Relative Permeability Properties Research Articles

Experiment on the Gas Permeability and Gas–Water Relative Permeability in High-Rank Coal with a Self-Developed Device

Water saturation, displacement pressure, and gas type are essential factors affecting the seepage characteristic of fluid in coal due to the swelling induced by gas adsorption. However, the understanding of the seepage behavior of water, CH4, and CO2 in coal seams is still poor owing to the lack of research. In this work, a series of gas permeability and gas–water relative permeability experiments were conducted by our self-developed device. The results can be summarized as follows: (1) with the increase in water saturation, the gas permeability decreased rapidly at first and then reduced sharply again after a period of slow decline; (2) the two-phase flow span showed no significant difference for He–water and CH4–water systems under different displacement pressures, but it increased for CO2-water system. The different behaviors of the two-phase flow span suggested that the effect of displacement pressure on relative permeability properties is dependent on the gas type. (3) The CO2–water relative permeability showed a sizeable two-phase flow span compared to the He–water or CH4–water system under the same displacement pressure, and the gas relative permeability decreased obviously in the following sequence: He > CH4 > CO2. The concept of relative permeability surface was proposed based on the experimental results. A parametric interpolation method was applied to determine the relative permeability surface, which could be used to accurately describe the flow characteristics of fluids in a mixed gas–water system.

Evaluation of van Genuchten-Mualem model on the relative permeability for unsaturated flow in aperture-based fractures

The relative permeability versus saturation relation is fundamental for modeling unsaturated flow processes in aperture-based fractures. On the basis of the local cubic law and the connectivity probability of aperture distribution within single fractures, an analytical relationship between the relative permeability and saturation is established. When the van Genuchten function on the description of the capillary pressure-saturation relationship is applied, an explicit mathematical expression between the relative permeability and saturation is gained similar to the form of the van Genuchten-Mualem (VG-M) model of porous media. Through the comparisons between the several series of laboratory-measured data available in the literature and theoretical results, good agreements are both presented and they suggest that the proposed VG-M model can be successfully used for aperture-based fractures as well as porous media. To understand aperture variation dependence of the relative permeability properties, a computational method combining fractal theory and the invasion percolation model to determine the empirical parameters associated with the spatial correlation of aperture distribution is developed. Simulated fractures with spatially correlated and uncorrelated aperture distributions corresponding respectively to small and large fractal dimensions are both studied. According to the simulated results, the residual saturation generally increases with fractal dimension increments. However, the value of m exhibits a weak dependence on fractal dimension. The proposed model can be applied to various engineering such as seepage control for rock slopes, petroleum reservoirs, nuclear waste disposal and geologic storage of carbon dioxide.

Robust optimization of subsurface flow using polynomial chaos and response surface surrogates

This study employs an inclusive framework for surrogate model-based optimization in the presence of parametric and spatial uncertainties. The framework is applied to optimize water injection rate for optimal hydrocarbon recovery from a synthetic subsurface model with uncertainty in the geological and fluid relative permeability properties. In one model of parametric uncertainty, geological properties such as the channel’s absolute permeability and the fault transmissibility multiplier and the fluid relative permeability parameters such as the residual oil saturation to water and the water relative permeability at residual oil are assumed to be non-informative. In another model, the channels positions are assumed uncertain and various realizations of the channelized permeability are parameterized and the spatial uncertainty is accounted for in the optimization. The uncertainty is quantified in each evaluation of the objective function via polynomial chaos expansions. The coefficients of polynomial chaos expansion are solved by probabilistic collocation method. The objective function is assigned with a risk-averse net present value computed from a distribution of values obtained from the probabilistic proxies. The proxies are updated for each round of objective function evaluation. Monte-Carlo simulations are also conducted to verify accuracy and to demonstrate the computational efficiency of the probabilistic collocation approach. The optimization is conducted in various random input cases (depending on the number of uncertain parameters) and for each case net present value is successfully maximized and optimal solutions of the water injection rates are determined.

