Flow In Media Research Articles

Reactive direct simulation Monte Carlo modeling of gas reactive transport in three dimensional porous fibrous media across rarefied to continuum regimes

Gas flow in complex porous media can vary across rarefied to continuum regimes depending on the characteristic size of porous media. To study the gas reactive transport process in three dimensional porous fibrous media across rarefied to continuum regimes, a comprehensive reactive direct simulation Monte Carlo model coupling with heat conduction and radiation model as well as reaction process is proposed. The results calculated by the proposed model are verified to fit well with those obtained using analytical model and experimental data. The “inlet” effect promoting the skeleton temperature is found. There are existing competitions between the heat conduction, reaction rate and convection, radiation process. The temperature of porous fibrous media skeleton increases with the catalyst coverage, and decreases with increase of Knudsen number. When the proportion of hydrogen increases, the increase in the temperature of the porous fibrous media skeleton is initially rapid and then gradual. These studies help to deeply understand the chemical reaction mechanism in porous media across rarefied to continuum regimes.

Flow-Driven Deformation in Granular Porous Media: Dimensionless Analysis

AbstractFluid injection can induce mechanical deformation in granular porous media due to the elevation of internal pore fluid pressure. This gains more significance when more than two immiscible fluids are involved, attributable to capillary and viscous drag forces. Such a coupled hydromechanical behavior associated with immiscible fluid flows plays an important role in injection, storage, and recovery of fluids in deformable porous media. This study presents a dimensionless map with newly proposed dimensionless parameters to predict deformation occurrence due to an immiscible fluid flow in deformable porous media. A series of hydromechanically coupled pore network simulations are first performed while varying the capillary number, mobility ratio, medium stiffness, and effective confining stress over orders of magnitudes. The compilation of simulation results with previously published Hele–Shaw experiment results is analyzed with the dimensionless parameters, such as the capillary number, mobility ratio, particle-level force ratios, and particle-level pressure ratios. Particularly, the particle-level pressure ratios include the capillary pressure ratio, defined as the ratio of capillary pressure to fracture pressure, and the viscous drag pressure, defined as the ratio of viscous drag pressure to fracture pressure. The dimensionless map based on the particle-level pressure ratios, where the capillary pressure ratio and viscous drag pressure ratio are defined as the ratios of capillary pressure and viscous drag pressure to fracture pressure, effectively delineates four deformation regimes—no deformation, capillary-induced deformation, drag-driven deformation, and mixed-mode deformation. The results demonstrate that capillary-induced deformation occurs when the capillary pressure ratio is greater than 10−1, while drag-driven deformation is observed when the viscous drag pressure ratio exceeds 10−2. The presented dimensionless map and dimensionless parameters are expected to be applicable for geological subsurface processes, including geological storage of carbon dioxide and hydrogen, and enhanced oil recovery.

Development of a Measurement Device for Micro Gas Flowrate Based on Laminar Flow Element with Micro-Curved Surface

The laminar flow meter (LFM) boasts several advantages such as no moving parts, a wide range ratio, high measurement accuracy, quick dynamic response, etc., and is a promising technology for micro gas flow measurement. In order to explore the influence of different curvature radii on curved surface gap LFM, three curved structures with different curvature radii were designed. The computational fluid dynamics method is applied to simulate the flow feature of three structures. The simulated velocity cloud and pressure distribution show that the larger the curvature radius, the more stable the flow of gas medium. The relationship between differential pressure and volume flow was obtained through the test within a flow range of 0~540 sccm. Regression analysis revealed that the volume flow measured by the curved surface LFM had a high linear relationship with the differential pressure. Experimental findings indicate that differential pressure of the structure with a curvature radius of 2 mm was greater than that of other two structures (curvature radius of 6 mm and 3 mm) at the same point. This indicates that adding the number of surfaces can effectively increase the pressure loss, so as to obtain a larger range ratio, but will increase the measurement error.

Enhancing Oil–Water Flow Prediction in Heterogeneous Porous Media Using Machine Learning

The rapid and accurate forecasting of two-phase flow in porous media is a critical challenge in oil field development, exerting a substantial impact on optimization and decision-making processes. Although the Convolutional Long Short-Term Memory (ConvLSTM) network effectively captures spatiotemporal dynamics, its generalization in predicting complex engineering problems remains limited. Similarly, although the Fourier Neural Operator (FNO) demonstrates adeptness at learning operators for solving partial differential equations (PDEs), it struggles with three-dimensional, long-term prediction. In response to these limitations, we introduce an innovative hybrid model, the Convolutional Long Short-Term Memory-Fourier Neural Operator (CL-FNO), specifically designed for the long-term prediction of three-dimensional two-phase flows. This model integrates a 3D convolutional encoder–decoder structure to extract and generate hierarchical spatial features of the flow fields. It incorporates physical constraints to enhance the model’s forecasts with robustness through the infusion of prior knowledge. Additionally, a temporal function, constructed using gated memory-forgetting mechanisms, augments the model’s capacity to analyze time series data. The efficacy and practicality of the CL-FNO model are validated using a synthetic three-dimensional case study and application to an actual reservoir model.

