Permeability Regime Research Articles

Pore-scale insights into relative permeability in strongly and weakly wet natural fractures: A Lattice Boltzmann Method 2D simulation study

The simplified view of two-phase flow, such as oil and gas, in a fracture is often assumed to occur in a stratified behavior. However, recent studies and production practices have revealed that two-phase flow in fractures exhibits diverse flow patterns. This paper investigates the control of the fracture aperture, fluids viscosity, and wettability on two-phase flow in a 2D cross section of a 3D Berea fracture. Lattice Boltzmann Method (LBM) simulations are used to model the impact of these properties on relative permeability curves. Notably, in strongly wet fractures, two distinct permeability regimes emerge. High aperture values exhibit behavior resembling parallel planes, while low aperture values lead to a linear decrease in permeability due to fluid interactions between fracture surfaces. Conversely, anomalous behavior of the relative permeability curves is identified in weakly wet fractures within specific aperture ranges. This behavior is associated with the occurrence of specific flow patterns within the fracture. Results also emphasize that changes in viscosity ratio do not affect the presence or the saturation range of the anomalous behavior but do influence its intensity for each fluid. Comparisons with Poiseuille profile equations reveal the limited impact of the fracture roughness. These findings enhance our understanding of the interactions between aperture, viscosity, and wettability and how they control the shape of the relative permeability curves. These curves are pivotal parameters for the continuum scale modeling (reservoir models) in oil and gas application, for instance.

Seismic Time-lapse Effects of Hydrocarbon Production on the Pressure, Porosity and Permeability Regimes in FUBA Field, Onshore Niger-Delta, Nigeria

Seismic Time-lapse Effects of Hydrocarbon Production on the Pressure, Porosity and Permeability Regimes in FUBA Field, Onshore Niger-Delta, Nigeria

A Model of Stress-Damage-Permeability Relationship of Weakly Cemented Rocks under Triaxial Compressive Conditions.

To unravel the permeability variation mechanism of weakly cemented rocks (WCR), the paper conducted triaxial permeability tests on weakly cemented sandstones (WCS) collected from the Jurassic formation in northwest China. The paper identified the correlation of WCS permeability versus porosity, cementation structure, and mineral composition, further developing a model to characterize the WCS stress-damage-permeability relationship. The research indicated that the WCS permeability was initially high due to the naturally high porosity, large pore diameter, and loose particle cementation, thus favoring a significant decline as pore convergence in the compaction stage. In the residual stage, kaolinite and montmorillonite minerals disintegrated into water and narrowed fractures, causing a slight permeability increase from the initial to the maximum and residual stages. The WCS matrix fracturing was phenomenologically accompanied by clay mineral disintegration. By assuming that the matrix can be compressed, jointed, and fractured, the paper defined a damage variable D and accordingly developed a stress-damage-permeability relationship model that incorporated matrix compression, jointing, and fracturing. The model can describe the WCS permeability regime regarding the high initial permeability and slight difference of the maximum and residual permeabilities versus the initial.

Acoustic Impedance Inversions for Offshore CO2 Storage: South Georgia Embayment, United States

This study builds and expands on previous CO2 storage resource assessment studies of the southeastern offshore Atlantic margin by providing a detailed evaluation on how rock porosities and permeabilities are distributed across the Upper Cretaceous strata restricted to the South Georgia Embayment (SGE). Using legacy industry two-dimensional seismic reflection and well data, this assessment is the first application of multiple seismic inversion techniques in this area. This workflow provides a reliable and repeatable model-based inversion which gives an improved image to discriminate lithology and predict porosity. The workflow is applicable to future CO2 storage resource assessment studies elsewhere. The inversion results indicate that distinct porosity and permeability regimes are present and distributed in the Upper Cretaceous strata within the SGE. The impedance and porosity relationships show well-founded and reliable correlation. These relationships reveal low impedance coincident to the high porosity intervals which are proposed as potential reservoir intervals for CO2 storage. In addition, the result shows that the Upper Cretaceous strata have two main potential reservoirs in the lower part. These are overlain by a thick impermeable interval, mostly shale, which has high impedance, low porosity, and low permeability and extends within the SGE. This result is in agreement with a previous study that also proposed two significant storage reservoirs for CO2 in the Upper Cretaceous strata. Since porosity distribution is estimated using multiple methods, it follows the trends of seismic signature and structures of the Upper Cretaceous strata. The extracted values of porosity, ranging from 15 to 36%, and permeability, ranging from 1 to 100 mD, are close to the measured values from the well core data at the Upper Cretaceous strata interval.

