Transport in Porous Media最新文献

The mechanical formation damage induced by pore collapse within production curve depletion-dependent reservoirs significantly influences oilfield development. This paper proposes a new perturbative solution for transient pores collapse hysteresis modeling in depletion-dependent oil reservoirs with compaction effects during alternating loading/unloading cycles. The nonlinear hydraulic diffusivity equation is perturbed through a first-order expansion technique using the depletion-dependent permeability, k(p) as a perturbation parameter, (epsilon). The practical uses of the model developed in this work are identifying flow regimes and hysteresis responses in pressure-sensitive reservoirs, estimating buildup pressure, specifying oil flow rate to prevent severe hysteretic behavior, and history matching during reservoir surveillance. The log–log analysis shows that the shut-in pressure has an influence on permeability loss. However, the comparisons between the permeability loss and its partial recovery curves show that this loss represents less than 5(%) of the permeability value from the previous drawdown cycle. The derivative was also used to compute the instantaneous permeability loss using the relationship: (partial m_textrm{D}/partial t_textrm{D}=k_textrm{D}(p_textrm{D})partial p_textrm{D}/partial t_textrm{D}). The main advantages of the solution derived in this work are the simple implementation, practical graphical analysis of the pores collapse hysteresis effect, the possibility of simulating different boundary conditions and well-reservoir settings, and the requirements of only a few pressure and permeability field data to input in the deviation factor. The solution proposed can be applied to choose the production time to shut the well and monitor the adequate oil flow rate during the production curve.

The effect of heterogeneity induced by highly permeable fracture networks on viscous miscible fingering in porous media is examined using high-resolution numerical simulations. We consider the planar injection of a less viscous fluid into a two-dimensional fractured porous medium that is saturated with a more viscous fluid. This problem contains two sets of fundamentally different preferential flow regimes; the first is caused by the viscous fingering, and the second is due to the permeability contrasts between the fractures and the rock matrix. We study the transition from the regime where the flow is dominated by the viscous instabilities, to the regime where the heterogeneity induced by the fractures define the flow paths. Our findings reveal that even minor permeability differences between the rock matrix and fractures significantly influence the behavior of viscous fingering. The interplay between the viscosity contrast and permeability contrast leads to the preferential channeling of the less viscous fluid through the fractures. Consequently, this channeling process stabilizes the displacement front within the rock matrix, ultimately suppressing the occurrence of viscous fingering, particularly for higher permeability contrasts. We explore three fracture geometries: two structured and one random configuration and identify a complex interaction between these geometries and the development of unstable flow. While we find that the most important factor determining the effect of the fracture network is the ratio of fluid volume flowing through the fractures and the rock matrix, the exact point for the cross-over regime is dependent on the geometry of the fracture network.

Biological tissue, pharmaceutical tablets, wood, porous rocks, catalytic reactors, concrete, and foams are examples of heterogeneous systems that may contain one or several fluid phases. Fluids in such systems carry chemical species that may participate in chemical reactions in the bulk of a fluid, as homogeneous reactions, or at the fluid/fluid or fluid/solid interfaces, as heterogeneous reactions. Magnetic resonance relaxation measures the return of ¹H nuclear magnetization in chemical species of these fluids to an equilibrium state in a static magnetic field. Despite the perceived difference between reaction–diffusion and relaxation–diffusion in heterogeneous systems, similarities between the two are remarkable. This work draws a close parallel between magnetic resonance relaxation–diffusion and chemical reaction–diffusion for elementary unitary reaction ({text{A}}to {text{B}}) in a dilute solution—both in heterogeneous systems. A striking similarity between the dimensionless numbers that characterize their relevant behavior is observed: the Damköhler number of the second kind ({{text{Da}}}^{{text{II}}}) for reaction and the Brownstein–Tarr number ({{text{BT}}}_{i}) for relaxation. The new vision of analogy between reaction- and magnetic resonance relaxation–diffusion in heterogeneous systems encourages the exploitation of similarities between reaction and relaxation processes to noninvasively investigate the dynamics of chemical species and reactions. One such example of importance in chemical engineering is provided for solid–fluid reaction in packed beds.

Quantifying the relationship between geometric descriptors of microstructure and effective properties like permeability is essential for understanding and improving the behavior of porous materials. In this paper, we employ a previously developed stochastic model to investigate microstructure–property relationships of nonwovens. First, we show the capability of the model to generate a wide variety of realistic nonwovens by varying the model parameters. By computing various geometric descriptors, we investigate the relationship between model parameters and microstructure morphology and, in this way, assess the range of structures which may be described by our model. In a second step, we perform virtual materials testing based on the simulation of a wide range of nonwovens. For these 3D structures, we compute geometric descriptors and perform numerical simulations to obtain values for permeability as an effective material property. We then examine and quantify the relationship between microstructure morphology and permeability by fitting parametric regression formulas to the obtained data set, including but not limited to formulas from the literature. We show that for structures which are captured by our model, predictive power may be improved by allowing for slightly more complex formulas.

