Transport in Porous Media最新文献

Spontaneous capillary imbibition in liquid–liquid systems with a shear-thinning wetting phase is crucial in natural and industrial processes yet remains underexplored. Shear-thinning fluids exhibit a continuous transition between power law and Newtonian behavior as the shear rate varies. To capture this rheological evolution during imbibition, we propose a Carreau–Yasuda-based transition function that quantitatively characterizes the relationship between wall shear rate and imbibition rate. Based on this function, we derive a governing equation, termed the transition model, to describe the capillary rise dynamics when Carreau–Yasuda fluid displaces a viscous liquid. The model is validated through multi-relaxation-time color-gradient lattice Boltzmann simulations. In parallel, capillary rise experiments using xanthan gum solutions and silicone oil are conducted to provide physical observations. The proposed transition function accurately captures the dynamic wall shear rate–imbibition rate relationship as Carreau–Yasuda fluids transition between power law and Newtonian behavior. Numerical solutions of the transition model closely align with experimental observation and lattice Boltzmann method simulation, whereas traditional power law model deviates at lower imbibition rates. Scaling analysis showed that, different from power law fluid, Carreau–Yasuda fluid imbibition in late viscous stage still obeys the classic square-root law when the imbibition rate falls below the critical value defined by the model and otherwise follows a power law scaling. This work provides new insights in shear-thinning fluids liquid–liquid imbibition and offers a robust framework for advancing the studies of non-Newtonian fluid imbibition in complex geometries.

This paper presents a comprehensive numerical framework for simulating convection-dominated transport phenomena in heterogeneous porous media, combining a weak Galerkin finite element method for spatial discretization on general polygonal meshes with a high-order diagonally implicit Runge–Kutta scheme for temporal integration. The method effectively addresses key challenges in porous media simulations, including handling of sharp gradients in convection-dominated flows, accurate representation of complex geometries and material interfaces, and robust treatment of nonlinear reaction terms. Theoretical analysis establishes unconditional stability and optimal convergence rates of (mathcal {O}(tau ^p + h^k)), where p and k represent the temporal and spatial orders of accuracy, respectively. The analysis is extended to mixed boundary conditions commonly encountered in practical applications. Numerical experiments demonstrate the method’s superiority over conventional approaches, particularly in maintaining solution quality for high Péclet number flows and complex heterogeneous domains. The scheme’s computational efficiency is validated through CPU-time comparisons against established methods for equivalent accuracy targets. Additional investigations confirm the method’s robustness for strongly nonlinear reactions and its extensibility to three-dimensional problems. The conservation properties and ability to handle general meshes make it particularly suitable for practical porous media applications including contaminant transport and enhanced oil recovery, as demonstrated through a realistic hydrogeological simulation.

Cement-based material fabrication typically involved cement-mix curing, followed by drying, which partially removed the evaporable water. The post-curing drying of cement-based materials is addressed with unprecedented determination of the drying-participating water (DPW) and drying-induced air voids (DIAV), which in this work involve drying at 23 °C and 40% relative humidity, and differ from the widely reported greater quantities for elevated-temperature drying. This work also provides a simple method for the determination in real time during drying. Prior methods, such as porosimetry and density measurement, are inadequate. Of significance is the finding that increasing the water/cement ratio caused the DPW and DIAV contents to grow, but the fraction of the drying-induced pore volume occupied by air remained unaffected. Here, “complete drying” means complete removal of the part of the evaporable water that can be removed under the drying conditions used (23 °C, 40% relative humidity, 30 days), i.e., DPW during post-curing drying. The cured material was saturated with water before drying started. During drying, the DPW content diminished while the drying-induced air voids (DIAV, the part of the total air voids resulting from drying under the drying conditions used) content grew, with air (rather than water) increasingly occupying the drying-induced pores. The density and DPW + DIAV (drying-induced porosity) decreased slightly during drying. Increasing the water/cement ratio caused the DPW and DIAV contents to grow, but the fraction of the drying-induced pore volume occupied by air remained unaffected. This work provides a new method of real-time determination of DPW and DIAV during drying.

To optimize recovery during shale gas operations and enable efficient CO₂ storage in depleted shale formations, it is crucial to accurately model all relevant transport and storage mechanisms. Despite significant progress in the technical literature, comprehensive modeling of diffusion and sorption in shale remains a major challenge due to the inherent complexity and scale of the system.

This study introduces a volume-averaged dual-porosity model for gas diffusion and sorption in shale. We focus on the matrix segments of the shale system where larger natural or induced fractures dictate the boundary conditions.

The new model, represented by coupled ordinary differential equations (ODEs), accommodates gases with a wide range of sorption affinities and extends the application of Vermeulen’s approximation to a broad range of the characteristic times for diffusion and sorption.

Calculation results are validated against fully discretized finite-difference numerical solutions to the governing partial differential equations (PDEs) for both inert gases (e.g., helium - He) and highly adsorptive gases (e.g., CO₂). The new model accurately captures gas transport and sorption in dual-porosity systems without requiring a full domain discretization. Additionally, we discuss its application in characterizing transport and storage mechanisms in shale cores using tandem experiments with He and CO₂.

In summary, this study introduces and validates a novel integral model for gas transport and sorption in dual-porosity systems. The model can serve as an efficient tool for the interpretation of core-scale experiments and provide a pathway for upscaling transport and sorption processes by translating relevant characteristic times.

