Analytical Theory for Three-Phase Partially Miscible Flow in Ternary Systems

2004 ◽  
Author(s):  
Tara LaForce ◽  
Russell T. Johns
Keyword(s):  
Ternary Systems ◽  
Analytical Theory ◽  
Miscible Flow ◽  
Three Phase ◽  
Partially Miscible

Composition Routes for Three-Phase Partially Miscible Flow in Ternary Systems

SPE Journal ◽  
2005 ◽  
Vol 10 (02) ◽  
pp. 161-174 ◽  
Author(s):  
Tara C. LaForce ◽  
Russell T. Johns
Keyword(s):  
Ternary Systems ◽  
Miscible Flow ◽  
Three Phase ◽  
Partially Miscible

Experimental Confirmation for Analytical Composition Routes in Three-Phase Partially Miscible Flow

2006 ◽  
Author(s):  
Tara C. LaForce ◽  
Yildiray Cinar ◽  
Russell Taylor Johns ◽  
Franklin M. Orr
Keyword(s):  
Experimental Confirmation ◽  
Miscible Flow ◽  
Three Phase ◽  
Partially Miscible

Experimental Confirmation of Analytical Composition Routes in Three-Phase Partially Miscible Flow

SPE Journal ◽  
2009 ◽  
Vol 15 (01) ◽  
pp. 160-170 ◽  
Author(s):  
T.. LaForce ◽  
Y.. Cinar ◽  
R.T.. T. Johns ◽  
F.M.. M. Orr
Keyword(s):  
Analytical Solutions ◽  
Permeability Model ◽  
Alcohol Injection ◽  
Miscible Flow ◽  
Three Phase ◽  
Partially Miscible ◽  
Simplifying Assumptions ◽  
Vertical Glass ◽  
Oil Injection ◽  
The Mathematical Model

Summary In this paper, effluent data from laboratory experiments are compared with analytical composition routes and profiles for three- phase partially miscible flow of three-component mixtures. Coreflood experiments were run in vertical glass bead packs to achieve approximately 1D displacements with stable displacement fronts. The displacements employed in this study include modest effects of dispersion, but dispersion does not substantially alter the composition routes. Analytical composition routes are developed by the method of characteristics (MOC) for 1D, dispersion-free flow where up to three flowing phases may be present. The exponents used in the relative permeability model were obtained by fitting profiles from one drainage (oil injection) and one imbibition (water/alcohol injection) displacement. The resulting parameters were used to construct the analytical solutions for the remaining displacements. Development of the analytical solutions to Riemann problems is outlined. Different parameters are obtained for the imbibition and drainage experiments, indicating that hysteresis occurs in the experiments. Comparison of the experimental results with the analytical solutions shows that the mathematical model captures the essential features of the experimental displacements. In the cases in which the analytical solutions fail to model accurately the physical displacements, the effects of simplifying assumptions in the model are examined.

Cosolvency effects, miscibility windows and two-phase lg holes in three-phase llg surfaces in ternary systems: a status report

2000 ◽  
Vol 171 (1-2) ◽  
pp. 127-149 ◽  
Author(s):  
Kerstin Gauter ◽  
Cor J Peters ◽  
Arndt L Scheidgen ◽  
Gerhard M Schneider
Keyword(s):  
Ternary Systems ◽  
Status Report ◽  
Two Phase ◽  
Three Phase

An analytical theory for the capillary bridge force between spheres

2016 ◽  
Vol 812 ◽  
pp. 129-151 ◽  
Author(s):  
N. P. Kruyt ◽  
O. Millet
Keyword(s):  
Laplace Equation ◽  
Capillary Force ◽  
Numerical Solutions ◽  
Analytical Theory ◽  
Phase Contact ◽  
Capillary Bridge ◽  
Contact Circle ◽  
Three Phase ◽  
Meridional Profile ◽  
Rupture Criterion

An analytical theory has been developed for properties of a steady, axisymmetric liquid–gas capillary bridge that is present between two identical, perfectly wettable, rigid spheres. In this theory the meridional profile of the capillary bridge surface is represented by a part of an ellipse. Parameters in this geometrical description are determined from the boundary conditions at the three-phase contact circle at the sphere and at the neck (i.e. in the middle between the two spheres) and by the condition that the mean curvature be equal at the three-phase contact circle and at the neck. Thus, the current theory takes into account properties of the governing Young–Laplace equation, contrary to the often-used toroidal approximation. Expressions have been developed analytically that give the geometrical parameters of the elliptical meridional profile as a function of the capillary bridge volume and the separation between the spheres. A rupture criterion has been obtained analytically that provides the maximum separation between the spheres as a function of the capillary bridge volume. This rupture criterion agrees well with a rupture criterion from the literature that is based on many numerical solutions of the Young–Laplace equation. An expression has been formulated analytically for the capillary force as a function of the capillary bridge volume and the separation between the spheres. The theoretical predictions for the capillary force agree well with the capillary forces obtained from the numerical solutions of the Young–Laplace equation and with those according to a comprehensive fit from the literature (that is based on many numerical solutions of the Young–Laplace equation), especially for smaller capillary bridge volumes.

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