scholarly journals Unified theory of global flow and squirt flow in cracked porous media

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA65-WA76 ◽  
Author(s):  
Morten Jakobsen ◽  
Mark Chapman
Keyword(s):  
Porous Media ◽  
Velocity Dispersion ◽  
Solid Matrix ◽  
Global Flow ◽  
Local Pressure ◽  
Fluid Mass ◽  
T Matrix ◽  
Wave Induced ◽  
Cracked Porous Media ◽  
Single Set

Approximations for frequency-dependent and complex-valued effective stiffness tensors of cracked porous media (saturated with a single fluid) are developed on the basis of an inclusion-based model (the T-matrix approach to rock physics) and a unified treatment of the global-flow and squirt-flow mechanisms. Essentially, this study corrects an inconsistency or error related to fluid-mass conservation in an existing expression for the t-matrix (wave-induced deformation) of a communicating cavity, a cavity that is isolated with respect to stress propagation (through the solid matrix) but that can exchange fluid mass with other cavities because of global and/or local pressure gradients associated with passage of a long viscoelastic wave. An earlier demonstration of Gassmann consistency remains valid because the new theory of global flow and squirt flow (which also takes into account solid mechanical effects of stress interaction by us-ing products of communicating t-matrices associated with two-point correlation functions of ellipsoidal symmetry) only differs from an earlier version by a correction term that goes to zero in the low-frequency limit. If the unified model is applied to the special case of a model involving a single set of spheroidal cavities (having the same aspect ratio and orientation), the results become identical with those obtained using a special theory of global flow that predicts that at zero frequency the cavities will behave as though they are isolated with respect to wave-induced fluid flow (in accordance with Gassmann’s formulas) and that at high frequencies, they will behave as though they are dry. Our theory predicts that there will be a continuous transition from a global-flow-dominated system (characterized by a negative velocity dispersion) to a squirt-flow-dominated system (characterized by a positive velocity dispersion) if one begins with a single set of cavities and then introduces a distribution of shapes and/or orientations that gradually becomes wider (more realistic).

Elastic waves in porous media saturated with non-wetting fluid

2020 ◽  
Vol 60 (1) ◽  
pp. 315
Author(s):  
Jimmy X. Li ◽  
Reza Rezaee ◽  
Tobias M. Müller ◽  
Mohammad Sarmadivaleh
Keyword(s):  
Porous Media ◽  
Apparent Viscosity ◽  
Elastic Waves ◽  
Solid Wall ◽  
Seismic Exploration ◽  
Solid Matrix ◽  
Biot Theory ◽  
Bulk Fluid ◽  
Wave Induced ◽  
Wetting Fluid

Elastic waves have widely been used as a non-destructive probing method in oilfield exploration and development, and the most well-known applications are in seismic exploration and borehole sonic logging. For waves in porous media, it is popular to use the Biot theory, which incorporates the wave-induced global flow, accounting for the frictional attenuation. The Biot theory assumes that the fluid is wetting to the solid matrix. However, the fluid is not always wetting the rock in real reservoirs. It was previously revealed that a non-wetting fluid parcel tends to slip on the solid wall pore boundary where the intermolecular potential between the fluid and solid wall is weaker than in wetting fluid conditions. This particular slippage feature means that the coupling relationship between the fluid and solid frame and frictional dissipation is likely to be very different between non-wetting and wetting fluid situations. We characterise this wave-induced slippage using an apparent viscosity for the non-wetting fluid within the thin viscous boundary layer. This apparent viscosity is smaller than the viscosity of the bulk fluid. We demonstrate that the slip correction affects the dynamic permeability and dynamic tortuosity and results in slippage/wettability dependent phase velocities and attenuation of the fully fluid-saturated rock.

