A New Method for Generating Pore-Network Models of Porous Media

In this study, we have developed a new method to generate a multi-directional pore network for representing a porous medium. The method is based on a regular cubic lattice network, which has two elements: pore bodies located at the regular lattice points and pore throats connecting the pore bodies. One of the main features of our network is that pore throats can be oriented in 13 different directions, allowing a maximum coordination number of 26 that is possible in a regular lattice in 3D space. The coordination number of pore bodies ranges from 0 to 26, with a pre-specified average value for the whole network. We have applied this method to reconstruct real sandstone and granular sand samples through utilizing information on their coordination number distributions. Good agreement was found between simulation results and observation data on coordination number distribution and other network properties, such as number of pore bodies and pore throats and average coordination number. Our method can be especially useful in studying the effect of structure and coordination number distribution of pore networks on transport and multiphase flow in porous media systems.     

A new stochastic method of reconstructing porous media

We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program. We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability. The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than 0.2 to ensure its connectivity and conductivity.     

Process Based Reconstruction of Sandstones and Prediction of Transport Properties

We present a process based method for reconstructing the full three-dimensional microstructure of sandstones. The method utilizes petrographical information obtained from two-dimensional thin sections to stochastically model the results of the main sandstone forming processes – sedimentation, compaction, and diagenesis. We apply the method to generate Fontainebleau sandstone and compare quantitatively the reconstructed microstructure with microtomographic images of the actual sandstone. The comparison shows that the process based reconstruction reproduces adequately important intrinsic properties of the actual sandstone, such as the degree of connectivity, the specific internal surface, and the two-point correlation function. A statistical reconstruction of Fontainebleau sandstone that matches the porosity and two-point correlation function of the microtomography data differs strongly from the actual sandstone in its connectivity properties. Transport properties of the samples are determined by solving numerically the local equations governing the transport. Computed permeabilities and formation factors of process based reconstructions of Fontainebleau sandstone compare well with experimental measurements over a wide range of porosity.     

Connectivity of Pore Space as a Control on Two-Phase Flow Properties of Tight-Gas Sandstones

We predict capillary-pressure (drainage) curves in tight-gas sandstones which have little matrix or microporosity using a quantitative grain-scale model. The model accounts for the geometric results of some depositional and diagenetic processes important for porosity and permeability reduction in tight-gas sandstones, such as deformation of ductile grains during burial and quartz cementation. The model represents the original sediment as a dense, disordered packing of spheres. We simulated the evolution of this model sediment into a low-porosity sandstone by applying different amounts of ductile grains and quartz precipitation. A substantial fraction of original pore throats in the sediment is closed by the simulated diagenetic alteration. Because the percolation threshold corresponds to closure of half of the pore throats, the pore space in this type of tight-gas sandstone is poorly connected and is often close to being completely disconnected. The drainage curve for different model rocks was computed using invasion percolation in a network taken directly from the grain-scale geometry and topology of the model. Some general trends follow classical expectations and were confirmed by experimental measurements: increasing the amount of cement shifts the drainage curve to larger pressures. This is related to reduction of the connectivity of pore space resulting from closure of throats. Existence of ductile grains in the ductile grain model also reduces the connectivity of pore space but it treats the throats distribution differently causing the drainage curves to be shifted to larger irreducible water saturation when cement is added to the model. The range of porosities in which these connectivity effects are important corresponds to the range of porosities common for tight gas sandstones. Consequently these rocks can exhibit small effective permeability to gas even at large gas saturations. This problem occurs at larger porosities in rocks with significant content of ductile grains because ductile deformation blocks a significant fraction of pore throats even before cementation begins. Predicted drainage curves agree with measurements on two samples with little microporosity, one dominated by rigid grains, the other containing a significant fraction of ductile grains. We conclude that connectivity of the matrix pore space is an important factor for an understanding of flow properties of tight-gas sandstones.     

Time-Dependent Diffusion and Surface-Enhanced Relaxation in Stochastic Replicas of Porous Rock

Understanding the connection between pore structure and NMR behavior of fluid-saturated porous rock is essential in interpreting the results of NMR measurements in the field or laboratory and in establishing correlations between NMR parameters and petrophysical properties. In this paper we use random-walk simulation to study NMR relaxation and time-dependent diffusion in 3D stochastic replicas of real porous media. The microstructures are generated using low-order statistical information (porosity, void–void autocorrelation function) obtained from 2D images of thepore space. Pore size distributions obtained directly by a 3D pore space partitioning method and indirectly by inversion of NMR relaxation data are compared for the first time. For surface relaxation conditions typical of reservoir rock, diffusional coupling between pores of different size is observed to cause considerable deviations between the two distributions. Nevertheless, the pore space correlation length and the size of surface asperity are mirrored in the NMR relaxation data for the media studied. This observation is used to explain the performance of NMR-based permeability correlations. Additionally, the early time behavior of the time-dependent diffusion coefficient is shown to reflect the average pore surface-to-volume ratio. For sufficiently high values of the self-diffusion coefficient, the tortuosity of the pore space is also recovered from the long-time behavior of the time-dependent diffusion coefficient, even in the presence of surface relaxation. Finally, the simulations expose key limitations of the stochastic reconstruction method, and allow suggestions for future development to be made.     

