scholarly journals The Investigation of Permeability Calculation Using Digital Core Simulation Technology

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3273 ◽  
Author(s):  
Lei Zhang ◽  
Wenlong Jing ◽  
Yongfei Yang ◽  
Hainan Yang ◽  
Yaohao Guo ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Pore Network Model ◽  
Direct Computation ◽  
Navier Stokes Equations ◽  
Digital Core ◽  
Core Simulation ◽  
Boltzmann Method

Digital core simulation technology, as an emerging numerical simulation method, has gradually come to play a significant role in the study of petrophysical properties. By using this numerical simulation method, the influence of micro factors on seepage properties of reservoir rock is taken into consideration, making up the shortcomings of the traditional physical experiment. Three-dimensional core images are reconstructed by a computed tomography scanning technique. Different sizes of the sub-region were simulated by three methods including the direct computation of Navier-Stokes equations, the simulation of the pore network model, and the lattice Boltzmann method. The permeability computed by each simulation was compared. After comparison between these three methods, the results of the direct computation method based on Navier-Stokes equations were found to be higher than the other two methods. The pore network model simulation has an obvious advantage on the computation speed and the simulation area. The lattice Boltzmann method shows the low efficiency due to the time-consuming process. At last, the permeability calculated by the three methods is matched by the Kozeny-Carman equation. A more accurate formula can be obtained by a series of numerical simulations, which can be applied to marco-scale simulation.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

Lattice Boltzmann Method for the Simulating Extrudate Swell of Viscoelastic Fluid

2015 ◽  
Vol 799-800 ◽  
pp. 784-787
Author(s):  
Wen Qin Liu ◽  
Yong Li
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Extrudate Swell ◽  
Navier Stokes Equations ◽  
New Approach ◽  
Moving Interface ◽  
Good Accord ◽  
Boltzmann Method

The main objective of this work is to develop a new approach based on the Lattice Boltzmann method (LBM) to simulate the extrudate swell of an Oldroyd B viscoelatic fluid. Two lattice Boltzmann equations are used to solve the Navier-Stokes equations and constitutive equation simultaneously at each time iteration. The single LBM model is used to track the moving interface in this paper. To validate the accuracy and stability of this new scheme, we study the steady 2D Poiseuille flow firstly, finding the numerical results be in good accord with the analytical solution. Then the die-swell phenomenon is solved, we successfully acquire the different swelling state of an Oldroyd B fluid at different time.

Lattice Boltzmann Models for Microflows

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Continuum Mechanics ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
The Past ◽  
Developed Turbulence ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method

The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fact remains that, with due extensions of the basic scheme, the LB has proven capable of providing several valuable insights into the physics of flows at micro- and nano-scales. This does not mean that LBE can solve the actual Boltzmann equation or replace Molecular Dynamics, but simply that it can provide useful insights into some flow problems which cannot be described within the realm of the Navier–Stokes equations of continuum mechanics. This Chapter provides a cursory view of this fast-growing front of modern LB research.

A LATTICE BOLTZMANN STUDY OF THE 2D BOUNDARY LAYER CREATED BY AN OSCILLATING PLATE

2006 ◽  
Vol 17 (01) ◽  
pp. 39-52 ◽  
Author(s):  
L. CAPPIETTI ◽  
B. CHOPARD
Keyword(s):  
Boundary Layer ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Exact Analytical Solution ◽  
Shear Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boltzmann Method ◽  
Stokes Second Problem ◽  
Oscillating Plate

We study the applicability of the Lattice Boltzmann Method (LBM) to simulate the 2D laminar boundary layer induced by an oscillating flat plate. We also investigate the transition to the disturbed laminar regime that occurs with a rough oscillating plate. The simulations were performed in two cases: first with a fluid otherwise at rest and second in presence of superimposed current. The generation of coherent vortex structures and their evolution are commented. The accuracy of the method was checked by comparisons with the exact analytical solution of the Navier–Stokes equations for the so-called Stokes' Second Problem. The comparisons show that LBM reproduces this time varying flow with first order accuracy. In the case of the wavy-plate, the results show that a mechanism of vortex-jet formations, low speed-streak and shear instability sustain a systems of stationary vortices outside the boundary layer. The vortex-jet takes place at the end of the decelerating phase whereas the boundary layer turns out to be laminar when the plate accelerates. In the presence of the superimposed current, the vortex-jet mechanism is still effective but the vortices outside the boundary layer are only present during part of the oscillating period. During the remaining part, the flow turns out to be laminar although a wave perturbation in the velocity field is present.

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