A phase field model for mass transport with semi-permeable interfaces

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field framework used here has several advantages over the sharp interface method. First of all, explicit tracking of the interface is no longer necessary. Secondly, the interfacial condition can be incorporated with a variable diffusion coefficient. A detailed asymptotic analysis confirms the diffusive interface model converges to the existing sharp interface model as the interface thickness goes to zero. A decoupled energy stable numerical scheme is developed to solve this system efficiently. Numerical simulations first illustrate the consistency of theoretical results on the sharp interface limit. Then a convergence study and energy decay test are conducted to ensure the efficiency and stability of the numerical scheme. To illustrate the effectiveness of our phase-field approach, several examples are provided, including a study of a two-phase mass transfer problem where drops with deformable interfaces are suspended in a moving fluid.Comment: 20 pages, 15 figure

Numerical upscaling for heterogeneous materials in fractured domains

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The main computational challenge is the high resolution needed to resolve the data variation. We propose a multiscale method that models the thin structures as interfaces and incorporate heterogeneities in corrected shape functions. The construction results in an accurate upscaled representation of the system that can be used to solve for several forcing functions or to simulate evolution problems in an efficient way. By introducing a novel interpolation operator, defining the fine scale of the problem, we prove exponential decay of the shape functions which allows for a sparse approximation of the upscaled representation. An a priori error bound is also derived for the proposed method together with numerical examples that verify the theoretical findings. Finally we present a numerical example to show how the technique can be applied to evolution problems

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.Comment: 16 pages, 4 figure

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy

Fluid permeation through a membrane with infinitesimal permeability under Reynolds lubrication

This article has been published in a revised form in Journal of Mechanics [https://doi.org/10.1017/jmech.2020.38]. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © 2020 The Society of Theoretical and Applied Mechanics

Modelling and quantification of structural uncertainties in petroleum reservoirs assisted by a hybrid cartesian cut cell/enriched multipoint flux approximation approach

Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir distributed properties and reservoir structure calls for History Matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history-matched models which might result in different predictions of reservoir performance. Uncertainty Quantification restricts the raised model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of Uncertainty Quantification ignore large scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more intensely compared with petrophysical uncertainty. What makes the quantification of structural uncertainty impracticable is the need for global regridding at each step of History Matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian Cut Cell Method which decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of History Matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of class Locally Conservative Flux Continuous Methods (Extended Enriched Multipoint Flux Approximation Method abbreviated to extended EMPFA). The robustness and consistency of proposed Hybrid Cartesian Cut Cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. In this research, the general framework of Uncertainty Quantification is extended and well-equipped by proposed approach to tackle uncertainties of different structures such as reservoir horizons, bedding layers, faults and pinchouts. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic models of uncertain structures. Also this thesis provides a comparative study of structural uncertainty influence on reservoir forecasts among various geological structures

A Numerical Study Of A Permeable Capsule Under Stokes Flows By The Immersed Interface Method

Ph.DDOCTOR OF PHILOSOPH

Sedimentation of self-propelled Janus colloids: polarization and pressure

We study experimentally-using Janus colloids-and theoretically-using Active Brownian Particles- the sedimentation of dilute active colloids. We first confirm the existence of an exponential density profile. We show experimentally the emergence of a polarized steady state outside the effective equilibrium regime, i.e. when v_s is not much smaller than the propulsion speed. The experimental distribution of polarization is very well described by the theoretical prediction with no fitting parameter. We then discuss and compare three different definitions of pressure for sedimenting particles: the weight of particles above a given height, the flux of momentum and active impulse, and the force density measured by pressure gauges

Dissolution of a CO2 spherical cap bubble adhered to a flat surface in air-saturated water

Bubbles adhered to partially hydrophobic flat surfaces often attain a spherical cap shape with a contact angle much greater than zero. We address the fundamental problem of the diffusion-driven dissolution of a sessile spherical cap bubble (SCB) adhered to a flat smooth surface. In particular, we perform experiments on the dissolution of CO2 bubbles (with initial radii similar to 1 mm) immersed in air-saturated water adhered to two substrates with different levels of hydrophobicity. It is found that the contact angle dynamics plays an important role in the bubble dissolution rate. A dissolution model for a multicomponent SCB in an isothermal and uniform pressure environment is then devised. The model is based on the quasi-stationary approximation. It includes the effect of the contact angle dynamics, whose behaviour is predicted by means of a simplified model based on the results obtained from adhesion hysteresis. The presence of an impermeable substrate hinders the overall rate of mass transfer. Two approaches are considered in its determination: (a) the inclusion of a diffusion boundary layer-plate interaction model and (b) a finite-difference solution. The model solutions are compared with the experimental results, yielding fairly good agreement.The authors gratefully acknowledge the support of Total E&P Recherche et Développement through study agreement FR00006995, and the Spanish Ministry of Economy and Competitiveness through grant DPI2014-59292-C3-1-P