Non-uniform Permeability Research Articles

Similarity Investigation of Thermosolutal Mixed Convection in a Saturated Porous Medium

This contribution investigates the thermosolutal convection phenomenon around a thin wall, vertically immersed in a fluid saturating a porous medium of non-uniform permeability, taking into account the thermal conditions of the wall which is exposed to a fluid suction/injection. The conservation equations with boundary conditions have been transformed by the similarity method into a set of nonlinear differential equations. The resulting equations are numerically resolved using a fifth-order Runge-Kutta scheme coupled with the shooting technique. A graphical and physical interpretation of the found results as a function of the control parameters was performed. It is noticed that the heat transfer rate and the mass transfer rate at wall, are intensified for free convection and for significant permeability.

Open-Circuit Electromagnetic Analysis of Interior Permanent Magnet Machines With Arbitrary Rotor Frame Using a 2-D Analytical Model

Two-dimensional (2-D) analytical modeling of interior permanent magnet (IPM) machines is quite challenging due to the nonuniform permeability of the rotor core. The choice of a non-cylindrical rotor frame (e.g., rotor frame with cosine shape) further increases the complexity of the model. This article presents a methodology for the 2-D modeling of IPM machines with cylindrical and non-cylindrical rotor frames. In this model, interior magnets are first mapped to the surface of the rotor body using the equivalent magnetic circuit model. In other words, the IPM machine is transformed into an equivalent surface-mounted permanent magnet (SPM) machine. The rotor shape is modeled by the proper adjustment of the permanent magnet (PM) magnetization pattern of the equivalent SPM machine. Next, the radial and tangential flux components of the equivalent (SPM) machine are computed by solving Maxwell’s relations and applying 2-D boundary conditions. The effect of the stator slotting on the distribution of magnetic flux is accounted using the theory of virtual current. The accuracy of the presented model is verified against the finite element (FE) and experimental measurements.

Analysis of Surrounding Rock Pressure of Deep Buried Tunnel considering the Influence of Seepage

This paper takes the surrounding rock of deep tunnel as the research object and considers the action mechanism under the influence of seepage. Based on the Mohr-Coulomb criterion, the stress mechanism of surrounding rock of deep buried tunnel is analyzed by a convergence constraint method. Based on the elastic-plastic solution, the nonlinear elastic-plastic solution of the interaction between surrounding rock and lining structure considering the effect of seepage force is proposed, and the radius of surrounding rock plastic zone is obtained. The relationship between surrounding rock stress and displacement, radial deformation of lining, and support reaction force was observed. At the same time, considering the effects of seepage, strain softening, and intermediate principal stress, the surrounding rock is divided into a plastic residual zone, plastic softening zone, and elastic zone, and the stress distribution expressions of the plastic zone and each zone of surrounding rock of circular tunnel are derived. The results show that with the change of nonuniform permeability coefficient, the seepage shows anisotropy in different directions, and the closer to the horizontal or vertical direction, the more obvious the influence of nonuniform permeability coefficient on pore water pressure distribution. Seepage and material softening have different effects on the distribution of surrounding rock stress field and the size of plastic zone. Material softening is more unfavorable to the stability of surrounding rock than seepage. The intermediate principal stress coefficient has a significant impact on the tangential stress and plastic zone of surrounding rock. When the intermediate principal stress effect is not considered, the calculation results are relatively conservative and cannot give full play to the strength of surrounding rock effectively. The research conclusion can provide a theoretical reference for studying the stability of surrounding rock in tunnel excavation under water-bearing rock.

Cell Interplay Model to Assess the Impact of Glioma Cells on Blood-Brain Barrier Permeability.

The blood-brain barrier (BBB) is the most selective protecting layer of the central nervous system (CNS) with unique neurovascular features. The BBB is known to undergo a process of molecular alterations during disease state, such as in the case of glioma. This results in a non-uniform permeability along the BBB layer, which retains intact regions but develops focal sites of higher leakiness, especially in the surrounds of the tumor core. Although essential to guarantee brain homeostasis, the BBB has been the Achilles heel of drug delivery to the brain since the early times of the first classification as "barrier," more than a century ago. Due to the presence of the BBB, the transport of drug molecules from the bloodstream to the brain parenchyma is highly restricted, and, therefore, clinically relevant therapeutic concentrations cannot be achieved. Research efforts have focused on the development of novel tools to ameliorate drug permeability across the BBB, including drug formulation into non-invasive delivery systems with brain targeting properties and techniques that allow a temporary disruption of the BBB. To strengthen the advancement of potential drug candidates, in vitro models that recapitulate the main in vivo features of BBB are required to perform a preliminary screening of permeability, both in health and disease conditions. Herein, a protocol to assemble a BBB in vitro model to screen drug permeability in a glioma disease state is detailed. The model consists of a BBB and glioma cell co-culture and aims at exploiting the effect of the interplay between the cell constituents on the permeability of drug molecules. Although simple and straightforward, the herein in vitro model presents a high reproducibility, cost-effectiveness, and a favorable time-benefit balance.

