Numerical simulation of displacement characteristics of CO_2 injected in pore-scale porous media

Pore structure of porous media, including pore size and topology, is rather complex. In immiscible twophase displacement process, the capillary force affected by pore size dominates the two-phase flow in the porous media, affecting displacement results. Direct observation of the flow patterns in the porous media is difficult, and therefore knowledge about the two-phase displacement flow is insufficient. In this paper, a two-dimensional(2D) pore structure was extracted from a sandstone sample, and the flow process that CO_2 displaces resident brine in the extracted pore structure was simulated using the Navier eStokes equation combined with the conservative level set method. The simulation results reveal that the pore throat is a crucial factor for determining CO_2 displacement process in the porous media. The two-phase meniscuses in each pore throat were in a self-adjusting process. In the displacement process,CO_2 preferentially broke through the maximum pore throat. Before breaking through the maximum pore throat, the pressure of CO_2 continually increased, and the curvature and position of two-phase interfaces in the other pore throats adjusted accordingly. Once the maximum pore throat was broken through by the CO_2, the capillary force in the other pore throats released accordingly; subsequently, the interfaces withdrew under the effect of capillary fore, preparing for breaking through the next pore throat.Therefore, the two-phase displacement in CO_2 injection is accompanied by the breaking through and adjusting of the two-phase interfaces.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

The impact of heterogeneity and pore network characteristics on single and multi-phase fluid propagation in complex porous media:An X-ray computed tomography study

This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifically,high-resolution or micro X-ray computed tomography(CT)imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada,considered flow analogous to the Brazilian Pre-salt carbonate reservoirs.The petrophysical results comprised two distinct stromatolite depositional facies,the columnar and the fine-grained facies.By generating pore network model(PNM),the study quantified the relationship between key features of the porous system,including pore and throat radius,throat length,coordination number,shape factor,and pore volume.The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores.Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length.Additionally,a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields.The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation.Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others.The relation between saturation profiles,porosity profiles,and the number of fluid flow patterns for the samples was evident.Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection(SB)observed.

Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

A study on the temperature sensitivity of NMR porosity in porous media based on the intensity of magnetization Dedicated to the special issue “Magnetic Resonance in Porous Media”

The measurement of nuclear magnetic resonance(NMR)porosity is affected by temperature.Without considering the impact of NMR logging tools,this phenomenon is mainly caused by variations in magnetization intensity of the measured system due to temperature fluctuations and difference between the temperature of the porous medium and calibration sample.In this study,the effect of temperature was explained based on the thermodynamic theory,and the rules of NMR porosity responses to temperature changes were identified through core physics experiments.In addition,a method for correcting the influence of temperature on NMR porosity measurement was proposed,and the possible factors that may affect its application were also discussed.

Empirical study of magnetohydrodynamic effect on fluid flow in clayey porous media

Enhancing oil recovery from clayey reservoirs is a significant challenge in petroleum industry due to complex interactions between fluids and rock surfaces,particularly clay swelling.This study presents the first empirical analysis of magnetic fields'impact on fluid flow in clayey porous media.Our core findings indicate that magnetic treatment of water increases oil recovery by an average of 15–30%in clayey media,with limited effectiveness in pure quartz media.Detailed experiments unraveled that improved recovery factor by magnetic treatment stem from both mitigated swelling and altered magnetic properties at clay surface;introducing 30%clay to porous medium decreased the recovery by 32%compared to pure quartz sand.Heating the clay to around 1000°C to reduce its swelling property improved the recovery by only 16%,suggesting magnetic treatment is not solely attributed to clay swelling mitigation.Treating ferromagnetic films at clay surface with HCl to produce non-magnetic FeCl_(3) resulted in a high recovery factor,similar to the clay-free medium.Moreover,it was determined that a magnetic field intensity of 43760–51740 A/m is optimal for fluid displacement in clayey media.Notably,the intensity of 47760 A/m increased recovery to 84.5%in a 30%clay medium,compared to 49.7%without treatment.Interestingly,it was observed that the maximum flow rate was associated with zero potential difference across the medium,providing a faster method to determine the optimum magnetic field intensity.Lastly,the concept of‘Magnetic memory’was investigated,referring to the persistence of magnetic field's influence after its removal.Our findings indicated that pressure build-up time stability lasted 10 days post-treatment,after which water behavior reverts,and clay swelling resumes.This insight into the temporal dynamics of magnetic field application provides a deeper understanding of its long-term impacts on fluid flow in clayey reservoirs.