Modeling Transport in Porous Media With Phase Change: Applications to Food Processing

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Amit Halder ◽  
Ashish Dhall ◽  
Ashim K. Datta
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Food Processing ◽  
Transport Processes ◽  
Phase Changes ◽  
Solid Matrix ◽  
Deep Fat Frying ◽  
Modeling Framework ◽  
Food Manufacturing ◽  
Food Processes

Fundamental, physics-based modeling of complex food processes is still in the developmental stages. This lack of development can be attributed to complexities in both the material and transport processes. Society has a critical need for automating food processes (both in industry and at home) while improving quality and making food safe. Product, process, and equipment designs in food manufacturing require a more detailed understanding of food processes that is possible only through physics-based modeling. The objectives of this paper are (1) to develop a general multicomponent and multiphase modeling framework that can be used for different thermal food processes and can be implemented in commercially available software (for wider use) and (2) to apply the model to the simulation of deep-fat frying and hamburger cooking processes and validate the results. Treating food material as a porous medium, heat and mass transfer inside such material during its thermal processing is described using equations for mass and energy conservation that include binary diffusion, capillary and convective modes of transport, and physicochemical changes in the solid matrix that include phase changes such as melting of fat and water and evaporation/condensation of water. Evaporation/condensation is considered to be distributed throughout the domain and is described by a novel nonequilibrium formulation whose parameters have been discussed in detail. Two complex food processes, deep-fat frying and contact heating of a hamburger patty, representing a large group of common food thermal processes with similar physics have been implemented using the modeling framework. The predictions are validated with experimental results from the literature. As the food (a porous hygroscopic material) is heated from the surface, a zone of evaporation moves from the surface to the interior. Mass transfer due to the pressure gradient (from evaporation) is significant. As temperature rises, the properties of the solid matrix change and the phases of frozen water and fat become transportable, thus affecting the transport processes significantly. Because the modeling framework is general and formulated in a manner that makes it implementable in commercial software, it can be very useful in computer-aided food manufacturing. Beyond its immediate applicability in food processing, such a comprehensive model can be useful in medicine (for thermal therapies such as laser surgery), soil remediation, nuclear waste treatment, and other fields where heat and mass transfer takes place in porous media with significant evaporation and other phase changes.

Experimental Validation of Non-Fourier Thermal Response in Porous Media

2001 ◽  
Author(s):  
A. G. Agwu Nnanna ◽  
K. T. Harris ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Experimental Validation ◽  
Thermal Response ◽  
Lag Time ◽  
Equation Model ◽  
Thermal Parameters ◽  
Solid Matrix ◽  
Microscale Model ◽  
Short Time

Abstract An experimental validation of non-Fourier behavior in porous media due to short time thermal perturbation is presented. The governing energy equation is formulated based on the two-equation model and the non-Fourier model. This formulation leads to the emergence of four thermal parameters: lag-time in heat flux τq, lag-time τt in temperature due to interstitial heat transfer coefficient h, and lag-time in the transient response of the temperature gradient τx in the heat flux equation. These parameters account for the microstructural thermal interaction between the fluid and neighboring solid matrix as well as the delay time needed for both phases to approach thermal equilibrium. An experimental verification of the microscale model was performed under standard laboratory conditions. The values of the aforementioned thermal parameters were determined to compute the fluid and solid temperatures. Results predicted from three models (classical Fourier, non-Fourier, and experimental) were compared. It indicates an excellent agreement between the non-Fourier and the experimental model, and a significant deviation of Fourier prediction from the experimental results.

scholarly journals Development of Embedded Element Technique for Permeability Analysis of Cracked Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Qian ◽  
Qianjun Xu
Keyword(s):  
Porous Media ◽  
Effective Permeability ◽  
Water Pressure ◽  
Crack Density ◽  
Mesh Size ◽  
Differential Method ◽  
Simulation Based ◽  
The Matrix ◽  
Element Technique ◽  
Cracked Porous Media

The widely used approach of mesoscale finite element modeling for permeability analysis is to simulate the matrix and cracks with continuum elements (CE), whereas this process brings technical difficulties in generating a satisfying mesh conformity at the interface. In this work, an alternative method based on embedded element (EE) technique is developed for the prediction of water pressure field and effective permeability in the numerical simulation. Based on the mathematical similarity between elasticity and seepage problems, water pressure can derive from the corresponding displacement through “elastic analogy.” To assess the capability of the EE technique, different cases are simulated and compared with the CE model. The results show that there is a satisfactory agreement in water pressures and velocities between the CE and EE modeling. In the CE model, different factors, such as permeability contrast between matrix and cracks (Kcrack/Kmatrix) and mesh size, are considered. It is obvious to find that results will become stable when Kcrack/Kmatrix reaches 104, and the mesh size has little impact. The effective permeability of 3D porous media with random cracks is evaluated and the results show that the differential method is accurate for 3D permeability analysis when the crack density is not large.

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