Relative Permeability In Porous Media Research Articles

Comparative Laboratory Wettability Study of Sandstone, Tuff, and Shale Using 12-MHz NMR T1-T2 Fluid Typing: Insight of Shale

Summary Wettability is a fundamental parameter significantly influencing fluid distributions, saturations, and relative permeability in porous media. Despite the availability of several wettability measurement techniques, obtaining consistent wettability index results, particularly in tight reservoirs, remains a challenge. Nevertheless, obtaining accurate wettability indices is crucial for gaining a more profound understanding of rock properties and precisely identifying and evaluating oil recovery processes. This study adapts T1-T2 nuclear magnetic resonance (NMR) in twin plugs (cores cut in half from the middle) style wettability measurement for different reservoirs. The fluid typing in different lithologies by T1-T2 NMR is proved to be effective by introducing D2O with a modified pressurization saturation process. Therefore, demarcating the regions requires multiple experiments, including sole brine, sole oil phase, and D2O imbibition processes, to define oil and water distribution regions. Such fluid typing ability enables better accuracy in wettability characterization. The weighing method shows good agreement with the T2 spectrum but lacks the ability to differentiate fluids. It is observed that the same fluid in various porous media displays different divisions of T1/T2 ratios. The wettability index of sandstone, tuff, and shale measured by weighing and T1-T2 NMR method are compared and studied to demonstrate the applicability of different methods. The weighing method and the NMR method, as modified-Amott methods, share the same fundamental principle but differ in their measurement techniques. This study’s T1-T2 NMR wettability indices are −0.52, 0.06, and 0.14, whereas the weighing wettability indices are −0.63, 0.07, and 0.34 of sandstone, tuff, and shale, respectively. In addition to the difference in shale wettability index, there are also differences in shale porosity measured by methods with/without the ability to differentiate the fluid types. The T1-T2 NMR method is more accurate in measuring the wettability of shale because it can distinguish among free water in pores, structural water, and clay-bound water in smectitic clay minerals. If the clay-related water is not treated properly, the hydrophilicity of the shale will be overestimated. Ultimately, four types of pores (water-wet, oil-wet, mixed-wet, and unconnected pores) are classified and quantified by the proposed NMR method.

Pore-scale numerical prediction of three-phase relative permeability in porous media using the lattice Boltzmann method

Three immiscible fluids systems are often encountered in energy and environmental disciplines, especially in the oil exploration field. It is essential to enhance oil recovery (EOR) by identifying the three-phase fluid flow mechanism of oil-gas-water system in complex geological structures. In the present study, a lattice Boltzmann (LB) color gradient model for three immiscible fluid flow in three-dimensional porous media is employed and validated using five benchmarks (i.e., the multiphase spinodal decomposition; the multiphase Young-Laplace test; the liquid lens; contact angles and 3D channel layered three-phase fluid flow). The effects of wettability, viscosity ratio (M) and capillary number (Ca) on the relative permeability curves are analyzed in detail. When the wetting condition is enhanced, the results indicate that the relative permeability of non-wetting phase raises while that for the wetting phase exhibits a decline. When M is not equal 1, the relative permeability of high viscosity phase is significantly increased, while the other two phases are less affected. Meanwhile, the maximal value of relative permeability does not exceed unity because of the low porosity in the porous medium. For the influence of Ca, simulation results indicate the relative permeability shows weak sensitivity to Ca.

Relative Permeability of Porous Media with Nonuniform Pores

Most classical predictive models of relative permeability conceptualize the pores in porous media as assemblies of uniform capillary tubes with different sizes. However, this simplification may overestimate the transport capacity of porous media due to overlooking the effects of the pore nonuniformity. This study presents a simple way to quantify the effect of the nonuniformity of pore cross section on the transport characteristic of unsaturated porous media. The way is based on the index relationship between the porosity of a newly defined reference cross section and that of porous media, which satisfies the intrinsic constraints for the nonuniform porosity of cross sections in porous media. Moreover, the index factor can be captured by a newly defined parameter, called the nonuniformity factor, which is used to establish an extended Darcy’s law. Based on these, a fractal-based continuous analytical model and a fractal-based Monte Carlo model of relative permeability as well as a permeability-porosity model are established. Experimental data of five wetting-nonwetting phase systems, including the water-air, water-steam, water-nitrogen, water-oil, and oil-gas systems, are selected to assess the performance of the proposed model. The results confirm the proposed model’s capacity in capturing the transport properties of various porous media. It is found that the nonuniformity of pores can significantly increase the resistance of fluid flow and thus reduce the transport capacity of porous media.