Recently, there has been interest in stabilizing mechanisms for the classical viscous fingering instabilities in Hele-Shaw cells. Here, we critically review the stability criterion and derive it more generally, going beyond the single-finger criterion and analytically deriving critical slowing-down times in the slow-flow regime. We rederive the stability analysis for the linear opening scenario, obtaining a multiple-finger instability phase diagram, where we determine that the linear opening profile does not increase the stability range in the (U, W) space unless velocity corrections are considered. Furthermore, we found a crossing in the stability ranges at critical values of ((U_c,W_c)), indicating an enlarged stability for Hele-Shaw cells with a linear profile, only for wide cells and low flow speeds. We further analyze other opening profiles amenable to analytical treatment, including the power-law and exponential profiles.

Spontaneous imbibition plays a significant role in numerous engineering problems, particularly in the context of oil and gas reservoir exploitation over several decades. To date, various models have been proposed to simulate this process. However, none of the existing models simultaneously consider the effects of variable cross-section, fluid viscosity, and gravity. This study assumes that capillaries exhibit tortuous, non-circular, and irregular axial variations. By fully considering the effects of fluid viscosity and gravity on imbibition behavior, it proposes a more generalized spontaneous imbibition model. The results calculated by the new model are compared with both published data and the numerical simulations conducted in this study, validating its predictive capability. The findings indicate that for symmetric C-D and D-C capillaries, the total imbibition time is independent of the arrangement order of capillaries with different diameters. In contrast, for asymmetric capillaries, the total imbibition time decreases as the number of pore-throat structures increases. When the number of pore-throat structures is large, the interface displacement is proportional to the square root of time (t^1/2), exhibiting behavior similar to that observed in uniform capillaries. Based on this observation, an expression for the equivalent diameter is derived. Additionally, the imbibition velocity in non-uniform capillaries is significantly lower than that in uniform ones, with greater differences in pore-throat lengths leading to shorter total imbibition times. Under consistent wetting phase viscosity, a higher non-wetting phase results in longer imbibition times.

The presence of methane hydrate reduces the permeability of sediment to both water and gas. Current models of relative permeability, based on heuristic concepts like pore filling or grain coating, do not accurately represent the complex nature of geologic media and often overlook three-phase scenarios involving gas, water, and hydrate. Here, we use a thermodynamic argument to determine the pore-scale positioning of hydrate and from this predict gas and water flow properties of methane hydrate-bearing sediments. We conduct gas and water flow experiments with and without hydrate, comparing the results to both our physical model and existing models. We show that the flow properties of gas and water in the presence of hydrate can be determined using measurements from sediment without hydrate. In lieu of two-phase experimental measurements, we give functional forms of the relative permeability that are based in measurements of sandy sediments.

The main theme of this article is to find analytically the solution of an irreversible reaction of two components in liquid chromatography. The two-dimensional flow is considered in a closed channel, namely, the chromatographic column. The mathematical model, known as the equilibrium dispersive model (EDM), comprises two partial differential equations. Chemical reaction, dispersion in both radial and axial directions, and convection occur and are reflected in the model. A linear Langmuir adsorption isotherm is used for continuous flow and rectangular pulse injection. Application of Laplace and Hankel transformations is used as a basic tool for the solution. Hankel transformation is useful to tackle the radial effect of the flow, and Laplace transformed solution is important in very important for moment analysis in chromatography. The analytical solution, if possible, is verified using the high-resolution finite volume scheme. In case where no exact analytical solution is possible, we used the numerical Laplace inversion for the solution. Two well-known boundary conditions Dirichlet and Danckwert’s are used at inlet of the flow channel in combination with Neumann condition at outlet of the flow channel. The effects of key parameters ((mu), (D_z), and v) involved in our model on the behavior of the solution concentration of the components, such as peak sharpness and retention time, have been discussed. This physically validates the transport mechanism involved in the process.

Foam is often used to displace liquid from porous media, as it produces more stable displacements than using solely gas as a displacing fluid. A model is considered for the foam displacement process in geological applications. The liquid saturation field is divided into an outer region (in which capillary suction effects can be neglected) and an inner region (in which capillary suction effects are retained). The outer region solution exhibits a discontinuous jump in liquid saturation, sometimes referred to as a shock. The inner region solution is a travelling wave that is superposed across that jump. The focus here is upon the inner region. The liquid saturation profile across the inner region is shown to be asymmetric, with abrupt changes for high liquid saturations but gradual changes for lower liquid saturations. These gradual changes should be taken into account when matching onto the outer region. The inner region is predicted to be of small extent, but also accesses fluid mobilities which are much lower than those in the outer region. However, the very lowest mobilities are only attained within a tiny part of the inner region in which saturation is still changing abruptly. In much of the inner region, mobility is only marginally less than in the outer region. Hence, the presence of the inner region does not significantly enhance flow resistance of the foam displacement process. Consequently, the inner region should have little impact on the ability of foam to produce stable displacement processes in porous media.

Understanding imbibition in multiscale porous carbonates is essential for predicting fluid distribution in subsurface applications. We measured the capillary pressure for spontaneous imbibition and forced water injection in a mixed-wet multiscale oolitic limestone with distinct macro-, intermediate-size-, and micropore structure using the differential imaging-based porous plate (DIPP) technique. Spontaneous imbibition was found to occur through water-wet micropore channels, whereas forced water injection was dominated by the flow in mixed-wet and oil-wet macro-pores with residual oil found in pores of intermediate size. The analysis of contact angle, curvature, macro-pore occupancy, and overall water Amott index demonstrated mixed-wet-to-oil-wet conditions, resulting in a percolation-like advance during forced water injection. The water Amott index calculated on each pore size classification indicated water-wet micropores and oil-wet intermediate-size- and macro-pores. Our results highlight the role of micropores in sustaining water flow at low saturation and the role of intermediate-size-pores in retaining residual oil, advancing the predictive understanding of fluid behavior in carbonate reservoirs.