A detailed study of a number of methods of relative permeability measurement has been made in a search for the technique most suited to routine analysis of cores taken from reservoir rock. It has been found from tests run on the same samples of core material by a number of techniques that the Penn State, Hassler, Hafford, and dispersed feed techniques all yield results which are felt to be reliable. Conditions under which the faster single core dynamic technique may be used are described. Further work on the calculation of relative permeabilities to oil from data obtained by the gas drive method is needed before this latter rapid method can be utilized.Correlations between theoretical studies and experimental results have been obtained in studies of the boundary effect, pressure distribution in two-phase flow, and gas expansion effects. Previous conclusions that the effects of the outflow boundary could be made negligibly small have been substantiated. Results of experimentally determined oil and gas pressure distributions along a core sample during flow are presented. Further studies of the effects of rate of flow in the measurement of relative permeability-saturation relations have shown that results are independent of the rate of flow as long as the flow rate is below the point where inertial effects commence. An analysis of the effects of a severalfold expansion of gas along the flow path indicates that while saturation gradients are induced in the test sample, the errors caused by this phenomenon in relative permeability measurements are ~mall.

This paper presents the results of laboratory measurements of relative permeabilities to oil and gas on small core samples of reservoir rock by five methods, and describes the influences of such factors as boundary effect, hysteresis, and rate upon these measurements. The five methods used were the "Penn State," the "single core dynamic," the "gas drive," the "stationary liquid," and the "Hassler" techniques.In those methods in which the results are subject to error because of the boundary effect, the error may be minimized by the use of high rates of flow. In order to avoid complexities introduced by hysteresis, it is necessary to approach each saturation unidirectionally. Observed deviations of relative permeabilities with rate can be explained as a manifestation of the boundary effect, and disappear as the boundary effect vanishes.The results indicate that all five methods yield essentially the same relative permeabilities to gas. Of the four methods applicable to the determination of relative permeability to oil, three, the Penn State, single core dynamic, and gas drive, gave relative permeabilities to oil which were in close agreement. The Hassler method gave relative permeabilities to oil which were consistently lower than the results obtained by the other methods.

A mathematical model is presented for analyzing the effect of small, discontinuous shales on oil recovery. The model was validated by calculations with a fine-grid computer model. The study illustrates the importance of teamwork between geologists and engineers when describing a reservoir and when predicting its performance. Introduction A complex problem when predicting reservoir performance is assessment of permeability of a formation performance is assessment of permeability of a formation perpendicular to bedding planes. Vertical permeabilities, perpendicular to bedding planes. Vertical permeabilities, which may be less than horizontal permeabilities because of orientation of rock particles and cementing material, can be measured on core samples. It also is necessary to determine distribution of nonpay intervals because small amounts of impermeable rock can profoundly affect vertical permeabilities, even if the rock is discontinuous and randomly distributed. Lateral dimensions of shale laminae, shale bodies, or other impervious materials and their distribution are difficult to describe solely from data on cores and logs. Proper description requires knowledge of depositional environment and detailed information from geologic studies of outcrops and recent sediments. Correct assessment of vertical permeability is particularly important in gas drive operations because high oil particularly important in gas drive operations because high oil recovery depends on effective oil drainage by gravity. For example, shale bodies may be large enough laterally in some reservoirs to prevent coning and yet be few enough to permit good vertical oil drainage. A laminate barrier in a pinnacle reef (carbonate reservoir) was extensive enough to cause loss of miscibility by collecting oil and part of an LPG bank above it. Recent studies indicate the presence of frequent, small, randomly distributed shale bodies in the upper formation of a large sandstone reservoir, which reduce vertical permeability in that interval. Fortunately, conceptual models based on geologic studies of recent sediments, outcrops, cores, and logs are available for describing the distribution and dimensions of pay and nonpay in both sandstone and carbonate reservoirs. Also, reservoir simulators are available for solving increasingly complex problems in practical times at reasonable costs. Construction of simulators is relatively straightforward when a reservoir is divided into separate zones by continuous barriers. Usually, at least three layers are provided in a computer model for each zone. Thin layers provided in a computer model for each zone. Thin layers are used above impervious boundaries to represent flow from gas-invaded regions. An alternative procedure is to generate pseudorelative permeabilities for layers above boundaries. Layers beneath impervious boundaries in water-invaded regions require similar treatment for accurate simulation of reservoir performance. However, no standard treatment is available for modeling reservoirs containing many small, discontinuous barriers. Adequate simulation of performance in large regions of a reservoir could requite many more small computer blocks than the user could afford. This paper illustrates how geologists and engineers can cooperate in describing and predicting oil recovery from complex distributions of permeable and impermeable intervals. A brief overview is given on geologic modeling of different types of deposits. A simple mathematical model is presented for assessing the impact of a given sized impervious body on oil recovery. JPT P. 1531