Optimizing the value of reservoir simulation through quality-assured initialization

The initialization of a reservoir simulator calls for the populating of a three-dimensional dynamic grid-cell model using subsurface data and interrelational algorithms that have been synthesized to be fit for purpose. These prerequisites are rarely fully satisfied in practice. This paper sets out to strengthen initialization through four key thrusts, all of which seek to optimize the bridgehead between reservoir geoscience and reservoir engineering, and thereby maximize value from reservoir simulation. The first addresses representative data acquisition, which includes the key-well concept as a framework for the cost-effective incorporation of free-fluid porosity and permeability within an initialization database. The second concerns the preparation of these data and their products for populating the static and dynamic models. Important elements are dynamically conditioned net-reservoir cut-offs, recognition of primary flow units, and establishing interpretative algorithms at the simulator grid-cell scale for application over net-reservoir zones. The third thrust is directed at the internal consistency of capillary character, relative permeability properties and petrophysically-derived hydrocarbon saturations over net reservoir. This exercise is central to the simulation function and it is an integral component of hydraulic data partitioning. The fourth concerns the handling of formation heterogeneity and anisotropy, especially from the standpoint of directional parametric averaging and interpretative algorithms. These matters have been synthesized into a workflow for optimizing the initialization of reservoir simulators. In so doing, a further important consideration is the selection of the appropriate procedures that are available within and specific to different software packages. It is the authors’ experience that implementation of these thrusts has demonstrably enhanced the authentication of reservoir simulators through more readily attainable history matches with less required tuning. This outcome is attributed to a more systematic initialization process with a lower risk of artefacts. Of course, these benefits feed through to more assured estimates of ultimate recovery and, thence, hydrocarbon reserves.

Core-scale experimental study of relative permeability properties of CO2 and brine in reservoir rocks

Experimental studies of both drainage and imbibition displacements are needed to improve our fundamental understanding of multi-phase flow and trapping in CO2-brine systems and effectively take advantage of the large storage capacity of saline aquifers. Very few relative permeability measurements have been made and even fewer with in situ saturation measurements. Two new sets of steady state relative permeability measurements have been made in two different rock samples, and over a range of injection flow rates. These studies show that multi-phase brine displacement efficiency is strongly affected by the heterogeneity of the core. Moreover, we observe that, at any given fractional flow, different flow rates result in different CO2 saturations. Similarly, different flow rates lead to different relative permeability curves. Numerical simulations of two phase displacement are performed on one sample, and at one fractional flow of CO2. Numerical simulations demonstrate that some of the features of the saturation distributions can be qualitatively replicated. However, improvements in the correlations between porosity, saturation and capillary pressure will be needed to replicate the saturation distributions measured in the experiments.

Depletion Performance of Gas-Condensate Reservoirs

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. Introduction This paper reviews basic methods for evaluating the depletion performance of a well producing a gas-condensate fluid. In particular, we discuss initial gas-in-place estimates, inflow-performance relationships, the development and behavior of liquid saturations over both time and drainage area, and the interpretation of pressure-transient tests. Every aspect of these calculations for depletion of a gas-condensate, or any other essentially two-phase system, is implicitly dictated by the interaction between the fluid properties of the initial gas-in-place and the relative permeability properties of the reservoir rock. The simple steady-state theory forms a useful framework for understanding these interactions and often yields practical approximations for some important quantities. This theory and its relationship to commonly available laboratory measurements form the foundation for many of the methods discussed. Fluid Determination, Properties, and Descriptions Classification of a reservoir fluid as a black oil, volatile oil, gas condensate, wet gas, or dry gas is important because application of appropriate engineering practices to predict reserves and rates traditionally requires this knowledge. Fig. 1 is a schematic of a pressure/temperature (p-T) diagram for a multicomponent hydrocarbon mixture of constant composition. The region inside the envelope formed by the bubblepoint curve, critical point (C), and dewpoint curve is where liquid and vapor exist in equilibrium. Lines of constant liquid volume are shown inside this region. Fluids initially at temperature and pressure Positions I through V would be classified as a black oil, volatile oil, gas condensate, wet gas, and dry gas, respectively. Gas condensates are separated from the other fluid types by two characteristics: the condensation of a liquid phase at reservoir conditions during isothermal depletion and the retrograde (revaporization) nature of this condensation. Retrograde behavior of the condensing liquid phase can be seen by tracing the change in liquid volume along the constant-temperature line beginning at Point M in Fig. 1. After crossing the dewpoint line, the volume of liquid increases to approximately 10%at Point N and then begins to decrease with continued reduction in pressure.