Anisotropic dynamic permeability model for porous media

Based on the tortuous capillary network model,the relationship between anisotropic permeability and rock normal strain,namely the anisotropic dynamic permeability model(ADPM),was derived and established.The model was verified using pore-scale flow simulation.The uniaxial strain process was calculated and the main factors affecting permeability changes in different directions in the deformation process were analyzed.In the process of uniaxial strain during the exploitation of layered oil and gas reservoirs,the effect of effective surface porosity on the permeability in all directions is consistent.With the decrease of effective surface porosity,the sensitivity of permeability to strain increases.The sensitivity of the permeability perpendicular to the direction of compression to the strain decreases with the increase of the tortuosity,while the sensitivity of the permeability in the direction of compression to the strain increases with the increase of the tortuosity.For layered reservoirs with the same initial tortuosity in all directions,the tortuosity plays a decisive role in the relative relationship between the variations of permeability in all directions during pressure drop.When the tortuosity is less than 1.6,the decrease rate of horizontal permeability is higher than that of vertical permeability,while the opposite is true when the tortuosity is greater than 1.6.This phenomenon cannot be represented by traditional dynamic permeability model.After the verification by experimental data of pore-scale simulation,the new model has high fitting accuracy and can effectively characterize the effects of deformation in different directions on the permeability in all directions.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Modeling of multiphase flow in low permeability porous media:Effect of wettability and pore structure properties

Multiphase flow in low permeability porous media is involved in numerous energy and environmental applications.However,a complete description of this process is challenging due to the limited modeling scale and the effects of complex pore structures and wettability.To address this issue,based on the digital rock of low permeability sandstone,a direct numerical simulation is performed considering the interphase drag and boundary slip to clarify the microscopic water-oil displacement process.In addition,a dual-porosity pore network model(PNM)is constructed to obtain the water-oil relative permeability of the sample.The displacement efficiency as a recovery process is assessed under different wetting and pore structure properties.Results show that microscopic displacement mechanisms explain the corresponding macroscopic relative permeability.The injected water breaks through the outlet earlier with a large mass flow,while thick oil films exist in rough hydrophobic surfaces and poorly connected pores.The variation of water-oil relative permeability is significant,and residual oil saturation is high in the oil-wet system.The flooding is extensive,and the residual oil is trapped in complex pore networks for hydrophilic pore surfaces;thus,water relative permeability is lower in the water-wet system.While the displacement efficiency is the worst in mixed-wetting systems for poor water connectivity.Microporosity negatively correlates with invading oil volume fraction due to strong capillary resistance,and a large microporosity corresponds to low residual oil saturation.This work provides insights into the water-oil flow from different modeling perspectives and helps to optimize the development plan for enhanced recovery.

Three-Dimensional Imaging of Pore-Scale Water Flooding Phenomena in Water-Wet and Oil-Wet Porous Media

The penetration of water during water flooding has been observed over many years using several methods. A microfocused X-ray computed tomography scanner can be used to directly observe 3D water flooding in a nondestructive manner. To eliminate the possibility of false images being produced because of X-ray broadening effects, we developed a visualization method by arranging the brightness distribution of all phases involved. Water flooding experiments were conducted using oil-wet and water-wet porous media. The water phase was injected upward into packed glass beads containing an oil phase, and the process was scanned every minute until steady state was reached. Using this scheme, real-time, the water invasion pattern and oil trapping process in clusters of pores and individual pores can be observed clearly. By eliminating false images, the boundary of each phase could be identified with high precision, even in a single pore. Porelevel phenomena, including snap off (which has never before been captured in a real 3D porous medium), piston-like displacement, and the curvature of the interface, were also observed. Direct measurement of the pore throat radius and the contact angle between the wetting and nonwetting phases gave an approximation of the capillary pressure during the piston-like displacement and snap-off processes.

