scholarly journals Numerical calculation of unstable immiscible fluid displacement in a two-dimensional porous medium or Hele-Shaw cell

1985 ◽  
Vol 26 (4) ◽  
pp. 452-469 ◽  
Author(s):  
M. R. Davidson
Keyword(s):  
Porous Medium ◽  
Numerical Procedure ◽  
Immiscible Fluids ◽  
Boundary Integral ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Time Step ◽  
Fluid Displacement ◽  
Numerical Errors ◽  
Hele Shaw Cell

AbstractA numerical procedure for calculating the evolution of a periodic interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell is described. The motion of the interface is determined in a stepwise manner with its new velocity at exach time step being derived as a numerical solution of a boundary integral equation. Attention is focused on the case of unstable displacement charaterised physically by the “fingering” of the interface and computationally by the growth of numerical errors regardless of the numerical method employed. Here the growth of such error is reduced and the usable part of the calculation extended to finite amplitudes. Numerical results are compared with an exact “finger” solution and the calculated behaviour of an initial sinusoidal displacement, as a function of interfacial tension, initial amplitude and wavelength, is discussed.

scholarly journals An integral equation for immiscible fluid isplacement in a two-dimensional porous medium or Hele-Shaw cell

1984 ◽  
Vol 26 (1) ◽  
pp. 14-30 ◽  
Author(s):  
M. R. Davidson
Keyword(s):  
Integral Equation ◽  
Porous Medium ◽  
Interfacial Tension ◽  
Immiscible Fluids ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Flat Interface ◽  
Hele Shaw Cell

AbstractAn integral equation for the normal velocity of the interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell (one fluid displaces the other) is derived in terms of the physical parameters (including interfacial tension), a Green's function and the given interface. When the displacement is unstable, ‘fingering’ of the interface occurs. The Saffman-Taylor interface solutions for the steady advance of a single parallel-sided finger in the absence of interfacial tension are seen to satisfy the integral equation, and the error incurred in that equation by the corresponding Pitts approximating profile, when interfacial tension is included, is shown. In addition, the numerical solution of the integral equation is illustrated for a sinusoidal and a semicircular interface and, in each case, the amplitude behaviour inferred from the velocity distribution is consistent with conclusions based on the stability of an initially flat interface.

scholarly journals Lattice Boltzmann Simulation of Immiscible Two-Phase Displacement in Two-Dimensional Berea Sandstone

2018 ◽  
Vol 8 (9) ◽  
pp. 1497 ◽  
Author(s):  
Qingqing Gu ◽  
Haihu Liu ◽  
Yonghao Zhang
Keyword(s):  
Interfacial Tension ◽  
Lattice Boltzmann ◽  
Viscosity Ratio ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Berea Sandstone ◽  
Fluid Saturation ◽  
Wetting Fluid

Understanding the dynamic displacement of immiscible fluids in porous media is important for carbon dioxide injection and storage, enhanced oil recovery, and non-aqueous phase liquid contamination of groundwater. However, the process is not well understood at the pore scale. This work therefore focuses on the effects of interfacial tension, wettability, and the viscosity ratio on displacement of one fluid by another immiscible fluid in a two-dimensional (2D) Berea sandstone using the colour gradient lattice Boltzmann model with a modified implementation of the wetting boundary condition. Through invasion of the wetting phase into the porous matrix, it is observed that the viscosity ratio plays an important role in the non-wetting phase recovery. At the viscosity ratio ( λ ) of unity, the saturation of the wetting fluid is highest, and it linearly increases with time. The displacing fluid saturation reduces drastically when λ increases to 20; however, when λ is beyond 20, the reduction becomes less significant for both imbibition and drainage. The front of the bottom fingers is finally halted at a position near the inlet as the viscosity ratio increases to 10. Increasing the interfacial tension generally results in higher saturation of the wetting fluid. Finally, the contact angle is found to have a limited effect on the efficiency of displacement in the 2D Berea sandstone.

Using Dissipative Particle Dynamics to Model Binary Immiscible Fluids

1997 ◽  
Vol 08 (04) ◽  
pp. 909-918 ◽  
Author(s):  
Keir E. Novik ◽  
Peter V. Coveney
Keyword(s):  
Phase Separation ◽  
Dissipative Particle Dynamics ◽  
Particle Dynamics ◽  
Immiscible Fluids ◽  
Promising Method ◽  
Domain Growth ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Fluid Systems

We investigate the domain growth and phase separation of two-dimensional binary immiscible fluid systems using dissipative particle dynamics. Our results are compared with similar simulations using other techniques, and we conclude that dissipative particle dynamics is a promising method for simulating these systems.

scholarly journals High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Alessandra Feo ◽  
Fulvio Celico
Keyword(s):  
Fluid Flow ◽  
High Resolution ◽  
Capillary Pressure ◽  
Immiscible Fluids ◽  
Shock Capturing ◽  
Immiscible Fluid ◽  
Saturated Zone ◽  
Time Step ◽  
Three Phase ◽  
Sharp Front

AbstractNumerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

scholarly journals Two-phase MHD Flow through Porous Medium with Heat Transfer in a Horizontal Channel

