Directional Permeability Research Articles

REV and Three-Dimensional Permeability Tensor of Fractured Rock Masses with Heterogeneous Aperture Distributions

This study performed a representative elementary volume (REV) and 3D equivalent continuum study of rock fractures based on fluid simulations of 3D discrete fracture networks (DFNs). A series of 3D DFNs with heterogeneous aperture distributions (the DFN-H model) and uniform apertures (the DFN-I model) were established, in which the fractures were oriented according to the geological field mapping of a high-level radioactive waste candidate site in China. The 3D DFNs of the different model sizes were extracted and rotated in a number of directions to check whether there was a tensor quality of the permeability at a certain scale. The results show that aperture heterogeneity increases the REV size and results in a necessarily larger model size to reach an equivalent continuum behavior, and this effect is more obvious when the fracture density is smaller. The shape of the 2D permeability contour is irregular, with some breaks when the model size is small. As the model size increases, its shape gradually tends to become smooth and approaches an ellipse. The shape of the permeability contours of the DFN-H model is slender compared to the DFN-I model, indicating a larger difference between the minimum and maximum values of the permeability. For the DFN-H model, there is no appropriate approximation for the equivalent permeability tensor over the studied model size range, whereas a good fit of the permeability ellipsoid is obtained for the DFN-I model, and the 3D directional permeability is calculated at this model scale. The corresponding magnitude and direction of the principal permeability are obtained, which can be viewed as the equivalent permeability tensor for the approximated continuum medium.

A semi-theoretical method for determining the permeability tensor of fractured rock masses in three-dimensional space

The permeability tensor is a critical parameter for analyzing the hydraulic behavior of anisotropic permeability in fractured rock masses. However, determining this tensor for three-dimensional (3D) fractured rock masses has proven to be challenging and resource-intensive. Both field tests, requiring numerous costly in situ tests, and numerical experiments, hindered by complex discrete fracture networks with a high fracture density, present difficulties in obtaining accurate results. In response, this study proposes a semi-theoretical method for determining the permeability tensor of 3D fractured rock masses, significantly reducing labor and economic costs. The proposed method focuses on establishing the theoretical relationship of directional permeabilities in a 3D space, with emphasis on the properties of the permeability tensor and the influence of fractures' geometry on the flow rate. To facilitate the construction of the method, anisotropic ellipse and ellipsoid are introduced, providing a description of permeability anisotropy. With this innovative approach, engineers can calculate the permeability tensor even when only one value of permeability is available along any flow direction. The utilization of the anisotropic ellipse and ellipsoid concepts helps simplify the determination process. Through numerical experiments, the method is validated and its accuracy demonstrated, making it a valuable tool for analyzing the hydraulic behavior of 3D fractured rock masses.

NUMERICAL SIMULATION METHOD IN LOW PERMEABLE ANISOTROPIC RESERVOIRS IN ORDER TO INCREASE OIL RECOVERY


 
 The object of study is the filtration process in weakly permeable anisotropic formations (SAP). The work is devoted to the evaluation of the process of oil-bearing formation depletion, using as a criterion the distribution of reservoir pressure near the system of production and injection wells, taking into account the anisotropy of the permeability of the oil phase. In the course of the study, a combined numerical modeling method based on the finite element and finite difference methods is presented, which allows determining the value of reservoir pressure at any point in the computational domain. The finite-element-difference method proposed in this paper, which combines the advantages of the finite-element method and the finite-difference method to solve the nonstationary piezoelectric conductivity problem, taking into account the heterogeneous distribution of various filtration parameters within the deformed formation and at its boundaries, allows us to adequately calculate the distribution of reservoir pressure in real-world well operation conditions, which gives a number of advantages over existing methods. It was found that the effect of oil phase permeability in the shear direction dominates the effect of permeability in the axial directions. This is due to the fact that, according to the information obtained, for the effective use of anisotropic low-permeability formations, it is necessary to place production and injection wells in areas with relatively low anisotropy of formation permeability, especially to avoid areas with the presence of shear permeability of the formation. It is important to locate wells so that, on the one hand, there is no blockage of oil from the low permeability side, and, on the other hand, there is no rapid depletion of the formation from the high permeability side and the mutual exchange between the production and injection wells does not stop. When placing a system of production and injection wells in anisotropic formations of an oil field, it is necessary to conduct a systematic analysis of the surrounding anisotropy of the formations in order to place them in such a way that would ensure effective dynamics of filtration processes around these wells and increase oil recovery.
 
