Equivalent Relative Permeability Research Articles

Comparative analysis of hydrogen, methane and nitrogen relative permeability: Implications for Underground Hydrogen Storage

Underground Hydrogen Storage (UHS) is an emerging technology which aims to store terawatt-scale energy in the subsurface to alleviate daily and seasonal fluctuations in the ever-increasing renewable energy market. Depleted gas reservoirs and aquifers will be the main targets of storage which requires an understanding of the interaction between formation or cushion gas with native brine. A comprehensive comparison of the petrophysical and two-phase flow properties of the hydrogen-water, methane-water and nitrogen-water systems at in-situ conditions is the focus of our work. We conduct steady-state relative permeability experiments at 2.13 MPa and 298 K using identical capillary numbers of Nc=2.92×10−7 for all three systems. The saturation and in-situ contact angles are determined with segmentation of 3D micro-CT images. The contact angle of each system is almost identical at the irreducible water saturation, Swi, 44°, 46°, 45°, respectively, as is the interfacial tension of 72.0, 71.5 and 71mN/m, respectively. The capillary pressure-saturation relationships for each system have a maximum difference of 3.8 % which leads to approximately equivalent relative permeability in the Bentheimer sandstone core. The end-point relative permeabilities are krg0=0.049, krg0=0.045 and krg0=0.062 at irreducible water saturations of Swi=0.24, Swi=0.25 and Swi=0.23, respectively. All three gases demonstrate equivalent flow properties which indicates that both nitrogen and methane are suitable analogue gases for laboratory multiphase flow experiments and cushion gas to improve safety and the economics of commercial UHS projects. The results enable history matched depleted gas reservoir performance to be used as a guide for UHS.

Numeric determination of relative permeability of heterogeneous porous media with capillary discontinuities

Performance assessment of CO2 storage sites requires realistic modelling of the impact of heterogeneous aquifer properties on brine-CO2 flow. Heterogeneity gives rise to non-uniform saturation distributions that are affected by the balance of capillary, gravitational, and viscous forces. Since equivalent relative permeability and capillary pressure depend on saturation, their shape also varies with flow rate and gravitational phase segregation. This must be considered during performance assessment.Here we present a new workflow for the computation of equivalent relative permeability from force-balance controlled saturation distributions in heterogeneous rocks, computed with a novel continuum-scale flow solver with special provisions for material interfaces. Instead of simulating core flooding, the solver is used to recirculate phases across periodic boundaries until their distribution is in equilibrium with the applied forces.Our workflow is demonstrated on a segmented X-ray scan of a core sample of a laminated sandstone from a potential CO2 storage site in the Surat Basin, Australia, and an outcrop analogue model from Argentina. This application highlights how heterogeneity manifests in multi-phase flow functions, confirming rate dependence after eliminating capillary end effects.

Optimization of the Guiding Stability of a Horizontal Axis HTS ZFC Radial Levitation Bearing

This document presents a study on the optimization of the 3D geometry of a horizontal axis radial levitation bearing with zero-field cooled (ZFC) high-temperature superconductor (HTS) bulks in the stator, and radially magnetized permanent magnet (PM) rings in the rotor. The optimization of component dimensions and spacing to minimize the volume or cost concerning only the maximization of the levitation force was previously studied. The guidance force and guiding stability depend on the spacing between PM rings in the rotor and between the rings of HTS bulks in the stator. This new optimization study aims to find the optimum spacing that maximize the guidance force with given HTS bulk and PM ring dimensions while maintaining the minimum required levitation force. Decisions are taken using the non-dominated sorting genetic algorithm (NSGA-II) over 3D finite element analysis (FEA). A simplified electromagnetic model of equivalent relative permeability is used on 3D FEA to reduce numerical processing and optimization time. Experimental prototypes were built to measure magnetic forces and validate appropriate values of equivalent magnetic permeability. An analysis of stable and unstable geometry domains depending on the spacing between rings of HTS bulks and PM rings is also done for two HTS bulk sizes.