Effects of Nonuniform Permeability in Variable Bdpm Under a Sinusoidal Arrangement to Control Heat Transfer and Fluid Flow in a Channel - a Numerical Simulation

Effects of Nonuniform Permeability in Variable Bdpm Under a Sinusoidal Arrangement to Control Heat Transfer and Fluid Flow in a Channel - a Numerical Simulation

Identification and research of factors affecting the optimal distribution of well flow rates in space

The paper discusses and research the factors affecting the filtration rate to reduce stagnant zones in the domain and spreading outside the block under consideration. The main hydrodynamic factors in production by In-Situ Leaching are the distribution of permeability in the reservoir and well flow rates. The study of the factors was carried out on the basis of mathematical models using Darcy Law and Law of Conservation of Mass. Calculation was accomplished on a two-dimensional area with an isotropic and non-uniform permeability distribution to determine the effect of permeability on the leached area. The permeability coefficient was distributed respectively over three zones, in the southern part the permeability was low, in the central transition from low to high, respectively, in the northern part there was a highly permeable zone. Three wells were located in the domain, with the production well in the center of the domain. Injection wells are located symmetrically with respect to a horizontal line passing through the center of the area under consideration. The calculation was carried out for three modes of well flow rates with the ratio of the flow rates of the injection wells 0.5 / 0.5, 0.2 / 0.8, 0.8 / 0.2 relative to the flow rate of the production well. On the basis of comparative analyzes of the obtained results, it is concluded that: at the same flow rates, regardless of the permeability of the zones, the results obtained show that the leaching area in the low-permeability zone is larger in comparison with the high-permeability zone; with an increase in permeability, the shape of the leaching zone tends from round to drop-shaped; with an increase in the flow rate of wells in the radius of the leaching zone, it increases if the flow rate of solutions is much higher than the filtration rate.

Fluid Migration Characterization of Full-Scale Annulus Cement Sections Using Pressure-Pulse-Decay Measurements

Abstract Fluid migration behind casings is a well integrity problem that can result in sustained casing pressure, undetected leaks to the environment, and potentially very challenging remediation attempts. Understanding the geometric dimensions and extent of annular migration paths is important for diagnosing and effectively treating fluid migration and sustained casing pressure problems in wells. In this study, permeability and micro-annuli sizes in two full-scale cemented annulus test sections are measured using transient pressure-pulse-decay and steady-state seepage measurements. One of the studied sections is a cemented 9 5/8-in. and 13 3/8-in. casing section from a 30 years old Norwegian North Sea production well. A model for predicting the transient pressure decay in annular sections with non-uniform permeability is presented and the permeabilities of the two sections are determined by fitting the transient model to pressure measurements at either side of the test sections and at selected axial positions. For both sections, measured micro-annulus sizes are within the range of effective wellbore permeabilities based on sustained casing pressure records and previous vertical interference tests from other wells. The test sections display measurable axial permeability variations with the bottom part of these vertical sections having the lower permeability. For the retrieved casing section, the axial permeability variation occurs close to the middle of the test section and is attributed to the top-of-cement. Increasing internal casing pressure is found to slightly reduce the equivalent micro-annulus size, indicative of fracture-like response of the migration paths. Using two independent test protocols, we have measured effective permeabilities as well as local permeability variations in full-scale test sections and found consistent results. The study suggests that the transient test procedure can be used to more effectively characterize low-permeable annular cement where it is otherwise time-consuming or difficult to establish steady-state flow conditions.

