Non-isothermal porous media

NUMERICAL IMPLEMENTATION OF THERMALLY AND HYDRAULICALLY COUPLED PROCESSES IN NON-ISOTHERMAL POROUS MEDIA... 

Xu T. and Pruess K. Coupled modeling of non-isothermal multiphase flow, solute transport and reactive chemistry in porous and fractured media 1. Model develop-... 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

De Jonge, J. and Kolditz, O. (2002) Non-Isothermal Flow Processes in Porous Media, Part I Governing Equations and Finite Element Implementation, Rockflow Preprint [2002-1]. 

This paper presents a numerical simulation of the swellin shrinking processes using the numerical model RF-TH/M - a fully coupled thermo-hydraulic model with mechanical coupling - which has been developed for the purpose of modelling non-isothermal multiphase flow in swelling porous media. In this paper details of the mathematical and numerical multiphase-multicomponental formulation for bentonite, as well as code implementation are described. As an example a test case is investigated. 

Kolditz, O. J. De Jonge. 2003. Non-isothermal two-phase flow in porous media. (Submitted to Computational Mechanics). 

Kolditz, O. Kohlmeier, M. 2001. /I Fully Coupled T-H-M Model for Non-isothermal Flow and Deformation Processes in Porous Media (Preprint). Institute for Fluid Mechanics, University of Hanover, Germany. 

Gens, A. Olivella, S. 2000. Non-isothermal multiphase flow in deformable porous media. Coupled formulation and application to nuclear waste disposal. In Developments in Theoretical Geomechanics. Smith Carter eds., Balkema, Rotterdam, p. 619-640. 

Abstract motif is a three-dimensional finite-element code developed to simulate groundwater flow, heat transfer and solute transport in deformable fractured porous media. The code has been subjected to an extensive verification and updating programme since the onset of its development. In this paper, additional verification and validation works with an emphasis on thermo-hydro-mechanical processes are presented. The verification results are based on cases designed to verify thermo-hydro-mechanical coupling terms, and isothermal and non-isothermal consolidations. A number of validation case studies have been conducted on the code. Example results are repotted in this paper. 

We present now the extension of the constitutive equation (7) to partially saturated porous media. The material is assumed to be saturated by a liquid phase (noted by index w) and a gas mixture (noted by index g ). The gas mixture is a perfect mixture of dry air (noted by index da) and vapour (noted by index va). Based on most experimental data of unsaturated rocks and soils (Fredlund and Rahardjo 1993), and on the theoretical background of micromechanical analysis (Chateau and Dormieux 1998), the poroelastic behaviour of unsaturated material should be non-linear and depends on the water saturation degree. We consider here the particular case of spherical pores which are dried or wetted under a capillary pressure equal to the superficial tension on the air-solid interface. By adapting the macroscopic non-linear poroelastic model proposed by Coussy al. (1998) to unsaturated damaged porous media, the incremental constitutive equations in isothermal conditions are expressed as follows ... 

In what follows the magnetoviscosity phenomenon is analyzed by formulating the local ferrohydrodynamic model, the upscaled volume-average model in porous media with the closure problem, and solution and discussion of a simplified zero-order steady-state isothermal incompressible axisymmetric model for non-Darcy-Forchheimer flow of a Newtonian ferrofluid in a porous medium of the... 

Prasad, K.V. Abel, M. S. Khan, S.K. Datti, P. S. (2002). Non-Darcy forced convective heat transfer in a viscoelastic fluid flow over a non-Isothermal stretching sheet, /. Porous Media, 5, pp. 41-47, ISSN 1091-028X. 

Hsiao, K.-T. and Advani, S. G., A method to predict microscopic temperature distribution inside aperiodic unit cell of non-isothermal flow in porous media . Journal of Porous Media, 5, 69-86, 2002. 

Abstract. This article describes a hydrodynamic model of collaborative flnids (oil, water) flow in porons media for enhanced oil recovery, which takes into account the influence of temperature, polymer and surfactant concentration changes on water and oil viscosity. For the mathematical description of oil displacement process by polymer and surfactant injection in a porous medium, we used the balance equations for the oil and water phase, the transport equation of the polymer/surfactant/salt and heat transfer equation. Also, consider the change of permeabihty for an aqueous phase, depending on the polymer adsorption and residual resistance factor. Results of the numerical investigation on three-dimensional domain are presented in this article and distributions of pressure, saturation, concentrations of poly mer/surfactant/salt and temperature are determined. The results of polymer/surfactant flooding are verified by comparing with the results obtained from ECLIPSE 100 (Black Oil). The aim of this work is to study the mathematical model of non-isothermal oil displacement by polymer/surfactant flooding, and to show the efficiency of the combined method for oil-recovery. 

Modeling of Three-Phase Non-isothermal Flow in Porous Media Using the Approach of Reduced Pressure... 

Let us describe the mathematical model of a three-phase non-isothermal compressible flow in porous media taking into account capillary effects. It is assumed that the movement of phases obeys the generalized Darcy s law. We assume that the phases are in the local thermal equilibrium, so that in any elementary volume the fluids saturating the porous medium and the rock have the same temperature. Furthermore, oil is assumed to be homogeneous non-evaporable fluid and oil reservoir consists of one type of rock. In this case, three-phase non-isothermal flow in a bounded domain 2 c M (d = 1, 2, 3) taking into account capillary forces and the phase transitions between the phases of water and heat transfer is described by the following system of equations ... 

The general phenomenon of polymer adsorption/retention is discussed in some detail in Chapter 5. In that chapter, the various mechanisms of polymer retention in porous media were reviewed, including surface adsorption, retention/trapping mechanisms and hydrodynamic retention. This section is more concerned with the inclusion of the appropriate mathematical terms in the transport equation and their effects on dynamic displacement effluent profiles, rather than the details of the basic adsorption/retention mechanisms. However, important considerations such as whether the retention is reversible or irreversible, whether the adsorption isotherm is linear or non-linear and whether the process is taken to be at equilibrium or not are of more concern here. These considerations dictate how the transport equations are solved (either analytically or numerically) and how they should be applied to given experimental effluent profile data. 

Liquid-vapor phase transitions of confined fluids were extensively studied both by experimental and computer simulation methods. In experiments, the phase transitions of confined fluids appear as a rapid change in the mass adsorbed along adsorption isotherms, isochores, and isobars or as heat capacity peaks, maxima in light scattering intensity, etc. (see Refs. [28, 278] for review). A sharp vapor-liquid phase transition was experimentally observed in various porous media ordered mesoporous sifica materials, which contain non-interconnected uniform cylindrical pores with radii Rp from 10 A to more than 110 A [279-287], porous glasses that contain interconnected cylindrical pores with pore radii of about 10 to 10 A [288-293], silica aerogels with disordered structure and wide distribution of pore sizes from 10 to 10" A [294-297], porous carbon [288], carbon nanotubes [298], etc. 

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