Hash Unit Cell Shape Used To Enhancement Gain and Bandwidth of Metasurface Antenna

In this paper, Low-profile, high gain and wideband antenna loaded with a single layer metasurface are proposed. The process of adding the metasurface layer depends on the Fabry Pérot technology, which required existing an air gap among the slot antenna and the metasurface layer. The metasurface layer consists of an array of 4 × 4 unit elements placed on a Roger Ro4003C substrate layer with a thickness of 2.5mm. Hash shape is used as a radiating element. The metasurface MS is acting as left-hand material in which both permittivity and permeability are negative, leading to negative refractive indexing. The emitted waves from the slot antenna are affected by a set of unit cells on the metasurface MS above the slot antenna because of the structure’s equivalent relative permeability and permittivity changes, and the slot antenna performance changes accordingly. The antenna works at a frequency of 6.75 GHz as a resonant frequency with an improvement in the bandwidth value for the metasurface antenna to get a value of 2.2 GHz instead of 390 MHz for the slot antenna. The proposed antenna has a 37 % bandwidth impedance starting at 4.7 GHz and ending at 6.9 GHz with a 7.43 dB gain value. The suggested antenna is useful for use with Wi-Fi applications.

Determination of the Effective Electromagnetic Parameters of Complex Building Materials for Numerical Analysis of Wireless Transmission Networks

In this paper, we present the method for determination of effective electromagnetic parameters of complex building materials. By application of the proposed algorithm, it is possible to analyze electromagnetic field distribution for large-scale problems with heterogeneous materials. The two-dimensional numerical model of building components (hollow brick) with periodic boundary conditions was solved using the finite-difference time-domain method (FDTD) and discussed. On this basis, the resultant transmission coefficient was found and then the equivalent relative permeability and electric conductivity of heterogeneous dielectric structures, in the developed homogenization algorithm, were identified. The homogenization of material properties was achieved by performing a multi-variant optimization scheme and finally, selecting optimal electric parameters. Despite the analysis of heterogeneous building materials, the presented algorithm is shown as a tool for the homogenization of complex structures when scattering of a high-frequency electromagnetic field is considered.

Tensor Analysis of the Relative Permeability in Naturally Fractured Reservoirs

Summary Fluid evidence shows that prediction of water breakthrough and oil recovery from fractured reservoirs cannot be performed accurately without upscaled relative permeability functions. Relative permeability is commonly assumed to be a scalar quantity, although the justification of that—specifically for naturally fractured reservoirs (NFRs)—is rarely attempted. In this study, we investigate the validity of this scalar-quantity assumption and how it affects fracture/matrix equivalent relative permeabilities, kri(Sw), achieved by a numerical simulation of unsteady-state waterflooding of discrete-fracture/matrix models (DFMs). Numerical determination of relative permeability requires a realistic model, a spatially adaptive simulation approach, and a sophisticated analysis procedure. To fulfil these requirements, we apply the discrete-fracture/matrix modeling to well-characterized outcrop analogs at the hectometer to kilometer scale. These models are parameterized with aperture and capillary entry pressure data, taking into account variations from fracture segment to segment, trying to emulate in-situ conditions. The finite-element-centered finite-volume method is used to simulate two-phase flow in the fractured rock, while also considering a range of wettability conditions from water-wet to oil-wet. Our results indicate that the fracture/matrix equivalent relative permeability is a weakly anisotropic property. The tensors are not necessarily symmetric, and the absolute-permeability tensor is the most influential factor, determining the level of anisotropy of kri. The anisotropy ratio (AR) changes with saturation, is influenced by the fracture/matrix-interface wetted area (Awf), and differs for each phase. In addition, the diagonal terms of the equivalent relative permeability tensor (krii), determined using our novel approach, can be different from those obtained using the assumption that kri is scalar. The magnitude of the difference is controlled by the absolute permeability, wettability, flow rate, and orientation of the fractures in the model. It is worth mentioning that the type and direction of imbibition can be determined by off-diagonal terms of the kri tensor. Furthermore, krii largely depends on the direction of the waterflood along the i-axis.