Robust modeling of hysteretic capillary pressure and relative permeability for two phase flow in porous media

We investigate a robust and systematic modeling approach for hysteretic capillary pressure and relative permeability in porous media by using the theory of plasticity, considering that plasticity and hysteresis exhibit both irreversible physical processes. Focusing on the immiscible two-phase flow, we investigate stability analysis and find that the method based on the plasticity can yield well posedness (contractivity) and algorithmic stability (B-stability). This modeling approach can track and compute history-dependent flow properties such as residual saturation. In numerical simulation, we apply the algorithm of the 1D isotropic/kinematic hardening plasticity to reservoir simulation of gas-water flow. For weak and strong capillarity, the modeling yields strong numerical stability even for several drainage-imbibition processes. We also identify differences between with and without hysteresis, showing the importance of hysteretic capillary pressure and relative permeability. Thus, the hysteresis modeling based on the theory of plasticity is promising for robust numerical simulation of strong hysteresis.

Relative permeability for water and gas through fractures in cement.

Relative permeability is an important attribute influencing subsurface multiphase flow. Characterization of relative permeability is necessary to support activities such as carbon sequestration, geothermal energy production, and oil and gas exploration. Previous research efforts have largely neglected the relative permeability of wellbore cement used to seal well bores where risks of leak are significant. Therefore this study was performed to evaluate fracturing on permeability and relative permeability of wellbore cement. Studies of relative permeability of water and air were conducted using ordinary Portland cement paste cylinders having fracture networks that exhibited a range of permeability values. The measured relative permeability was compared with three models, 1) Corey-curve, often used for modeling relative permeability in porous media, 2) X-curve, commonly used to represent relative permeability of fractures, and 3) Burdine model based on fitting the Brooks-Corey function to fracture saturation-pressure data inferred from x-ray computed tomography (XCT) derived aperture distribution results. Experimentally-determined aqueous relative permeability was best described by the Burdine model. Though water phase tended to follow the Corey-curve for the simple fracture system while air relative permeability was best described by the X-curve.

THEORETICAL AND EXPERIMENTAL STUDY ON STRESS-DEPENDENCY OF OIL–WATER RELATIVE PERMEABILITY IN FRACTAL POROUS MEDIA

The coupled flow deformation behavior in the porous media has drawn tremendous attention in various scientific and engineering fields. It is reported that the porous media will be compressed and relative permeability in porous media will be changed as the effective stress increases. However, previous studies provided contradictory evidence for the stress-dependent irreducible water saturation and stress-dependent relative permeability. Until now, appropriate stress-dependent relative permeability curve for two-phase flow through porous media remains unclear. The goal of this work was to theoretically and experimentally study the stress-dependent relative permeability. Laboratory sample flooding tests were conducted to measure two-phase relative permeability in porous media under changing effective stress, and a corresponding theoretical model of stress-dependent relative permeability was derived to interpret the experimental results. The predictions from the proposed analytical model exhibited similar variation trends as the experimental data, which verified the theoretical model. Though the results for the stress-dependent relative permeability from previous studies are different, or even opposite, our proposed model with different conditions can provide explanations to these different results. This work provides a comprehensive experimental and theoretical study of stress-dependent relative permeability in porous media, which is beneficial to accurate performance forecasts for the coupled flow deformation behavior in porous media.

Analyzing Permeability of the Irregular Porous Media Containing Methane Hydrate using Pore Network Model Combined with CT

Gas hydrate as the 21st century new energy is viewed as prospective energy with clean, smaller pollution, and large storage characteristics. The permeability is a key parameter for gas hydrate production. In this work, pore network models combined with X-ray computed tomography (CT) were proposed to analyze the properties of gas hydrate in porous media. We studied the permeability in porous media, used the different shapes of sand including quartz, dolomite and feldspar. Experimental results show that in these three kinds of sand, the absolute permeability of quartz is the largest, feldspar is minimal. Under the same water saturation, capillary pressure of dolomite is less than quartz; water-phase relative permeability in porous media did not obvious change, while gas phase relative permeability is a big difference. Gas phase relative permeability of dolomite is smaller than the other two kinds of sand with low water saturation. However, under the high water saturation, gas phase relative permeability of dolomite is greater than the other two kinds of sand.