Pore Network Modelling of Electrical Resistivity and Capillary Pressure Characteristics

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.     

A Numerical Study of the Distribution of Water in Partially Saturated Porous Rock

The distribution of water and air phases in small blocks of porous sandstone is examined by using a simulated annealing technique that finds the minimum interfacial energy distributions at different saturations. Simulations are based on existing sandstone microstructures that were determined by X-ray microtomography. At low saturations, some of the water is distributed in films along the walls of larger pore spaces, and connects to pendular structures in the crevices and smaller pores. As the amount of water in the pores increases the water films become thicker and pores fill from the pendular structures. The distribution of water voxels in the pore space is examined by calculating interfacial areas, by classifying water voxels as to whether they lie within films or clusters, and by determining the size and distribution of these film clusters. An exponential relationship is found between the fraction of water voxels in the films and the degree of saturation. In addition, the dependency of small-sample electrical conductivity on saturation is examined by using a random walk method.     

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas?Cwater interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.     

A Semi-analytical Model for Pressure-Dependent Permeability of Tight Sandstone Reservoirs

In tight gas reservoirs, permeability is pressure dependent owing to pore pressure reduction during the life of the reservoir. Empirical models are commonly used to describe pressure-dependent permeability. In this paper, it was discussed a number of issues which centered around tight sandstone pressure-dependent permeability experiment, first to apply core aging on permeability test and then to develop a new semi-analytical model to predict permeability. In tight sandstone permeability test experiment, the microinterstice between core and sleeves resulted in over estimation of dependency of permeability on pressure. Then, a new semi-analytical model was developed to identify the relation between permeability and fluid pressure in tight sandstone, which indicates there is a linear relation between pore pressure changes and the inverse of permeability to a constant power. Pressure-dependent permeability of 8 tight sandstone core samples from Ordos Basin, China, was obtained using the modified procedure, and results were perfectly matched with the proposed model. Meanwhile, the semi-analytical model was also verified by pressure-dependent permeability of 16 cores in the literature and experiment results of these 24 cores were matched by empirical models and the semi-analytical model. Compared with regression result of commonly used empirical models, the semi-analytical model outperforms the current empirical models on 8 cores from our experiment and 16 cores from the literature. The model verification also indicates that the semi-theoretical model can match the pressure-dependent permeability of different rock types. In addition, the permeability performance under reservoir condition is discussed, which is divided into two stages. In most tight gas reservoirs, the permeability performance during production is located in stage II. The evaluation result with proposed experiment procedure and the stress condition in stage II will reduce permeability sensitivity to stress.     

基于核磁共振孔隙划分的致密油藏自发渗吸原油可动性研究

自发渗吸驱油是致密油藏提高采收率的有效手段,但不同的孔隙划分方法会导致原油可动性精细定量表征存在差异性.基于此,以鄂尔多斯盆地延长组致密油藏为研究对象,开展了四种典型致密岩心的自发渗吸驱油实验,利用基于核磁共振分形理论的流体分布孔隙精细划分方法,区分了致密砂岩岩心孔隙类型,明确了不同类型岩心孔隙结构对原油可动性和自发渗吸驱油速率的控制特征.研究结果表明不同类型岩心自发渗吸模拟油动用程度介于22.07%～33.26%,核磁共振T2谱双峰型岩心自发渗吸模拟油动用程度高于单峰型岩心;不同类型致密砂岩岩心中流体分布孔隙可初步划分出P1和P2两种类型, P1类型孔隙则可进一步划分出P1-1, P1-2和P1-3三种亚类型孔隙;致密砂岩岩心中P1和P2类孔隙中模拟油均有不同程度的动用, P1类孔隙作为致密岩心中主要孔隙,尤其是P1类孔隙中P1-2和P1-3类孔隙的数量决定了自发渗吸模拟油动用程度;P1-1, P1-2和P1-3类孔隙结构差异性对自发渗吸模拟油动用程度起决定性作用,较小尺寸孔径孔隙较大的孔隙结构差异性不仅提升了自发渗吸模拟油动用程度,而且提升了自发渗吸驱油速率;流体可动性指数较高的P...     

Multi-scale Image-Based Pore Space Characterisation and Pore Network Generation: Case Study of a North Sea Sandstone Reservoir

Transport in Porous Media - In this paper, we examine the pore space geometry and topology of a North Sea sandstone reservoir rock based on multi-scale scanning electron microscopy. The reservoir...     

