scholarly journals DOUBLE POROSITY MODELS FOR LIQUID FILTRATION IN INCOMPRESSIBLE POROELASTIC MEDIA

2010 ◽  
Vol 20 (04) ◽  
pp. 635-659 ◽  
Author(s):  
ANVARBEK MEIRMANOV
Keyword(s):  
Pore Space ◽  
Double Porosity ◽  
Homogenization Theory ◽  
Darcy Law ◽  
Solid Skeleton ◽  
Fractured Reservoir ◽  
Liquid Filtration ◽  
Liquid Domain ◽  
Poroelastic Media ◽  
The Common

Double porosity models for the liquid filtration in a naturally fractured reservoir is derived from the homogenization theory. The governing equations on the microscopic level consist of the stationary Stokes system for an incompressible viscous fluid, occupying a crack-pore space (liquid domain), and stationary Lame equations for an incompressible elastic solid skeleton, coupled with the corresponding boundary conditions on the common boundary "solid skeleton-liquid domain". We assume that the liquid domain is a union of two independent systems of cracks (fissures) and pores, and that the dimensionless size δ of pores depends on the dimensionless size ε of cracks: δ = εr with r > 1. The rigorous justification is fulfilled for homogenization procedure as the dimensionless size of the cracks tends to zero, while the solid body is geometrically periodic. As the result we derive the well-known Biot–Terzaghi system of liquid filtration in poroelastic media, which consists of the usual Darcy law for the liquid in cracks coupled with anisotropic Lame's equation for the common displacements in the solid skeleton and in the liquid in pores and a continuity equation for the velocity of a mixture. The proofs are based on the method of reiterated homogenization, suggested by Allaire and Briane. As a consequence of the main result we derive the double porosity model for the filtration of the incompressible liquid in an absolutely rigid body.

Analysis of Heterogeneous Cores Using SN Code With Discontinuity Factor

2014 ◽  
Author(s):  
Jing Zhao ◽  
Zhihong Liu ◽  
Chunlin Wei ◽  
Yongming Hu
Keyword(s):  
Common Method ◽  
Diffusion Equations ◽  
Homogenization Theory ◽  
Discrete Ordinates ◽  
The Common ◽  
Transport Method ◽  
Diffusion Computation ◽  
Heterogeneous Cores

Solving diffusion equations with the equivalence homogenization theory is the common method in reactor neutronics. But for some case, as for stronger absorbers, the diffusion equations will bring great errors and the transport method will be more suitable. The discontinuity factor theory has been successfully used in core diffusion computation programs and effectively reduced the homogenization error. The method of using the discontinuity factor in the transport method were studied. The result shows that higher accuracy was obtained from the discrete ordinates core transport computation program with discontinued factor.

scholarly journals Continuous dependence on modelling for temperature-dependent bidispersive flow

2017 ◽  
Vol 473 (2208) ◽  
pp. 20170485 ◽  
Author(s):  
Franca Franchi ◽  
Roberta Nibbi ◽  
Brian Straughan
Keyword(s):  
Temperature Effects ◽  
Continuous Dependence ◽  
Double Porosity ◽  
Interaction Coefficient ◽  
Solid Skeleton ◽  
Temperature Dependent ◽  
Porosity Structure ◽  
Viscosity Coefficients ◽  
The Third ◽  
Single Temperature

We consider a model for flow in a porous medium which has a double porosity structure. There is the usual porosity herein called macro porosity, but in addition, we allow for a porosity due to cracks or fissures in the solid skeleton. The cracks give rise to a micro porosity. The model considered also allows for temperature effects with a single temperature T . This paper analyses three aspects of structural stability. The first establishes continuous dependence of the solution on the interaction coefficient between the velocities associated with the macro and micro porosity. The second analyses continuous dependence on the viscosity coefficients, while the third establishes continuous dependence on the radiation constant when Newton’s law of cooling is involved on the boundary.

scholarly journals Horizontally isotropic double porosity convection

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180672 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Porous Medium ◽  
Nonlinear Stability ◽  
Vertical Component ◽  
Vertical Direction ◽  
Transversely Isotropic ◽  
Double Porosity ◽  
Solid Skeleton ◽  
The Difference

We analyse instability and nonlinear stability in a layer of saturated double porosity medium. In a double porosity or bidisperse porous medium, there are normal pores which give rise to a macroporosity. But, there are also cracks or fissures in the solid skeleton and these give arise to another porosity known as micro porosity. In this paper, the macropermeability is horizontally isotropic, in the sense that the vertical component of permeability is different to the horizontal one which is the same in all horizontal directions. Thus, the permeability is transversely isotropic with the isotropy axis in the vertical direction of gravity. We also allow the micro permeability to be horizontally isotropic, but the permeability ratios of vertical to horizontal are different in the macro- and micro-phases. The effect of the difference of ratios is examined in detail.