2020 ◽  
pp. 79-90
Author(s):  
Devendra Kumar ◽  
B. Satyanarayana ◽  
Rajesh Kumar ◽  
Bholey Singh ◽  
R. K. Shrivastava
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Differential Equations ◽  
Velocity Profile ◽  
Parallel Plate ◽  
Immiscible Fluids ◽  
Immiscible Fluid ◽  
Flow Through ◽  
Plate Channel

The present study deals with two layered MHD immiscible fluid flow through porous medium in presence of heat transfer through parallel plate channel. The fluids are incompressible, and flow is fully developed. The fluids are of different viscosities and thermal conductivities so flowing without mixing each other. Two different phases are accounted for study and are electrically conducting. Temperature of the walls of parallel plate channel is constant. Rheological properties of the immiscible fluids are constant in nature. The flow is governed by coupled partial differential equations which are converted to ordinary differential equations and exact solutions are obtained. The velocity profile and temperature distribution are evaluated and solved numerically for different heights and viscosity ratios for the two immiscible fluids. The effect of magnetic field parameter M and porosity parameter K is discussed for velocity profile and temperature distribution. Combined effects of porous medium and magnetic fields are accelerating the flow which, can be helpful in draining oil from oil wells.

Self-similar flows of multi-phase immiscible fluids

2000 ◽  
Vol 11 (6) ◽  
pp. 529-559
Author(s):  
A. OZTEKIN ◽  
B. R. SEYMOUR ◽  
E. VARLEY
Keyword(s):  
Viscous Fluid ◽  
Unsteady Flows ◽  
Immiscible Fluids ◽  
Newtonian Fluids ◽  
Two Dimensional ◽  
Constant Strength ◽  
Self Similar ◽  
Multi Phase ◽  
Similar Flows ◽  
Hele Shaw Cell

Exact analytical representations are obtained describing self-similar unsteady flows of multi-phase immiscible fluids in the vicinity of non-circular, but constant strength, fronts. It is assumed that Darcy's law holds for each phase and that the mobilities are known functions of the saturations. Equivalent representations are obtained for Hele-Shaw cell flows that are produced when a viscous fluid is injected into a region containing some other viscous fluid. The fluids may be Newtonian fluids or non-Newtonian fluids for which the coefficients of viscosity depend on the shear stress. Even though the flows are unsteady and two dimensional, the representations are obtained by using hodograph techniques.

Moving boundary problems in the flow of liquid through porous media

1982 ◽  
Vol 24 (2) ◽  
pp. 171-193 ◽  
Author(s):  
A. A. Lacey
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytic Functions ◽  
Moving Boundary ◽  
Immiscible Fluids ◽  
The Other ◽  
Two Dimensional ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
Time Singularities

AbstractThe movement of the interface between two immiscible fluids flowing through a porous medium is discussed. It is assumed that one of the fluids, which is a liquid, is much more viscous than the other. The problem is transformed by replacing the pressure with an integral of pressure with respect to time. Singularities of pressure and the transformed variable are seen to be related.Some two-dimensional problems may be solved by comparing the singularities of certain analytic functions, one of which is derived from the new variable. The implications of the approach of a singularity to the moving boundary are examined.

scholarly journals Well-posedness of the Muskat problem in subcritical L p -Sobolev spaces

2021 ◽  
pp. 1-43
Author(s):  
H. ABELS ◽  
B.-V. MATIOC
Keyword(s):  
Porous Medium ◽  
Vertical Motion ◽  
Parabolic Type ◽  
Immiscible Fluids ◽  
Well Posedness ◽  
Two Dimensional ◽  
Critical Space ◽  
Smoothing Property ◽  
Muskat Problem ◽  
Homogeneous Porous Medium

We study the Muskat problem describing the vertical motion of two immiscible fluids in a two-dimensional homogeneous porous medium in an L p -setting with p ∈ (1, ∞). The Sobolev space $W_p^s(\mathbb R)$ with s = 1+1/p is a critical space for this problem. We prove, for each s ∈ (1+1/p, 2) that the Rayleigh–Taylor condition identifies an open subset of $W_p^s(\mathbb R)$ within which the Muskat problem is of parabolic type. This enables us to establish the local well-posedness of the problem in all these subcritical spaces together with a parabolic smoothing property.

Analysis of Linear Encroachment in Two-Immiscible Fluid Systems in a Porous Medium

1994 ◽  
Vol 116 (1) ◽  
pp. 135-139 ◽  
Author(s):  
Vijayaraghavan Srinivasan ◽  
Kambiz Vafai
Keyword(s):  
Porous Medium ◽  
Theoretical Study ◽  
Saturated Porous Medium ◽  
Immiscible Fluids ◽  
The Other ◽  
Immiscible Fluid ◽  
Fluid System ◽  
Inertia Effects ◽  
Fluid Systems ◽  
First Time

The flow of two immiscible fluids in a porous medium was analyzed accounting for boundary and inertia effects. This problem was first solved by Muskat using Darcy’s equation for fluid flow in a saturated porous medium. In the present analysis the boundary and inertia effects have been included to predict the movement of the interfacial front that is formed as one fluid displaces the other. In the present work a theoretical study that accounts for the boundary and inertia effects in predicting the movement of the interface for linear encroachment in two immiscible fluid system in a porous material is presented for the first time. The results of the present study when compared with the Muskat’s model show that consideration of the boundary and inertia effects becomes important for low values of mobility ratio (ε<1.0) and higher values of permeability (K>1.0 × 1.0−10 m2).

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