FRACTAL ANALYSIS OF DIMENSIONLESS PERMEABILITY OF SPHERICAL PARTICLES IN POROUS MEDIA WITH RANDOMLY DAMAGED DISTRIBUTED TREE-LIKE BRANCHING NETWORKS CONSIDERING THE INFLUENCE OF ROUGHNESS

Fluid flow in porous media is the key scientific problem in the development of oil and gas reservoirs. The traditional mechanics of fluid flow in porous media which based on the continuum hypothesis and Darcy′s law plays an important role in developing conventional oil and gas resources. In recent years, unconventional reservoirs are drawing more and more attention all over the world, therefore the development theory and technology, especially the corresponding flow mechanisms have become the hot research issues. The unconventional reservoirs exhibit distinct multiscale characteristics, even with six orders of magnitude difference. In addition, the application of massive multi-stage hydraulic fracturing can induce strong stress interactions. Therefore, the traditional theory of fluid flow in porous media cannot accurately describe the flow characteristics in unconventional reservoirs. In essence, the development of unconventional oil and gas resources involves multiphase fluids (e.g. oil, water and gas) flow in multi-scale porous media with multi-field coupling and various flow patterns. Therefore, the concept of modern system of multiphase flow in porous media is proposed, which means multiphase fluids flowing in multi-scale porous media with multi-field coupling and various flow patterns. The research status and development tendency are reviewed from the aspects of: (1) micro- and nanoscale oil and gas flow simulation; (2) upscaling for reservoir simulation, (3) macroscale flow simulation of unconventional oil and gas reservoirs; (4) simulation of flow in large scale fractured and vuggy carbonate reservoirs and (5) physical simulation of hydrocarbon transport in porous media. More specifically, in nanoscale the density functional theory and molecular simulation method can be used to study the interfacial phenomena to understand the hydrocarbon transport behavior in nanopores and provide key parameters for mesoscale flow simulation. The current study of nanoscale simulation mainly focuses on developing more realistic molecular structure model to represent the heterogeneous shale samples. Microscale simulation methods involve pore network model, lattice Boltzmann method, direct simulation of Navies-Stokes equation, level-set method and smoothed particle hydrodynamics, etc. Digital core and pore network model are the fundamental research platforms. Various methods can be used to reconstruct digital cores with multiscale pore structures and mineral compositions. The complex physicochemical phenomena namely adsorption/desorption, wettability change and boundary effect should be considered in the microscale flow simulations and extensive works have been done in microscale gas flow simulations. The future work on microscale simulation should focus on the multiphase flow mechanisms with multi-field coupling. The multiscale characteristics of unconventional reservoirs indicate the necessity of upscaling process to introduce the microscale flow mechanisms to macroscale. Homogenization theory and volume averaging method are the main upscaling approaches. Current upscaling methods are mostly based on the periodic boundary condition and are unreliable to be used in complex oil and gas reservoirs, which needs further study. In addition, more research needs to be conducted on the upscaling from molecular scale to mesoscale. In macroscale simulations of unconventional oil and gas reservoirs, the fluid-structure interaction should be considered and high efficiency numerical algorithm needs to be established. For large scale fractured and vuggy carbonate reservoirs, the non-Darcy flow characteristics and different flow regimes in vugs and fractures should be taken into account during flow simulation. Physical simulations of hydrocarbon transport in porous media are conducted at two scales: macroscale, nano- and microscale. Macroscale physical simulations aim at monitoring the dynamic saturation and pressure fields change under the realistic reservoir conditions. Nano- and microscale physical simulations are mainly applied to study the fluid transport mechanisms in single pore or throat. In summary, the proposed theory of multiphase fluids flowing in multi-scale porous media with multi-field coupling and various flow patterns can be applied to study the fluid flow problems in unconventional oil and gas industries.

A sequential fully implicit multi-scale meshless multi-point flux method (MS-MMPFA) for nonlinear hyperbolic partial differential equations of fluid flow in heterogeneous porous media is described in this paper. The method extends the recently proposed the meshless multi-point flux approximation (MMPFA) for general fluid flow in porous media [Lukyanov, “Meshless Upscaling Method and its Application to a Fluid Flow in Porous Media”, Proceeding ECMOR XII, 2010] by utilizing advantages of the existing multi-scale finite volume (MSFV) schemes. The MMPFA is based on a gradient approximation commonly used in meshless method and combined with the mixed corrections which ensure linear completeness. In corrected meshless method, the domain boundaries and field variables at the boundaries are approximated with the default accuracy of the method. The MMPFA method was successfully tested for a number of problems where it was clearly shown that the MMPFA gives a good agreement with analytical solutions for a given number of particles. However, the level of detail and range of property variability included in reservoir characterization models leads to a large number of particles to be considered in MMPFA method. In this paper this problem is resolved using a sequential fully implicit MS-MMPFA method. The results are presented, discussed.