Stochastic quantification of flow field variability in complex geologic formations under uncertainty is expected to provide valuable information for rational management of regional groundwater resources and analysis of solute transport processes for stochastic environmental risk assessment. Studies of fluid flow behavior in confined aquifers of variable thickness presented in the literature assume that the thickness of the aquifer varies linearly or nonlinearly. However, natural variations, such as the thickness of the aquifer caused by complex natural events, cannot be accurately predicted. Therefore, quantifying the variability of the flow field in heterogeneous, non-uniform, confined aquifers may be done from a stochastic perspective. In this study, the spatial variations in hydraulic conductivity are considered as a stationary random process, while the spatial variations in aquifer thickness are treated as a nonstationary random process with homogeneous (stationary) increments. General expressions for the spatial covariance functions and the evolutionary power spectra of the depth-averaged hydraulic head and integrated specific discharge in the direction of x₁ are derived using the Fourier–Stieltjes spectral representation approach and representation theorem. Closed-form solutions for the evolutionary power spectra of depth-averaged hydraulic head and integrated specific discharge are used to analyze the effect of variation in the thickness of the confined aquifer on the variability of depth-averaged head and integrated discharge. An application of the theory developed here to the case of random aquifer thickness fields exhibiting a power-law semivariogram is given. The results of this study improve the understanding and quantification of flow field variability in natural confined aquifers.

We address the two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations in the case of a weak miscibility of a two-component fluid. To this end a notion of the miscibility strength is formulated on the basis of a correlation between the upscaling parameter and the surface tension. As a result, a two-scale model is derived. Macro-equations turn out to be a generalization of the Darcy law enjoying cross-coupling permeability tensors. It implies that the Darcy velocity of each phase depends on pressure gradients of both phases. Micro-equations serve for determination both of the permeability tensors and the capillary pressure. An example is constructed by analytical tools to describe capillary displacement of oil by mixture of water with carbon dioxide in a system of hydrophobic parallel channels.

Tortuosity ((tau)) is one of the key parameters controlling flow and transport in porous media. Although the concept of tortuosity is straightforward, its estimation in porous media has yet been challenging. Most models proposed in the literature are either empirical or semiempirical including some parameters whose values and their estimations are in prior unknown. In this study, we modified a previously presented geometric tortuosity (({tau }_{g})) model based on percolation theory and validated it against a methodology based on the pathfinding A* algorithm. For this purpose, we selected 12 different porous materials including four sandstones, three carbonates, one salt, and four synthetic media. For all samples, five sub-volumes at different lengths with fifty iterations were randomly selected except one carbonate sample for which three sub-volumes were extracted. Pore space properties, such as pore radius, throat radius, throat length, and coordination number distributions were determined by extracting the pore network of each sub-volume. The average and maximum coordination numbers and minimum throat length were used to estimate the ({tau }_{g}). Comparison with the A* algorithm results showed that the modified model estimated the ({tau }_{g}) accurately with absolute relative errors less than 28%. We also estimated the ({tau }_{g}) using two other models presented in the literature as well as the original percolation-based tortuosity model. We found that our proposed model showed a significantly higher accuracy. Results also indicated more precise estimations at the larger length scales demonstrating the effect of uncertainties at the smaller scales.

Abstract

Hygric pore network modelling, which characterises the macroscopic moisture storage and transport properties by simulating the microscopic storage and transport of moisture in the pore elements of the pore network, is a novel method to characterise the hygric properties of building materials. To analyse, verify and/or compare pore networks, a wide array of parameters (both geometrical and topological) exists. This paper aims to comprehensively investigate these parameters, targeting their impacts on the moisture retention and permeability curves of porous materials. The maximum-inscribed-ball method is employed to extract the pore networks of three real porous materials, which are further scaled down to provide three complementary virtual pore networks in order to cover a wider spectrum of pore sizes. Subsequently, these pore networks are modified to obtain variations in the parameter distributions, and then, a sensitivity analysis is implemented to determine the impact of the pore network parameters on the hygric property prediction. The results indicate that the moisture retention curve is most related to the radius and volume distributions of pore bodies and throats, whilst the distribution of coordination number is the most crucial parameter for the moisture permeability curve. The conclusions are further confirmed through an improved stochastic pore network generation algorithm. With preserved radius and volume distributions for pore bodies and pore throats, the moisture retention curve is predicted accurately. Adding information on the coordination number distribution to the algorithm then ensures the successful prediction of the moisture permeability curve.

Article Highlights

• Key pore network parameters governing the moisture transfer are determined, valid in both micro- and nano-scale.

• An improved stochastic pore network generation algorithm is proposed.

• Surface adsorption and surface flow are crucial in nanometre region.