Transport in Porous Media最新文献

Solute transport in unsaturated conditions is important in various applications and natural environments, such as groundwater flow in the vadose zone. Studies of unsaturated solute transport show complex characteristics (e.g. non-Fickian transport) due to larger variations in the pore-scale velocities compared to transport in saturated conditions. However, the physical processes at the pore scale are still not completely understood because direct three-dimensional observations at the pore scale are very limited. In this study, single-phase and two-phase solute transport was directly characterized by performing tracer injection experiments in a sintered glass and Bentheimer sandstone sample. These experiments were imaged by continuous scanning with fast laboratory-based micro-computed tomography. The network-scale flow velocities and transport properties were characterized by using the pore-based transient concentration fields to determine the tracer’s arrival time and filling duration in every pore. Important measures for dispersion (the scalar dissipation rate and filling duration) were determined and indicated a wide range in pore-scale velocities and the existence of stagnant and flowing pores for the unsaturated experiments. Furthermore, we performed the first quantification of the mass transfer coefficient between stagnant and flowing pores on three-dimensional experimental data. We also calculated the tortuosity directly from the interstitial velocity and the pore-based velocity. This was found to be 13% higher in unsaturated conditions compared to saturated conditions. Our results indicate that pore-scale structural heterogeneity increases the differences between saturated and unsaturated solute transport. This study thus provides further insight into pore-scale spreading and mixing of dissolved substances in unsaturated porous media.

The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (Front Phys 8:4, 2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. We analyzed 46 relative permeability curves based on the Lattice–Boltzmann color fluid model and two experimentally determined relative permeability curves. The analysis of the relative permeability data followed the methodology proposed by Roy et al. (Front Phys 8:4, 2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, the coefficients of the constitutive equation were found to be nearly the same for all wetting conditions. On the basis of these results, a simple approach was proposed to reconstruct the relative permeability of the oil phase using only the co-moving velocity relationship and the relative permeability of the water phase. This proposed method provides new information on the interdependence of the relative permeability curves, which has implications for the history matching of production data and the solution of the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before.

We present a comprehensive theoretical analysis which integrates the Klinkenberg plot into the pulse decay method (PDM) to effectively address the slippage effect on permeability measurement of micro/nanoporous media. Employing an asymptotic perturbation analysis on the Navier–Stokes equation within a capillary model, our work fills a critical gap in the interpretation of PDM experimental data, particularly by considering the influence of Knudsen number on permeability. Our findings substantiate the reliability of the Klinkenberg plot in interpreting PDM data, particularly when the ratio between the pore volume and the upstream or downstream chamber is below 0.1. It is noteworthy that our study underscores the persistent presence of the slippage effect when one chamber is sealed, emphasizing the necessity for careful consideration in permeability measurements under such conditions. The robustness of the theoretical framework is validated through experimental results, providing strong supports for the accuracy and applicability of our approach in heat and mass studies in micro/nanoporous media.

A method for calculating capillary pressure functions and saturation-dependent permeabilities of geometries containing several length scales is presented. The method does not require the exact geometries of the smaller length scales. Instead, it requires the effective two-phase flow parameters. It does this by generating phase distributions that form static equilibria at a selected capillary pressure value, similar to pore-morphology methods. Within a porous material, the effective parameters are used to obtain the corresponding phase saturation. It is shown how these phase distributions can be used in geometries spanning several length scales to calculate the capillary pressure function and saturation-dependent permeabilities. The method is tested on a geometry containing a simple isotropic porous material and it is applied to a complex textile stack geometry from a liquid composite molding process. In this geometry, three different length scales can be distinguished. The effective two-phase flow parameters of the textile stack are calculated by the proposed method, avoiding expensive simulations.

Numerical simulation studies of water–rock interaction mechanisms and pore-scale multiphase flow properties often require high computational efficiency and realistic geometries to enable a fast and accurate description of hydrodynamic behavior. In this paper, we have chosen to use deep learning models to achieve these requirements, firstly by using encoder structures to refine the image segmentation of void-solid structures on complex geometries of scanning electron microscopy (SEM) images of porous media through few-shot learning (FSL), not only obtaining an accuracy of 0.97, but also reducing the amount of annotation work. We then focus on pore-scale three-dimensional (3D) structural reconstruction using the unpaired image-to-image translation method, optimizing the cycle-consistent adversarial network (cycle-GAN) model via sliced Wasserstein distance (SWD) to transfer marine sedimentary sandstone features to the initial image, and the geometric stochastic reconstruction problems are transformed into optimization problems. Subsequently, the computational efficiency was improved by a factor of 21 by implementing the lattice Boltzmann simulation method (LBM) accelerated by GPU through compute-unified device architecture (CUDA). The flow field distribution and absolute permeability of the extracted 2D samples and the reconstructed 3D porous media structure were simulated. The results showed that our method could rapidly and accurately reconstruct the 3D structures of a given feature, ensuring statistical equivalence between the 3D reconstructed structures and 2D samples. We solve the problem of extrapolation-based 3D reconstruction of porous media and significantly reduce the time spent on structure extraction and numerical calculations.