Finite Element-Based Characterization of Pore-Scale Geometry and Its Impact on Fluid Flow

We present a finite element (FEM) simulation method for pore geometry fluid flow. Within the pore space, we solve the single-phase Reynold’s lubrication equation—a simplified form of the incompressible Navier–Stokes equation yielding the velocity field in a two-step solution approach. (1) Laplace’s equation is solved with homogeneous boundary conditions and a right-hand source term, (2) pore pressure is computed, and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field, we estimate the effective permeability of porous media samples characterized by section micrographs or micro-CT scans. This two-step process is much simpler than solving the full Navier–Stokes equation and, therefore, provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier–Stokes’ equation. Given the realistic laminar flow field, dispersion in the medium can also be estimated. Our numerical model is verified with an analytical solution and validated on two 2D micro-CT scans from samples, the permeabilities, and porosities of which were pre-determined in laboratory experiments. Comparisons were also made with published experimental, approximate, and exact permeability data. With the future aim to simulate multiphase flow within the pore space, we also compute the radii and derive capillary pressure from the Young–Laplace’s equation. This permits the determination of model parameters for the classical Brooks–Corey and van-Genuchten models, so that relative permeabilities can be estimated.     

Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network

A stochastic approach to network modelling has been used to simulate quasi-static immiscible displacement in porous media. Both number-based and volume-based network saturation results were obtained. Number-based results include: number-based saturation curves for primary drainage, secondary imbibition and secondary drainage, fluid distribution data, and cluster trapping history. Using pore structure data of porous media, it is possible to convert the number-based curves to capillary pressure — saturation relationships. Pore size distribution functions and pore shapes which are thought to closely represent Berea sandstone samples were used to predict the capillary curves. The physical basis of these calculations is a one-to-one correspondence between the cumulative node and bond index fractions in the network analysis, and the cumulative number-based distributions of pore body and pore throat diameters, respectively. The oil-water capillary pressure curve simulated for primary drainage closely resembles those measured experimentally. The agreement between the simulated and the measured secondary imbition and secondary drainage curves is less satisfactory.     

Pore-by-Pore Modelling,Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data

We predict waterflood displacement on a pore-by-pore basis using pore network modelling. The pore structure is captured by a high-resolution image. We then use an energy balance applied to images of the displacement to assign an average contact angle, and then modify the local pore-scale contact angles in the model about this mean to match the observed displacement sequence. Two waterflooding experiments on oil-wet rocks are analysed where the displacement sequence was imaged using time-resolved synchrotron imaging. In both cases the capillary pressure in the model matches the experimentally obtained values derived from the measured interfacial curvature. We then predict relative permeability for the full saturation range. Using the optimised contact angles distributed randomly in space has little effect on the predicted capillary pressures and relative permeabilities, indicating that spatial correlation in wettability is not significant in these oil-wet samples. The calibrated model can be used to predict properties outside the range of conditions considered in the experiment.

     

Predicting the Onset of Inertial Effects in Sandstone Rocks

This study presents a method to determine the onset of inertial effects at the microscopic level, to distinguish between Darcy and non-Darcy flow regions within porous media at the pore level, and to quantify the effects of retained polymer on gas mobility. Capillary pressure and polymer flood experiments were conducted using Elgin and Okesa sandstone samples. The pore-size distributions were used to study the high-velocity flow effects. A modified capillary-orifice model was used to determine the non-Darcy flow effects at the pore level, with and without residual polymer.The overall flow behavior at any flow rate may be described as the average of all contributions from the Darcy and the non-Darcy terms in all pores. Results of this study suggest that the conventional Reynolds number may lead to incorrect analysis of flow behavior when evaluating non-Darcy flow effects in porous media. The Forchheimer number, defined as the ratio of inertial forces to viscous forces, is found more adequate for analyzing microscopic flow behavior in porous media.     

Experimental Study of Seepage Properties of Broken Sandstone Under Different Porosities

In coal mining the water flow in broken rock is a very common phenomenon. Study of seepage properties of broken rock is one of the basic subjects required in order to understand the stability of rock surrounding roadways, preventing disasters such as water inrush and gas outbursts and developing underground resources. So far, quantitative studies on the nonlinear seepage properties of broken sandstone under different porosities are not extensive in the research literature. In this article, by means of an electro-hydraulic servo-controlled test system (MTS815.02) and a patent seepage device, the seepage properties under different conditions of porosity were tested on broken sandstone of five different grain sizes. Based on the loading method of controlling the axial compression displacement and steady permeating method, we obtained curves of the relation of pore pressure with time, as well as the relation curves between the pore pressure gradient for steady seepage and velocity. Furthermore, we calculated the permeability k and non-Darcy coefficient β corresponding to different porosities by fitting these curves with the binomial expression. This study indicates that: (1) the seepage properties of broken sandstone are closely related to grain size, load levels, and porosity structure; (2) the permeability k decreases, while the coefficient β increases with a decrease in porosity φ, but both the k − φ and the β − φ curves show some local fluctuations; (3) the permeability k of the broken sandstone has a magnitude of 10⁻¹⁴–10⁻¹² m², while the coefficient β ranges from 10¹⁰ to 10¹² m⁻¹. The results obtained provide some information for further study of the nonlinear seepage behavior of broken rock theoretically.