A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks

The seepage of porous media has garnered significant interest due to its ubiquitous presence in nature, but most of the research is based on the model of a single dendritic branching network. In this study, we derive a fractal model of the dimensionless permeability and the Kozeny–Carman (KC) constant of porous media consisting of spherical particles and randomly distributed tree-like branching networks based on fractal theory. In addition, three different types of corrugated pipes are considered. Then, the relationships between the KC constant, dimensionless permeability, and other structural parameters were discussed in detail. It is worth noting that the KC constant of the porous media composed of three types of pipes decreases sharply first and then increases with the increase in the internal diameter ratio, while the dimensionless permeability has the opposite trend and conforms to the physical law. In addition, empirical constants are not included in the analytical formulas of the present model, and the physical mechanism of fluid flow in spherical granular porous media with randomly distributed tree-like branching networks is clearly revealed.

This study investigates novel solitary wave solutions of the Gilson–Pickering ([Formula: see text]) equation, which is a model that describes the motion of a fluid in a porous medium. An analytical scheme is applied to construct these solutions, utilizing the extended Khater method in conjunction with the homogenous balance technique. The derived expressions for the solitary wave solutions are exact and are presented in terms of hyperbolic functions. The [Formula: see text] equation is valuable for a wide range of applications, including oil and gas reservoir engineering, groundwater flow, and flow in biological tissues. Additionally, this model is employed to describe the behavior of waves in various physical systems such as fluids and plasmas. Specifically, it models the propagation of dispersive waves in a media that exhibits both dispersion and dissipation. To ensure the accuracy of the constructed solutions, a numerical scheme is employed. The properties of the solitary wave solutions are analyzed, and their physical implications are explored. The results of this investigation reveal a rich variety of solitary wave solutions that exhibit interesting behaviors, including oscillatory and non-oscillatory behavior, which are elucidated through various types of distinct graphs. Consequently, this study provides significant insights into the behavior of fluid flow in porous media and its applications in various fields, including oil and gas reservoir engineering and groundwater flow modeling. The analytical and numerical methods employed in this investigation demonstrate their potential for studying nonlinear evolution equations and their applications in the physical sciences.

Understanding fluid flow in porous media is essential with complex and multiphase fluid flow. We demonstrate that high-resolution in-line density measurements are a valuable tool in this regard. An in-line densitometer is used in fluid flow in porous media applications to quantify fluid production and obtain quantitative and qualitative information such as breakthrough times, emulsion/foam generation, and steam condensation. In order to determine the potential applications for in-line densitometry for fluid flow in porous media, a series of sand pack floods were performed with a densitometer placed at the outlet of a sand pack. All fluids passed through the measurement cell at experiential temperatures and pressures. An algorithm was developed and applied to the density data to provide a quantitative determination of oil and water production. The second series of tests were performed at high temperature and pressure, with a densitometer placed at the inlet and outlet of a sand pack, for steam applications. In both series of experiments, data acquisition was collected at 1 hertz and the analyzed density data was compared to results from the conventional effluent analysis, including Dean-Stark, toluene separations, magnetic susceptibility measurement, and flash calculations where applicable. The high-resolution monitoring of effluent from a flow experiment through porous media in a system with two phases of known densities enables two-phase production to be accurately quantified in the case of both light and heavy oil. The frequency of measurements results in a high-resolution history of breakthrough times and fluid behavior. In the case of monitoring steam injection processes, reliable laboratory tests show that in-line density measurements enable the determination of steam quality at the inlet and outlet of a sand pack and qualitative determination of steam condensation monitoring The use of in-line densitometry provides insight on the monitoring of complex fluid flow in porous media, which typical bulk effluent analysis is not able to do. The ability to measure produced fluids at high resolution and extreme temperatures reduces mass balance error associated with the effluent collection and broadens our understanding of complex fluid flow in porous media.

1 - Modelling fluid flow in saturated porous media and at interfaces

A fractal analytical model for Kozeny-Carman constant and permeability of roughened porous media composed of particles and converging-diverging capillaries

In the study of heat transfer in tree-like branching network, neither the heat convection caused by fluid flow in the tree-like branching network nor the asymmetric structure of the tree-like branching network can be ignored. In this work, we assume the porous media is embedded with a tree-like branching network that are characterized by damaged pipes. We investigated the effects of surface roughness on heat conduction and heat convection in the porous media embedded with the damaged tree-like branching network based on the fractal features of tree-like branching networks and the basic theory of thermodynamics. The proposed model for thermal conductivity can be expressed as a function of micro-structural parameters of the composite, such as the relative roughness, the ratio of thermal conductivity of the wall to that of the fluid in the micro-channel, the diameter ratio, the length ratio, the branching level, the number of damaged channels, the total number of branching levels, and the main tube porosity of the porous media. The effects of the micro-structural parameters of the model on its effective thermal conductivity have been analyzed in detail. It is believed that the joint expression of heat conduction and heat convection could enrich and develop the physical study of heat transport in porous media.