Real-time prediction and assessment of hydrogeological conditions in pit wall rock mass using advanced computer technologies

For the feasibility study of preventive drainage, it is often required to evaluate groundwater inflows in specific pit areas, to identify seepage height in pit wall, and to determine hydrodynamic parameters of flow in the existing geological and hydrogeological conditions. The authors have identified methodological approaches, technological methods and schemes, and combinations of software tools that allow automation of evaluating and predictive studies of hydrogeological conditions in certain areas of open pits using 3D models and finite element methodbased calculations. To solve these tasks, we have tested the dynamic geological simulation software system Leapfrog Geo (Seequent) in combination with the dedicated calculation module Slide2 (Rocscience Inc.). A promising area of joint application of Leapfrog Geo and Slide software is real-time permeation calculations in areas of complex geological and hydrogeological conditions, where grapho-analytical methods provide very approximate and rough results, whereas 3D software products (like MODFLOW or FEFLOW) require too much time and labor input, or even are inapplicable due to lack of modeling source data. The water inflow estimation procedure included determination of specific water inflow in the profile which passed through the center of the flow path, and multiplication of the result by the width of the pit wall intake area with regard to nonuniform permeability of rocks.

Benchmarking a reduced order finite element method for multiphase carbon sequestration models

Carbon sequestration in deep saline aquifers has been proposed for long-term storage of CO2 as an alternative to the release of CO2 into the atmosphere. In this article, we present a computationally efficient numerical model based on a sequentially coupled Finite Element Method (FEM) and Streamline Upwind Finite Element Method (SU-FEM)-Finite Difference Method (FDM). An adaptive timestep strategy is implemented which allows computationally efficient and stable solutions as time progresses. The computational efficiency of the formulation is demonstrated by four examples that consider nonuniform permeability, multiple injection wells, an upsloping aquifer, and a dome-shaped aquifer. The adaptive timesteps reduce the computational cost by 75-82% compared to constant timesteps in the four examples considered. The proposed formulation is compared against a benchmark study where eleven different simulators were used to determine the arrival time of the CO2 plume at a leaky well. The original benchmark study did not include an FEM-based discretization of the reduced order equations. To the authors’ best knowledge, the current work is the first FEM based implementation of reduced order (vertically averaged) multiphase flow equations evaluated against this benchmark. The proposed formulation is in good general agreement with the results from the various simulators studied in the benchmark, and excellent agreement with an FDM discretization of the vertically averaged governing equations.

Numerical Analysis of the Magnetomechanical Effect in Heating Pipes

A physical and mathematical model is considered to support the investigation of the prospects of using the effect of metal’s “magnetic memory” for the nondestructive testing of items made from ferromagnetic materials located in the Earth’s magnetic field. Based on the finite-element method, an algorithm and a computer code for the 3D computations of the magnetic potential distribution in a medium with nonuniform magnetic permeability are worked out. The developed methods and software tools are used to model the leakage field near the clamped heating pipes of steam boilers. Relationships demonstrating the interdependence between the change in magnetic induction and the magnetic leakage field are obtained. Satisfactory agreement is observed between the calculated and experimental data on the distribution of the field strength of the magnetic leakage on the surface of the heating pipe.

Predictive Inverse Model for Advective Heat Transfer in a Short‐Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

AbstractIdentifying fluid flow maldistribution in planar geometries is a well‐established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two‐dimensional Hele‐Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C‐Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir‐scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding‐plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. The results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

A generalized analytical model for hydrocarbon production using multi-fractured horizontal well with non-uniform permeability distributions

The multi-fractured horizontal well (MFHW) has significantly facilitated the exploitation of unconventional hydrogen-carbon compound reservoirs, which is an abundant source of fossil hydrogen energy. The composite linear flow models were frequently adopted to analytically evaluate the hydrocarbon production using MFHW. Most of the existing composite linear flow models assume uniform permeability in the primary fractures and the Stimulated Reservoir Volume (SRV) region. However, due to the non-uniform proppant distribution in the primary fractures and the heterogeneity in the density of the secondary fractures in SRV region, the permeability field in both regions are non-uniform. For the first time, a generalized analytical model incorporating continuous permeability heterogeneity in both the primary fractures and SRV region is proposed for the hydrocarbon production of MFHW. Any arbitrary permeability distribution functions can be treated as inputs to the proposed model. The mathematical model is solved using the perturbation technique and the Laplace transform method.The good match with the numerical solution verifies the accuracy of the proposed analytical model. Subsequently, the proposed solution is assigned with different modes of permeability heterogeneity to investigate their impacts on well production performances, i.e., cumulative hydrocarbon production and transient bottom-hole pressure (BHP). The results reveal that the incorporation of permeability heterogeneity will enhance the production rate and lower the BHP drawdown compared to the homogeneous case with the same average permeability. Besides, a field case is presented to demonstrate the applicability of the proposed model.