The purpose of this paper is to present the results of theoretical and experimental studies of water imbibition. The imbibition processes are involved in recovery of oil from stratified and fractured-matrix formations in natural water drives and water flooding. An understanding of the role of imbibition in implementing the recovery of oil from such formations is deemed essential to proper control of these reservoirs to achieve maximum recovery. The theoretical studies involved development of the differential equations which describe the spontaneous imbibition of water by an oil-saturated rock. The dependence of the rate of water intake by the rock on the permeability, interfacial tension, contact angles, fluid viscosities and fluid saturations is discussed. A few experiments were performed using core samples to determine the effects of core length and presence of a free gas saturation. The role of water imbibition in recovery of oil from a fractured-matrix reservoir by water flooding was investigated by use of a laboratory model. This model was scaled to represent one element of a fractured-matrix formation. Water floods were made at various rates with several fracture widths. Interpretations were made of the behavior expected in a system containing many matrix blocks. The presence of a free gas saturation was found to reduce the rate of water imbibition. In the reservoir prototype of the fractured-matrix model, water imbibition rather than direct displacement by water was the dominant mechanism in the recovery of oil at low rates. Introduction Imbibition may be defined as the spontaneous taking up of a liquid by a porous solid. The spontaneous process of imbibition occurs when the fluid-filled solid is immersed or brought in contact with another fluid which preferentially wets the solid. In the process of wetting and flowing into the solid, the imbibing fluid displaces the non-wetting resident fluid. Common examples of this phenomenon are dry bricks soaking up water and expelling air, a blotter soaking up ink and expelling air and reservoir rock soaking up water and expelling oil.

Here is an approach for solving reservoir flow problems where behavior is dominated by a rate-limiting step. Simple models are developed for gravity drainage where vertical flow occurs, for water underrunning of viscous oils, for gravity segregation of water banks in gas caps, and for control of coning by injection of oil. Introduction Forecasting the behavior of a reservoir is one of the more important but complicated tasks of engineers in the oil industry. Knowledge of reserves remaining in a reservoir is vital to planning optimum depletion of a field. Unfortunately, the engineer assigned the task of predicting reserves often faces a difficult choice. For the most accurate answer, he can use a computer program that takes into account all of the pertinent factors, but this approach is usually pertinent factors, but this approach is usually expensive and time consuming, and requires a detailed knowledge of the reservoir. On the other hand, he can use conventional one-dimensional displacement calculations that are easily applied but that in some cases do not adequately describe the reservoir flow system. The purpose of this paper is to describe a middle-ground approach that in special situations has many of the advantages of the above methods with out their more serious drawbacks. This approach uses mathematical models that describe the principal flow mechanisms and can be quickly applied by hand calculations. The technology of predicting reservoir behavior has grown steadily since the pioneering work of Muskat and of Buckleys and Leverett. Muskat's tank-type or zero-dimensional method of predicting behavior in dissolved gas drive reservoirs has been invaluable to the industry. Another milestone was reached with the Buckley-Leverett method of predicting linear displacement of oil by water or gas when flow was principally along the bedding plane. The classic work of Hurst, Muskat, and van Everdingen and Hursts laid a firm foundation for problems involving unsteady-state flow of fluids. Later, progress was made by Welge in solving one-dimensional progress was made by Welge in solving one-dimensional displacement equations more easily. The advent of digital computers led to the development of methods of solving problems of greater and greater complexity. Indicating the progress being made with computers, Douglas et al. in one paper, included the effect of capillary pressure in one-dimensional flow, and in another paper dealt with the flow of two phases in two dimensions. The utility of computers in predicting reservoir behavior has continued to grow as programs have become more user-oriented and as computers have become faster and more economical to employ. But even today, the time, effort, and money required to use computers to solve reservoir problems cannot always be justified. Thus, other tools are needed. An excellent example of another approach is given in a paper by Joslin. In analyzing a gas injection project in a large Venezuelan reservoir, Joslin realized project in a large Venezuelan reservoir, Joslin realized that gas had overridden the entire oil sand because production was above the critical rate. However, the production was above the critical rate. However, the presence of pancake-like shale members penetrated presence of pancake-like shale members penetrated by the wells prevented coning of gas into perforations located below the shale near the base of the sand. Oil recovery was predicted by assuming that gas displaced oil vertically downward throughout the producing area. Another paper demonstrating the practical use of simple mathematical models is that of Matthews and Lefkovits for predicting producing rates for wells in depletion-type reservoirs. JPT P. 1145