Development and calibration of a bio-geo-reactive transport model for UHS

The increased share of renewable energy sources will lead to large fluctuations in energy availability and increases energy storage’s significance. Large-scale hydrogen storage in the subsurface may become a vital element of a future sustainable energy system because stored hydrogen becomes an energy carrier available on demand. Large hydrogen amounts can be stored in porous formations such as former gas fields or gas storages, while caverns can contribute with high deliverability. However, the storage of hydrogen induces unique processes in fluid-fluid and rock-fluid interactions (for example, bio- and geochemical reactions), which may affect the efficiency of the storage. In the present study, a mathematical model describing the two-phase multicomponent flow in porous media, including bio- and geochemical reactions, is developed to predict these hydrogen-related processes. The proposed model extends an existing model in the open source simulator DuMux describing the bio-reactive transport process considering methanation and sulfate-reduction by geochemical reactions. Significant attention is placed on the reduction from pyrite-to-pyrrhotite coming with the generation of harmful hydrogen sulfide. This reaction is calibrated by developing a kinetic model in DuMux that mimics the observations of reactor experiments from literature. The developed and calibrated model is afterwards used for simulation runs on field scale to assess the impact on Underground Hydrogen Storage (UHS) operations. The developed kinetic model describes the reduction from pyrite-to-pyrrhotite in agreement with the observations in the literature, whereby particular focus was placed on the hydrogen sulfide production rate. The consecutive implementation of the transport model in DuMux on field scale, including the bio- and geochemical reactions, shows the potential permanent hydrogen losses caused by reactions and temporary ones induced by gas-gas mixing with the initial and cushion gas.

Oxidation Study and Mechanism Analysis of Desulfurization Ash in Dense-Phase Tower

Dense-phase-tower desulfurization technology is an emerging semi-dry flue-gas desulfurization ash process, i.e., the flue gas is allowed to enter the desulfurization tower from the bottom up and, at the same time, is sprayed with a desulfurizing agent that undergoes an acid–base reaction with the flue gas in the ascent process. The calcium sulfite and calcium sulfate produced by the reaction and the part of the desulfurization agent that is not involved in the reaction will enter the subsequent dust removal system, and what is retained is the by-product desulfurization ash. This desulfurization ash contains a large amount of calcium sulfite, which leads to its unstable nature; it is easily oxidized and expands in volume, and, if used in the field of building materials, it will lead to cracking and other problems, so it is difficult to effectively use it. In order to solve this problem, XRF, XRD, and iodometric and other analytical methods were used to determine the specific composition of desulfurization ash, and the muffle furnace and vertical tube furnace were used to study the thermal oxidative modification of calcium sulfite in desulfurization ash, to investigate the effects of the oxygen content, reaction temperature, medium flow rate, and chloride content on the oxidation of calcium sulfite, and to analyze the thermodynamics in the high-temperature oxidation reaction. The results showed that the oxidation rate of calcium sulfite increased with higher reaction temperatures. Increased oxygen content promoted the oxidation rate, particularly at low oxygen levels. The oxidation rate of calcium sulfite correlated positively with the medium flow rate until a rate of 75 mL·min− was reached. At a reaction temperature of 420 °C and a gas flow rate of 85 mL·min−1, the oxidation conversion efficiency exceeded 89%. Chloride content significantly reduced the oxidation rate of calcium sulfite, although this inhibition weakened at temperatures above 500 °C. Kinetic analysis suggested that the oxidation reaction of calcium sulfite predominantly occurred below 500 °C. These findings have both theoretical and practical implications for the thermal oxidation treatment and disposal of desulfurization ash.

A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales

AbstractIn this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.

Modeling of heat conduction through rate equations

AbstractStarting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following a variant of the Coleman-Noll procedure where the entropy production too is given by a non-negative constitutive equation. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive function for the heat flux that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to providing already known models (e.g., Maxwell-Cattaneo-Vernotte’s and Jeffreys-like heat conductors), this scheme allows the formulation of new models of heat transport that are likely to apply also in nanosystems. This is consistent with the fact that higher-order time derivatives of the heat flux are in order when high-rate regimes occur.