Heterogeneity Affects Intertidal Flow Topology in Coastal Beach Aquifers

AbstractIntertidal aquifers are hotspots of biogeochemical cycling where nutrients and contaminants are processed prior to discharge to the ocean. The nature of the dynamic subsurface mixing zone is a critical control on mitigating reactions. Simulation of density‐dependent, variably saturated flow and salt transport incorporating realistic representations of aquifer heterogeneity was conducted within a Monte Carlo framework to investigate influence of nonuniform permeability on intertidal groundwater flow and salt transport dynamics. Results show that heterogeneity coupled with tides creates transient preferential flow paths within the intertidal zone, evolving multiple circulation cells and fingering‐type salinity distributions. Due to heterogeneity, strain‐dominated (intense mixing) and vorticity‐dominated (low mixing) flow regions coexist at small spatial scales, and their spatial extent reaches peaks at high tide and low tide. Such topological characteristics reveal complex tempo‐spatial mixing patterns for intertidal flow with localized areas of high and low mixing intensities, which have implications for intertidal biogeochemical processing.

Mathematical modeling and simulation of molecular mass transfer across blood brain barrier in brain capillary

The blood brain barrier (BBB) is a unique anatomical structure tightly regulated by the interplay of cellular and acellular components, thus providing maintenance of brain homeostasis, regulation of influx and efflux and protection from harm. In both health and disease, the BBB acts as a mediator between the peripheral and the central nervous system (CNS). Understanding the BBB is considered as a key for developing effective treatments for a wide range of CNS disorders. The main novelty of this study is to develop a 2-dimensional and 3-dimensional model of BBB mass transfer resistance to investigate effective diffusion and molecular mass transfer from inside the capillary to the extravascular space. In this study, the capillary and the tissue around it with non-uniform permeability are numerically simulated. The endothelial cells, basement membrane and astrocyte foot processes are modeled as a porous medium. Moreover, a correlation of mass transfer resistance between the capillaries and astrocytes was established to estimate an effective diffusion coefficient. Model validation is done according to the comparison of simulation results and experimental data for the nanodrug mass transfer resistance in a wide range of red blood cell distance in the capillary. This comparison corroborates an excellent agreement with an average deviation of 6%. It is well perceived that the internal diameter of capillaries and the distance between the outside of the capillary and astrocyte have significant effects on delivering materials to neurons. Moreover, blood flow velocity and the number of red blood cells dramatically deteriorate the nano-particles' concentration due to increasing the mass transfer resistance.

Structural Optimization of Slotting Nozzle Used to Improve Coal-Seam Permeability

Slotting directional hydraulic fracturing is a new method for improving permeability of a coal seam in underground coal mines that can solve problems related to non-uniform permeability enhancement in the seam. A slotting nozzle is the key to this technology: its performance determines the length and stability of the slotted hole. In this study, computational fluid dynamics was used to study the effects of stable segment length L, convergent angle θ, and straight segment length l on the performance of slotting nozzles. The results showed that the order of parameters affecting nozzle performance is: θ > L > l. When the total length of the slotting nozzle was fixed, the dynamic pressure gradually decreased with an increase of L and the rate of decrease slowed down. With an increase of θ, dynamic pressure increased quadratically and the rate of change gradually decreased. With an increase of l, the dynamic pressure decreased quadratically and the rate of change gradually increased. A slotting nozzle (L = 0 mm, θ = 30°, l = 9 mm) was manufactured and measurements of flow coefficient, water jet morphology, and a slotting experiment were carried out. The experimental results showed that the flow coefficient, water jet convergence, and slotting depth of the optimized slotting nozzle were obviously higher than those of the original design, which proved the validity of using this numerical method to optimize the slotting nozzle structure.

3D MHD cross flow over an exponential stretching porous surface

AbstractThe present study aims to investigate the effects of thermal‐diffusion and diffusion‐thermo onan magnetohydrodynamic convective flow of viscous fluids over an exponentially stretching sheet. Thermal radiation effects are also considered in the study. This analysis is carried out in three dimensions and a similarity transformation is adopted to get a set of ordinary differential equations from a set of partial differential equations. And the Fourth‐order Runge‐Kutta method and shooting technique along with the secant method are employed to find out an iterative solution. We also analyze here the influence of the variable magnetic field, nonuniform permeability and variable chemical reaction on the fluid flow. The impact of various pertinent parameters of interest has extensively been explored through graphs and tables. The major findings of the present study are that resistive Lorentz force diminishes the fluid velocity and uplifts the thermal as well as concentration fields. Inclusion of porous matrix improves the viscous drag force which in turn augments wall shear stresses and peters out the heat and mass transfer rates from the sheet. In addition, the thermal expansion coefficient has an inverse relation with temperature.