The Effect OfWettability On Two-Phase Relative Penneabilities

Abstract Relating have been determined between wettability and the two-phase relative permeability saturation properties of three consolidation intergranular cores. Wettability was defined by the contact angel (θ), measured external to the porous medium, and by the ability of a fluid to spontancously imbibe into the porous system. Close control over the wettability was achieved in these tests by using synthetic cores composed of polytetrafluoroethylene (PTPE) and various pure fluid paris which displayed essencially uniform wetting behaviour with the solid. The PTPE media, which were of widely differing porousity and permeability, provided systems of fixed pore geometry which were ideal for systematic studies of the wettability variable. Certain comparisons with published work suggested that the PTPE cores were representative models of naturally occurring intergranular porous media. Results determined during the study suggested that wettability effects may predominate over influences from the detailed pore structure. Relative permeability test results indicated that the most efficient immiscible displacement was obtained with fluids capable of spontaneously imbibing into the porous media. Relative permeability saturation relations were media. Relative permeability saturation relations were virtually independent of (θ) for displacements with imbibing fluids. As (θ) was increased through values for which imbibitions did not occur, a consistent shift in the relative permeability properties of both phases was found when the media contained an initial irreducible saturation of the displacing phase. For drainags or forced displacements from a core initially saturated with one fluid, relative permeability curves were little affected when the system contact angel through the displacing phase was varied over the range of 180 to 90 degrees. The sensitivity of the relative permeability relations to contact-angel changes was strongly influenced by the saturation history of a core. Introduction and Background EFFECT OF WETIABILITY ON DISPLACEMENT THE EFFECT of wettability on immiscible displacement has been studied by many investigators over the past few decades(1). It is well recognized that the relative wetting preference displayed by oil and water for the reservoir rock has a strong influence on the behaviour of a waterflood or natural water drive. Wettability has, in fact, been described as the single most important variable affecting the recovery history of a Waferflood(2,3). Reservoir performance calculations and estimates of residual oil saturation are often based on laboratory flow tests with representative core samples believed to possess the wetting characteristics of the reservoir. An accurate assessment of the residual oil saturation is also very important for the evaluation of tertiary recovery processes(4). The influence that wettability has on the microscopic distribution and configuration of residual oil within the pore spaces of the rock could be important in the design and application of surfactant or micro-emulsion floods. Despite the large past effort that has been devoted to studies of wettability effects in porous media, the large number of recent reports on this subject indicate that many aspects are still not well understood. Rathmell et al.(4) have recently summarized some of the areas of conflict.

Discussion of the Use of Capillary Tube Networks in Reservoir Performance Studies

Abstract The paper is presented as a discussion of the work of Simon and Kelsey on the use of capillary tube networks in reservoir performance studies. The author believes that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions that are too optimistic for reservoir-scale predictions that are too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. The reason for this is that the networks are too small to permit proper scaling of longitudinal and transverse dispersion effects. Hence, as early a breakthrough as will occur with fully developed viscous fingers is not observed. Introduction It appears to us that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions which are much too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. We believe that the principal reason for this is that the Simon-Kelsey networks are too small to permit proper scaling of longitudinal and transverse proper scaling of longitudinal and transverse dispersion effects. Hence, the authors do not observe as early a breakthrough as will occur with fully developed viscous fingers. Since the authors oil recovery predictions are too optimistic for any given degree of heterogeneity, but decrease with increasing heterogeneity, Simon and Kelsey have attributed too great a degree of heterogeneity to some of the laboratory models involved in previously reported work in attempting to match the observed recovery data. Data derived from the models themselves indicate a much lesser degree of heterogeneity. MODELLING OF PORE STRUCTURE AND THE H FACTOR The mathematical model of reservoir displacement processes described by Simon and Kelsey is related processes described by Simon and Kelsey is related to the capillary network model of pore structure devised by Fatt. However, Fatt intended his model to describe the capillary pressure and relative permeability properties of small samples of reservoir rock, rather than large-scale oil reservoirs. Fatt emphasized the relationship between the form of the network as expressed by his connectivity number, 8, and the degree of similarity of the capillary pressure and relative permeability curves for his model to those of typical reservoir rocks. Fatt found that similarity required a value of 8 in the interval from 7 to 25. This is the average number of other tubes connected to the two ends of a given tube. It means that from 4 to 13 flow channels meet at each junction, on the average. For this reason, Fatt favored the use of a triple hexagonal network (B = 10) in which six tubes meet at each junction. This judgment of natural rock pore structure is supported by more recent scanning electron microscope studies. Simon and Kelsey used the double hexagonal network (B = 7) in part of the work reported in Ref. 1; but the remainder and the second article are based on a diamond grid (B = 6). Fact also found that a reciprocal relationship between tube radius and tube length was required to simulate actual rock permeability-porosity relationships. Simon and Kelsey permeability-porosity relationships. Simon and Kelsey have instead used tubes of constant length. A wide distribution of cube radii was found by Fatt to be necessary to simulate the capillary pressure curves of consolidated porous media. Pore radius distributions are typically log-normal, and the distributions used by Fatt were of this shape. They are not flat-topped distributions such as that used by Simon and Kelsey to define a heterogeneity factor, H, as the ratio of the maximum to the minimum channel radius. However, it is easy to derive for such a flat-topped distribution that the fractional average deviation for a total number of flow channels, N, is given by the following equations: ............(1a) ............(1b) SPEJ P. 352