Evaporation-induced salt crystallization in complex porous structures is highly important for diverse scientific and industrial fields. Individual capillary tubes are elementary components used for investigating flow and transport in the interparticle interstices of porous media. In this study, the effects of the angularity and size of capillary tubes on water evaporation and salt crystallization were investigated through monitoring the receding meniscus, salt crystal morphology and growth process in capillary tubes with different cross sections. The Stefan diffusive and two-regional models were used to simulate evaporation from capillaries of different cross-sectional shapes in the absence and in the presence of salt, respectively. The evaporation process of deionized water in round tubes could be divided into two stages: the falling rate and the receding front stages. However, the evaporation process of deionized water for the square tubes, where a liquid film was formed, could be divided into three stages: a constant rate, receding front and falling rate stages. The salt evaporation rate was lower than that of deionized water owing to the lower water activity and obstruction from the salt crystals. The evaporation rate was proportional to the tube diameter for the round capillaries and inversely proportional to the inner side length of the square capillaries for both deionized water and the salt solution. Owing to the effect of thick liquid films on both the drying rate and ion transport, crystallization occurred in the bulk meniscus within a round tube, while crystallization preferentially occurred at the tube entrance for the square tubes. The agreement between the experimental observations and model simulations revealed that the two-region model was capable of describing the evaporation-induced salt crystallization in the square tubes.

The important problem of the flow through a star-shaped crack is studied. Both clear and porous medium-filled ducts are solved for the first time. An accurate modified Ritz method is used to accommodate concave sharp corners. Flow rates and Poiseuille numbers are determined for star ducts with 2–6 pointy branches. Asymptotic approximations and corner singularities are discussed.

Mobilization of in situ fine particles in geothermal reservoirs is a key contributor to permeability damage and clogging of the reservoir rock, leading to a decline in well productivity during enhanced geothermal operations. This phenomenon is a result of disturbance in the mechanical equilibrium of the forces acting on a given fine particle, most significant of which are electrostatic and drag forces. These forces are affected by changes in fluid flow velocities, in situ temperatures, or ionic strength of in situ fluids. Theoretical formulation of migration of fine particles in porous media driven by non-isothermal flow remains challenging, and requires a considerable number of parameters to quantify the characteristics of a given colloidal particle-pore fluid–solid grain system. The identification of all the involved parameters often necessitates costly, intricate, and time-consuming physical experiments. Moreover, implementing the complete form of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, commonly adopted to evaluate changes in electrostatic forces, is complicated, computationally demanding, and impractical, particularly when applied to evaluate fines migration at a reservoir scale. This study presents a theoretical framework for accurate and practical prediction of fine particle migration driven by non-isothermal flow in a clay-NaCl-quartz system. The novel contributions of this study are twofold. Firstly, a new numerical model is developed based on the complete DLVO theory, which integrates for the first time the effects of both thermal and hydraulic loads on all underlying parameters including both the static dielectric constant and the refractive index of the pore fluid. Secondly, an innovative simplified DLVO-based model has been introduced, requiring notably fewer parameters compared to existing models, thus offering a practical and efficient solution. The proposed models are utilized to conduct a comprehensive assessment of the fundamental mechanisms involved in fine particle liberation. Findings are key to predict fines-migration-induced permeability damage in geothermal reservoirs to achieve a sustainable design of energy storage/production operations as well as to develop effective strategies to prevent or mitigate the decline in well productivity in time.

Abstract

Reservoir modeling consists of two key components: the reproduction of the historical performance and the prediction of the future reservoir performance. Industry-standard reservoir simulators must run fast on enormous and possibly unstructured grids while yet guaranteeing a reasonable representation of physical and chemical processes. However, computational demands limit simulators in capturing involved physical and geochemical mechanisms, especially when chemical reactions interfere with reservoir flow. This paper presents a mathematical workflow, implemented in IORSim, that makes it possible to add geochemical calculations to porous media flow simulators without access to the source code of the original host simulator. An industry-standard reservoir simulator calculates velocity fields of the fluid phases (e.g., water, oil, and gas), while IORSim calculates the transport and reaction of geochemical components. Depending on the simulation mode, the geochemical solver estimates updated relative and/or capillary pressure curves to modify the global fluid flow. As one of the key innovations of the coupling mechanism, IORSim uses a sorting algorithm to permute the grid cells along flow directions. Instead of solving an over-dimensionalized global matrix calling a Newton–Raphson solver, the geochemical software tool treats the species balance as a set of local nonlinear problems. Moreover, IORSim applies basis swapping and splay tree techniques to accelerate geochemical computations in complex full-field reservoir models. The presented work introduces the mathematical IORSim concept, verifies the chemical species advection, and demonstrates the IORSim computation efficiency. After validating the geochemical solver against reference software, IORSim is used to investigate the impact of seawater injection on the NCS Ekofisk reservoir chemistry.

Article Highlights

• The IORSim sorting algorithm decouples the nonlinear geochemical reaction calculations into recurring one-dimensional problems to assure numerical stability and computation efficiency. To the best of our knowledge, this work presents the mathematical concept, implementation, and application of topological sorting for the first time on (industry) field-scale problems.

• IORSim combines topological sorting with basis swapping and splay trees to significantly reduce computation times. Moreover, a high-speed forward simulation mode was developed to allow the post-advection of chemical components to visualize species distribution, water chemistry, and mineral interactions. If the geochemical reactions interfere with the fluid flow, the IORSim backward mode uses relative permeability curves to update the global fluid flow at each time step.

• We validate the implemented topological scheme on a reservoir grid, show the computation efficiency, and compar

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.