Modeling of viscoelastic properties of nonpermeable porous rocks saturated with highly viscous fluid at seismic frequencies at the core scale

2017 ◽  
Vol 122 (8) ◽  
pp. 6067-6086 ◽  
Author(s):  
Zizhen Wang ◽  
Douglas R. Schmitt ◽  
Ruihe Wang
Keyword(s):  
Viscous Fluid ◽  
Viscoelastic Properties ◽  
Porous Rocks ◽  
The Core ◽  
Seismic Frequencies

scholarly journals Gravitational differentiation in the regimes from stokes settling to Rayleigh–Raylor flows

2019 ◽  
pp. 15-30
Author(s):  
V. P. Trubitsyn
Keyword(s):  
Viscous Fluid ◽  
Interacting Particles ◽  
Small Particles ◽  
Continuous Transition ◽  
New Approach ◽  
Earth's Core ◽  
The Core ◽  
The Earth ◽  
Large Particles ◽  
Two Component

The Earth’s core was formed under gravitational differentiation in the course of the separation of iron and silicates. Most of the iron has gone into the core as early as when the Earth was growing. However, iron continued to precipitate even during the subsequent partial solidification which developed from the bottom upwards. At the different stages and in the different layers of the mantle, iron was deposited in different regimes. In this paper, the mechanisms of the deposition of a cloud of heavy interacting particles (or drops) in a viscous fluid are considered. A new approach suitable for analytical and numerical tracing the changes in the structure of the flows in a two-component suspension under continuous transition from the Stokessettling (for the case of a cloud of large particles) to the Rayleigh–Taylor flows and heavy diapirs (for the case of a cloud of small particles) is suggested. It is numerically and analytically shown that the both regimes are the different limiting cases of the sedimentation convection in suspensions.

Convective/absolute instability in miscible core-annular flow. Part 2. Numerical simulations and nonlinear global modes

2009 ◽  
Vol 618 ◽  
pp. 323-348 ◽  
Author(s):  
B. SELVAM ◽  
L. TALON ◽  
L. LESSHAFFT ◽  
E. MEIBURG
Keyword(s):  
Viscous Fluid ◽  
Numerical Simulations ◽  
Annular Flow ◽  
Nonlinear Oscillations ◽  
Variable Viscosity ◽  
Base Flow ◽  
Absolute Instability ◽  
Infinite Domain ◽  
Global Mode ◽  
The Core

The convective/absolute nature of the instability of miscible core-annular flow with variable viscosity is investigated via linear stability analysis and nonlinear simulations. From linear analysis, it is found that miscible core-annular flows with the more viscous fluid in the core are at most convectively unstable. On the other hand, flows with the less viscous fluid in the core exhibit absolute instability at high viscosity ratios, over a limited range of core radii. Nonlinear direct numerical simulations in a semi-infinite domain display self-excited intrinsic oscillations if and only if the underlying base flow exhibits absolute instability. This oscillator-type flow behaviour is demonstrated to be associated with the presence of a nonlinear global mode. Both the parameter range of global instability and the intrinsically selected frequency of nonlinear oscillations, as observed in the simulation, are accurately predicted from linear criteria. In convectively unstable situations, the flow is shown to respond to external forcing over an unstable range of frequencies, in quantitative agreement with linear theory. As discussed in part 1 of this study (d'Olce, Martin, Rakotomalala, Salin and Talon,J. Fluid Mech., vol. 618, 2008, pp. 305–322), self-excited synchronized oscillations were also observed experimentally. An interpretation of these experiments is attempted on the basis of the numerical results presented here.

Dynamics of the axisymmetric core-annular flow. II. The less viscous fluid in the core, saw tooth waves

2002 ◽  
Vol 14 (3) ◽  
pp. 1011-1029 ◽  
Author(s):  
Charalampos Kouris ◽  
John Tsamopoulos
Keyword(s):  
Viscous Fluid ◽  
Annular Flow ◽  
The Core

scholarly journals Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2797-2807 ◽  
Author(s):  
Leon Thomsen
Keyword(s):  
Bulk Modulus ◽  
Model Theory ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Porous Rocks ◽  
Seismic Frequencies ◽  
New Formulation ◽  
Special Case ◽  
Finite Concentrations

The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.

Stability of miscible core–annular flows with viscosity stratification

2007 ◽  
Vol 592 ◽  
pp. 23-49 ◽  
Author(s):  
B. SELVAM ◽  
S. MERK ◽  
RAMA GOVINDARAJAN ◽  
E. MEIBURG
Keyword(s):  
Viscous Fluid ◽  
Viscosity Ratio ◽  
Variable Viscosity ◽  
Sudden Change ◽  
Plane Channel ◽  
Critical Value ◽  
Interface Thickness ◽  
Axisymmetric Mode ◽  
The Core ◽  
Annular Flows

The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

Generalized Maxwell Model as Viscoelastic Lubricant in Journal Bearing

2011 ◽  
Vol 478 ◽  
pp. 64-69 ◽  
Author(s):  
M. Guemmadi ◽  
A. Ouibrahim
Keyword(s):  
Viscoelastic Properties ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Maxwell Model ◽  
Load Bearing Capacity ◽  
The Core ◽  
Generalized Maxwell Model ◽  
Computational Code ◽  
Flow Velocity Profile

The hydrodynamic lubrication interest is still of great importance, so that more and more elaborated lubricants are considered. They, however, involve consequently more and more hydrodynamic complexity as a result of the rheological properties of the additives. In our case, we consider lubricants having viscoelastic properties described by a generalized Maxwell model used in the case of journal bearing lubrication. The complexity of the coupled associated equations (momentum and constitutive) to describe the hydrodynamic prevailing in such a geometry requires numerical solutions. Using the commercial Finite Volume software Fluent 6.3 together with an appropriate developed computational code, via UDF (User Defined Functions), we determine the pressure distribution as well as the flow velocity profile and the stress field in the core, the load bearing capacity developed and the attitude angle; all together with the effects of the viscoelastic lubricant parameters (relaxation time and shear viscosity).

Connection between viscoelastic properties of polymers and the technological parameters of spinning fibres of the ?core-shell? type

1988 ◽  
Vol 19 (6) ◽  
pp. 395-397
Author(s):  
V. P. Kostromin ◽  
N. B. Buleva ◽  
S. N. Kolomiets ◽  
V. M. Levin
Keyword(s):  
Viscoelastic Properties ◽  
Core Shell ◽  
Technological Parameters ◽  
The Core ◽  
Shell Type
Sign in / Sign up

Export Citation Format

Share Document