Marcio S. Carvalho

Pore Scale and Macroscopic Displacement Mechanisms in Emulsion Flooding

The flow properties of complex fluids through porous media give rise to multiphase flow displacement mechanisms that operate at different scales, from pore-level to Darcy scale. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced-oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Pore-scale flow visualization as well as core flooding results available in the literature have demonstrated that the enhanced recovery factor is regulated by the capillary number of the flow. However, the mechanisms by which additional oil is displaced during emulsion injection are still not clear. In this work, we carried out two different experiments to evaluate the effect of emulsion flooding both at pore and macro scales. Visualization of the flow through sand packed between transparent plexiglass parallel plates shows that emulsion flooding improves the pore-level displacement efficiency, leading to lower residual oil saturation. Oil recovery results during emulsion flooding in tertiary mode (after waterflooding) in parallel sandstone cores with very different absolute permeability values prove that emulsion flooding also leads to enhancement of conformance or volumetric sweep efficiency. Combined, the results presented here show that injection of emulsion offers multiscale mechanisms resulting from capillary-driven mobility control.

Immiscible Liquid-Liquid Displacement in Capillary Tubes

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

Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders

Circular Couette flow of inelastic shear-thinning materials in annuli is examined. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the processes at which this type of flow occurs. Therefore, it is quite important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (dilute polymeric solutions) liquids. Te effect of the shear-thinning behavior of high concentration suspensions on the onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and searching for the critical conditions. This procedure avoids the need for a stability analysis of the flow and the solution of an eigenproblem. The differential equations were solved by the Galerkin/finite-element method and the resulting set of nonlinear algebraic equations, by Newtons method

Dynamic Network Model of Mobility Control in Emulsion Flow Through Porous Media

Modeling the flow of emulsion in porous media is extremely challenging due to the complex nature of the associated flows and multiscale phenomena. At the pore scale, the dispersed phase size can be of the same order of magnitude of the pore length scale and therefore effective viscosity models do not apply. A physically meaningful macroscopic flow model must incorporate the transport of the dispersed phase through the porous material and the changes on flow resistance due to drop deformation as it flows through pore throats. In this work, we present a dynamic capillary network model that uses experimentally determined pore-level constitutive relationships between flow rate and pressure drop in constricted capillaries to obtain representative transient macroscopic flow behavior emerging from microscopic emulsion flow at the pore level. A parametric analysis is conducted to study the effect of dispersed phase droplet size and capillary number on the flow response to both emulsion and alternating water/emulsion flooding in porous media. The results clearly show that emulsion flooding changes the continuous-phase mobility and consequently flow paths through the porous media, and how the intensity of mobility control can be tuned by the emulsion characteristics.

Efficient computation of the spectrum of viscoelastic flows

The understanding of viscoelastic flows in many situations requires not only the steady state solution of the governing equations, but also its sensitivity to small perturbations. Linear stability analysis leads to a generalized eigenvalue problem (GEVP), whose numerical analysis may be challenging, even for Newtonian liquids, because the incompressibility constraint creates singularities that lead to non-physical eigenvalues at infinity. For viscoelastic flows, the difficulties increase due to the presence of continuous spectrum, related to the constitutive equations. The Couette flow of upper convected Maxwell (UCM) liquids has been used as a case study of the stability of viscoelastic flows. The spectrum consists of two discrete eigenvalues and a continuous segment with real part equal to -1/We (We is the Weissenberg number). Most of the approximations in the literature were obtained using spectral expansions. The eigenvalues close to the continuous part of the spectrum show very slow convergence. In this work, the linear stability of Couette flow of a UCM liquid is studied using a finite element method. A new procedure to eliminate the eigenvalues at infinity from the GEVP is proposed. The procedure takes advantage of the structure of the matrices involved and avoids the computational overhead of the usual mapping techniques. The GEVP is transformed into a non-degenerate GEVP of dimension five times smaller. The computed eigenfunctions related to the continuous spectrum are in good agreement with the analytic solutions obtained by Graham [M.D. Graham, Effect of axial flow on viscoelastic Taylor-Couette instability, J. Fluid Mech. 360 (1998) 341].

Flow of Oil‐Water Emulsion Through Constricted Capillary Tubes

The flow of oil‐in‐water emulsions through a constricted capillary tube was analyzed by experiments and theory. The experiments consisted of flow visualization and pressure drop measurements of the flow. A number of different emulsions were prepared using synthetic oils and deionized water. The average drop size varied from smaller to larger than the neck radius. Fluid mobility, defined as flow rate over pressure drop, was used to quantify the magnitude of the pore‐blocking caused by drops larger than the constriction radius. The effect of the interfacial tension and viscosity ratio between the two phases on the changes of the local mobility was determined by solving the free surface flow of an infinite oil drop immersed in water flowing through a constricted capillary tube by Finite Element Method.

