Contribution to the Modelling of Coupled Heat and Mass Transfers on 3D Real Structure of Heterogeneous Building Materials: Application to Hemp Concrete

Hydraulic flow, electrical flow and the passage of elastic waves through porous media are all linked by electrokinetic processes. In its simplest form, the passage of elastic waves through the porous medium causes fluid to flow through that medium and that flow gives rise to an electrical streaming potential and electrical counter-current. These processes are frequency-dependent and governed by coupling coefficients which are themselves frequency-dependent. The link between fluid pressure and fluid flow is described by dynamic permeability, which is characterised by the hydraulic coupling coefficient (C_hp). The link between fluid pressure and electrical streaming potential is characterised by the streaming potential coefficient (C_sp). While the steady-state values of such coefficients are well studied and understood, their frequency dependence is not. Previous work has been confined to unconsolidated and disaggregated materials such as sands, gravels and soils. In this work, we present an apparatus for measuring the hydraulic and streaming potential coefficients of high porosity, high permeability consolidated porous media as a function of frequency. The apparatus operates in the range 1 Hz to 2 kHz with a sample of 10 mm diameter and 5–30 mm in length. The full design and validation of the apparatus are described together with the experimental protocol it uses. Initial data are presented for three samples of Boise sandstone, which present as dispersive media with the critical transition frequency of 918.3?±?99.4 Hz. The in-phase and in-quadrature components of the measured hydraulic and streaming potential coefficients have been compared to the Debye-type dispersion model as well as theoretical models based on bundles of capillary tubes and porous media. Initial results indicate that the dynamic permeability data present an extremely good fit to the capillary bundle and Debye-type dispersion models, while the streaming potential coefficient presents an extremely good fit to all of the models up to the critical transition frequency, but diverges at higher frequencies. The streaming potential coefficient data are best fitted by the Pride model and its Walker and Glover simplification. Characteristic pore size values calculated from the measured critical transition frequency fell within 1.73% of independent measures of this parameter, while the values calculated directly from the Packard model showed an underestimation by about 12%.

     

Use of a Downscaling Procedure for Macroscopic Heat Source Modeling in Porous Media

Many porous media such as rocks have mesoscale inhomogeneities. The characteristic sizes of such inhomogeneities are much larger than the pore size but much less than the characteristic scale of the problem, such as the length of the sample on which measurements are taken. In this paper, we have solved the one-particle problem for depolarization of an ellipsoidal particle located in a porous medium with electrokinetic effect. To calculate the effective physical properties of a porous medium with many ellipsoidal inclusions, we have applied the effective field method. The application of this method allows us to take into account the texture of an inhomogeneous medium. The analysis performed has shown that three effective properties of inhomogeneous media (permeability, electroosmotic coupling coefficient and electrical conductivity) are not completely independent variables. General theory is illustrated by calculations of the effective properties of media containing spherical and spheroidal inclusions.     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

Percolation models of the permeability properties of media

Models that describe the permeability of media with allowance for the structure of the pore space are considered. It is proposed to use percolation theory to describe the topology of the pore space. If the distribution of the pore channels in the medium is random, percolation theory makes it possible to determine the percolation threshold, and also to estimate the fluid conductivity of the cluster that then results. Results obtained for models of granular, porous, and cracked media are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–86, May–June, 1984.     

Two-Phase Flow Properties Prediction from Small-Scale Data Using Pore-Network Modeling

The objective of this work is to evaluate the prediction accuracy of network modeling to calculate transport properties of porous media based on the interpretation of mercury invasion capillary pressure curves only. A pore-scale modeling approach is used to model the multi-phase flow and calculate gas/oil relative permeability curves. The characteristics of the 3-D pore-network are defined with the requirement that the network model satisfactorily reproduces the capillary pressure curve (P_c curve), the porosity and the permeability. A sensitivity study on the effect of the input parameters on the prediction of capillary pressure and gas/oil relative permeability curves is presented. The simulations show that different input parameters can lead to similarly good reproductions of the experimental P_c, although the predicted relative permeabilities K_r are somewhat widespread. This means that the information derived from a mercury invasion P_c curve is not sufficient to characterize transport properties of a porous medium. The simulations indicate that more quantitative information on the wall roughness and the node/bond aspect ratio would be necessary to better constrain the problem. There is also evidence that in narrow pore size distributions pore body volume and pore throat radius are correlated while in broad pore size distributions they would be uncorrelated.     