Modeling relative permeability of water in soil: Application of effective‐medium approximation and percolation theory

AbstractAccurate prediction of the relative permeability to water under partially saturated condition has broad applications and has been studied intensively since the 1940s by petroleum, chemical, and civil engineers, as well as hydrologists and soil scientists. Many models have been developed for this purpose, ranging from those that represent the pore space as a bundle of capillary tubes, to those that utilize complex networks of interconnected pore bodies and pore throats with various cross‐section shapes. In this paper, we propose an approach based on the effective‐medium approximation (EMA) and percolation theory in order to predict the water relative permeability. The approach is general and applicable to any type of porous media. We use the method to compute the water relative permeability in porous media whose pore‐size distribution follows a power law. The EMA is invoked to predict the relative permeability from the fully saturated pore space to some intermediate water saturation that represents a crossover from the EMA to what we refer to as the “critical region.” In the critical region below the crossover water saturation Swx, but still above the critical water saturation Swc (the residual saturation or the percolation threshold of the water phase), the universal power law predicted by percolation theory is used to compute the relative permeability. To evaluate the accuracy of the approach, data for 21 sets of undisturbed laboratory samples were selected from the UNSODA database. For 14 cases, the predicted relative permeabilities are in good agreement with the data. For the remaining seven samples, however, the theory underestimates the relative permeabilities. Some plausible sources of the discrepancy are discussed.

A NOVEL FRACTAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY IN POROUS MEDIA

Multiphase flow in porous media is very important in various scientific and engineering fields. It has been shown that relative permeability plays an important role in determination of flow characteristics for multiphase flow. The accurate prediction of multiphase flow in porous media is hence highly important. In this work, a novel predictive model for relative permeability in porous media is developed based on the fractal theory. The predictions of two-phase relative permeability by the current mathematical models have been validated by comparing with available experimental data. The predictions by the proposed model show the same variation trend with the available experimental data and are in good agreement with the existing experiments. Every parameter in the proposed model has clear physical meaning. The proposed relative permeability is expressed as a function of the immobile liquid film thickness, pore structural parameters (pore fractal dimension Dfand tortuosity fractal dimension DT) and fluid viscosity ratio. The effects of these parameters on relative permeability of porous media are discussed in detail.

A Fractal Model for the Stress-Dependent Permeability and Relative Permeability in Tight Sandstones

Stress-dependent permeability and relative permeability in porous media are important in petroleum-engineering fields. It has been shown that stress-dependent permeability and relative permeability play important roles in determination of flow characteristics for tight-sandstone porous media. In this work, novel predictive models for stress-dependent permeability and relative permeability in microporous media with lower permeability are developed on the basis of fractal theory. The predictions of irreducible water saturation, normalized porosity, normalized permeability, and the ratio Krw/Krg by the proposed model show a variation trend similar to that of the available experimental data. On the basis of the proposed normalized porosity and normalized permeability model, it is found that the normalized porosity and permeability decrease with effective stress, thus predicted results are in good agreement with former experiments. The proposed normalized porosity and normalized permeability are expressed as a function of the effective stress, rock elastic modulus, microstructural parameters, and initial irreducible water saturation. The theoretical study of relative permeability under stress demonstrates that wetting phase relative permeability is related to the effective stress, microstructural parameters, and initial irreducible water saturation.

Prediction of Relative Permeability for Multiphase Flow in Fractured Oil Reservoirs by using a Soft Computing Approach

Artificial neural networks (ANNs) are weightily parallels, distributed processors, constituting of numerous simple processing units that are used to solve the complex problems. In this paper ANN was used to present complex relation between water-oil relative permeability key points and rock and fluid properties for multiphase flow in porous media. In this research 200 relative permeability curves from Iranian carbonate were used to reach the ultimate goal. 6 key points which contains end points and the crossover points, were considered for each curve. ANN was then used to predict these key points from different rock and fluid properties. ANN presents very high correlation coefficients in the range of 0. 85 to 0. 95 for Kr key points. The results proved that ANN is an appropriated tool to predict water-oil relative permeability in porous media with high accuracy when the needed core and fluid properties are available.

Experimental Study of Temperature Effect on Oil Relative Permeability in Porous Media

In the modeling of thermal recovery processes of heavy oil, it is important to know the oil primary relative permeability in the reservoir; moreover we have to be aware of effects of the temperature on oil relative permeability as well. In this study, a sand pack of quartz (SiO2) has been used to simulate and make a porous medium. Quartz is naturally water wet. During experiments there was no change in the pore volume of the media at different temperatures because of the low expansion coefficient of quartz. The fluid used in experiments is engine oil 50. Glass pipes with length of 91cm and diameter of 2.6cm have been used in the experiments. At first, columns have been filled with sand, which sand grains had different diameters, then carbon dioxide was injected to the columns to deplete the air in the pores , then the porous media have been saturated with water to calculate the porosity using the scale model. In addition according to Darcys law in steady state, the absolute permeability was calculated. In the next step, oil was injected to columns until the water saturation reached connate water saturation and finally, water injection was begun to get residual oil saturation (Sor). Experiments results showed that increase of temperature increases the oil relative permeability, note that wetability was constant. Increasing the temperature decreases the oil viscosity then this reduction causes the fluid to move easier and its velocity increases as well.