Resistance and mobility functions for the near-contact motion of permeable particles

A lubrication analysis is presented for the resistances between permeable spherical particles in near contact,$h_0/a\ll 1$, where$h_0$is the minimum separation between the particles, and$a=a_1 a_2/(a_1+a_2)$is the reduced radius. Darcy's law is used to describe the flow inside the permeable particles and no-slip boundary conditions are applied at the particle surfaces. The weak permeability regime$K=k/a^{2} \ll 1$is considered, where$k=\frac {1}{2}(k_1+k_2)$is the mean permeability. Particle permeability enters the lubrication resistances through two functions of$q=K^{-2/5}h_0/a$, one describing axisymmetric motions, the other transverse. These functions are obtained by solving an integral equation for the pressure in the near-contact region. The set of resistance functions thus obtained provide the complete set of near-contact resistance functions for permeable spheres and match asymptotically to the standard hard-sphere resistances that describe pairwise hydrodynamic interactions away from the near-contact region. The results show that permeability removes the contact singularity for non-shearing particle motions, allowing rolling without slip and finite separation velocities between touching particles. Axisymmetric and transverse mobility functions are presented that describe relative particle motion under the action of prescribed forces and in linear flows. At contact, the axisymmetric mobility under the action of oppositely directed forces is$U/U_0=d_0K^{2/5}$, where$U$is the relative velocity,$U_0$is the velocity in the absence of hydrodynamic interactions and$d_0=1.332$. Under the action of a constant tangential force, a particle in contact with a permeable half-space rolls without slipping with velocity$U/U_0=d_1(d_2+\log K^{-1})^{-1}$, where$d_1=3.125$and$d_2=6.666$; in shear flow, the same expression holds with$d_1=7.280$.

Utilizing cores for characterising the temperature and permeability regimes in a litho-stratigraphic model of the Montserrat geothermal system, Montserrat (Lesser Antilles arc, West Indies)

Cores samples are vital in the characterization of heterogeneous volcanic geothermal environments. Continuous cored intervals, representative of the subsurface formation, can help to validate geological and thermal classifications previously interpreted from drill cuttings. More importantly, core samples can help to improve our understanding of controls on fluid flow, as direct permeability measurements are attainable. In this study, we conduct petrological and petrophysical analyses on three cores (Core 1, Core 2 and Core 3) obtained from the well MON-3, drilled within the hydrothermal system located in Montserrat, Lesser Antilles arc, West Indies. We present a litho-stratigraphic model of the geothermal system. Contrasting lithologies (sandstone, limestone and interbedded silicified tuff) and mineralogies (calcite vs plagioclase) from Core 3 (2109 – 2116.5 mbsl) contributed to constraining a volcanic-sedimentary unit (∼1900 – 2200 mbsl) while pumice textures of Core 1 (1478 – 1482.6 mbsl) and Core 2 (1700 – 1705.3 mbsl) helped to classify a subaerial volcanic unit (∼1200 – 1900 mbsl). Integrating classified alteration assemblages in the model with downhole temperature logs, we propose that the thermal regime of the hydrothermal system was hotter in the past based on evidence of epidote and actinolite observed at depths less than 1200 mbsl. Lastly, we infer that the primary permeability of carbonate formations or secondary fracture permeability developed by a SW and WNW fault zone in a shallower volcanic sedimentary unit (∼900 – 1200 mbsl) could be influences on potential feedzone locations in the wellbore. This could be supported by the relatively highest measured permeabilities (10−18 – 10−17 m2) in a carbonate sample of Core 3 and fractured samples of Core 2. Overall, the improved characterization of litho-units, alteration assemblages and permeable zones with possible influences on fluid flow, can be used to enhance previous numerical and geophysical models of Montserrat's geothermal system.

Pressure-driven pipe flow of semi-dilute and dense suspensions over permeable surfaces

We study pressure-driven suspensions of non-colloidal, non-Brownian, and rigid spheres in a Newtonian solvent where the pipe surface is replaced by porous media using numerical simulations. We examine various values of the permeability of the porous medium K, while we keep the porosity and the thickness of the porous layer constant to clarify the effect of the permeable wall on the suspension flows at bulk particle volume fractions 0.1 ≤ ϕb ≤ 0.5. In the limit of vanishing inertia, the rate of suspension flow decreases as the bulk volume fraction ϕb increases and it builds up as the permeability of the porous media increases. There are also two different regimes characterizing the dimensionless slip velocity normalized by both shear rate and penetration depth, namely, the strong permeability regime and the weak permeability regime. In the former, the solvent penetrates deeper and the streamwise velocity at the interface increases with the porous media permeability, while in the latter, the fluid cannot go through the porous media deeply and the variation of the slip velocity with the permeability is small. Our results might suggest a new passive technique to reduce drag by enhancing the rate of suspension flow in devices where the suspension transport is crucial. It might also offer basic insights for the extension to the flow of suspensions over and through complex porous media.

