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Register a new userEstimating nonlinearities in twophase flow in porous media
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Added by
Jeereome Jaffree
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in one-dimensional two-phase displacements in porous media that are performed in laboratories. This is an example of the problem of estimating nonlinear coefficients in a system of nonlinear partial differential equations.
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We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.
In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards equation. The submodels are coupled by physical transmission conditions expressing the continuity of the normal fluxes and of the pressures. We start by analyzing the case of a fracture having a fixed width-length ratio, called $varepsilon > 0$. Then we take the limit $varepsilon to 0$ and give a rigorous proof for the convergence towards effective models. This is done in different regimes, depending on how the ratio of porosities and permeabilities in the fracture, respectively matrix scale with respect to $varepsilon$, and leads to a variety of effective models. Numerical simulations confirm the theoretical upscaling results.
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.
Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason why has been a puzzle for over half a century. Here, by directly visualizing the flow in a transparent 3D porous medium, we demonstrate that this anomalous increase is due to the onset of an elastic instability. We establish that the energy dissipated by the unstable flow fluctuations, which vary across pores, generates the anomalous increase in flow resistance through the entire medium. Thus, by linking the pore-scale onset of unstable flow to macroscopic transport, our work provides generally-applicable guidelines for predicting and controlling polymer solution flows.
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