Flow characteristics and regime transition of aqueous foams in porous media over a wide range of quality,velocity,and surfactant concentration

Aqueous foam is broadly applicable to enhanced oil recovery(EOR).The rheology of foam as a function of foam quality,gas and liquid velocities,and surfactant concentration constitute the foundation of its application.The great variations of the above factors can affect the effectiveness of N2 foam in EOR continuously in complex formations,which is rarely involved in previous relevant studies.This paper presents an experimental study of foam flow in porous media by injecting pre-generated N2 foam into a sand pack under the conditions of considering a wide range of gas and liquid velocities and surfactant concentrations.The results show that in a wide range of gas and liquid velocities,the pressure gradient contours are L-shaped near the coordinate axes,but V-shaped in other regions.And the surfactant concentration is a strong factor influencing the trend of pressure gradient contours.Foam flow resistance is very sensitive to the surfactant concentration in both the high-and low-foam quality regime,especially when the surfactant concentration is less than CMC.The foam quality is an important variable to the flow resistance obtained.There exists a transition point from low-to high-quality regime in a particular flow system,where has the maximum flow resistance,the corresponding foam quality is called transition foam quality,which increases as the surfactant concentration increases.The results can add to our knowledge base of foam rheology in porous media,and can provide a strong basis for the field application of foams.

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Two-phase flow in porous media is a very active field of research,due to its important applications in groundwater pollution,CO_(2)sequestration,or oil and gas production from petroleum reservoirs,just to name a few of them.Fractional flow equations,which make use of Darcy's law,for describing the movement of two immiscible fluids in a porous medium,are among the most relevant mathematical models in reservoir simulation.This work aims to solve a fractional flow model formed by an elliptic equation,representing the spatial distribution of the pressure,and a hyperbolic equation describing the space-time evolution of water saturation.The numerical solution of the elliptic part is obtained using a finite-element(FE)scheme,while the hyperbolic equation is solved by means of two dif-ferent numerical approaches,both in the finite-volume(FV)framework.One is based on a monotonic upstream-centered scheme for conservation laws(MUSCL)-Hancock scheme,whereas the other makes use of a weighted essentially non-oscillatory(ENO)reconstruc-tion.In both cases,a first-order centered(FORCE)-αnumerical scheme is applied for inter-cell flux reconstruction,which constitutes a new contribution in the field of fractional flow models describing oil-water movement.A relevant feature of this work is the study of the effect of the parameterαon the numerical solution of the models considered.We also show that,in the FORCE-αmethod,when the parameterαincreases,the errors diminish and the order of accuracy is more properly attained,as verified using a manufactured solution technique.

Computer simulation of Cu:AlOOH/water in a microchannel heat sink using a porous media technique and solved by numerical analysis AGM and FEM

Extensive improvements in small-scale thermal systems in electronic circuits,automotive industries,and microcomputers conduct the study of microsystems as essential.Flow and thermic field characteristics of the coherent nanofluid-guided microchannel heat sink are described in this perusal.The porous media approximate was used to search the heat distribution in the expanded sheet and Cu:γ-AlOOH/water.A hybrid blend of Boehme copper and aluminum nanoparticles is evaluated to have a cooling effect on the microchannel heat sink.By using Akbari Ganji and finite element methods,linear and non-linear differential equations as well as simple dimensionless equations have been analyzed.The purpose of this study is to investigate the fluid and thermal parameters of copper hybrid solution added to water,such as Nusselt number and Darcy number so that we can reach the best cooling of the fluid.Also,by installing a piece of fin on the wall of the heat sink,the coefficient of conductive heat transfer and displacement heat transfer with the surrounding air fluid increases,and the efficiency of the system increases.The overall results show that expanding values on the NP(series heat transfer fluid system maximizes performance with temperatures)volume division of copper,as well as boehmite alumina particles,lead to a decrease within the stream velocity of the Cu:AlOOH/water.Increasing the volume fraction of nanoparticles in the hybrid mixture decreases the temperature of the solid surface and the hybrid nanofluid.The Brownian movement improves as the volume percentage of nanoparticles in the hybrid mixture grows,spreading the heat across the environment.As a result,heat transmission rates rise.As the Darcy number increases,the thermal field for solid sections and Cu:AlOOH/water improves.