Collision rates of permeable particles in creeping flows

Binary collision rates are calculated for the permeable particles undergoing (i) Brownian motion, (ii) gravity sedimentation, (iii) uniaxial straining flow, and (iv) shear flow. Darcy's law is used to describe the flow inside the permeable particles, and no-slip boundary conditions are applied at particle surfaces. A leading-order asymptotic solution of the problem is developed for the weak permeability regime K=k/a2≪1, where k=12(k1+k2) is the mean permeability and a=a1a2/(a1+a2) is the reduced radius; ai, ki (i = 1, 2), respectively, is the radius and permeability of each particle. The resulting collision rates are given by the quadrature of the pair mobility functions for permeable particles in the near-contact lubrication region and size-ratio-dependent parameters obtained from standard hard-sphere pair mobility functions. Collision rates in shear flow vanish below a critical value of the permeability parameter K* that increases with diminishing size ratio. The analogous problem of pair collision rates of particles with small-amplitude surface roughness δa is also analyzed. The formulas for the collision rates of rough particles provide accurate analytical approximations for the collision rates of permeable particles for all four aggregation mechanisms and a wide range of size ratios using an equivalent roughness δ=0.72K2/5.

Tunneling modes induced by interface states in 1D photonic crystals with single negative materials

We investigate the electromagnetic wave propagating in one dimensional photonic crystals with alternating layers of negative permittivity materials and negative permeability metamaterials. The band structure and transmission spectra are obtained. In the negative effective permittivity and negative effective permeability regime, we find new interface modes propagating along the interfaces between the two different media with even and odd parities, respectively. For the oblique incident case, the new propagation modes result in the emergence of a transmission band within the zero-ϕeff gap of these photonic crystals. By adjusting the plasma density or the thickness of the plasma layer, the zero-ϕeff gap as well as the transmission band of the interface modes can be tuned, which can facilitate the design of tunable filters at the microwave frequency range.

Computational study of cobalt-modified nickel-ferrite/PZT magnetoelectric composites for voltage tunable inductor applications

Control of magnetic permeability through voltage in magnetoelectric materials promises to create novel voltage tunable inductors. Domain-level phase field modeling and computer simulation are employed to study magnetoelectric composites of Co-modified NiCuZn ferrite and PZT, where ferrite outperforms metallic magnetostrictive materials at high frequencies important for inductor applications. The simulations focus on the interplay between magnetocrystalline anisotropy and stress-induced anisotropy and reveal different regimes of permeability and tunability behaviors. It is shown that the permeability and its tunability can be significantly increased by reducing the intrinsic magnetocrystalline anisotropy through doping NiCuZn-ferrite with Co2+ to form solid solution (1-x)(Ni0.6Cu0.2Zn0.2)Fe2O4-xCoFe2O4, and the optimal performance is achieved at vanishing magnetocrystalline anisotropy constant K1 = 0 corresponding to composition x∼0.02. The findings are confirmed by complementary experiments with good agreements. The effect of internal bias stress is further investigated, which is shown to shift the permeability regimes and thus provides an effective engineering technique to optimize the voltage tunable inductor performance. A tunability as high as ∼500% is obtained under the optimal condition, which is much higher than that obtained in conventional high-frequency voltage tunable inductors.

The effect of the dielectric layer thickness on the negative permeability in metamaterials

In this work, we investigate the influences of the dielectric layer on the magnetic resonance of the cut-wire pair structure (CWP). The interaction between the cut-wires is modeled through a LC circuit, based on which, the magnetic resonant frequency is calculated. Furthermore, the dependence of the resonant bandwidth on the structure parameters is also determined. By tuning the dielectric layer thickness, we obtained a noticeable broadening of the negative permeability regime of 17%, which represents the enhancement of the magnetic resonance. A good agreement between the theory, simulation, and practical experiment has been demonstrated. We believe that our results should be consequential with regard to the determination of the mechanism behind the wave-matter interaction in the GHz frequency regime.

