A lattice Boltzmann (LB) model is proposed for simulating fluid flow in porous media by allowing the aggregates of finer-scale pores and solids to be treated as ‘equivalent media’. This model employs ...a partially bouncing-back scheme to mimic the resistance of each aggregate, represented as a gray node in the model, to the fluid flow. Like several other lattice Boltzmann models that take the same approach, which are collectively referred to as gray lattice Boltzmann (GLB) models in this paper, it introduces an extra model parameter, ns, which represents a volume fraction of fluid particles to be bounced back by the solid phase rather than the volume fraction of the solid phase at each gray node. The proposed model is shown to conserve the mass even for heterogeneous media, while this model and that model of Walsh et al. (2009) 1, referred to the WBS model thereafter, are shown analytically to recover Darcy–Brinkman’s equations for homogenous and isotropic porous media where the effective viscosity and the permeability are related to ns and the relaxation parameter of LB model. The key differences between these two models along with others are analyzed while their implications are highlighted. An attempt is made to rectify the misconception about the model parameter ns being the volume fraction of the solid phase. Both models are then numerically verified against the analytical solutions for a set of homogenous porous models and compared each other for another two sets of heterogeneous porous models of practical importance. It is shown that the proposed model allows true no-slip boundary conditions to be incorporated with a significant effect on reducing errors that would otherwise heavily skew flow fields near solid walls. The proposed model is shown to be numerically more stable than the WBS model at solid walls and interfaces between two porous media. The causes to the instability in the latter case are examined. The link between these two GLB models and a generalized Navier–Stokes model 2 for heterogeneous but isotropic porous media are explored qualitatively. A procedure for estimating model parameter ns is proposed.
The capability to simulate real gas flow in porous materials with micro- and nano-meter-scale pores is of importance in many applications, such as gas extraction from shale reservoirs, and the design ...of gas-based fuel cells. A node-bond pore-network flow model (PNFM) has been developed for gas flow where it is the only fluid phase. The flow conductance equation includes the usual Darcy flow terms, and additional terms that capture the contributions from slip flow to Knudsen diffusion. With respect to the case for a non-ideal gas, the extra contributions, which are necessary, to the coefficients of the Darcy and Knudsen terms, are expressed in terms of reduced temperature and pressure, using van der Waals’s two-parameter principle of corresponding states. Analysis on cylindrical pores shows that the coefficient deviates from that of the non-ideal gas case by more than 80% in the Darcy term, while between −80% and 150% in the Knudsen term, when the physical states approach to the critical state of the fluid. Although the deviations become smaller when the states are away from the critical state, they remain relatively large even at conditions relevant to practical applications. The model was applied to a pore network of a realistic 3D shale model to show slippage and Knudsen effects on the predicted permeability and the sensitivity to pore sizes. Simulations were carried out for methane under the operational conditions of typical shale-gas reservoirs, and nitrogen under the conditions of laboratory experiments. The results show that the ratio of gas and Darcy permeability correlates positively and strongly with the pore size but inversely with the gas pressure and Tangential Momentum Accommodation Coefficient (TMAC) in the slip term, which can impact gas permeability disproportionally. The results are in favour of controlling the rate of gas depressurisation to avoid early depletion in shale gas production. The methane permeability is shown to be 30% greater, relatively, than that when the ideal gas law is applied, even under normal field operational conditions, while the nitrogen permeability can only approximate the methane permeability within a certain range of field operational conditions when the slip flow is not dominating.
In geoenergy applications, mudrocks prevent fluids to leak from temporary (H
2
, CH
4
) or permanent (CO
2
, radioactive waste) storage/disposal sites and serve as a source and reservoir for ...unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.
We have developed a new method for calculating permeability and capillary pressure from the pore skeleton that is extracted from a fractured rock model, which might comprises medial axes of matrix ...pores and/or medial surfaces of fracture voids. Such a skeleton, therefore, is able to encapsulate the total connected fluid flow paths in the pore-void space. To do pore-network flow simulations, the pore skeleton needs to be further “discretised” into a network of interconnected nodes and bonds to capture local pore morphology. Jiang et al. (Adv Water Resour 107:280–289,
2017
) developed a method to extract pore skeletons of this type and a discretisation to construct a pore-network model that is optimal in many aspects. In this work, we develop a new in-place discretisation method, by simply inserting a virtual link, a bond, between every pair of skeleton voxels, nodes, which are either face or only edge adjacent under certain conditions. This new method results in a simpler pore-network model, i.e. a virtual network, in which each node or bond is assumed as either a cylinder or a tiny fracture, as well as prescribed with length and inscribed radius/aperture only. As a result, a simpler pore-network simulator is also developed using improved formulae of conductance and capillary pressure according to where each virtual link falls, appropriately distinguishing every local configuration within matrixes or fractures. We verify our methods by comparing the simulation results against with those of lattice Boltzmann methods and a laboratory flooding experiment and demonstrate the accuracy and efficiency of our methods with sensitivity analysis.
Fracture aperture change under stress has long been considered as one of primary causes of stress sensitivity of fractured gas reservoirs. However, little is known about the evolution of the ...morphology of fracture apertures on flow property in loading and unloading cycles. This paper reports a stress sensitivity experiment on carbonate core plugs in which Computed Tomography (CT) technology is applied to visualize and quantitatively evaluate morphological changes to the fracture aperture with respect to confining pressure. Fracture models were obtained at selected confining pressures on which pore-scale flow simulations were performed to estimate the equivalent absolute permeability. The results showed that with the increase of confining pressure from 0 to 0.6 MPa, the fracture aperture and equivalent permeability decreased at a greater gradient than their counterparts after 0.6 MPa. This meant that the rock sample is more stress-sensitive at low effective stress than at high effective stress. On the loading path, an exponential fitting was found to fit well between the effective confining pressure and the calculated permeability. On the unloading path, the relationship is found partially reversible, which can evidently be attributed to plastic deformation of the fracture as observed in CT images.
