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Pore-scale modeling of viscoelastic flow and the effect of polymer elasticity on residual oil saturation
textPolymers used in enhanced oil recovery (EOR) help to control the mobility ratio between oil and aqueous phases and as a result, polymer flooding improves sweep efficiency in reservoirs. However, the conventional wisdom is that polymer flooding does not have considerable effect on pore-level displacement because pressure forces would not be enough to overcome trapping caused by capillary forces. Recently, both coreflood experiments and field data suggest that injecting viscoelastic polymers, such as hydrolyzed polyacrylamide (HPAM), can result in lower residual oil saturation. The hypothesis is that the polymer elasticity provides several pore-level mechanisms for oil mobilization that are generally not significant for purely-viscous fluids. Both experiments and modeling need to be performed to investigate the effect of polymer elasticity on residual oil saturation. Pore-scale modeling and micro-fluidic experiments can be used to investigate pore-level physics, and then used to upscale to the macro-scale. The objective of this work is to understand the effect of polymer elasticity on apparent viscosity and residual oil saturation in porous media. Single- and multi-phase pore-level computational fluid dynamics (CFD) modeling for viscoelastic polymer flow is performed to investigate the dominant mechanisms at the pore level to mobilize trapped oil. Several interesting results are found from the CFD results. First, the elasticity of the polymer results in an increase in normal stress at the pore-level; therefore, the normal stresses exerted on a static oil droplet are significant and not negligible as for a purely-viscous fluid. The CFD results show that viscoelastic fluid exerts additional forces on the oil-phase which may help mobilize trapped oil out of the porous medium. Second, due to the elasticity of polymer, the viscoelastic polymer has some level of pulling effect; while passing above a dead-end pore it can pull out the trapped oil phase and then mobilize it. However, both CFD modeling and micro-fluidic experiments show the pulling-effect is not likely the main mechanism to reduce oil saturation at pore-level. Third, dynamic CFD simulations show less deformation of the oil phase while viscoelastic polymer is displacing fluid compared to purely viscous fluid. It may justify the hypothesis that polymer elasticity resists against snap-off mechanism. As a result, when viscoelastic polymer displaces the oil ganglia, the oil phase does not snap off, and the oil phase remains connected, and therefore easier to move in porous media compared to disconnected oil. For single phase flow, a closed-form flow equation has been developed based on CFD modeling in converging/diverging ducts representative of pore throats. The pore-level equations were substituted into a pore-network model and validated against experimental data. Good agreement is observed. This study reveals important findings about the effect of polymer elasticity to reduce the residual oil saturation; however, more experiments and simulations are recommended to fully-understand the mobilization mechanisms and take advantage of them to optimize the polymer-flooding process in the field.Petroleum and Geosystems Engineerin
An Extended Volume of Fluid Method and its Application to Single Bubbles Rising in a Viscoelastic Liquid
An extended volume of fluid method is developed for two-phase direct
numerical simulations of systems with one viscoelastic and one Newtonian phase.
A complete set of governing equations is derived by conditional
volume-averaging of the local instantaneous bulk equations and interface jump
conditions. The homogeneous mixture model is applied for the closure of the
volume-averaged equations. An additional interfacial stress term arises in this
volume-averaged formulation which requires special treatment in the
finite-volume discretization on a general unstructured mesh. A novel numerical
scheme is proposed for the second-order accurate finite-volume discretization
of the interface stress term. We demonstrate that this scheme allows for a
consistent treatment of the interface stress and the surface tension force in
the pressure equation of the segregated solution approach. Because of the high
Weissenberg number problem, an appropriate stabilization approach is applied to
the constitutive equation of the viscoelastic phase to increase the robustness
of the method at higher fluid elasticity. Direct numerical simulations of the
transient motion of a bubble rising in a quiescent viscoelastic fluid are
performed for the purpose of experimental code validation. The well-known jump
discontinuity in the terminal bubble rise velocity when the bubble volume
exceeds a critical value is captured by the method. The formulation of the
interfacial stress together with the novel scheme for its discretization is
found crucial for the quantitatively correct prediction of the jump
discontinuity in the terminal bubble rise velocity
A phase-field model for active contractile surfaces
The morphogenesis of cells and tissues involves an interplay between chemical
signals and active forces on their surrounding surface layers. The complex
interaction of hydrodynamics and material flows on such active surfaces leads
to pattern formation and shape dynamics which can involve topological
transitions, for example during cell division. To better understand such
processes requires novel numerical tools. Here, we present a phase-field model
for an active deformable surface interacting with the surrounding fluids. The
model couples hydrodynamics in the bulk to viscous flow along the diffuse
surface, driven by active contraction of a surface species. As a new feature in
phase-field modeling, we include the viscosity of a diffuse interface and
stabilize the interface profile in the Stokes-Cahn-Hilliard equation by an
auxiliary advection velocity, which is constant normal to the interface. The
method is numerically validated with previous results based on linear stability
analysis. Further, we highlight some distinct features of the new method, like
the avoidance of re-meshing and the inclusion of contact mechanics, as we
simulate the self-organized polarization and migration of a cell through a
narrow channel. Finally, we study the formation of a contractile ring on the
surface and illustrate the capability of the method to resolve topological
transitions by a first simulation of a full cell division
A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law
In this paper, we investigate numerically a diffuse interface model for the
Navier-Stokes equation with fluid-fluid interface when the fluids have
different densities \cite{Lowengrub1998}. Under minor reformulation of the
system, we show that there is a continuous energy law underlying the system,
assuming that all variables have reasonable regularities. It is shown in the
literature that an energy law preserving method will perform better for
multiphase problems. Thus for the reformulated system, we design a finite
element method and a special temporal scheme where the energy law is preserved
at the discrete level. Such a discrete energy law (almost the same as the
continuous energy law) for this variable density two-phase flow model has never
been established before with finite element. A Newton's method is
introduced to linearise the highly non-linear system of our discretization
scheme. Some numerical experiments are carried out using the adaptive mesh to
investigate the scenario of coalescing and rising drops with differing density
ratio. The snapshots for the evolution of the interface together with the
adaptive mesh at different times are presented to show that the evolution,
including the break-up/pinch-off of the drop, can be handled smoothly by our
numerical scheme. The discrete energy functional for the system is examined to
show that the energy law at the discrete level is preserved by our scheme
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