The blood–brain barrier and blood–tumour barrier in brain tumours and metastases

For a blood-borne cancer therapeutic agent to be effective, it must cross the blood vessel wall to reach cancer cells in adequate quantities, and it must overcome the resistance conferred by the local microenvironment around cancer cells. The brain microenvironment can thwart the effectiveness of drugs against primary brain tumours as well as brain metastases. Inthis Review, we highlight the cellular and molecular components of the blood-brain barrier (BBB), a specialized neurovascular unit evolved to maintain brain homeostasis. Tumours are known tocompromise the integrity of the BBB, resulting in a vasculature known as the blood-tumour barrier (BTB), which is highly heterogeneous and characterized by numerous distinct features, including non-uniform permeability and active efflux of molecules. We discuss the challenges posed by the BBB and BTB for drug delivery, how multiple cell types dictate BBB function and the role of the BTB in disease progression and treatment. Finally, we highlight emerging molecular, cellular and physical strategies to improve drug delivery across the BBB and BTB and discuss their impact on improving conventional as well as emerging treatments, such as immune checkpoint inhibitors and engineered T cells. A deeper understanding of the BBB and BTB through the application of single-cell sequencing and imaging techniques, and the development of biomarkers of BBB integrity along with systems biology approaches, should enable new personalized treatment strategies for primary brain malignancies and brain metastases.

Patterns of recovery and injection wells in deposits of high-viscosity oil with reservoir decompression zones

The issue of patterns of injection and recovery wells in zones of non-uniform permeability reservoirs is discussed by many researchers. The researchers aim to identify the influence of well patterns in reservoir zones with different permeability on the efficiency of oil recovery. This issue is particularly acute for systems maintaining reservoir pressure. The location of injection wells in low-permeable zones, and recovery wells - in high-permeability zones helps increase the coverage of the impact. Moreover, even in the conditions of a partially developed reservoir, transformation of the existing development system has significant potencies for increasing the ORC. One more crucial problem is the study of the effect of extensive highly permeable inclusions (faults, zones of reservoir loosening) on the effectiveness of regular development systems.

Effects of non-uniform permeability on vortex shedding and noise control of blunt trailing edge

In this paper, the characteristics of the vortex shedding and noise of the blunt trailing edge with different porous permeable segment are studied by numerical simulation. The permeability distribution is adjusted through continuously changing the viscous drag of porous region to achieve uniformity and non-uniformity. The simulation results firstly show that the porous trailing edge can stabilize the free shear layer in a certain range of viscous drag coefficient to suppress the vortex shedding and reduce the overall noise level significantly. The optimized non-uniform permeability can further reduce the noise by 3dB than that of uniform permeability for porous blunt trailing edge. The discrete strip-shaped porous blunt trailing edge is proposed for more practical engineering application. It is found that the noise level is increased by 2 dB rather than optimal function distribution. However, the discrete strip porous trailing edge still has significant noise reduction capacity with respect to solid blunt trailing edge. The three-dimensional simulation demonstrates further that the non-uniform permeable trailing edge behaves more potential than uniform permeable trailing edge and reveals the crucial spanwise synergy effects by porous treatment.

Toward Incorporation of Membrane Properties Non-Uniformity in Spiral Wound Module Performance Simulators—Effect of Non-Uniform Permeability on Fouling Layer Evolution

A performance simulator of spiral wound membrane (SWM) modules used for desalination is a valuable tool for process design and optimization. The existing state-of-the-art mesoscale simulation tools account for the spatial non-uniformities created by the operation itself (flow, pressure, and concentration distributions) but they assume uniform membrane properties. However, experimental studies reveal that membrane properties are by no means uniform. Therefore, the need arises to account for this non-uniformity in simulation tools thus enabling a systematic assessment of its impact, among other benefits; a first step toward this goal is presented herein. In particular, the issue of an organic fouling layer growing on a membrane with non-uniform permeability is analyzed. Several mathematical treatments of the problem are discussed and indicative results are presented. The concept of fouling layer thickness probability density function is suggested as a means to introduce sub-grid level calculations in existing simulation tools. The analysis leads to the selection of an appropriate methodology to incorporate this effect in the dynamic simulation of fouling layer evolution at the membrane-sheet scale.