Learning a general model of single phase flow in complex 3D porous media

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R 2 = 0.9) when tested on extremely diverse real domains at multiple scales.

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

In this paper, a homogenized multiphase lattice Boltzmann (LB) model is established for parallelly simulating immiscible two-phase flow in both solid-free regions (pore scale) and porous areas (continuum scale). It combines the color-gradient multiphase model with the Darcy–Brinkman–Stokes method by adding a term that includes surface force and drag force of porous matrix to multiple-relaxation-time LB equation in moment space. Moreover, an improved algorithm is proposed to characterize and implement the apparent wettability in the locally homogenized porosity field. Validations and test cases are given to demonstrate the accuracy and robustness of this new model, as well as its applicability for trans-scale fluid simulation of transport and sorption behavior from porous (Darcy flow) area to free (Stokes flow) area. For practicality, the two-phase seepage flow in a composite rock structure with multiscale pores is simulated by this new model, and the effects of viscosity ratio and wettability on the displacement process are discussed.

Modeling gas flow in low-permeability formations: An efficient combination of mixed finite elements and high order time integration schemes

Numerical simulation of gas flow in low permeability formations is a challenging task due to the high nonlinearity induced by (i) the compressibility of the gas, (ii) the Klinkenberg slippage effect and (iii) the Langmuir adsorption of the gas on the pore surface. Because of these nonlinearities, modeling gas flow in low permeability formations requires a great deal of computational effort. In this work, we develop an efficient numerical model using advanced spatial and temporal discretization methods for a simultaneous solution of the coupled equations of gas flow, cubic Peng-Robinson equation of state, slippage effect and Langmuir adsorption. The spatial discretization is performed with the lumped hybrid formulation of the mixed finite element method which is well adapted for fluid flow in heterogeneous porous media. The time integration is performed with high-order methods via the method of lines (MOL) which allows large time steps and efficient solution of the nonlinear system of equations. Numerical experiments, performed for gas extraction in a heterogeneous domain, point out the high efficiency of the new model since it can be until 10 times more efficient than the classical first-order time discretization method. Results of global sensitivity analysis show that the intrinsic gas-phase permeability and the Klinkenberg factor are the most influential parameters controlling the pumping rate in the case of gas extraction in a homogeneous domain.

A lattice Boltzmann approach to mathematical modeling of myocardial perfusion.

A mathematical model of myocardial perfusion based on the lattice Boltzmann method (LBM) is proposed and its applicability is investigated in both healthy and diseased cases. The myocardium is conceptualized as a porous material in which the transport and mass transfer of a contrast agent in blood flow is studied. The results of myocardial perfusion obtained using LBM in 1D and 2D are confronted with previously reported results in the literature and the results obtained using the mixed-hybrid finite element method. Since LBM is not suitable for simulating flow in heterogeneous porous media, a simplified and computationally efficient 1D-analog approach to 2D diseased case is proposed and its applicability discussed.

Adaptive Space-Time Domain Decomposition for Multiphase Flow in Porous Media with Bound Constraints

Adaptive Space-Time Domain Decomposition for Multiphase Flow in Porous Media with Bound Constraints

Active Media Perfusion in Bioprinted Highly Concentrated Collagen Bioink Enhances the Viability of Cell Culture and Substrate Remodeling.

The bioprinting of high-concentrated collagen bioinks is a promising technology for tissue engineering and regenerative medicine. Collagen is a widely used biomaterial for bioprinting because of its natural abundance in the extracellular matrix of many tissues and its biocompatibility. High-concentrated collagen hydrogels have shown great potential in tissue engineering due to their favorable mechanical and structural properties. However, achieving high cell proliferation rates within these hydrogels remains a challenge. In static cultivation, the volume of the culture medium is changed once every few days. Thus, perfect perfusion is not achieved due to the relative increase in metabolic concentration and no medium flow. Therefore, in our work, we developed a culture system in which printed collagen bioinks (collagen concentration in hydrogels of 20 and 30 mg/mL with a final concentration of 10 and 15 mg/mL in bioink) where samples flow freely in the culture medium, thus enhancing the elimination of nutrients and metabolites of cells. Cell viability, morphology, and metabolic activity (MTT tests) were analyzed on collagen hydrogels with a collagen concentration of 20 and 30 mg/mL in static culture groups without medium exchange and with active medium perfusion; the influence of pure growth culture medium and smooth muscle cells differentiation medium was next investigated. Collagen isolated from porcine skins was used; every batch was titrated to optimize the pH of the resulting collagen to minimize the difference in production batches and, therefore, the results. Active medium perfusion significantly improved cell viability and activity in the high-concentrated gel, which, to date, is the most limiting factor for using these hydrogels. In addition, based on SEM images and geometry analysis, the cells remodel collagen material to their extracellular matrix.

