Consolidation in Compressible Mixtures

1978 ◽  
Vol 45 (4) ◽  
pp. 727-732 ◽  
Author(s):  
D. E. Kenyon
Keyword(s):  
Porous Media ◽  
Boundary Layers ◽  
Fluid Pressure ◽  
Transient Behavior ◽  
Present Theory ◽  
Small Departure ◽  
Small Measure

Comparisons between linear theories of incompressible and compressible porous media reveal two phenomena unique to phase compressibility: (1) boundary layers of fluid pressure and filtration will appear at noncontact loading surfaces in a compressible mixture, and (2) a small measure of mixture compressibility does not always imply that the transient behavior of a compressible mixture is only a small departure from that of an incompressible mixture. The relationships between the compressibility parameters of the present theory and those of Biot are given.

Thermally driven cavity flows in porous media II. The horizontal boundary layer structure

1982 ◽  
Vol 382 (1782) ◽  
pp. 135-154 ◽  
Keyword(s):  
Porous Media ◽  
Boundary Layers ◽  
Layer Structure ◽  
Present Theory ◽  
Cavity Flows ◽  
Driven Cavity ◽  
Double Structure ◽  
Horizontal Boundary ◽  
Thermally Driven ◽  
Entire Flow

An analysis is given of the structure, at high Rayleigh numbers, of thermally driven cavity flows in fluid-saturated porous media. Particular emphasis is placed on the description of the diffusive layers near the horizontal surfaces. Solutions consistent with the core behaviour determined in part I of this series are obtained. These solutions, which are new, indicate that the horizontal boundary layers have a double structure in which the outer layer has a thickness O ( R -¼ ), where R is the Rayleigh number. Corner interactions between the horizontal and the vertical boundary layers are also discussed, and the present theory provides a first-order description of the entire flow field.

scholarly journals The Single-Blow Problem Including the Effects of Longitudinal Conduction

1964 ◽  
Author(s):  
C. P. Howard
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Conduction ◽  
Transient Behavior ◽  
Step Change ◽  
Graphical Form ◽  
Compact Heat Exchanger ◽  
Fluid Temperature ◽  
Transfer Data ◽  
Method Of Calculation

The results are presented from a numerical finite-difference method of calculation for the transient behavior of porous media when subjected to a step change in fluid temperature considering the case where the longitudinal thermal heat conduction cannot be neglected. These results, given in tabular and graphical form, provide a useful means for evaluating the heat-transfer data obtained from the transient testing of compact heat-exchanger surfaces.

Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Minh H. Tran ◽  
Younane N. Abousleiman
Keyword(s):  
Porous Media ◽  
Fluid Pressure ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Analytical Models ◽  
Combined Effects ◽  
Saturated Porous Media ◽  
Stress Distributions ◽  
Shale Formations ◽  
Electrically Charged

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.

Dynamic Interactions Between the Vadose and Phreatic Zones During Breaking Solitary Wave Runup and Drawdown Over a Fine Sand Beach

2009 ◽  
Author(s):  
Heng Xiao ◽  
Yin L. Young ◽  
Jean H. Pre´vost
Keyword(s):  
Porous Media ◽  
Solitary Wave ◽  
Fluid Pressure ◽  
Fine Sand ◽  
Laboratory Scale ◽  
Slope Instability ◽  
Multiphase Model ◽  
Wave Runup ◽  
Sand Beach ◽  
Dynamic Interactions

The objective of this work is to investigate the dynamic interactions between the vadose and the phreatic zones during breaking solitary wave runup and drawdown over a fine sand beach. Extreme wave runup and drawdown in the nearshore region can lead to soil failure in the form of severe erosion, liquefaction, or slope instability. However, the physics of the nearshore region is difficult to simulate numerically due to the greatly varying time scales between the four governing processes: loading and unloading caused by wave runup and drawdown, propagation of the saturation front, pore pressure diffusion, and soil consolidation. Such processes are also difficult to simulate experimentally via model-scale wave tank studies due to the inability to satisfy all the similarity requirements for both the wave and the porous media in a 1g environment. Hence, the goal of this work is to perform a 1D study using a multiphase model to describe the transient responses of the species saturation, pore fluid pressure, effective stresses, and skeleton deformation. Results are shown for three simulations: (1) full-scale simulation, (2) 1:20 laboratory-scale simulation without scaling of the porous media, and (3) 1:20 laboratory-scale with consistent scaling of the soil permeability. The results suggest that the scaling of porous media between the pore fluids and soil skeleton has a significant influence on the transient response of both the vadose and the phreatic zones.

