Transport in Porous Media最新文献

This study investigates multiphase flow with non-Newtonian fluid at pore scale, using the Compressive Continuum Species Transfer (C-CST) method in a microchannel and 2D porous media, with emphasis on drainage and mass transfer between fluids through the Volume of Fluid (VOF) method. The object of study is the multiphase flow in oil reservoirs, where immiscible fluids coexist in the porous media. The use of recovery methods becomes relevant in scenarios of low reservoir energy or when the physical properties of the oil compromise the flow. The influence of petroleum rheology, especially heavy crude oil with non-Newtonian viscoelastic behaviour, is considered. Recovery methods, such as the injection of CO₂, aim to optimize the flow by modifying the rheological properties of the fluid. This article aims to conduct a numerical analysis using the C-CST method with Direct Numerical Simulation (DNS) and volume tracking techniques to capture an interface between fluids. The main objective is to numerically implement a non-Newtonian rheological model in the linear momentum conservation equation, comparing the flow between non-Newtonian and Newtonian fluids at pore scale, and analysing the mass transfer at the flow interface with this new approach.

Understanding the dynamics of the filling process of a pore body with a nonwetting fluid is important in the context of dynamic pore network models and others. It can justify many of the assumptions behind the different rules that describe how the network behaves during imbibition and drainage processes. It also provides insight into the different regimes pertinent to this system. The filling process starts with the contact line pinning at the pore entrance. Three regimes can be identified during the filling process that is related to how the contact line advances. In the first two regimes, the contact line pins at the pore entrance while the emerging droplet develops, and in the third one, the contact line departs the entrance of the pore and advances along the pore surface. During the first regime, which is brief, the curvature of the meniscus increases, and likewise, the corresponding capillary pressure, while in the other two regimes, the curvature decreases and so does the capillary pressure. Such behavior results in the rate at which the nonwetting fluid invades the pore to change. It initially decreases, then increases as the meniscus advances. The radius of curvature of the meniscus, eventually, increases to infinity for which the interface assumes a flat configuration. A one-dimensional modeling approach is developed that accounts for all these regimes. The model also considers the two immiscible fluids over a wide spectrum of contrast in viscosity. Information about the mean velocity of the invading fluid, the location of the contact line, the radius of curvature of the meniscus, the volume of the emerging droplet, and several others are among the details that the model provides. A computational fluid dynamics (CFD) simulation has also been considered to confirm the proposed fates of the interface and to provide a framework for comparisons. The results of the validation process show, generally, a very good match between the model and the CFD analysis.

We review models for unsteady porous media flow in the volume-averaging framework and we discuss the theoretical relations between the models and the definition of the model coefficients (and the uncertainty therein). The different models are compared against direct numerical simulations of oscillatory flow through a hexagonal sphere pack. The model constants are determined based on their definition in terms of the Stokes flow, the potential flow and steady nonlinear flow. Thus, the discrepancies between the model predictions and the simulation data can be attributed to shortcomings of the models’ parametrisation. We found that an extension of the dynamic permeability model of Pride et al. (PRB 47(9):4964–4978, 1993) with a Forchheimer-type nonlinearity performs very well for linear flow and for nonlinear flow at low and medium frequencies, but the Forchheimer term with a coefficient obtained from the steady-state overpredicts the nonlinear drag at high frequencies. The model reduces to the unsteady Forchheimer equation with an acceleration coefficient based on the static viscous tortuosity for low frequencies. The unsteady Forchheimer equation with an acceleration coefficient based on the high-frequency limit of the dynamic tortuosity has large errors for linear flow at medium and high frequencies, but low errors for nonlinear flow at all frequencies. This is explained by an error cancellation between the inertial and the nonlinear drag.

Porous ionic electrospray emitters have received significant interest for space propulsion due to their performance and operational simplicity. We have developed a diffusion equation for describing the transient flow response in a porous electrospray emitter, which allows for the prediction of the settling time for flow in the porous emitter. This equation accounts for both the change in liquid storage at exposed pores on the emitter with pressure and viscous diffusion through Darcy’s law. Transient flow solutions are provided for the most common emitter topologies: pillar, cone, and wedge. Transient flow solutions describe the settling time and magnitude of current overshoot from porous electrosprays, while providing useful guidelines for reducing transient response time through emitter design. Comparing diffusion of pressure to the onset delay model for electrospray emission shows that diffusion is most relevant at higher voltages and when a porous reservoir is used. Accounting for multiple emission sites on the wedge geometry shows that emission sites settle in proportion to emission site spacing to the power − 1.74.

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.

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.