Transport in Porous Media最新文献

Water seepage in rocks, in geotechnical engineering such as the hydrofracturing of hard rocks, excavation of underground chambers, and prevention of mine water disasters, is a common problem. According to rock mechanics theory, the deformation and stress of rocks influence seepage behavior. In this study, a modified permeability model of argillaceous sandstone under coupled hydromechanical conditions was established to reveal the relationship between permeability and effective stress, including external stress and internal water pressure. The modeling results indicate a negative exponential relationship between the argillaceous sandstone permeability and the effective stress. The proposed effective stress-sensitive permeability model was validated by conducting two sets of seepage experiments based on controlling the water pressure and external stress, with the results obtained considered satisfactory. Based on the proposed permeability model, a fully coupled multifield model of the water seepage and rock deformation was developed. Fully coupled scenario-based numerical simulations were conducted in a finite element environment to investigate water seepage evolution and rock deformation. The experimental and numerical results show that the trends in the evolution of the entire compressive stress–strain and permeability curves are reversed, and the maximum value of the permeability was not consistent with the failure of argillaceous sandstone. This model and corresponding numerical simulations can provide insights for water seepage research and serve as a reliable theoretical basis for evaluating roof water injection and hydraulic fracturing in rock and mining engineering.

Abstract

Wettability is one of the critical parameters affecting multiphase flow in porous media. The wettability is determined by the affinity of fluids to the rock surface, which varies due to factors such as mineral heterogeneity, roughness, ageing, and pore-space geometry. It is well known that wettability varies spatially in natural rocks, and it is still generally considered a constant parameter in pore-scale simulation studies. The accuracy of pore-scale simulation of multiphase flow in porous media is undermined by such inadequate wettability models. The advent of in situ visualization techniques, e.g. X-ray imaging and microtomography, enables us to characterize the spatial distribution of wetting more accurately. There are several approaches for such characterization. Most include the construction of a meshed surface of the interface surfaces in a segmented X-ray image and are known to have significant errors arising from insufficient resolution and surface-smoothing algorithms. This work presents a novel approach for spatial determination of wetting properties using local lattice-Boltzmann simulations. The scheme is computationally efficient as the segmented X-ray image is divided into subdomains before conducting the lattice-Boltzmann simulations, enabling fast simulations. To test the proposed method, it was applied to two synthetic cases with known wettability and three datasets of imaged fluid distributions. The wettability map was obtained for all samples using local lattice-Boltzmann calculations on trapped ganglia and optimization on surface affinity parameters. The results were quantitatively compared with a previously developed geometrical contact angle determination method. The two synthetic cases were used to validate the results of the developed workflow, as well as to compare the wettability results with the geometrical analysis method. It is shown that the developed workflow accurately characterizes the wetting state in the synthetic porous media with an acceptable uncertainty and is better to capture extreme wetting conditions. For the three datasets of imaged fluid distributions, our results show that the obtained contact angle distributions are consistent with the geometrical method. However, the obtained contact angle distributions tend to have a narrower span and are considered more realistic compared to the geometrical method. Finally, our results show the potential of the proposed scheme to efficiently obtain wettability maps of porous media using X-ray images of multiphase fluid distributions. The developed workflow can help for more accurate characterization of the wettability map in the porous media using limited experimental data, and hence more accurate digital rock analysis of multiphase flow in porous media.

Fines detachment, migration and pore clogging are important processes in diverse problems in underground formations. Recent works have analyzed the idea of employing fines detached by low-salinity water injection to modify water trajectories in a rock formation. In oil and geothermal reservoirs, fines can play, in this context, a beneficial role in water production control. In underground pollution processes, fines can serve as a potential mechanism for isolating soil or water contaminants. In this work, a new application to block the fluid flow in a conducting fault that directly links the injection well with extraction wells by using a slug of low-salinity water is explored. This technique could bear significant relevance, particularly in scenarios where water is injected to displace oil or soil contaminants from the formation into extraction wells. The existence of this type of highly conductive pathways can significantly reduce the efficiency of oil or contaminant sweeping. To analyze the problem, we consider here a low-salinity water slug that is introduced in the injection stream of a standard inverse five-spot well array, in which a high-permeability fault-like streak directly connects the injector with two of the four extraction wells. The mathematical model to describe fines detachment, migration, pore clogging and permeability impairment is revisited and adapted. The nonlinear coupled equation set for single-phase fluid flow, salinity transport and fines dynamics is numerically solved by a finite element method. The efficiency of the low-salinity fines detaching method to block water flow in conductive faults is discussed in terms of slug injection period, slug salinity and flow injection rate. The most sensitive parameters are injection period and injection rate. It was found that fines are equally effective at obstructing broad or narrow faults.

In this Letter, it is shown how the determination of the effective coefficients involved in the macroscopic model for pressure driven and/or Couette flow in a rough fracture can be simplified by solving only one closure problem instead of two as originally reported in Prat et al. (Transp Porous Media 48(3):291–313, 2002. https://doi.org/10.1023/a:1015772525610).

