Transport in Porous Media最新文献

This work conducts pore-scale numerical computations to reveal the hydrodynamic characteristics of the fully-developed flow through a fixed-bed reactor regularly packed with mono-sized spheres. One of the main purposes is to obtain invariant standard values which can be used as the benchmarks for those results from randomly packing methods such as Monte Carlo or DEM. Also, a repeatable and verifiable process is introduced to forecast the pressure drop and the mass flow rate in a packed bed without running any numerical simulation.

The mono-sized spheres in the present simulations are in FCC, BCC, or SC arrangement. For each packing, different Reynolds numbers and lattice angles are considered. For these regular arrangements, it is revealed that the cross-section of the reactor can be clearly separated into two regions: the more loosely-packed near-wall region and the densely-packed core region, with a boundary at a half-sphere diameter distance from the wall. The mass flow rates into the two regions will self-adjust themselves in proportion. Consequently, separate average Reynolds numbers in the near-wall, Re_w, and the core region, Re_co, are defined. Comparison of our computational results for fully-developed conditions with the experimental data for regular packings is presented. However, the inevitable presence of the entrance effect in the experiments on insufficiently-long regular packed beds forbids pertinent comparison. This work then continues to present a simplified model to predict the pressure drop through a reactor randomly packed with mono-sized spheres. The empirical correlations of C_D (times) d/L with Re_w or Re_co in respective regions are derived. These correlations can be used to evaluate the pressure drop through a reactor at a given total mass flow rate, which is proportioned in each region. A linear interpolation or extrapolation procedure is proposed to evaluate the (Delta) P based on the ((1/Delta) P_FCC)-({varepsilon }_{text{FCC}}), ((1/Delta Ptext{BCC}))-({varepsilon }_{text{BCC}}), and ((1/Delta) P_SC)-({varepsilon }_{text{SC}}) relations, with given average void fraction (varepsilon), diameter and length of the container, particle diameter, and total mass flow rate. The reliability of the simplified model has been validated through the comparison with empirical correlations and Monte Carlo simulation in the literature.

Multi-scale modelling techniques are commonly used to characterize heterogeneous rock samples. However, open challenges limit the efficiency of these models. A significant issue is the tradeoff between resolution and field of view (FoV) during imaging. Capturing an image of a heterogeneous rock sample that includes pores of different scales with a large FoV is impossible. Various novel approaches have attempted to solve this problem, but they have inherent limitations such as unrealistic results and high computational costs. In this study, we propose a novel method to generate 3D multiscale images of two heterogeneous rock samples: Berea sandstone and Edward Brown carbonate. We scanned both samples at low and high (HR) resolutions using X-ray microtomography. Our approach involves distinct reconstruction of resolved and unresolved porosity in rock images at lower resolutions. We divide the unresolved porosity into smaller sections, called unresolved templates, using the watershed algorithm to reduce memory allocation. The cross-correlation based simulation approach then finds a suitable replacement template from the HR images, which contain a significant number of micro-pores, using a modified overlap region selection procedure in 3D. We compare the geometrical and petrophysical properties of the reconstructed multi-scale images with those of the HR rock images. The results show good agreement with the HR image properties computed from the direct numerical simulation approach. Additionally, our thus validated method is two to four times faster in constructing multi-scale images.

Thermal consolidation of soil is a significant concern in buried geothermal pipeline engineering. Soil consolidation begins immediately upon pipeline completion, while a stable temperature field does not instantly form after soil backfilling. Therefore, considering the heat diffusion process post-pipeline installation is crucial for accurately predicting consolidation completion time. This study proposes a novel mathematical model integrating the heat diffusion process and continuous drainage boundary conditions. Based on the newly proposed model, the early-stage consolidation during the heat diffusion process can be accurately accounted so that the accelerated consolidation caused by the thermal effect would not be overestimated. In order to facilitate the application of the proposed model, a semi-analytical solution is derived by utilizing the integral transform method, variable separation method, and the inverse Fourier transform, the correctness of which has been validated through comparisons with the existing simplified studies. Additionally, a parametric study investigating the potential influencing parameters on thermal consolidation is conducted.