Embedded Finite Element formulation for fluid flow in fractured porous medium

The presence of discontinuities, such as fractures or geological faults, can significantly influence the fluid flow in a porous medium. In general, the discontinuities can act as preferential flow paths. However, depending on their aperture and filling material, they can act as barriers to fluid flow. To model these different possibilities, this paper presents an embedded approach in the context of the finite element method to model the presence of discontinuities inside a porous medium in transient analyses. The formulation is attractive since it does not require the mesh used to discretize the porous medium to conform to the discontinuities. The derivation of the formulation is based on the Strong Discontinuity Approach by enriching the pressure field of the finite element with a Heaviside function. The enriched part of the pressure field is discretized based on the pressure jumps evaluated at the nodes where the discontinuity intersects the finite element. The discontinuity internal pressure is taken as an independent field, allowing the modeling of high pressures inside the discontinuity. A strategy to condense the discontinuity internal pressure degrees of freedom is presented. Numerical examples are presented showing the flexibility of the formulation to capture the influence of discontinuities on the fluid flow in porous medium. The results obtained with the proposed formulation are compared with interface element models, showing a good agreement between the two approaches.

Effect of particle size distribution variability on the permeability of hydrate-bearing sediments: A CFD study

Natural gas hydrates (NGH) are considered as a future clean energy in the era of carbon neutrality. The seepage behaviour of hydrate-bearing sediment (HBS) and its controlling factors are significant for developing effective production strategies. In this study, we aim to elucidate how the heterogeneous spatial distribution of clayey-silty sediment particles, particularly the non-uniform particle size distribution (PSD) affects the permeability of HBS. An algorithm was developed to generate the heterogeneous spatial distribution of sediment particles based on the PSD of hydrate-bearing cores extracted from Japan Nankai Trough (D50 = 122 μm). A series simulation of fluid flow in porous media based on CFD was conducted for the HBS with varying hydrate saturations (SH). The watershed segmentation algorithm was employed for the identification of pore structure, including pore space and pore throat with a detailed analysis on the pore structure evolution with SH. Host sediments with higher uniformity result in initial high permeability but the permeability reduction with increasing SH is more significant compared with that of lower uniformity. Pore throat width reduced to less than 5 μm with SH above 50% compared with its original width of ∼30 μm. Tortuosity exhibits a linear increase with SH, while permeability decreases exponentially with increasing tortuosity. We propose an improved permeability model (KCpro) based on the classical Kozeny-Carman model accounting for the change in specific surface area for non-uniform PSD in HBS with good agreement. This study confirmed the applicability of CFD modelling as a promising tool to study the seepage behaviour of HBS complementary to classical permeability experimental tests. Results of this study provide fundamental understanding on how permeability evolves in HBS with significant PSD variations in natural gas hydrate reservoirs in nature.

Open and remotely accessible Neuroplatform for research in wetware computing.

Wetware computing and organoid intelligence is an emerging research field at the intersection of electrophysiology and artificial intelligence. The core concept involves using living neurons to perform computations, similar to how Artificial Neural Networks (ANNs) are used today. However, unlike ANNs, where updating digital tensors (weights) can instantly modify network responses, entirely new methods must be developed for neural networks using biological neurons. Discovering these methods is challenging and requires a system capable of conducting numerous experiments, ideally accessible to researchers worldwide. For this reason, we developed a hardware and software system that allows for electrophysiological experiments on an unmatched scale. The Neuroplatform enables researchers to run experiments on neural organoids with a lifetime of even more than 100 days. To do so, we streamlined the experimental process to quickly produce new organoids, monitor action potentials 24/7, and provide electrical stimulations. We also designed a microfluidic system that allows for fully automated medium flow and change, thus reducing the disruptions by physical interventions in the incubator and ensuring stable environmental conditions. Over the past three years, the Neuroplatform was utilized with over 1,000 brain organoids, enabling the collection of more than 18 terabytes of data. A dedicated Application Programming Interface (API) has been developed to conduct remote research directly via our Python library or using interactive compute such as Jupyter Notebooks. In addition to electrophysiological operations, our API also controls pumps, digital cameras and UV lights for molecule uncaging. This allows for the execution of complex 24/7 experiments, including closed-loop strategies and processing using the latest deep learning or reinforcement learning libraries. Furthermore, the infrastructure supports entirely remote use. Currently in 2024, the system is freely available for research purposes, and numerous research groups have begun using it for their experiments. This article outlines the system's architecture and provides specific examples of experiments and results.