The physical process in which a substance moves from a location with a higher concentration to a location with a lower concentration is known as molecular diffusion. It plays a crucial role during the mixing process between different gases in porous media. Due to the petrophysical properties of the porous medium, the diffusion process occurs slower than in bulk, and the overall process is also affected by thermodynamic conditions. The complexity of measuring gas–gas diffusion in porous media at increased pressure and temperature resulted in significant gaps in data availability for modelling this process. Therefore, correlations for ambient conditions and simplified diffusivity models have been used for modelling purposes. In this study, correlations in dependency of petrophysical and thermodynamic properties were developed based on more than 30 measurements of the molecular diffusion of the binary system hydrogen–methane in gas storage rock samples at typical subsurface conditions. It allows reproducing the laboratory observations by evaluating the bulk diffusion coefficient and the tortuosity factor with relative errors of less than 50 % with minor exceptions, leading to a strong improvement compared to existing correlations. The developed correlation was implemented in the open-source simulator DuMu^x and the implementation was validated by reproducing the measurement results. The validated implementation in DuMu^x allows to model scenarios such as Underground Hydrogen Storage (UHS) on a field-scale and, as a result, can be used to estimate the temporary loss of hydrogen into the cushion gas and the purity of withdrawn gas due to the gas–gas mixing process.

Water Alternated Gas (WAG) flooding is largely used as an Enhanced Oil Recovery (EOR) method in oil fields. It is based on the high sweep efficiency of the water phase and the high displacement efficiency of the gas phase. Additionally, other components may be dissolved in both displacing phases, increasing the oil recovery factor and leading to modern WAG schemes such as PWAG (Polymer WAG), MWAG (Miscible WAG), and others. In this paper, we present approximate analytical solutions for the linear immiscible Water Alternated Gas problem. The mathematical model is composed by a 2×2 system of nonlinear hyperbolic Partial Differential Equations (PDE), solved by the Method of Characteristics (MOC) for a set of reservoir properties. The analytical solution is compared with numerical simulation showing the accuracy and robustness of the method under different WAG configurations. The presented solutions can be used to select the best recovery technique for a particular field in a fast and efficient way.

Abstract

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise.

Article Highlights

• A two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem.

• The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven.

• Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

Complex physical phenomena take place while dealing with the convective heat transfer in porous medium. Due to involved complexities, most of the earlier numerical studies are performed using various porous models compromising the detailed phenomena. Therefore, a pore-scale simulation has been performed for convective heat transfer in triply-periodic-minimal-surface lattices, with identical void fraction and unit-cell size, but different geometrical shapes (tortuosity), namely Diamond, Inverted Weaire–Phelan, Primitive, and Gyroid. Further, each lattice derived into three different types of porous structures by designing second subdomain as solid (in Type 1), fluid (in Type 2), and microporous zones (in Type 3). The convective heat transfer in a square mini-channel filled with the porous structures is investigated for the range of flow Reynolds number (0.01<mathrm{Re}<100) and (mathrm{Pr}=7). The temperature distributions, solid and fluid Nusselt numbers on the external walls and on the internal walls, and quantitative departure from local thermal equilibrium (LTE) assumption are calculated for different porous media. The effect of porous morphology/tortuosity and effective porosity on the heat transfer is examined. The results revealed that the maximum temperature within the domain is found in Type 2 treatment, leading to inferior heat transfer performance compared to Type 1 and Type 3. Among all the lattices, the Diamond lattice provides more uniform temperature distribution over the external walls and within the volume including solid and fluid. The effective and the internal Nusselt numbers increase drastically for Re > 10. For the range of Re considered here, the Primitive lattice shows the maximum deviation from LTE assumption.

Realistic immiscible viscous fingering, showing all of the complex finger structure observed in experiments, has proven to be very difficult to model using direct numerical simulation based on the two-phase flow equations in porous media. Recently, a method was proposed by the authors to solve the viscous-dominated immiscible fingering problem numerically. This method gave realistic complex immiscible fingering patterns and showed very good agreement with a set of viscous unstable 2D water → oil displacement experiments. In addition, the method also gave a very good prediction of the response of the system to tertiary polymer injection. In this paper, we extend our previous work by considering the effect of wettability/capillarity on immiscible viscous fingering, e.g. in a water → oil displacements where viscosity ratio (left( {mu_{{text{o}}} /mu_{{text{w}}} } right) gg 1). We identify particular wetting states with the form of the corresponding capillary pressure used to simulate that system. It has long been known that the broad effect of capillarity is to act like a nonlinear diffusion term in the two-phase flow equations, denoted here as (D(S_{w} )). Therefore, the addition of capillary pressure, (P_{c} (S_{w} )), into the equations acts as a damping or stabilisation term on viscous fingering, where it is the derivative of this quantity that is important, i.e. (D(S_{w} )simleft( {dP_{c} (S_{w} )/dS_{w} } right)). If this capillary effect is sufficiently large, then we expect that the viscous fingering to be completely damped, and linear stability theory has supported this view. However, no convincing numerical simulations have been presented showing this effect clearly for systems of different wettability, due to the problem of simulating realistic immiscible fingering in the first place (i.e. for the viscous-dominated case where (P_{c} = 0)). Since we already have a good method for numerically generating complex realistic immiscible fingering for the (P_{c} = 0) case, we are able for the first time to present a study examining both the viscous-dominated limit and the gradual change in the viscous/capillary force balance. This force balance also depends on the physical size of the system as well as on the length scale of the capillary damping. To address these issues, scaling theory is applied, using the classical approach of Rapport (1955), to study this scaling in a systematic manner. In this paper, we show that the effect of wettability/capillarity on immiscible viscous fingering is somewhat more complex and interesting than the (broadly correct) qualitative description above. From a “lab-scale” base case 2D water → oil displacement showing clear immiscible viscous fingering which we have already matched very well using our numerical method, we examine the effects of introducing either a water wet (WW) or an oil wet (OW) capillary pressure, of different