| The foam drive process is a technique for enhancing the production of oil from underground reservoirs. The idea behind foam drive is to inject gas and aqueous surfactant solution into a well to force oil trapped in the reservoir towards a surrounding array of collection wells. The surfactant solution generates foam in the reservoir and acts to increase the "effective viscosity" of the drive fluid--increasing the sweep efficiency of the process. While this is a promising technique, the Darcian theory of capillary flow is unable to properly correlate or predict many aspects of this process.; An analysis of the Darcian theory suggests that while the forces in the phase momentum balances describe foam, the interfacial momentum balances are incomplete. Furthermore, known forms of the interfacial constitutive equation relating the texture of the fluid/fluid interfaces to capillary pressure, gas phase pressure drop and saturation do not properly account for the relaxation and hysteresis exhibited by capillary processes. So our goal is to obtain a constitutive theory characterizing the variables and equations that describe the evolution of interfacial texture in response to changes in controlled variables.; First, energy and entropy balances for a thermodynamic analysis of an open multiphase body are derived. The energy balances obtained here contain three new terms accounting for the work to displace non-equilibrium interfaces and contact lines. These balances are applied to a discontinuous model of a capillary system to enforce conservation of energy and the second law. The resulting isothermal entropy change is shown to be a sum of the internal and external virtual work. Second, by eliminating the isoperimetric constraint on the internal virtual work it is converted into parametric form which shows that while the non-equilibrium configuration of an interface is defined by an infinite number of parameters, only a finite number are required to define the equilibrium configuration. So the second law implies that the motion of a single interface constrained to an equilibrium path is described by: (1) a single internal parameter, (2) the path of vanishing internal affinity, and (3) a rate equation implied by the external virtual work. An analysis of snap-off on a sinusoidal pore shows that these constitutive equations describe both relaxation and hysteresis. |