The Effect of Temperature on the Permeability Ratio of Different Fluid Pairs in Two-Phase Systems

Results of experiments involving the isothermal displacement of a refined oil by water, nitrogen, and steam indicate that gas-oil and water-oil permeability ratios may be functions of temperature. Introduction The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made. permeability at elevated temperatures been made. Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigation are dissimilar. Edmondson found that in Berea sandstone a temperature-dependent effect was present, while Shilobod, using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A and M U. found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge permeability ratios were calculated using the Welge procedure. procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75 degrees F to 540 degrees F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study. It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system. Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75 degrees F to 500 degrees F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effects to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated). JPT P. 1037

The basis of differential staining of ascospores and vegetative cells of yeasts.

An investigation of the staining reactions of ascospores from 10 species of yeasts with 19 different dyes, showed that differentiation of spores from vegetative cells by staining depends on their relative permeability properties. Three possible staining mechanisms are discussed and examined for consistency with the data. It was also discovered that ascospores of Hansenula saturnus, which are not stained by the malachite green method, could be differentiated very satisfactorily from the vegetative cells by staining with hot rose bengal, followed by counter-staining with cold victoria blue B.

The Calculated Performance of Solution-Gas-Drive Reservoirs

Abstract Several methods are available for calculating the performance of solution-gas-drive reservoirs from the PVT properties of the oil and from the relative permeability and other properties of the formation. These methods require a number of simplifying assumptions. The present method of computation has made use of a high-speed computer to solve simultaneously the nonlinear partial differential equations that describe two-phase flow by solution-gas drive in order to calculate the performance of a reservoir. Some of the results obtained by the nonlinear partial differential equation solution are compared with those obtained with an approximate method, which has been called the semi-steady-state solution. The pressure and saturation profiles from the wellbore to outer boundary calculated by the two methods are compared for one constant-terminal-rate case and two constant-terminal-pressure cases. The agreement in these profiles, as well as in the values of average reservoir pressure and cumulative recovery, leads to the conclusion that, for most engineering calculations, the semi-steady-state method will give a reasonable approximation to the numerical solution of the differential equations describing solution-gas drive. An unfavorable (as regards ultimate oil production) set of relative permeability curve was used in the calculations in the belief that the effect of the parameters which were studied would be emphasized to a greater degree. Furthermore, the reservoir was assumed to be completely homogeneous, and these results should not be considered applicable to any other type of reservoir. Gravity effects are not considered. The absolute permeability was varied from 25 to 0.5 md. At an economic limit of 2 B/D, the recovery for a 25-md reservoir is about 1.8 times as great as that for a 0.5-md reservoir. The effect of permeability on the producing gas-oil ratio is minor. Once PVT properties of the oil and the relative permeability properties of the reservoir are fixed, the producing gas-oil ratio is found to be a function of the fraction of oil recovered.