Heat Transfer in the Non-Newtonian Axisymmetric Flow in the Neighborhood of a Sudden Contraction

The flow pattern at low Reynolds number in the neighborhood of a sudden contraction is very sensitive to the mechanical behavior of the flowing fluid. A large extensional viscosity leads to vortex enhancement in the corner region of the flow of a non-Newtonian fluid in such geometry. In the corresponding flow of a Newtonian fluid, these vortices are much weaker and smaller. Moreover, the extension-thickening behavior of most polymeric liquids leads to higher viscous dissipation effects in the predominantly extensional flow, as compared to typical shear flows. The flow and temperature fields for this problem have been obtained from numerical integration of the conservation equations, aiming at applications related to extrusion and capillary rheometry of polymeric liquids. To account for the flow dependence of the stress tensor, a generalized Newtonian model has been employed, including the dependence of the viscosity function on both the second and the third invariants of the rate-of-deformation tensor. The numerical solutions have been obtained via a finite-volume method. The case of a 4:1 circular contraction was investigated, with uniform temperature distribution at the solid boundaries. The fluid inlet temperature is equal to the temperature at the walls, so that thermal gradients in the fluid are due to viscous dissipation effects only. Comparisons between Newtonian and non-Newtonian results showed that the combined effect of viscous dissipation and enhancement of vortex activity significantly affects the temperature field. The practical significance of the results is discussed for extrusion processes and capillary rheometry.

Snap-off in constricted capillary with elastic interface

Snap-off of bubbles and drops in constricted capillaries occurs in many different situations, from bio-fluid to multiphase flow in porous media. The breakup process has been extensively analyzed both by theory and experiments, but most work has been limited to pure interfaces, at which the surface stress is isotropic and fully defined by the interfacial tension and interface curvature. Complex interfaces may present viscous and elastic behavior leading to a complex stress state that may change the dynamics of the interfacedeformation and breakup. We extend the available asymptotic model based on lubrication approximation to include elastic interfacial stress. Drop breakup time is determined as a function of the capillary geometry and liquidproperties, including the interfacial elastic modulus. Results show that the interfacial elasticity has a stabilizing effect by slowing down the growth of the liquid collar, leading to a larger break-up time. This stabilizing effect has been observed experimentally in different, but related flows [Alvarado et al., “Interfacial visco-elasticity of crude oil-brine: An alternative EOR mechanism in smart waterflooding,” in SPE-169127 Improved Oil Recovery Symposium (Society of Petroleum Engineers, 2014)].

Immiscible liquid-liquid displacement in capillary tubes: viscoelastic effects

The displacement of a fluid by liquid injection occurs in some practical applications like oil recovery in porous media and cementation of drilling wells. The dimensionless numbers that govern this problem are the capillary number, Reynolds number and viscosity ratio. An overview of selected oil recovery processes shows that hydrolyzed polyacrilamide and bio-polymers, as xanthan gun, are commonly pumped into oil reservoir in order to aid oil recovery. These materials are non-Newtonian, presenting high viscoelastic effects. The fractional mass deposited on the tube wall and the shape of the interface on liquid-liquid displacement of two Newtonian materials was studied previously by Soares et al. (2005). The goal of the present work is to conduct an experimental investigation analyzing viscoelastic effects on the fractional coverage and on the shape of the interface for both: a polymer displacing a Newtonian liquid and a Newtonian liquid displacing a polymer.

Filtering the eigenvalues at infinite from the linear stability analysis of incompressible flows

Steady state, two-dimensional flows may become unstable under two and three-dimensional disturbances if the flow parameters exceed some critical values. In many practical situations, determining the parameters at which the flow becomes unstable is essential. Linear hydrodynamic stability of a laminar flow leads to a generalized eigenvalue problem (GEVP) where the eigenvalues correspond to the rate of growth of the disturbances and the eigenfunctions to the amplitude of the perturbation. Solving GEVPs is challenging, because the incompressibility of the liquid gives rise to singularities leading to non-physical eigenvalues at infinity that require substantial care. The high computational cost of solving the GEVP has probably discouraged the use of linear stability analysis of incompressible flows as a general engineering tool for design and optimization. In this work, we propose a new procedure to eliminate the eigenvalues at infinity from the GEVP associated to the linear stability analysis of incompressible flow. The procedure takes advantage of the structure of the matrices involved and avoids part of the computational effort of the standard mapping techniques used to compute the spectrum of incompressible flows. As an example, the method is applied in the solution of linear stability analysis of plane Couette flow.