A lattice model of foam flow in porous media: A percolation approach

Because fluid flow in porous media is opaque to most observational techniques simulations of the processes occurring in porous media have become important. Typical reservoir simulations treat the flow as taking place in some averaged (Darcy-scale) medium but simulations can also be carried out at the level of the network of pores and throats of the porous medium. We report the results of a pore-scale investigation of mechanisms for the alteration of mobility by foam lamella blockage in a network of these spaces and channels of porous media. Saturation and relative permeability curves are obtained using well-known power-law expressions of percolation theory and a rescaling of the percolation parameter readily permits a number of lamella-blocking mechanisms to be treated. An explanation of the shift in breakthrough gas saturation and the deformation of the shape of permeabilityvs saturation curves upon introduction of foam is provided for a variety of blocking mechanisms. The qualitatively different features seen in experimental studies of modification of gas mobility by foam can be rationalized using only two parameters which characterize the throat-size at which blockage commences and the degree of blockage.     

Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach

The finite deformation of an unsaturated porous medium is analysed from first principles of mixture theory. An expression for Bishop’s effective stress is derived from (1) the deformation-dependent Brooks and Corey’s water retention curve and (2) the restrictions on the constitutive relationships of an unsaturated medium subject to finite deformation. The resulting expression for the effective stress parameter \(\chi \) is reasonably consistent with experimental data from the literature. Hence, it is shown that Bishop’s equation is constitutively linked to water retention curves in deforming media.     

Contrôle passif d'écoulements incompressibles autour d'obstacles à l'aide de milieux poreux

Passive control of the flow behind a bluff-body is obtained by integrating porous area on the body. The penalisation method is used to modelize the flow in three different media. In fact each medium can be considered as a porous medium. The fluid is identified as a porous medium of infinite permeability and the solid is identified as a porous medium of zero permeability. This way, it is easy to compute the flow in each medium using the same parameter. Some benefical effects are due to the porous interface: the flow is smoothed, and the enstrophy and drag are significantly reduced.     

Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable,heterogeneous porous media

This paper presents a numerical approach for the simulation of fluid flow through porous media by proposing a theoretical and numerical meso-to-macro multiscale framework, which combines the advantages of the lattice Boltzmann method (LBM) with the continuum Theory of Porous Media (TPM) to efficiently and accurately model fluid transport in heterogeneous porous media. In particular, LBM presents an alternative to experiments by studying the flow from a mesoscopic perspective, which in turn, allows the derivation of the material parameters needed for simulating the flow in the macroscopic TPM model. In this work, a meso-macro hierarchic upscaling scheme is applied to investigate the deformation-dependent intrinsic permeability properties and the Darcy/non-Darcy fluid flow regime. Concerning the mesoscale, the intrinsic permeability of the porous domain is computed by means of the LBM model at the first stage. Subsequently, deformation of the medium takes place in furtherance of determining the relation of the aforementioned deformation dependency. Thereupon, these findings are input into the TPM model in order to compute the primary unknown variables, where special focus is laid on the stability challenges in the compaction and near compaction states. With respect to the criteria of non-Darcy fluid flow, the conditions of its onset, i.e. the induced pressure gradient and mean fluid flow velocity, are computed as well using the LBM solver and conveyed afterwards to the macroscopic TPM model. Herein, the non-Darcy intrinsic permeability has been investigated in the TPM approach based on the Forchheimer equation. Simulations done on a synthetic porous micro-structure show that the combined framework proved to stand well between the two approaches.     

基于介观结构的饱和与非饱和多孔介质有效应力

基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.      

定量开采条件下径向渗流的液固耦合问题

考虑到多孔介质渗透率随孔隙度变化的特点，建立了力学模型，研究定量抽放问题；对于广义平面应力状态下的非线性渗流耦合问题，提出了解的构造方法和解耦方法；求出了耦合条件下的孔隙压力，多孔介质总应力、总应变和总位移的解析解；进行了实例计算，并与Biot理论进行了对比，结果表明两种理论的差别很大。因此在渗透系数有较明显变化的场舍下不能采用Biot理论进行分析。     

The Effect of varying correlation lengths on Anomalous Transport

Conventional concepts for transport in porous media assume that the heterogeneous distribution of hydraulic conductivities is the source for the contaminant temporal and spatial heavy tail. This tailing, known as anomalous or non-Fickian transport, can be captured by the β parameter in the continuous-time random walk framework. This study shows that with the increase in spatial correlation length between these heterogeneous distributions of hydraulic conductivities, the transport’s anomaly reduces; yet, the β value is unchanged, suggesting a topological component of the conductivity field, captured by the β. This finding is verified by an analysis of the solute transport, showing that the changing conductivity values have a moderate effect on the transport shape.