A pressure-projection pre-conditioning multi-fractional-step method for Navier–Stokes Flow in Porous Media

A new pressure-projection pre-conditioning multi-fractional-step (PPP-MFS) method for incompressible Navier–Stokes flow in porous media is presented. This fractional step method is applied to decouple the pressure and the velocity; thereby, overcoming the computational costs and difficulty associated with the resolution of the nonlinear term in the Navier–Stokes equation for fine geometric models. Specifically, time evolution is decomposed into a sequence of multi-fractional solution steps. In the first step, an elliptic problem is solved for pressure (p) with a no-slip boundary condition. This gives the Stokes pressure and velocity fields. In the second step, the obtained pressure p is then projected onto the field p∗ and used to solve for velocity field (u) required for the pre-conditioning of the solution to the Navier–Stokes equation. The pressure and velocity fields are obtained from the solution of the Navier–Stokes equation in the third step. Numerical and geometric discretisation of porous samples were carried out using finite-element method. For flow in simple channel models represented by two- and three-dimensions and in systems with high conductivity, the Stokes and Navier–Stokes numerical solutions produced close pressure and velocity field approximations. For flow around a cylinder, computation time is consistently higher in the Navier–Stokes equation by a factor of 2 with a pronounced non-symmetric pressure field at high mesh refinements. This computation time is desirable given that Navier–Stokes computation without preconditioning can be orders of magnitude more expensive.

Assessing Rheology Effects and Pore Space Complexity in Polymer Flow Through Porous Media: A Pore‐Scale Simulation Study

AbstractNon‐Newtonian fluid flow within porous media, exemplified by polymer remediation of contaminated groundwater/aquifer systems, presents complex challenges due to the fluids' complex rheological behavior within 3D tortuous pore structures. This paper introduces a pore‐scale flow simulator based on the OpenFOAM open‐source library, designed to model shear‐thinning flow within porous media. Leveraging this developed solver, extensive pore‐scale flow simulations were conducted on μ‐CT images of various real and synthetic porous media with varying complexity for both power‐law and Cross‐fluid models. We focused on the macroscale‐averaged deviation between bulk viscosity and the in‐situ viscosity, commonly denoted by a shift factor. We provided an in‐depth evaluation of the shift factor's dependency on the fluid's rheological attributes and the rock's pore space complexity. The least‐squares fitted values of the shift factor fell in the range of 1.6–9.5. Notably, the most pronounced shift factor emerged for extreme flow behavior indices. Our findings highlight not just the critical role of rheological parameters, but also demonstrate how the shift factor fluctuates based on tortuosity, characteristic pore length, and the cementation exponent. In particular, less porous/permeable systems with smaller characteristic pore lengths exhibited larger shift factors due to higher variations of shear rate and local viscosity in narrower flow paths. Additionally, the shift factor increased as rock became more tortuous and heterogeneous. The introduced pore‐scale simulation proves instrumental in determining the macroscopic averaged shift factor. This, in consequence, is vital for precise computations of viscosity and pressure drop when dealing with non‐Newtonian fluid flow in porous media.

Quantitative characterization of imbibition in fractured porous media based on fractal theory

In low-permeability reservoirs, such as shale and tight sandstone, imbibition is an important mechanism for enhancing oil recovery. After hydraulic fracturing treatment, these reservoirs create a network of fracture pathways for fluid flow. Therefore, understanding the imbibition mechanisms in fractured porous media and quantitatively characterizing oil–water distribution are crucial for the development of low-permeability reservoirs. In this study, a mathematical model of two-phase flow in porous media with branching fractures was established. The phase-field method was employed to track the oil–water interface, and quantitative characterization of imbibition was conducted based on fractal theory, and the effects of wetting phase injection rate, the number of disconnected fractures, fracture spacing, and fracture morphology on imbibition in branched fracture porous media were discussed. The research findings indicate that in branched fracture porous media, both co-current and countercurrent imbibition processes occur simultaneously, and there exists a diffusion interface layer with a certain thickness at the oil–water interface. The hydraulic pressure generated by the wetting phase injection rate provides the driving force for imbibition oil recovery, but it also affects the contact time between the wetting and non-wetting phases. The presence of disconnected fractures hinders the propagation of hydraulic pressure, reducing the effectiveness of imbibition. The imbibition displacement zone is limited and occurs only within a certain range near the fractures. As the number of branching fractures increases, the channels for the wetting phase to enter matrix pores are enhanced, resulting in higher efficiency of imbibition displacement of the oil phase. The results of this research can provide guidance for the design of fracturing programs and recovery prediction in low-permeability reservoirs.