Experimental study on moving boundaries of fluid flow in porous media

A finite-element scheme has been formulated, which is capable of solving transient analysis of both conductive and convective heat transfers due to fluid flow in porous media. The model also includes the latent heat effect to consider the phase change aspect of a frozen medium. To test the validity of the model, it was applied to six cases for which analytical solutions are available. The test cases cover (i) single-phase fluid flow through porous media, (ii) radial conduction with and without phase change, (iii) conductive and convective heat transfer in an aquifer, and (iv) two-phase immiscible flow in porous media. In all these cases, good agreement with analytical solutions are observed validating the computational scheme. This computational scheme should be useful in solving frozen ground problems, thermal stimulation technique for natural gas recovery from hydrates, and single-phase and two-phase convective heat transfer problems in enhanced oil recovery scheme in petroleum engineering.

Hele-Shaw cells are used to model creeping flow through porous media (where Darcy's law is valid). The effects of inertia on flow about obstructions in a Hele-Shaw cell can be calculated by a perturbation method if one can determine a solution to Laplace's equation. Results of a computer solution for flow about circular, square and elliptical obstructions are presented These results show that for a modified presented These results show that for a modified Reynolds number of less than 1, the inertia terms are small; and for values of less than 3, the average streamline predicts the ideal flow. Therefore, the analogy might be used for studying flow in porous media up to a modified Reynolds number of at least 3. Introduction The nature of fluid flow in porous media is of interest in the fields of soil mechanics, ground water flow, petroleum production, filtration and flow, in packed beds. Because it is very difficult to study the phenomenological behavior of flow in porous media, homologs and analogs are used to study flow characteristics. A Hele-Shaw model, made of two closely spaced plates - usually glass - is often used as an analogy to two-dimensional flow in porous media. Hele-Shaw showed experimentally that the streamline configuration for creeping flow around an obstacle located between two closely spaced parallel plates is the same as for two-dimensional parallel plates is the same as for two-dimensional ideal flow about the same obstacle. Stokes verified these observations mathematically. The usual equation of motion for flow in porous media is Darcy's law. The form of the mathematical statement of Darcy's law is identical, within a multiplicative constant, to the expression for the average velocity over the place gap in the plane of a Hele-Shaw model. These models may be used to describe flow in both homogeneous and heterogeneous porous media.

This research reports on the development of a two dimensional lattice gas automata (LGA) model to simulate fluid flow in porous media. In lattice gas automata simple rules of particle interactions at a lattice are used to simulate complex flow phenomena. Since the numerical operations involved are largerly bit manipulations, lattice gas automata can be potentially more efficient in memory usage than conventional methods, such as finite difference or finite element methods. There are basically two motivations for the utilisation of lattice-gas automata methods for studying fluid flow in porous media. First, the no-slip boundary condition of hydrodynamics is easily implemented as a simple bounce-back reflection at solid walls. Second, the discrete nature of the lattice-gas method makes it computationally efficient in terms of the work necessary to update a single site of the lattice. Fluid flow in porous media is generally described by Darcy's law, which linearly relates fluid velocity to pressure gradient. Other research on the use of lattice gas automata to model fluid flow in porous media primarily focuses on Stokes flow at the pore level with the intent of understanding flow at the core scale. This work concentrates on modeling Darcy flow in a heterogeneous field. Permeability variations and anisotropy are modeled by a distribution of scatter. Collision of incoming particles with scatterers is a stochastic process.

ABSTRACT: Geomaterials are porous, and there are air, water and other liquids inside the pore space. Pore pressure fluctuation may result in the change of contact forces between the solid grains. The deformation of solid skeleton changes the size of pore and therefore the fluid flows inside the pore space. The coupled process is often described with the mixture theory in continuum mechanics. Localized deformation may lead to the displacement discontinuity or the fracture, increasing the complexity of the whole fluid-solid coupled process. Numerical simulations of the complex processes in the subsurface are essential in understanding many geoengineering systems, such as hydraulic fracturing, geological fault reactivation, waste water management, geothermal energy extraction and CO2 sequestration and so on. This paper presents an assumed enhanced strain (AES) finite element method to model the fracture evolution in porous media, where the discontinuous function enrichments are introduced into the displacement approximation to simulate fracture deformation. The enriched degrees of freedom can be removed by the standard static condensation method, which means the method does not introduce additional global system of equations. The mass and stress coupling is described by the standard Biot’s poro-elasticity theory. The numerical method is verified by the mesh sensitivity studies and comparisons with analytical solutions. Particularly, with the AES framework, we have numerically compared the cohesive fracture model and linear elastic fracture mechanics model for simulating hydraulic fracture propagation in porous media. 1 INTRODUCTION Predicting the mechanical behavior of subsurface fractures is crucial to many engineering practices, especially in the industry of energy resources. Subsurface processes, such as hydraulic fracturing and induced seismicity, pertains to the fracture deformation and propagation driven by fluid flows in subsurface porous media. Hydraulic fracturing is dominated by the opening mode, while induced seismicity may be dominated by the shear modes. Fracture deformation and propagation can also significantly impact subsurface fluid flows, by providing additional flow conduits or barriers to the subsurface. Therefore, understanding the interaction between fractures and fluid flows in porous media is key for the comprehension of those subsurface processes. The motivation of this work is to provide a convenient finite element framework to simulate fracture propagation coupled with fluid flows in the complex subsurface environment.

An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media