Wave simulation in double-porosity media based on the Biot-Rayleigh theory

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. WA11-WA21 ◽  
Author(s):  
Enjiang Wang ◽  
José M. Carcione ◽  
Jing Ba
Keyword(s):  
Wave Energy ◽  
Mode Conversion ◽  
Pore Space ◽  
Time Integration ◽  
Grid Method ◽  
Double Porosity ◽  
P Wave ◽  
Biot Theory ◽  
Integration Algorithm ◽  
Diffusive Modes

We have developed a numerical algorithm for simulation of wave propagation in double-porosity media, where the pore space is saturated with a single fluid. Spherical inclusions embedded in a background medium oscillate to yield attenuation by mode conversion from fast P-wave energy to slow P-wave energy (mesoscopic or wave-induced fluid-flow loss). The theory is based on the Biot theory of poroelasticity and the Rayleigh model of bubble oscillations. The differential equation of the Biot-Rayleigh variable is approximated with the Zener mechanical model, which results in a memory-variable viscoelastic equation. These approximations are required to model mesoscopic losses arising from conversion of the fast P-wave energy to slow diffusive modes. The model predicts a relaxation peak in the seismic band, depending on the diameter of the patches, to model the attenuation level observed in rocks. The wavefield is obtained with a grid method based on the Fourier differential operator and a second-order time-integration algorithm. Because the presence of two slow quasistatic modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modeling has spectral accuracy in the calculation of the spatial derivatives.

scholarly journals Cenomanian-Early Campanian Carbonate Reservoir Rocks of Northwestern Iraq: Diagenesis and Porosity Development

2018 ◽  
Vol 2 (2) ◽  
pp. 1-19
Author(s):  
Mohamed Al-Haj ◽  
Ali Al-Juboury ◽  
Aboosh Al-Hadidy ◽  
Dalia Hassan
Keyword(s):  
Upper Cretaceous ◽  
Gamma Ray ◽  
Carbonate Reservoir ◽  
Fractured Reservoir ◽  
Burial Diagenesis ◽  
Near Surface ◽  
Reservoir Rocks ◽  
Zone Ii ◽  
The Common ◽  
Highly Porous

The present work focuses on the upper Cretaceous (Cenomanian-early Campanian) carbonate successions in selected wells from northwestern Iraq. These successions are represented by Gir Bir (Cenomanian-early Turonian), Wajna (late Santonian) and Mushorah (early Campanian) Formations. The succession has affected by early burial near-surface, unconformity-related and deep burial diagenesis represented by cementation, neomorphism, dolomitization, dedolomitization, silicification, authigenesis of glauconite and pyrite, compaction, micritization, solution and porosity formation. The common porosity types are intergranular, fenestral, intercrystalline, moldic, vuggy, channel and fracture. Three porosity zones (I, II, and III) are identified depending on variation in gamma ray which reflects their shale content. The upper part of zone (II) is highly porous and regarded on the main reservoir unit in the middle and upper parts of the Gir Bir Formation. Fracture and moldic and vuggy dissolution features in addition to karstic and fissure features are responsible for the porosity increase in the fractured reservoir unit.

scholarly journals On models of double porosity poroelastic media

2015 ◽  
Vol 203 (3) ◽  
pp. 1694-1725 ◽  
Author(s):  
Claude Boutin ◽  
Pascale Royer
Keyword(s):  
Double Porosity ◽  
Poroelastic Media

scholarly journals Analysis of a multiple-porosity model for single-phase flow through naturally fractured porous media

2003 ◽  
Vol 2003 (7) ◽  
pp. 327-364 ◽  
Author(s):  
Anna Maria Spagnuolo ◽  
Steve Wright
Keyword(s):  
Single Phase ◽  
Flow System ◽  
Double Porosity ◽  
Phase Flow ◽  
Fractured Reservoir ◽  
Single Phase Flow ◽  
Naturally Fractured ◽  
Flow Through ◽  
Multiple Porosity ◽  
Porosity Model

A derivation of a multiple-porosity model for the flow of a single phase, slightly compressible fluid in a multiscale, naturally fractured reservoir is presented by means of recursive use of homagnetization theory. We obtain a model which generalizes the double-porosity model of Arbogast et al. (1990) to a flow system with an arbitrary finite number of scales.

Sign in / Sign up

Export Citation Format

Share Document