 
 
 
 

Physics of generalized couette flow of immiscible fluids in anisotropic porous medium

This study presents an investigation on the generalized Couette flow of two immiscible Newtonian fluids in an anisotropic porous medium. The flow occurs between two parallel plates, driven by the combined effects of an axial pressure gradient and the movement of the upper plate. The region between the plates is filled with an anisotropic porous medium characterized by directional permeability. An exact solution is derived for the proposed problem by considering appropriate boundary and interface conditions. The slip condition is employed at the lower plate of the channel which has a significant role in the flow mechanics of fluids flowing through porous medium. The effects of directional permeability on the flow of immiscible fluids are explored, and specific cases are presented. This study reveals a significant influence of directional permeability on the flow velocity of both fluids. Furthermore, quantitative conclusions are drawn regarding the shear stress at the lower and upper wall of the channel, with implications for the anisotropic nature of blood arteries. The findings contribute to a deeper understanding of fluid flow in anisotropic porous media and have potential applications in various engineering domains.

Numerical study on effect of anisotropic permeability of porous electrodes on PEM fuel cell performance

ABSTRACT The permeability of porous medium characterizes the ability of fluid flowing in the porous medium. The porous electrode of proton exchange membrane fuel cell consists of gas diffusion layer and catalytic layer, with the gas diffusion layer carrying the transport of the reaction gas and the catalytic layer being the main site of chemical reactions within the PEM fuel cell, both of which play a key role in the PEM fuel cell. In this paper, the effect of permeability in different directions within the porous electrode on the performance of PEM fuel cell was investigated in terms of polarization curves, oxygen distribution, and membrane water content distribution. It is found that under the same working conditions, the permeability in X-direction has the greatest influence on the PEM fuel cell performance and the PEM fuel cell performance is proportional to the magnitude of the permeability in X-direction, when the permeability in X-direction change to 0.1 and 0.2 of the original value, the PEM fuel cell performance decreases by 11.36% and 8.01%, and when the permeability in X-direction change to 5 and 10 of the original value, the PEM fuel cell performance increases by 10.18% and 13.79%. The effect of permeability in the Y-direction of porous electrodes on the performance of PEM fuel cells can be neglected. In porous electrodes, the PEM fuel cell performance reaches a peak when the permeability in the Z-direction of the gas diffusion layer is 1.18e-11 m2 and the permeability in the Z-direction of the catalytic layer is 2.36e-12 m2, therefore, increasing or decreasing the permeability in this direction leads to a decrease in the performance of the PEM fuel cell.

Predicting 3D Physical Properties From a Single 2D Slice Based on Convolutional Neural Networks: 2D‐Slice‐To‐3D‐Properties for Porous Rocks

AbstractThe 3D physical properties of porous rocks directly determine the subsurface flow and modeling. However, predicting a wide range of 3D physical rocks remains a formidable challenge and requires a large amount of input. Reliable microstructure‐property correlations can accurately predict 3D physical properties, avoiding time‐consuming experimental testing. Here, we propose a new dimensionless convolutional neural network (CNN)‐based method to find inherent correlations for accurately predicting 3D properties of porous rocks using only a single 2D slice or a series of 2D slices. Training and testing were conducted on 9 properties of 16,409 semi‐realistic 3D porous rocks. Eight properties, except for the formation factor, were predicted with an acceptable correlation coefficient of 0.92. Furthermore, the modeling results indicate that the network architecture of the model has a significant impact on its performance. The classical CNN Model 4 achieved an average validating loss of 1.0 × 10−3. Interval 2D slice sampling can significantly reduce the computational cost in training model. The developed model was verified and tested by five independent porous samples. Additionally, the proposed method accurately predicted permeability in different directions using only 2D slices trained in one direction, for porous rocks where anisotropy is not significant. This work demonstrates the ability to predict various 3D properties rapidly and accurately using only a single 2D slice from semi‐realistic 3D volumes. It provides insights into the conversion of 2D slices to 3D properties for porous media in a wide range of applications, including property estimation from 2D images without structural construction and simulation in 3D.