     

Influence of phase behavior on chemical flood transport phenomena

We propose that there are two classes of temporal development in the degradation of permeability of porous media due to deposition of fines: (1) Deposition, and therefore permeability degradation, is localized to bands growing orthogonally to the average local flow direction, and (2) permeability degradation occurs in stripes parallel to the local flow direction. These latter stripes do not influence total permeability much as they develop. When these stripes are allowed to develop, they coalesce and worm holes form. We discuss how imposing different flow conditions such as constant flow and constant pressure influence the deposition process. Our conclusion is that constant pressure conditions typically lead to a slower permeability degradation compared to constant flow conditions as a direct consequence of the formation of low-permeability bands. We test our ideas by numerical simulations on a simple model for fines migration and deposition in porous media.     

Two-phase flow in heterogeneous porous media: The method of large-scale averaging

The analysis of two-phase flow in porous media begins with the Stokes equations and an appropriate set of boundary conditions. Local volume averaging can then be used to produce the well known extension of Darcy's law for two-phase flow. In addition, a method of closure exists that can be used to predict the individual permeability tensors for each phase. For a heterogeneous porous medium, the local volume average closure problem becomes exceedingly complex and an alternate theoretical resolution of the problem is necessary. This is provided by the method of large-scale averaging which is used to average the Darcy-scale equations over a region that is large compared to the length scale of the heterogeneities. In this paper we present the derivation of the large-scale averaged continuity and momentum equations, and we develop a method of closure that can be used to predict the large-scale permeability tensors and the large-scale capillary pressure. The closure problem is limited by the principle of local mechanical equilibrium. This means that the local fluid distribution is determined by capillary pressure-saturation relations and is not constrained by the solution of an evolutionary transport equation. Special attention is given to the fact that both fluids can be trapped in regions where the saturation is equal to the irreducible saturation, in addition to being trapped in regions where the saturation is greater than the irreducible saturation. Theoretical results are given for stratified porous media and a two-dimensional model for a heterogeneous porous medium.     

Linking Morphology of Porous Media to Their Macroscopic Permeability by Deep Learning

Flow, transport, mechanical, and fracture properties of porous media depend on their morphology and are usually estimated by experimental and/or computational methods. The precision of the computational approaches depends on the accuracy of the model that represents the morphology. If high accuracy is required, the computations and even experiments can be quite time-consuming. At the same time, linking the morphology directly to the permeability, as well as other important flow and transport properties, has been a long-standing problem. In this paper, we develop a new network that utilizes a deep learning (DL) algorithm to link the morphology of porous media to their permeability. The network is neither a purely traditional artificial neural network (ANN), nor is it a purely DL algorithm, but, rather, it is a hybrid of both. The input data include three-dimensional images of sandstones, hundreds of their stochastic realizations generated by a reconstruction method, and synthetic unconsolidated porous media produced by a Boolean method. To develop the network, we first extract important features of the images using a DL algorithm and then feed them to an ANN to estimate the permeabilities. We demonstrate that the network is successfully trained, such that it can develop accurate correlations between the morphology of porous media and their effective permeability. The high accuracy of the network is demonstrated by its predictions for the permeability of a variety of porous media.

     

Simulation of the dynamic (frequency-dependent) permeability and electrical conductivity in porous materials based on the concept of an ensemble of pores

The class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometrical parameters (e.g., pore size) is studied. The case of the saturation of the pore space with a single-phase multicomponent fluid mixture is studied with and without taking into account the transfer of electric charges. Transfer laws are derived from the condition of decreasing free energy. The hydrodynamic connectivity of pores (and electrical conductivity) is described by two kernels: one kernel describes the connectivity of pores in space, and the other describes the connectivity of pores in the elementary macrovolume. The frequency dependences of the dynamic permeability determined in laboratory experiments and the electrical conductivity of the porous medium were determined using the concept of an ensemble of pores. The relationship between the models considered and relaxation filtration models is established.     

Onset of Convection in a Porous Layer with Continuous Periodic Horizontal Stratification. Part I. Two-Dimensional Convection

The onset of convection in a horizontal porous layer is investigated theoretically. The permeability of the porous medium is a continuous periodic function of the horizontal x coordinate. Floquet theory has been employed to determine the favoured two-dimensional mode of convection. For a wide range of periods of the permeability variation, a matrix eigenvalue technique with eighth order accuracy has been employed to find the critical Darcy– Rayleigh number. This is supplemented by a multiple-scales analysis of the large-period limit, and a brief consideration of the anisotropic limit for very short periods.