Characterization of Hysteretic Multiphase Flow from the MM to M Scale in Heterogeneous Rocks

Incorporating mm-m scale capillary pressure heterogeneity into upscaled numerical models is key to the successful prediction of low flow potential plume migration and trapping at the field scale. Under such conditions, the upscaled, equivalent relative permeability incorporating capillary pressure heterogeneity is far from that derived conventionally at the viscous limit, dependent on the heterogeneity structure and flow rate, i.e. dependent on the capillary number. Recent work at the SCA 2017 symposium (SCA2017-022) demonstrated how equivalent functions can be obtained on heterogeneous rock cores from the subsurface under drainage conditions; going beyond traditional SCAL. Experimental observations using medical CT scanning can be combined with numerical modelling so that heterogeneous subsurface rock cores can be directly characterized and used to populate field scale reservoir models. In this work, we extend this characterization approach by incorporating imbibition cycles into the methodology. We use a Bunter sandstone core with several experimental CO2 – Brine core flood datasets at different flow rates (2x drainage, 1x imbibition and 2x trapping) to demonstrate the characterization of hysteretic multiphase flow functions in water-wet rocks. We show that mm-m scale experimental saturations and equivalent, low flow potential relative permeabilities can be predicted during drainage and imbibition, along with trapping characteristics. Equivalent imbibition relative permeabilities appear as a function of capillary number, as in the drainage cases. We also find that the form of capillary pressure function during imbibition has a large impact on the trapping characteristics, with local heterogeneity trapping reduced (or removed), if the capillary pressure drops to zero, or below at the residual saturation.

Cyclic injection of CO<SUB align="right">2 into a saline aquifer with extended interface

Cyclic CO2 injection is considered to be an effective method to maximise CO2 dissolution in hydrocarbon reservoirs (Reznik et al., 1984; Monger et al., 1991) and saline aquifers (Zhang and Agarwal, 2012; Dusseault et al., 2012). Gravity override and evolution of a transition zone have large effects on the development of a saturation transition zone between the pure host fluid and the injected gas. In this paper, equivalent relative permeability functions are derived to address the effect of gravity override, allowing reduction of the problem dimension from 2D to 1D. An analytical solution for saturation distribution in a cyclic drainage-imbibition process is obtained. To incorporate the solubility of CO2 in the aqueous phase, a one-way coupled approximation is used and a numerical solution is proposed for derivation of compositional distribution of the chemical species. Information about saturation distribution from the analytical solution provides saturation distribution over time and distance, and this is substituted in the concentration distribution equation. In contrast to previously well-studied analytical solutions (e.g., Orr, 2007), this hybrid scheme includes the effect of kinetic mass transfer and dispersion, and provides a reasonable approximation for saturation-concentration distribution during injection.

Obtaining the secondary impedance of single-sided linear induction motor with a double layer reaction rail: a new approach

In the performance calculations of single-sided linear induction motor (SLIM),the equivalent circuit technique (ECT) is used. In this paper, a new approach is proposed for obtaining the secondary impedance of single-sided linear induction motor (SLIM) with a double layer reaction rail by using the layered secondary model. The proposed method improves the ECT technique by considering the saturation effect and the non-linear complex equivalent relative permeability. This study also examines the contributions of other electromagnetic effects, such as longitudinal end effect and transverse edge effect as well. Our method is applied to the SLIM and computed results of the method are compared to the experimental results of the previous studies. This evaluation proved that the outcomes of the proposed method are in accordance with the experimental results widely studied in the literature.

Power-frequency magnetic shielding of heavy-current conductors by rectangular shields

Metallic enclosures of rectangular shape (e.g. galvanised iron trunking) are often installed in large buildings for the purpose of mechanical protection. Recently shielding performance of such enclosures has been of interest as a result of concerns about power-frequency magnetic field interference. The paper addresses shielding characteristics of rectangular shields, based on theoretical discussion, numerical simulations and laboratory experiments. It is found that both field reflection and field attenuation are two key factors, determined by impedance and skin depth ratios, respectively. Galvanised iron trunking can be approximately modelled as a linear shield with a constant equivalent relative permeability, the value of which is proportional to current magnitude. Shielding impact of shield parameters and source orientation, as well as guidelines for trunking design also discussed.