Prediction of Noise from Turbulent Boundary Layers Attached to Porous Media

AIAA Journal ◽  
2019 ◽  
Vol 57 (6) ◽  
pp. 2457-2464 ◽  
Author(s):  
Steven A. E. Miller ◽  
Elisha R. Pager
Keyword(s):  
Porous Media ◽  
Boundary Layers ◽  
Turbulent Boundary Layers

Analysis of the Influence of Fluid Flow on the Plasticity of Porous Rock Under an Axially Symmetric Punch

1974 ◽  
Vol 14 (03) ◽  
pp. 271-278 ◽  
Author(s):  
Milos Kojic ◽  
J.B. Cheatham
Keyword(s):  
Plastic Deformation ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Unit Volume ◽  
Fluid Pressure ◽  
The Body ◽  
Axially Symmetric

Introduction A number of problems occur in the fields of drilling and rock mechanics for which consideration must be given to the interaction of fluid flow and rock deformation. Such problems include those of borehole stability, chip removal from under a drill bit, drilling in the presence of a fluid pressure gradient between the drilling fluid and formation fluid, and drilling by use of hydraulic jets. We have recently developed a general theory of the influence of fluid pressure gradients and gravity on the plasticity of porous media. The solution of the problem considered here serves as an example of the application of that theory. The illustrative problem is to determine the load required on a flat problem is to determine the load required on a flat axially symmetric punch for incipient plasticity of the porous medium under the punch when fluid flows through the bottom face of the punch. The rock is assumed to behave as a Coulomb plastic material under the influence of body forces plastic material under the influence of body forces due to fluid pressure gradients and gravity. Numerical methods that have been used by Cox et al. for analyzing axially symmetric plastic deformation in soils with gravity force are applied to the problem considered here. Involved is an iterative process for determining the slip lines. The fluid flow field ‘used for calculating the fluid pressure gradient is based upon the work by Ham pressure gradient is based upon the work by Ham in his study of the potential distribution ahead of the bit in rotary drilling. The effective stresses in the porous rock and the punch force for incipient plasticity are computed in terms of the fluid plasticity are computed in terms of the fluid pressure and the cohesive strength and internal pressure and the cohesive strength and internal friction of the rock. PLASTICITY OF POROUS MEDIA PLASTICITY OF POROUS MEDIA A recently developed general theory of plasticity of porous media under the influence of fluid flow is summarized in this section. The equation of motion for the porous solid for the case of incipient plastic deformation reduces to the following equilibrium equation:(1) where Ts is the partial stress tensor of the solid; Fs is the body force acting on the solid per unit volume of the solid material; P is the interaction force between the solid and the fluid; and is the porosity, which is defined as the ratio of the pore porosity, which is defined as the ratio of the pore volume to the total volume of the solid-fluid mixture. The partial stress tensor Ts can be considered as the effective stress tensor that is used in sod mechanics. With the acceptance of the effective stress principle defined in Ref. 5, the yield function, f, in the following form is satisfied for plastic deformation of the porous medium. plastic deformation of the porous medium.(2) where EP is the plastic strain tensor and K and the work-hardening parameter. From the equation of motion for the fluid, the interaction force P can be expressed in the form(3) where is the inertial force of the fluid per unit volume of the mixture and F is the body force acting on the fluid per unit volume of fluid. For the case of incipient plastic deformation the solid can be considered static (velocities of the solid particles are zero), and the problem of determining particles are zero), and the problem of determining the fluid flow field is the one usually analyzed in petroleum engineering. petroleum engineering. Consider a flow of be fluid such that the inertial forces of the fluid can be neglected and assume that Darcy's law is applicable. SPEJ P. 271

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