Pore connectivity is an important property of coal. To explore the connectivity of pore-fractures in terms of macropores and mesopores in high-rank coal, two coal samples collected from the coal seam ...#3 in the southern Qinshui basin were selected. A pore-fracture network model of high-rank coal on the nanometer (10–100 nm) to micrometer (0.1–10 μm) scale is constructed, and key parameters are extracted using the 3D (three-dimensional) digital spatial characterization based on 3D scanning with FIB-SEM (Focused Ion Beam Scanning Electron Microscopy). Then, the connectivity of the pore-fractures and the contribution of pores with different genetic types to the connectivity of the high-rank coal are confirmed. The results show that the pores and throats of high-rank coal in coal seam #3 in the southern Qinshui basin are very narrow, with predominant mesopores < 50 nm in width. The tortuosity of the coal samples is low, and the cross-section is predominantly square and triangular in shape, which means that the capillary resistance is small. The connectivity of the pores is poor, and mesopores play an important role in the pore connectivity. Linear differential shrinkage pores are the main connected pores on the nanometer scale and communicate with irregularly rounded and elliptic differential shrinkage pores, secondary pores, and mineral pores. The types and contents of the minerals in coals determine the morphological characteristics and degree of development of the differential shrinkage pores, and have an important influence on the pore connectivity in high-rank coal. The content of quartz determines the degree of development of the linear differential shrinkage pores, and is the primary reasons for the differences in the connectivity of the two samples.
The migration of expelled hydrocarbon from source rock into unconventional tight reservoirs is subject to different pore-scale fluid transport mechanisms as opposed to the conventional counterparts ...and therefore plays a crucial role in controlling the hydrocarbon distribution and accumulation in the former. One of the different mechanisms is related to the formation of a more viscous boundary layer (BL) of brine, i.e., wetting phase fluid on pore surfaces, giving rise to the so-called BL effect. In this work, a two-phase pore network model (PNM) that considers this BL effect is developed to study the influences of pore-scale characteristics on the oil migration process, manifested through the BL effect in tight-sandstone media. Good agreements are reached between experimentally derived relative permeability curves and predicted ones, by applying this model to the pore-network networks extracted from the same samples. Then, this validated model was used to evaluate the impacts of the following factors on the oil migration process: pore radius, coordination number, aspect ratio, brine viscosity, and wettability. The results show that all factors can influence the oil migration process but at different magnitudes. The applicability and significance of the developed tight oil migration PNM are discussed in this work.
Edge detection is one of the key issues in the field of computer vision and remote sensing image analysis. Although many different edge-detection methods have been proposed for gray-scale, color, and ...multispectral images, they still face difficulties when extracting edge features from hyperspectral images (HSIs) that contain a large number of bands with very narrow gap in the spectral domain. Inspired by the clustering characteristic of the gravitational theory, a novel edge-detection algorithm for HSIs is presented in this paper. In the proposed method, we first construct a joint feature space by combining the spatial and spectral features. Each pixel of HSI is assumed to be a celestial object in the joint feature space, which exerts gravitational force to each of its neighboring pixel. Accordingly, each object travels in the joint feature space until it reaches a stable equilibrium. At the equilibrium, the image is smoothed and the edges are enhanced, where the edge pixels can be easily distinguished by calculating the gravitational potential energy. The proposed edge-detection method is tested on several benchmark HSIs and the obtained results were compared with those of four state-of-the-art approaches. The experimental results confirm the efficacy of the proposed method.
Microfractures have great significance in the study of reservoir development because they are an effective reserving space and main contributor to permeability in a large amount of reservoirs. ...Usually, microfractures are divided into natural microfractures and induced microfractures. Artificially induced rough microfractures are our research objects, the existence of which will affect the fluid-flow system (expand the production radius of production wells), and act as a flow path for the leakage of fluids injected to the wells, and even facilitate depletion in tight reservoirs. Therefore, the characteristic of the flow in artificially induced fractures is of great significance. The Lattice Boltzmann Method (LBM) was used to calculate the equivalent permeability of artificially induced three-dimensional (3D) fractures. The 3D box fractal dimensions and porosity of artificially induced fractures in Berea sandstone were calculated based on the fractal theory and image-segmentation method, respectively. The geometrical parameters (surface roughness, minimum fracture aperture, and mean fracture aperture), were also calculated on the base of digital cores of fractures. According to the results, the permeability lies between 0.071–3.759 (dimensionless LB units) in artificially induced fractures. The wide range of permeability indicates that artificially induced fractures have complex structures and connectivity. It was also found that 3D fractal dimensions of artificially induced fractures in Berea sandstone are between 2.247 and 2.367, which shows that the artificially induced fractures have the characteristics of self-similarity. Finally, the following relations were studied: (a) exponentially increasing permeability with increasing 3D box fractal dimension, (b) linearly increasing permeability with increasing square of mean fracture aperture, (c) indistinct relationship between permeability and surface roughness, and (d) linearly increasing 3D box fractal dimension with increasing porosity.
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