Perspiration permeable, textile embeddable microfluidic sweat sensor

Epidermal microfluidic devices are continuously being developed for efficient sweat collection and sweat rate detection. However, most microfluidic designs ignore the use of airtight/adhesive substrate will block the natural perspiration of the covered sweat pores, which will seriously affect normal sweat production and long-term wearable comfort. Herein, we present a Janus textile-embedded microfluidic sensor platform with high breathability and directional sweat permeability for synchronous sweat rate and total electrolyte concentration detection. The device consists of a hollowed-out serpentine microchannel with interdigital electrodes and Janus textile. The dual-mode signal of the sweat rate (0.2–4.0 μL min−1) and total ionic charge concentration (10–200 mmol L−1) can be obtained synchronously by decoupling conductance step signals generated when sweat flows through alternating interdigitated spokes at equal intervals in the microchannel. Meanwhile, the hollowed-out microchannel structure significantly reduces the coverage area of the sensor on the skin, and the Janus textile-embedded device ensures a comfortable skin/device interface (fewer sweat pores are blocked) and improves breathability (503.15 g m−2 d−1) and sweat permeability (directional liquid transportation) during long-term monitoring. This device is washable and reusable, which shows the potential to integrate with clothing and smart textile, and thus facilitate the practicality of wearable sweat sensors for personalized healthcare.

Estimating the permeability of fractured rock masses for design of construction dewatering systems

A comprehensive data on dewatering and pumping-well systems installed in fractured rock is compiled and analyzed to estimate the permeability of fractured rock masses. The data covers construction activities of different nature and dewatering depths, and considered the richest of its kind. Due to the relatively small volume and the nature of rock masses involved in the analyzed systems, the effect of having predominant oriented fracture sets, and consequently different directional permeabilities (i.e., scale-dependent permeabilities) are minimal. As a result, the current study is a clear advancement on state-of-the art given that the vast majority of the related studies available in the literature are presented to estimate the directional permeability of rock masses. The analyses showed a significant discrepancy between the coefficients of permeability estimated from field packer and falling-head tests and those back-calculated from the actual discharge pumped out of rock masses using dewatering or pumping-well systems. Back-calculated permeabilities can be up to five orders of magnitude larger than the measured values. Such discrepancy increases with increasing permeability of rock mass. The sensitivity of the estimated permeability to the difference in rock formation, utilized fracturing index, test type, and depth of test is studied. A data-driven approach is used to develop a novel correlation between the measured and back-calculated coefficients of permeability. Accordingly, a procedure is proposed to estimate the permeability of fractured rock masses involved in construction dewatering as a function of the measured permeability and rock degree of fracturing.

Impact assessment of strain-dependent permeability on reservoir productivity in CSS

Geomechanical analysis is essential to assess the productivity forecast of cyclic steam simulation (CSS) operations in heavy oil reservoirs. The high-temperature and high-pressure fluid injection, as well as depletion in unconsolidated and poorly cemented porous media during CSS, may generate a relevant stress–strain response at levels that can lead to irreversible changes in reservoir permeability. Therefore, it is fundamental to consider permeability dependence on rock strain to properly analyze the impact of geomechanics, pressure, and temperature on reservoir performance. This paper implements a proposed directional strain-dependent permeability model to assess the productivity and compare it with a conventional volumetric permeability model through numerical simulation, considering the effects of wellbore creation on the stress–strain initial state. An explicit coupling between CMG-STARS and the geomechanics in-house simulator GSIM is carried out to perform the simulations using the proposed model. The results of oil production rates and permeability profiles show competitiveness between dilation and compaction periods that modify the structure of the porous media. There is a significant influence of stress state, strain, and injected energy on the permeability parameter. The approximations of this study might be used for feasibility assessment and optimization of CSS when integrating reservoir flow and geomechanical behavior analysis in productivity forecast.

Evaluation of structural damage and gas transportability change in coal subjected to ultrasound stimulation using image-based modeling and permeability tests

Ultrasound stimulation will cause structural damage and modify gas transportability in coal, which is beneficial to enhance coalbed methane production. The image-based modeling and permeability tests were conducted to examine the structural damage and gas transportability change in coal subjected to ultrasound stimulation. The results show that the fracture space volume and structural complexity in coal significantly increased after 2 h’ ultrasound stimulation. The fracture porosity increased by 8.1%∼11.9%, and the interconnected fracture proportion increased by 17.2%∼21.2%. The anisotropy permeability was estimated using gas transport simulation in 3D coal structure, and the average permeability in three-dimensional directions increased by 95.2%∼113.5% after ultrasound stimulation, which implies that ultrasound stimulation can induce multi-dimensional structural damage and expand interconnected fracture networks. The permeability tests show that gas permeability in stressed coal was significantly improved by 34.3%∼43.8% with half an hour of ultrasound stimulation. With continuous ultrasound stimulation, the gas permeability increased rapidly with increasing stimulating duration at the initial stage. Subsequently, the permeability continued to increase, but the trend of permeability increase gradually slowed down. Finally, after several cycles of stimulation, the permeability tended to be constant. It implies that the performance of ultrasound stimulation on enhancing coal permeability is time-effective, and there is an optimal stimulating duration parameter for the target CBM reservoir, which is critical for pursuing the high efficiency application of ultrasound in CBM engineering operations.