Seismic Signatures of Hydrothermal Pathways Along the East Pacific Rise Between 9°16′ and 9°56′N

AbstractWe apply wave equation‐based techniques to 2‐D seismic data to characterize the nature of zero‐age upper crust at the East Pacific Rise from 9°16′ to 9°56′N. The final velocity model reveals a number of low‐velocity anomalies, complex in shape, extending down to ~1 km below the seafloor. We attribute them to the presence of hydrothermal flow. Depending on their spatial correlation with the previously identified tectonic discontinuities in bathymetry and presence of venting, we classify them as downgoing and upgoing pathways, respectively. This distinction is not always clear; within the third‐order discontinuities at 9°20′ and 9°37′N, both pathways may be present. The region north of 9°44′N, known for its magmatic robustness and volcanic activity, is represented by five low‐velocity perturbations. Three of these anomalies are spatially correlated with the fourth‐order discontinuities and attributed to the presence of the on‐axis recharge zones. The remaining two anomalies underlie two vent clusters, marked as hydrothermally active sites after the last documented eruption event. These velocity anomalies can be thus identified as the up‐flow pathways or at least their remnants. By comparing our results to the available interdisciplinary data sets, we show that the interaction between the tectono‐magmatic and hydrothermal processes is not straightforward due to different timescales at which they operate. However, for developing, maintaining, and driving vigorous, high‐temperature hydrothermal flow, the high crustal permeability and high thermal regime must coexist in time and space.

Fluid mud consolidation delayed by extracellular polymer substances

ABSTRACTA strain of bacterium identified as Burkholderia vietnamiensis was newly isolated and screened from mud deposited in a harbour basin. The effects of B. vietnamiensis on the fluid mud consolidation and the extracellular polymer substances (EPS) secreted by the microorganisms were examined in laboratory experiments. The experiments revealed the important characteristics of the EPS and their critical contents for nautical-depth applications. The self-weight consolidations in the settling and permeability regimes were best predicated by an exponential equation and a logarithmic equation, respectively. EPS cannot change the trend of sediment settling and consolidation, but its content is negatively correlated with the velocity of sediment consolidation. EPS with high polysaccharide/protein ratio is a potential reference to select bacteria for nautical-depth applications. The critical EPS content that would effectively extend the usage time of nautical depths was estimated as 2.34 g/l.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule.For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations.The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

A study of gas transport and production characteristics with non-Darcy flow in tight gas reservoirs

Tight gas reservoirs (TGRs) are important unconventional resources. In such reservoirs, the permeability is much lower than that in conventional gas reservoirs. While, the Klinkenberg effect is widely considered in gas reservoirs, it is not enough to depict complicated non-Darcy effects in certain TGRs including the nano-scale pores. It is also not clear that when complicated non-Darcy effects should be considered, and how strong these effects in TGRs. In this paper, a new model which couples both non-Darcy flow and stress effects was established. The flow regimes involve viscous flow, slippage flow, transition flow, and molecular-free flow. The impacts of stress effect on both the absolute permeability and non-Darcy flow regimes were incorporated as well. After that, the model was validated using experimental data. Finally, the model was employed to identify the critical conditions that Darcy flow, slippage flow, or complicated non-Darcy flow regimes should be accounted in different TGRs. The results show that when the permeability is lower than 10−2 md, there is transition flow in TGRs, and the gas production will be underestimated if only viscous and slippage flows are considered; when the permeability is higher than 10−1 md, Knudsen number is small which indicates that the slippage flow is slight, and the non-Darcy flow has very little impact on gas production. [Received: December 9, 2015; Accepted: June 4, 2016]

A study of gas transport and production characteristics with non-Darcy flow in tight gas reservoirs

Tight gas reservoirs (TGRs) are important unconventional resources. In such reservoirs, the permeability is much lower than that in conventional gas reservoirs. While, the Klinkenberg effect is widely considered in gas reservoirs, it is not enough to depict complicated non-Darcy effects in certain TGRs including the nano-scale pores. It is also not clear that when complicated non-Darcy effects should be considered, and how strong these effects in TGRs. In this paper, a new model which couples both non-Darcy flow and stress effects was established. The flow regimes involve viscous flow, slippage flow, transition flow, and molecular-free flow. The impacts of stress effect on both the absolute permeability and non-Darcy flow regimes were incorporated as well. After that, the model was validated using experimental data. Finally, the model was employed to identify the critical conditions that Darcy flow, slippage flow, or complicated non-Darcy flow regimes should be accounted in different TGRs. The results show that when the permeability is lower than 10−2 md, there is transition flow in TGRs, and the gas production will be underestimated if only viscous and slippage flows are considered; when the permeability is higher than 10−1 md, Knudsen number is small which indicates that the slippage flow is slight, and the non-Darcy flow has very little impact on gas production. [Received: December 9, 2015; Accepted: June 4, 2016]

