shale-Uvigerina Zone C Obispo Sand and fractured shale equivalent Pacific Shale Zone The productive interval of the Lakeview Pool is limited to Upper Miocene and Lower Pliocene deposition. In this general area, the most prevalent type of accumulation results from stratigraphic traps or permeability pinchouts. As is the case of the Lakeview Pool, strati-graphic traps resulting from angular unconformities are present. The structure within the Miocene does not parallel that of the Etchegoin (Pliocene), as the Miocene beds were folded, and in places faulted, and subjected to erosion prior to Pliocene deposition. The Lakeview horizon consists of truncated sands which occur on the northeast flank of the Thirty-Five anticline. The direction of strike is west and northwesterly through sections 25 and 36 and continues northwesterly through sections 26 and 33, to the approximate center of section 32. At this point the strike swings to the northeast and the horizon re-enters section 33. in the northwest corner. The change in strike in section 32 affords synclinal accumulation at that point. The Lake-view sand is truncated updip by the Etchegoin overlap. To the southeast, the sand shales out, while to the northwest, the productive interval appears to be limited by a combination of stratigraphic pinchout and permeability barrier. Structurally, the Lakeview reservoir presents three areas of interest, as shown on Fig. 3. Area I in section 32 is a region in which a productive Sub-Lakeview Miocene sand is present. It occurs from 10 feet to 30 feet below the base of the Lakeview sand and attains a maximum thickness of 25 feet in Well No. 21, section 32. The producing characteristics of the Sub-Lakeview Miocene sand differ radically from those of the Lakeview sand. Water production at high structural locations and abnormally high fluid levels indicate that there was no communication with the Lakeview sand. Wells in Area I penetrated this sand and produced it in conjunction with the Lakeview sand. In Area 11, the Lakeview sand is a

Jan 1, 1950

By A. S. Michaels, R. S. Timmins

A study of the effect upon oil recovery from an un-consolidated porous medium of chromatographic transport of selected reverse-wetting additives during water displacement is described. Flow tests were performed on hydrocarbon oil-saturated sand columns (containing connate water) into which small volumes of short-chain aliphatic amine solutions were introduced during water flooding. Concurrently, meusurements of oil-silica contact angles, oil-water interfacial tensions and oil-water distribution coefficients were measured us a function of additive concentration. Certain treatments were found to cause a slight reduction in oil recovery, while others produced a significant increase (up to 50 per cent of the normtzl irreducible rninimum oil saturation). Recovery eficiency was correlated most satisfactorily with the maximum degree of reverse wetting produced during additive transport; conditions which resulted in only mild oil wettability of the sand reduced recovery, while those favoring strong oil wetting increased recovery. A mechanism of reverse-wetting additive action during chromatographic transport is developed which ascribes the results to transient changes in oil-solid contact angle during flow, with consequent release of oil trapped by capillary forces. Implications of these observations with regard to improved waterflood efficiencies are discussed. INTRODUCTION The need for finding improved methods of oil production is amply illustrated by the large volume of oil considered economically unrecoverable by existing production practice. Water flooding has long been an excellent method of secondary recovery. However, even in those areas of a formation which are well swept by a water flood, 20 per cent or more of the oil remains trapped within the formation and is not recovered. This trapping of oil within the pores of the rock structure results primarily from interfacial forces. If these interfacial forces were altered, it is possible that the trapped oil could be released and recovered. The addition of surface-active agents to a water flood to alter the interfacial properties of the oil-water-solid system has received considerable attention as a method of increasing oil recovery. Studies of surfactant treatment have yielded varied and, in some cases, apparently conflicting results. Increased oil recovery using surface-active agents has been reported by a number of investigators. Others have found that use of surfactants in a water flood either has no effect upon oil recovery or decreases it. Since surface-active agents tend to alter the formation wettability and oil-water interfacial tension simultaneously, several investigators have tried to determine the role these two factors play in oil recovery. Data have been presented which indicate that the most desirable condition for the solid surface is strongly water-wet. Other results indicate that, although breakthrough recovery may be less, the greatest ultimate recovery is obtained when neutral wettability prevails.", " The desirability of low interfacial tension seems to depend upon the wettability of the formation. Reports of higher recoveries, when the interfacial tension is high in a water-wet system and low in an oil-wet system, are at odds with reports of increased recovery in water-wet systems when surfactants which decrease the interfacial tension are added to the water flood. A review of previous work studying the effects of using surface-active agents in a water flood shows that these agents produce widely different effects and that opinions as to the role of the various interfacial properties are diverse. The consensus, however, is that the interfacial properties are quite important in the displacement of oil from a porous medium by water. Even in those investigations where appreciable increases in oil recovery resulted from treatment with a surface-active agent, economic considerations generally made practical application of the treatment unattractive because surfactants tend to be adsorbed within the formation. This adsorption would necessitate using large quantities of surfactant if all of the flood water were treated to contain a given surfactant concentration, even if this concentration were quite low. Preston and Calhoun suggested that the principles of chromatography could be applied to the use of surface-active agents as a means of increasing oil recovery. A small volume of surface-active material is injec-