Digital Rock Analysis on the Influence of Coarse Micro-Fractures on Petrophysical Properties in Tight Sandstone Reservoirs

Tight sandstone reservoirs, as typical unconventional reservoirs, have attracted more and more attention worldwide. Compared to conventional reservoirs, the complex microscopic pore structures and micro-fractures of the tight reservoirs are developed, and fluid flow in the tight sandstone reservoir is very complicated. Therefore, studying the influence of fractures on the rock topological structure and the flow characteristics between micro-fractures and the matrix is critical to the development of tight sandstone reservoirs. In light of the intricate nature of micro-fractures, digital rock analysis technology is utilized to address this issue instead of traditional experimental methods. Firstly, the selected tight rock is scanned by X-ray computed tomography (XCT), and then the natural tight digital rock is reconstructed by filtering and binary segmentation. Secondly, micro-fracture with different shapes is added to the digital rock. Then, a pore network model extracted by the maximum ball method is adopted to conduct the flow simulation. The study finds that the distribution of pore throat radius changes with increasing fracture aperture and length and that the permeability and capillary pressure curves are influenced by fracture aperture and length in the direction of connectivity. The impact of micro-fracture dip angle on pore throat structure is significant with changes in permeability and fluid flow in different directions. Overall, the study emphasizes the importance of fracture aperture and length in determining the properties and behavior of tight sandstone reservoirs and highlights the usefulness of digital rock analysis technology in providing insights into complex microstructures.

Influence mechanism of brine-gas two-phase flow on sealing property of anisotropic caprock for hydrogen and carbon energy underground storage

As the simplest saturated hydrocarbon, methane is an important hydrogen and carbon energy. The stability and sealing of caprock are keys to ensure the safe storage of energy in the process of hydrogen and carbon energy underground storage. A fully coupled two-phase flow model is established to analyze the migration mechanism of methane in caprock. This model considers the characteristics of dual porosity medium composed of caprock fractures and matrix, including the seepage of methane and brine. In the model, the replacement process of methane and brine exists in the fracture network, and the dynamic adsorption desorption process of methane exists in the matrix. Under the action of tectonic stress, obvious differences are observed in the fracture and permeability in different directions. All these characteristics are considered in the fully coupled two-phase flow model. The restraining and strengthening effects of caprock in the process of methane leakage are analyzed. The results show that the gas induces the adsorption expansion of the caprock matrix and reduces the fracture opening and permeability of the caprock. With the gradual invasion of gas into the caprock, the sealing characteristics of caprock show the evolution of self-inhibition first and then self-enhancement. With the increase in dip angle, gas tends to invade vertically rather than horizontally. Realizing gas–brine replacement is easier with the existence of large fractures. This study provides an effective numerical analysis method, which can be used to evaluate the sealing efficiency in the caprock in underground methane storage.

Directional Dependency of Relative Permeability in Vugular Porous Medium: Experiment and Numerical Simulation

Carbonate reservoirs are a highly heterogeneous type of reservoir characterized by the presence of a large amount of vugs and pores. During two-phase displacement, the two-phase flow regime in the vugs might be gravity segregated. The distribution pattern of two-phase fluid in the vugs would accelerate the water flow in downward and horizontal directions, meanwhile decelerating in an upward direction, resulting in a different oil recovery ratio. This gives rise to the question of whether the relative permeability should be modeled as a directional dependent in a vugular porous medium since it is usually treated as an isotropic quantity. In this study, via both experiment and numerical simulation, we demonstrate that the relative permeability of vugular porous medium is dependent on the angle between the flow direction and the horizontal plane and should be considered for oil recovery estimation for carbonate reservoirs. Using the transmissibility-weighted upscaling method and a single-vug model, the relative permeability curves for different flow directions are obtained by numerical simulation. A directional relative permeability model for a vugular porous medium is also proposed.