Multiple flow mechanisms that coexist in nanoscale porous media are responsible for deviations from the linear Klinkenberg equation. The use of mathematical models in the literature has obvious limitations in evaluating this flow phenomenon because the viscosity/diffusion coefficients of nanoscale porous media are more accurate only in the limited Knudsen number region. By introducing, the concept of an effective molecular mean free path, this paper proposes single models of viscosity/diffusion for the full Knudsen number range to replace the combination model in the literature. On this basis, a new apparent permeability model is developed with multiple coexisting mechanisms for the full Knudsen number range, and the effectiveness of the proposed model is verified by using published data. The discontinuous problem of the combination model of the viscosity/diffusion coefficient in the literature for the full Knudsen number range is solved using the new viscosity and diffusion coefficient models. The new apparent permeability model accurately predicts the absolute permeability and explains the phenomenon of deviation from the linear Klinkenberg equation. This paper further discusses the influence of different mechanisms on the permeability. The rarefaction effect weakens the diffusion ability in porous media but increases the contribution of Darcy flow to permeability. The viscous flow increment, absolute permeability and slippage effect were the most important flow mechanisms in nanopores.

Investigating the spatial and size distributions of fracture structures formed by various external stresses in coal is essential for understanding fracture evolution and methane percolation behavior in coal reservoirs. To estimate the characteristics of microscale fractures in three-dimensional space, X-ray computed microtomography was used to establish digital reconstructed fracture models. Two algorithms that reflect topological features were applied to quantitatively characterize coal fractures. The results show that tectonic stress negatively affects the anisotropy of fractures, reducing the frequency of fractures that are approximately parallel or perpendicular to the main direction. A new fracture connectivity evaluation parameter, calculated by the integral average of the linear fitting curve between the coordination number and the corresponding average radius of many maximum spheres in the pore network model, is proposed. This method is more objective for evaluating fracture connectivity. The results indicate that with increasing tectonic action, fracture connectivity improves. Based on skeleton model data, we found a power-law relationship between the equivalent diameter of the fracture and the cumulative volume. Using this relationship and the capillary model assumption, we rederived expressions for total gas seepage flux and permeability applicable to fractures that do not conform to the tortuous fractal theory. Additionally, we discovered that the fracture aperture follows a log-normal distribution and derived an improved cube model’s mathematical formula based on this. These findings are significant for revealing how different fracture structures affect gas seepage and provide a foundation for developing theoretical models to predict gas seepage in coal reservoirs.

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 success of foam-induced flow diversion in fractured carbonates hinges on proper injection strategies, requiring an in-depth understanding of the factors responsible for stimulating fracture–matrix interactions. In this study, we present a novel investigation of the interactions between the fracture and the matrix influenced by the mobility control effect during CH₄-foam injections. These interactions were probed at the pore scale using a three-phase flow system integrated with a high-resolution micro-CT scanner. In situ phase saturations were monitored and quantified to interpret the resulting fluid transport at various injection parameters. At the initial stage of foam injection, the surfactant solution was able to invade the matrix leading to water/oil displacement events, however, impeding gas penetration. Increasing total injection velocity produced higher in situ foam quality in the fracture than the injected quality, where significant fraction of the surfactant solution from the foam was primarily diverted into the matrix. A pronounced increase in the average gas saturation within the matrix was only observed at the highest injection velocity. The pore-scale evidence showed the occurrence of combined displacement processes (water/oil, gas/oil, gas/oil/water) in the matrix, attributed to the established mobility control in the fracture, which contributed to the diversion of surfactant solution and gas to the matrix. Lastly, the injection–soaking–production technique effectively mobilized the residual oil after a long injection process of CH₄-foam. At this stage, the surfactant solution was no longer playing a role as the primary invading fluid; rather, it was the diverted gas that led to the increase in the matrix-oil production.

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.