Experimental Study of Relative Permeability of Porous Media Used in PEM Fuel Cells

This study investigated gas and liquid relative permeability, one of the important two-phase transport properties of the porous media used in proton exchange membrane (PEM) fuel cells. The experiment showed that the gas relative permeability obtained by the gravimetric analysis and neutron imaging agreed at low saturation levels, but differs at high saturation levels. The liquid relative permeability in the saturation level range of 0.3 to 0.8 was measured by neutron imaging. Because of dead air pockets in the porous materials and certain saturation levels are required to establish continuous flow of liquid water through gas diffusion media, liquid permeability at both high and low saturation levels could not be obtained. It was shown that the 3rd-order power correlation of gas permeability generally used in numerical simulation only fitted the porous media of A1 and A3 at low saturation levels.

Experimental Study of Relative Permeability of Porous Media Used in PEM Fuel Cells

not Available.

Fractal analysis of permeabilities for porous media

AbstractA fractal analysis of permeabilities for porous media, both saturated and unsaturated, is presented based on the fractal nature of pores in the media. Both the fractal‐phase permeability and the fractal relative permeability are derived and found to be a function of the tortuosity fractal dimension, pore‐area fractal dimension, phase fractal dimension, saturation, and microstructural parameters. The proposed models for permeabilities—both the phase permeability and the relative permeability—do not contain any empirical constant. The validity of the present analysis is verified by a comparison with the existing measurements, and excellent agreement between the model predictions and experimental data is found. In addition, the present work reveals that the relative permeability depends not only on saturation but also on the two fractal dimensions, pore fractal dimension (at porosity greater than 0.90), and tortuosity fractal dimension, which characterize the fractal characters of capillaries in porous media. The two fractal dimensions may be the two of the important mechanisms affecting the relative permeability in porous media, and this is a supplement to the available conclusion on relative permeability. © 2004 American Institute of Chemical Engineers AIChE J, 50: 46–57, 2004

Reconstruction of Berea sandstone and pore-scale modelling of wettability effects

We present an integrated procedure for estimating permeability, conductivity, capillary pressure, and relative permeability of porous media. Although the method is general, we demonstrate its power and versatility on samples of Berea sandstone. The method utilizes petrographical information obtained from 2D thin sections to reconstruct 3D porous media. The permeability and conductivity are determined by solving numerically the local equations governing the transport. The reconstructed microstructure is transformed into a topologically equivalent network that is used directly as input to a network model. Computed two-phase and three-phase relative permeabilities for water wet conditions are in good agreement with experimental data. We present a method for characterizing wettability on the pore-scale from measured Amott wettability indices. Simulated effects of wettability on waterflood relative permeabilities and oil recovery compare favourably with experimental results.

A technique for measuring two-phase relative permeability in porous media via X-ray CT measurements

A novel method for computing two-phase relative permeability curves from the results of spontaneous imbibition experiments is presented. Using a specially constructed imbibition cell and an X-ray Computed Tomography (CT) scanner, we obtain accurate measurement of saturation profiles along the length of cores as a function of time. The saturation profile history allows direct computation of the relative permeability for both phases from a single experiment when used in combination with a previously measured capillary pressure curve. Results are unique within experimental error. The proposed procedure works equally well for spontaneous and forced cocurrent imbibition. It was tested thoroughly using synthetic and experimental spontaneous imbibition data, for water–air and water–oil systems. Study showed that the pressure-gradient history can be neglected during calculations of air–water relative permeability; however, pressure-gradient data improves the accuracy of measurement for viscous oil flowing at high water saturation. Test results are described within the paper. Advantages include the incorporation of capillary forces and no requirement for steady-state conditions. This method is useful to measure imbibition relative permeability curves, especially in low permeability rocks at relatively low wetting phase saturations. In such systems, it is laborious to reach multiple steady states and capillary forces are significant so that classical unsteady-state techniques do not apply.

A New Method for the Analysis of Relative Permeability in PorousMedia

By combining three-dimensional digital microtomographytechniques with the lattice Boltzmann method, a new methodology is usedto analyse the relative permeability of multiphase flow in porousmedia. The results indicate that the two coupling coefficients K12 andK21 have the same magnitude, therefore the Onsager reciprocity stillholds. The results also agree well with the results of pipe flownumerical experiments.

Influence of Dead-End Pores on Relative Permeability of Porous Media

The network model is used to show that wetting phase relative permeability of porous media is only slightly influenced by the fraction of that phase trapped in dead-end pores. On the other hand, the trapping of nonwetting phase in dead-end pores is a major influence on the shape of the nonwetting phase relative permeability curve. Laboratory experiments on porous media are suggested to test these network model predictions.