By R. N. Upadhyay, M. Maleki, I. Fatt

Conventional laboratory core analysis tests on samples of two limestone reservoir rocks indicate that about 20 per cent of PV is in dead-end pores. These tests (electric logging formation factor, mercury injection capillary pressure and miscible displacement) were carried out on 1/4-in. diameter test plugs. Test results show a clear dilference between these samples and sandstone or homogeneous limestone reservoir rock. Although the amount of dead-end pore space can be only roughly estimated, the presence of such pore space seems clearly indicated. Pressure transient studies also show presence of deadend PV. Although they do not give quantitative results, pressure transient data yield a reasonable estimate of the size of the neck connecting dead-end pores to the main flow channels. INTRODUCTION Equations conventionally used to describe reservoir flow behavior contain the implicit assumption that all connected pore spaces contributed to both porosity and permeability. Several authors3-7 have pointed out the changes in pressure transient behavior and in electric log interpretation that may result if this assumption is incorrect and, instead, dead-end or cul-de-sac pores are present. There is a need for laboratory tests that can detect presence of dead-end pores in core samples. With such information on hand the petroleum engineer can make more rational use of the mathematical tools now available for analysis of reservoir flow behavior. This paper describes laboratory studies designed to detect and, if possible, give a quantitative measure of dead-end PV in laboratory-size core plugs. Three reservoir rocks were used, two of which were limestones suspected of having deadend pore spaces and a well-known sandstone, used as a comparison standard, in which there is believed to be little or no dead-end pore space. All the studies were designed to measure the natural dead-end PV; i.e., the pore space which is dead-ended because of rock structure. During multiphase flow in a rock without dead-end pores, some parts of one of the phases can become surrounded by the other, thereby giving (for certain flow behavior) an effective dead-end pV8,9. Such behavior will not be described here.