Data inversion of multi-dimensional magnetic resonance in porous media

Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral information.The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media.Apart from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion spectra.Through the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases.Signals in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore scales.The separation of contributions from different environments is a common ill-posed problem,which can be resolved numerically.Moreover,the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra.This paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different scenarios.Detailed information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.

Synthesis of waterborne polyurethane-humic acid cross-linked biomass porous materials for the adsorption of methylene blue

A series of adsorbent materials(WPU-HAx-y)with a three-dimensional porous structure,green sustainability,and excellent performance were prepared and evaluated for the removal of methylene blue using nontoxic and environmentally friendly waterborne polyurethane as the matrix material and humic acid,a biomass material,as the functional material.The newly synthesized adsorbents were characterized by infrared spectroscopy,scanning electron microscopy,specific surface area,and thermogravimetric.The effects of contact time(0-8 h),starting concentration(10-100 mg·L^(-1)),pH(3-11),solution temperature(30-60℃),and coexisting ions(Ca2+,Na+,K+,Mg2+)on the performance were investigated.Pseudo-first-order,pseudo-second-order,elovich,and intra-particle diffusion models were used to analyze the adsorption kinetics;the Langmuir,Freundlich,Temkin,and Dubin-Radushkovich adsorption isotherms were evaluated;and the adsorption behavior of the adsorbent materials was found to be more appropriate for the pseudo-second-order model for chemical pollutant removal than the Langmuir model,which depends on monolayer adsorption.WPU-HA2-3 stood out with a maximum adsorption capacity of 813.0081 mg·g^(-1) fitted to the pseudo-second-order and 309.2832 mg·g^(-1) fitted to the Langmuir model,showing superior adsorption performance and regenerability.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

A Fractal Orifice-Throat Model for Seepage Characteristics of Multiscale Porous Media

The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.

Numerical Investigation of Heat and Mass Transfer in Nanofluid-Filled Porous Medium

In this work, we numerically study the laminar mixed convection of fluid flow in a vertical channel filled with porous media during the drying process. The porous medium, modeled as a vertical wall, consists of solid and nanofluid phase (Water-Al2O3 or Water-Cu), as well as a gas phase. The established model is developed based on Whitaker’s theory and resolved by our numerical code using Fortran. Results principally show the influence of various physical parameters, such as nanoparticle volume fraction, ambient temperature, and saturation on heat and mass transfer on the drying process. This study brings the effect of the presence of nanofluids in porous media. It contributes not only to our fundamental understanding of drying processes but also provides practical insights that can guide the development of more efficient and sustainable drying technologies. .

Pore structure and liquid flow velocity distribution in water-saturated porous media probed by MRI

Magnetic resonance imaging （MRI） was used to probe the structure and flow velocity within the interparticle space of a packed bed of agar beads under water-saturated condition. The images of the velocity field at three different flow rates were obtained. To determine the pore-parameter of the porous media, the internal structure of the bed was also obtained using image processing technique. The results show that the porosity of the sample is 31.28% and the fitting curve for the distribution of pore equivalent diameter follows Gaussian distribution. The velocity profiles do shift as the flow rate varies and the solution flow through the void space is not a homogeneous flow in any pores. The velocity distributions within the pore are roughly parabolic with the local maximum being near the center. About half of the velocity components are in the class of 0-1 cm/s. The frequency of lower velocity components is lower at higher flow rate, but to higher velocity components, it is just the opposite.