Anisotropic wood–water interactions determined by gravimetric vapor sorption experiments

Gravimetric vapor sorption experiments were performed on beech wood samples to determine the directional permeability, diffusion and sorption coefficients in the three orthotropic wood directions. Dynamic Vapor Sorption (DVS) experiments allowed for the direct evaluation of the diffusion coefficient from the analysis of the kinetic sorption profile using a double stretched exponential model with values ranging from 0.10 × 10−10 to 1.52 × 10−10 m2/s and depending on the wood direction of the sample and the RH-values. Moisture sorption isotherms (MSIs) were constructed and fitted to a modified Guggenheim-Anderson-de Boer and a Sorption Site Occupancy model, which allowed for the calculation of the sorption coefficient which was found to be between 2.4 and 3.0 mol/(m3 Pa). Dynamic Vapor Transport (DVT) experiments were performed to calculate the permeability coefficient from the vapor flow rate and it ranges between 0.56 × 10−10 and 4.38 × 10−10 mol/(m s Pa) as a function of the flow direction and RH conditions. These results indicate that such an experimental approach is suitable for determining wood–moisture interactions.

Analysis of fluid-structure interaction in a directional permeability membrane in pressure-driven flow

Finite volume and finite element analysis of fluid-structure interaction is performed to understand the behavior of a directional permeability membrane in pressure-driven flow. The membrane is comprised of two flexible porous sheets separated by a spacer. The porous sheets each have a different thickness with pores that are offset from each other. The design allows flow when the thicker sheet is on the high pressure side, but prevents flow if the pressure gradient is reversed. Flow through the membrane is studied for a pressure range of 0.01–0.1 m H2O in forward flow to understand the complex fluid motion and dependence of membrane deformation on sheet thickness, downstream pore diameter, and initial gap between the sheets. In forward flow, maximum mass flow rate of 0.2 g s−1 (or flow rate of 12.024 ml min−1) can be obtained at 0.1 m H2O pressure head. Reverse flow conditions are modeled to study the effect of design parameters on the required closing pressure, indicating that as little as 0.0325 m H2O of pressure head is required for closing.

Bestrophin-2 and glutamine synthetase form a complex for glutamate release.

Bestrophin-2 (Best2), a member of the bestrophin family of calcium-activated anion channels, is expressed in nonpigmented epithelium (NPE) of the ciliary body with critical involvement in aqueous humor homeostasis. Best2 knockout mice exhibit a reduced intraocular pressure, suggesting the pharmaceutical potential of Best2 as a target for lowering ocular hypertension. However, little is known about the physiological binding partners and/or regulators of Best2. In this study, we performed a proteomic pulldown of bovine ciliary body lysate using purified Best2 proteins as the bait, and identified glutamine synthetase (GS), which catalyzes the conversion of glutamate and ammonia into glutamine, as a Best2 binding partner. We assessed the functional consequences of the interaction and discovered a mutually inhibitory effect: GS decreases Best2-mediated chloride conduction, while Best2 reduces cytosolic GS activity by tethering GS to the cell membrane. Since glutamate is the substrate of GS and an anion, we investigated the ability of Best2 to conduct glutamate. Remarkably, Best2 exhibits a directional permeability to glutamate heavily favoring glutamate exit from the cell, and the binding of GS to Best2 sensitized Best2 to intracellular glutamate, which promotes opening of Best2 and thus relieves the inhibitory effect of GS. We further demonstrated the physiological role of Best2 in conducting chloride and glutamate and the influence of GS in NPE cells. Moreover, by single-particle cryo-EM, we solved the structure of the Best2-GS complex, illustrating the interacting residues and extension of the Best2 ion conducting pathway through the GS central cavity. Together, our results reveal a novel mechanism of glutamate release through Best2-GS.

Value of core for reservoir and top-seal analysis for carbon capture and storage projects

Abstract Carbon capture and storage (CCS) initiatives to mitigate greenhouse gas emissions are being planned in many countries, including offshore settings in the UK. To start with, almost all of these initiatives have utilized core that was originally collected to help with oil and gas exploration, appraisal and development projects. The objectives of core-based studies for CCS are subtly different to those for oil and gas studies. There are several significant reasons why core should be valued in CCS projects. Data from core provide a chance to calibrate lithology and porosity interpretations made from wireline logs that are used to characterize the subsurface and populate geocellular models. Permeability-related attributes, especially directional permeability ( k v and k h ) and relative permeability in CO 2 –water mixed fluid systems, are essential to predict CO 2 injection rates and CO 2 movement patterns in the reservoir and can only be acquired from core. Although many geomechanical data, necessary to undertake safe injection of CO 2 and avoid induced fracturing, can be acquired from wireline logs, borehole imaging and downhole tests, core samples from the reservoir and top-seal are required to reveal tensile strength and to calibrate elastic and other geomechanical properties acquired from logs. Top-seal performance is critical for carbon capture and storage; core samples from top-seals are the best way to determine capillary entry pressure and so define the maximum CO 2 column height and possible CO 2 leakage rates. The possibility of dissolution reactions between formation water, acidified by high pressure CO 2 , and minerals in both the reservoir and top-seal is best assessed by detailed petrographic and mineralogical study of core samples and a combination of modelling and core flow-through experiments. In summary, core is essential to CCS projects to determine CO 2 storage efficiency, CO 2 injection rates and the optimum way to safely store CO 2 .