Jan 1, 1967

By P. D. White, J. T. Moss, J. S. McNiel

Results of experimental work on the in situ combustion process were first published in this country in 1953' when Kuhn and Koch described results of a three-well test in Jefferson County, Okla. Shortly there-after Grant and Szasz2 described field studies in Nowata County, Okla., in which several modifications of the basic combustion process were investigated by injection of various oxidizing gas mixtures other than air. In the past five years speculation concerning this method of oil recovery has continued, with a number of interesting papers on various aspects of in situ combustion appearing in the literature3,4,5,6,7. However, only one of these' provided actual engineering information on pattern-type field experiments. The primary objectives of the Oklahoma three-well test were to check operation of specially designed electrical ignition equipment and evaluate problems associated with initiation of combustion in a natural oil sand reservoir. Immediately following successful completion of this test in the Pontotoc sand, plans were activated for a second field experiment to be conducted in the same sand a short distance away. The objective of this second field test1 as to establish a relationship between field observations and information derived from laboratory experimentation and computations. Secondary objectives of the test were to develop operating tech- niques and define operating problems, and to obtain information that would assist in the economic and engineering appraisals of the process. Careful planning was required since this test was designed with the hope of providing basic information on the characteristics and operation of a combustion drive. It was necessary to include test facilities which would not only permit precise control and measurement of the process variables but would also provide sufficient flexibility of control to insure that variables in the combustion process could be studied during the course of the test under a wide range of conditions. In order to accomplish these objectives elaborate instrumentation and several control wells were included in the design of the test installation. This type installation was felt to be well suited for an experimental study, but was in no respect intended as a counterpart of a commercial-scale operation. PRELIMINARY LABORATORY WORK An important objective of the field experiment, as stated previously, has been to obtain reliable data on operating variables which might be compared with similar data obtained in laboratory combustion tests. The value of successful correlations between quantities that can be measured in the laboratory and those obtained in a full-scale commercial venture has been well established for other industrial processes. The difficulty of following a process underground should make such correlations even more essential here. Also. approaching the field test phase of development of in situ combustion, it was considered desirable to precede design of test equipment with laboratory combustion studies under a variety of conditions to establish likely ranges of variables. These included temperature, air injection rate, frontal advance rate and produced gas composition.

By R. R. Harvey

Recent evidence has indicated that the films forming at crude oil-water interfaces are the result of naturally occurring su,rface-active components in the crude oil rather than oxidation products resulting from exposure of the oil to air. Since the presence of such films may strongly affect the displacement of oil from porous media, a knowledge of their composition and formatiorz is of fundamental importance. In this study, without the assumption of a specific mechanism, film formation is considered to involve the transfer of a weakly surface-active species in solution in the oil to the oil-water interface. The film gas law and the Gibbs adsorption equation may thus he applied to the system. The rigid films which form upon decrease of the oil-water interfacial area are considered a result of the very slow rate of re-solution of the film material into the oil. When the shrinkage of the interface is very rapid, the amount of film material leaving the interface is negligible, and the system may then be treated in the same manner as an insoluble film. The combination of these treatments leads to a new concept of the film factor in which it may he quantitatively related to the concentration of film-forming material at the interface. Suitable experiments can then yield the following information. 1. Original concentration of surface-active species in the oil. 2. The change of concentration with time. 3. Concentration of surface active species at the interface. 4. The change of this concentration with time. 5. Interfacial tension of the system at any time and its variation with time. 6. Equilibriunz concentrations for a given set of conditions. 7. Concentration requirements for solid film formation. 8. Molecular diameter of the adrorbed species. These calculations may be made solely from data taken from measurements on the original oil. While using the pendant drop method of interfacial tension measurement of crude oil-water systems, Bartell and Niederhauser' remarked on the thin, transparent, pliable, solid films or membranes which were often formed at the interface between crude oil and water. As a result of their observations of these films, Bar-tell and Niederhauser concluded: 1. The films are formed by material from the oil adsorbed at the interface rather than by a reaction at the interface. 2. The adsorption of the film-forming material is a rather slow process. 3. There are good indications that the process is reversible; i.e., the film constituents may re-dissolve into the oil. 4. The film will spontaneously spread over any new surface formed. 5. The process of adsorption at the interface is accompanied by a decrease in the interfacial tension of the system. Although they had proved that film formation was not due to a reaction at the interface, Bartell and Niederhauser were unable to demonstrate conclusively whether these film-forming constituents were present in the original reservoir oil or whether they were formed as oxidation products after exposure of the oil to air. Recent evidence seems to point to their presence in the original oil. Although the true nature of the film-forming constituents is still uncertain, these conditions would be fulfilled by the assumption of the presence of a slightly soluble surface-active component in the original oil. This component would migrate to a freshly formed interface because it would thereby lower the free energy of the system. The component at the surface constitutes an expanded monolayer which would become compressed, upon retraction of drop, due to the slow rate of re-solution of the film components into the bulk of the oil. It is possible, by involved extraction processes, to separate or at least concentrate this film-forming fraction. However, using the assumptions made above, the technique of monolayer film study may be applied to reveal much of the nature of the adsorbing material without resorting to an actual separation of the film-forming constituents.