Flow regimes for the immiscible liquid–liquid displacement in capillary tubes with complete wetting of the displaced liquid

2009 ◽  
Vol 641 ◽  
pp. 63-84 ◽  
Author(s):  
EDSON J. SOARES ◽  
RONEY L. THOMPSON

The motion of two immiscible liquids in a capillary tube is analysed, theoretically and numerically, for the case in which a residual film confines the displacing liquid to the core of this tube. The theoretical analysis has shown that the three flow regimes predicted by Taylor (J. Fluid Mech., vol. 10, 1961, pp. 161–165), for the case of gas-displacement, can only be achieved when the ratio of the viscosity of the displaced fluid to that of the displacing one is greater than 2. An elliptic mesh generation technique, coupled with the Galerkin finite-element method, is used to compute the velocity field and the configuration of the interface between the two fluids. A map of cases in the Cartesian space defined by the capillary number (Ca) and the viscosity ratio (Nμ) is constructed in order to locate the different flow patterns the problem exhibits. The critical capillary number at which the flow enters the transition range between the bypass regime and the full-recirculating one is given. While a decrease of the fraction of mass attached to the wall is achieved by decreasing Ca or increasing Nμ, bypass flow patterns are formed as a consequence of high values of the capillary number and viscosity ratio.

1966 ◽  
Vol 6 (03) ◽  
pp. 247-253 ◽  
Author(s):  
Necmettin Mungan

Abstract A study was made of the effects of wettability and interfacial tension the immiscible displacement of a liquid by another liquid for porous media. The influence of viscosity ratio was also investigated. Porous media used were polytetrafluoroethylene (TFE) cores prepared by compressing TFE powder under different pressures. It is shown that displacement of a wetting by a nonwetting liquid is always less efficient than the displacement of a nonwetting by a wetting fluid, all other things being equal. In the former case, the recovery efficiency can be increased substantially by either reducing the interfacial tension or increasing the viscosity of the displacing fluid. A qualitative discussion is given on the implications of this work to the recovery of crude oil by waterflooding. Introduction The high cost of oil exploration and new recovery schemes makes it imperative that waterflooding be conducted under conditions favoring most efficient oil recovery. To improve oil recovery by waterflooding, it is essential that the role played by interfacial forces in the entrapment of residual oil be studied and understood. Interfacial phenomena in natural rock, connate water and crude oil systems are very complicated because of the complexity of the natural liquids found in petroleum reservoirs, because of our inability to adequately describe the geometrical structure of the porous media and because of a lack of understanding of physical and chemical interactions between the liquids and surface of the pores. The problem becomes further complicated when one tries to elucidate the role of interfacial phenomena in fluid flow. Numerous studies of the displacement of oil by water under different interfacial tension or wettability conditions have been made. These studies have been performed in silica, alundum or sandstone systems using water and paraffin oil and also some surface active material to control the interfacial tension or and the contact angle. Unfortunately, the high energies of various interfaces involved favor adsorption and orientation of the surface active material at the intrafaces. Also the surface active material concentration at the interfaces exceeds that in the bulk of the liquid phases. Such surface excess may cause the surfactant distribution, the contact angle and the interfacial tension to differ from their measured static equilibrium values and makes interpretation of the displacement experiments difficult. Furthermore, as changes in also lead to changes in cos, the role played individually by one of these parameters in the displacement becomes obscured by the effect of the other. To circumvent these difficulties, a low surface energy solid and true solutions or pure liquids should be used. Use of a low surface energy solid minimizes adsorption and orientation effects at the solid-liquid interfaces. By controlling and cos through use of selected pairs of pure liquids or true solutions rather than by surfactants, the adsorption effects at liquid-liquid interfaces are eliminated. In the present study TFE cores were used as me porous media. Liquids used were water sucrose solutions, paraffin oils and benzyl, n-butyl and isobutyl alcohols. The interfacial tension was varied from 40 to 1.1 dynes/cm by suitably choosing the liquid pair. A surface above material was added to the water-oil system only in the case where interfacial tension of 0.5 dynes/ cm was desired. No precise changes of cos were attempted. However, either the displaced or the displacing liquid could be made the one which preferentially wets the TFE surface. Using sucrose solutions and blends of paraffin oils proved to be a convenient way of changing the viscosity ratio between the displaced and displacing liquids. The present investigation examines the effect of interfacial tension, wettability and viscosity ratio on the immiscible liquid-liquid displacement from porous media. SPEJ P. 217ˆ


2005 ◽  
Vol 127 (1) ◽  
pp. 24-31 ◽  
Author(s):  
E. J. Soares ◽  
M. S. Carvalho ◽  
P. R. Souza Mendes

We analyze the liquid-liquid displacement in capillary tubes. The goal is to determine the amount of displaced liquid that remains attached to the tube wall and the configuration of the liquid-liquid interface at different operating parameters. The study encompasses both numerical and experimental approaches. The finite element method is used to solve the governing equations and, in order to validate the predictions, visualization experiments are performed to capture images of the interface. The numerical results were obtained for the assumption of negligible inertia, and the effects of viscosity ratio and capillary number are investigated. The predictions and experimental observations are in good agreement.


2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.


Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.


Author(s):  
Jeremy Rice ◽  
Amir Faghri

A new technique, called the surface velocity correction technique (SVC), is developed to track a free surface such as a liquid-vapor interface. SVC is a computationally inexpensive, and accurate method to capture interfacial fluid phenomena. This method uses a finite volume technique to discretize the governing equations, and a semi-Legrangian mesh to locate the interface between two fluids. The effectiveness of this technique is demonstrated through several classical examples and the results are also compared to both analytical and VOF solutions. The examples include: the shape of a meniscus in a capillary tube in mechanical equilibrium, the rise of a meniscus in a capillary tube, and the instability growth of a free flowing cylindrical column of fluid.


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