Modelling of Hydrogen Permeability of Structural Materials Through Protective Coating Defect

An efficient reduction of gaseous hydrogen isotope permeation through a metal wall is essential in several applications like hydrogen storage and distribution, hydrogen embrittlement protection, and tritium inventory in future fusion reactors like ITER. Hydrogen permeation barrier films often exhibit lower efficiency than anticipated. It is very difficult to identify and quantify the responsible mechanism since the defects can be of submicrometer dimensions and very sparsely populated. We considered hydrogen permeability through a cylindrical membrane (barrier) in the presence of protective coating defect at the inlet surface of a structural material. For various materials, when the processes of diffusion, desorption and dissolution are limiting, we present the mathematical models in the form of boundary value problems with non-linear and dynamic boundary conditions. On the basis of the implicit difference scheme, a computational algorithm of a boundary value problems solution is developed. Numerical simulation results of hydrogen permeation flux and diffusant distribution are presented. Qualitative regularities of steady state permeability regime establishment and delay times registered experimentally and depending on geometric characteristics of the membrane and physical parameters are identified.

Analytical modeling of the transient response of a coil encircling a ferromagnetic conducting rod in pulsed eddy current testing

Analytical solutions are obtained in the time domain for the electromagnetic response to the leading edge of a square pulse excitation of a multiple turn current coil, encircling a long ferromagnetic rod, in the linear permeability regime. The resulting equations, obtained using a magnetic vector potential formalism, describe the time-dependent progression of flux into and along the rod. Results are in agreement with finite element solutions obtained for the same geometry. The work is motivated by the requirement for rapid analytical solutions and insight into pulsed eddy current response during inspection of multilayer aluminum aircraft structures in the vicinity of ferrous fasteners.

Petrophysical characterization of the South Georgia Rift Basin for supercritical CO2 storage: a preliminary assessment

The Triassic–Jurassic South Georgia Rift (SGR) Basin, buried beneath Coastal Plain sediments of southern South Carolina, southeastern Georgia, western Florida, and southern Alabama, consists of an assemblage of continental rift deposits (popularly called red beds), and mafic igneous rocks (basalt flows and diabase sills). The red beds are capped by basalts and/or diabase sills, and constitute the target for supercritical CO2 storage as part of a Department of Energy funded project to study the feasibility for safe and permanent sequestration. The purpose of this research is to evaluate subsurface suitability for underground CO2 storage in terms of the local and regional distribution of porous and permeable reservoirs. In addition, unlike shale-capped CO2 reservoirs, very little is known about the ability of basalts and diabase sills to act as viable seals for CO2 storage. New results demonstrate the presence of confined porous rocks that may be capable of storing significant quantities of supercritical CO2. Reservoir thicknesses as high as 420 m and an average porosity as high as 14 % were obtained. The SGR Basin manifests distinct porosity–permeability regimes that are influenced by the depositional environments. These are: a high-porosity, medium/low-permeability zone associated with lacustrine deposits, a medium/low-porosity, low-permeability zone dominated by fluvial fine- to very fine-grained sandstone, and an extremely low porosity and permeability zone characterized by fluvial and alluvial-fan deposits. Analyses further show that the basalt flows and diabase sills are characterized by low porosity as well as high seismic velocities and densities that are favorable to caprock integrity.

A comparison of variational formats for porous media subjected to dynamic loading

AbstractThis paper presents a comparison of two variational formats for fully saturated porous media subjected to dynamic loading, whereby the general situation of relative fluid acceleration is considered: (1) the classical three‐field (u, p, w)‐format and (2) a novel two‐field (u, p)‐format, where the seepage velocity w is a spatially ‘local’ field whose treatment resembles that of internal variables in material models. The limited numerical comparison shows that the (u, p)‐format competes well with the (u, p, w)‐format. Indeed, it is consistent with the general acceleration modeling in the full range of permeabilities. Moreover, in the low permeability regime (where the magnitude of w is insignificant), the new format reflects the situation pertinent to ‘added‐mass’ and is more efficient than the classical (u, p, w)‐format. Finally, the (u, p)‐formatcan conveniently be implemented in existing FE‐codes based on the ‘added mass’ formulation. Copyright © 2010 John Wiley & Sons, Ltd.