Bestrophin-2 and glutamine synthetase form a complex for glutamate release.

Bestrophin-2 (BEST2) is a member of the bestrophin family of calcium-activated anion channels that has a critical role in ocular physiology1-4. Here we uncover a directional permeability of BEST2 to glutamate that heavily favours glutamate exit, identify glutamine synthetase (GS) as a binding partner of BEST2 in the ciliary body of the eye, and solve the structure of the BEST2-GS complex. BEST2 reduces cytosolic GS activity by tethering GS to the cell membrane. GS extends the ion conducting pathway of BEST2 through its central cavity and inhibits BEST2 channel function in the absence of intracellular glutamate, but sensitizes BEST2 to intracellular glutamate, which promotes the opening of BEST2 and thus relieves the inhibitory effect of GS. We demonstrate the physiological role of BEST2 in conducting chloride and glutamate and the influence of GS in non-pigmented ciliary epithelial cells. Together, our results reveal a novel mechanism of glutamate release through BEST2-GS.

An optimum solution for coal permeability estimation from mesoscopic scale calibrated stochastic and deterministic discrete fracture network models

The efficiency of a coal bed as a reservoir of methane and CO2 sink primarily depends on its fracture permeability. Conventional techniques of permeability estimation from drilled-core plugs in the laboratory and analytical computations are often different from in-situ measurements by multiple orders. Hence, pre-drill estimation of coal bed permeability remains one of the major challenges for the operators. Researchers usually try to solve this issue by building DFN models based on the direct use of µCT images of millimeters scale coal chips. However, such small-scale DFN models also overestimate permeability by many folds. As a solution, we propose the deployment of calibrated Discrete Fracture Network (DFN) modeling technique based on mesoscale coal images. Deterministic and stochastic DFN models are simulated by replicating thirteen coal specimens collected from the Gondwana coal seams in the Raniganj coalfield of India. Different model outputs such as directional permeabilities, permeability anisotropy, connectivity, etc. are used to distinguish and calibrate these models. The derived average permeabilities from these models closely match with available field measurements. Thus, the proposed technique helps in minimizing the huge gap between the laboratory and well-test measurements. In the process, we derive the threshold sample/model size that would sufficiently address the average cleat permeability at the well-drainage scale. Additionally, sensitivity analysis of key fracture attributes is carried out to quantify their effect on coal permeability.

Characterization of Tensile Stress-Dependent Directional Magnetic Incremental Permeability in Iron-Cobalt Magnetic Sheet: Towards Internal Stress Estimation through Non-Destructive Testing.

Iron-Cobalt ferromagnetic alloys are promoted for electrical energy conversion in aeronautic applications, but their high magnetostrictive coefficients may result in undesired behaviors. Internal stresses can be tuned to limit magnetostriction but must be adequately assessed in a non-destructive way during production. For this, directional magnetic incremental permeability is proposed in this work. For academic purposes, internal stresses have been replaced by homogenous external stress, which is easier to control using traction/compression testbench and results in similar effects. Tests have been limited to tensile stress stimuli, the worst-case scenario for magnetic stress observation on positive magnetostriction coefficient materials. Hysteresis cycles have been reconstructed from the incremental permeability measurement for stability and reproducibility of the measured quantities. The directionality of the sensor provides an additional degree of freedom in the magnetic response observation. The study reveals that an angle of π/2 between the DC (Hsurf DC) and the AC (Hsurf AC) magnetic excitations with a flux density Ba at Hsurf DC = 10 kA·m−1 constitute the ideal experimental situation and the highest correlated parameter to a homogeneous imposed tensile stress. Magnetic incremental permeability is linked to the magnetic domain wall bulging magnetization mechanism; this study thus provides insights for understanding such a mechanism.