Begell House Inc.
Journal of Porous Media
JPM
1091-028X
14
8
2011
EFFECT OF NONUNIFORM TEMPERATURE GRADIENTS ON THERMOGRAVITATIONAL CONVECTION IN A POROUS LAYER USING A THERMAL NONEQUILIBRIUM MODEL
659-669
Jinho
Lee
School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea
I. S.
Shivakumara
Department of Mathematics, Bangalore University, Bangalore-560 056, India
A. L.
Mamatha
Department of Mathematics, UGC-Center for Advanced Studies in Fluid Mechanics, BangaloreUniversity, Bangalore 560001, India
The effect of various forms of nonuniform basic temperature gradients on the onset of convection in a Newtonian fluid-saturated isotropic porous layer is investigated when the fluid and solid phases are not in local thermal equilibrium. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation and the Forchheimer-extended Darcy model is used to describe the flow. The eigen value problem is solved numerically using the Galerkin technique. Comparisons are also made of the critical stability parameters between the present results and published ones for the linear basic temperature profile case, and the agreement is found to be good. The possibility of delaying or hastening the on set of convection by the basic state temperature gradients along with the influence of parameters representing the local thermal non-equilibrium effect is analyzed in detail. When compared with the nonuniform temperature gradients, it is found that the linear temperature profile indicates a reinforcement of stability. In addition, the role of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles.
MODELLING AND SIMULATION OF TEMPERATURE-DENSITY-DRIVEN FLOW AND THERMODIFFUSION IN POROUS MEDIA
671-690
Alfio
Grillo
DISMA "G.L. Lagrange", Politecnico di Torino, C.so Duca degli Abruzzi 24, I-10129, Torino
(TO), Italy
Michael
Lampe
G-CSC Goethe-Universität Frankfurt am Main,Kettenhofweg 139, D-60325 Frankfurtam Main, Germany
Gabriel
Wittum
G-CSC Goethe-Universität Frankfurt am Main,Kettenhofweg 139, D-60325 Frankfurtam Main, Germany
We investigate some aspects of thermodiffusion in saturated porous media in the presence of both density- and temperature-driven single-phase flow. This type of flow is sometimes referred to as thermohaline flow. We also review some fundamental thermodynamic concepts that are necessary for the formulation of the examined problem and compare our approach with some other models of thermodiffusion available in the literature. Our constitutive description and mathematical modeling are framed with in the hybrid mixture theory. Finally, we show and discuss the results of numerical simulations of some selected test cases in which thermodiffusion as well as thermohaline flow are considered.
SIMULATION AND CHARACTERIZATION OF MULTIPHASE FLOW AND PARTICLE TRANSPORT IN POROUS MEDIA
691-698
Ana
Serrenho
Geophysics Centre of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal; and Department of Civil Engineering, Nationa lUniversity of Ireland, Galway, Ireland
Murat
Aydin
Geophysics Centre of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal; and Institute of Energy, Istanbul Technica lUniversity, 34469 Maslak-Istanbul, Turkey
Antonio Ferreira
Miguel
Department of Physics, School of Sciences and
Technology, University of Evora, Institute of Earth Sciences (ICT) Pole of Evora,
Portugal
The study of multiphase flow through porous structures is of considerable importance in many fields of science and technology. This paper analyzes numerically low and medium Reynolds number flows in a cavity filled with porous materials and with a stagnant zone. Simulations were carried out with both a single-phase and two-phase flow. The transport of solid particles through the porous structure is also analyzed. This study covers Reynolds numbers ranging from 0.1 to10 and Peclet numbers ranging from 0.5 to 105.
COMPARISON OF RESIDUAL OIL SATURATION FOR WATER AND SUPERCRITICAL CO2 FLOODING IN A LONG CORE, WITH LIVE OIL AT RESERVOIR CONDITIONS
699-708
R. Z.
Moreno
Department of Petroleum Engineering, State University of Campinas, UNICAMP, Ch P. 6122, Campinas, San Paulo, 13083-970, Brazil
R. G.
Santos
Department of Petroleum Engineering, State University of Campinas, UNICAMP, Ch P. 6122, Campinas, San Paulo, 13083-970, Brazil
C.
Okabe
Petrobras S. A., San Paulo, Brazil
D. J.
Schiozer
Department of Petroleum Engineering, State University of Campinas, UNICAMP, Ch P. 6122, Campinas, San Paulo, 13083-970, Brazil
O. V.
Trevisan
Department of Petroleum Engineering, School of Mechanical Engineering, University of Campinas, Mendeleyev Street 200, Cidade Universitaria Zeferino Vaz − Barao Geraldo, Campinas − Sao Paulo, Brazil, 13083-860
E. J.
Bonet
Department of Petroleum Engineering, State University of Campinas, UNICAMP, Ch P. 6122, Campinas, San Paulo, 13083-970, Brazil
S.
Iatchuk
Department of Petroleum Engineering, State University of Campinas, UNICAMP, Ch P. 6122, Campinas, San Paulo, 13083-970, Brazil
The measurement of residual oil saturation (ROS) is of paramount importance in predicting the expected recovery in a producing field. It is also a key factor for reservoir management and for defining possible long-term enhanced oil recovery (EOR) targets. Even though ROS has been known to depend on different factors, such dependence has not been investigated extensively in the laboratory, at reservoir conditions. This paper describes an experimental work focusing on the rock formation and conditions of a very highly productive field that is offshore Brazil. The objective was to compare the recovery efficiency between water and supercritical CO2 flooding at reservoir conditions in terms of ROS evolution. A careful program of displacement tests was conducted using long real unconsolidated porous media and live reservoir fluid at reservoir pressure and temperature. An improved version of a conventional test apparatus has been implemented successfully to allow high pressure displacements through long cores. A linear x-ray monitoring device permitted us to follow water and CO2 in situ saturations along the core. A numerical simulation study was developed to scrutinize possible effects from varying conditions. The results obtained in this work led to lower residual oil saturation in the CO2 flooding than water flooding. Experimental and numerical simulation results are compared.
THE GAS-OIL GRAVITY DRAINAGE MODEL IN A SINGLE MATRIX BLOCK: A NEW RELATIONSHIP BETWEEN RELATIVE PERMEABILITY AND CAPILLARY PRESSURE FUNCTIONS
709-720
Mohammadreza
Kamyab
Department of Petroleum Engineering, Curtin University, Bentley, WA, Australia
Morteza
Dejam
Department of Petroleum Engineering, College of Engineering and Applied Science, University
of Wyoming, 1000 E. University Avenue, Laramie, Wyoming 82071-2000, USA
Mohsen
Masihi
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
Mohammad Hossein
Ghazanfari
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
This work concerns modeling of gas-oil gravity drainage for a single block of naturally fractured reservoirs. The non-linearity induced from saturation-dependant capillary pressure and relative permeability functions makes a gravity drainage model difficult to analytically and numerically solve. Relating the capillary pressure and relative permeability functions is a potential method to overcome this problem. However, no attempt has been made in this regard. In this study a generalized one-dimensional form of gas-oil gravity drainage model in a single matrix block, presented in the literature, is considered. In contrast with commonly used forms of capillary pressure and relative permeability functions, more realistic models, which are in power law, are used in the model. It has been found that the nonlinearity of the generalized model is canceled only if the powers of capillary pressure and relative permeability functions are related as n = m + 1. The Fourier Laplace inversion method is applied to numerically solve the developed model and generate the drainage flow rate and the oil saturation profiles at different values of m and n powers. The results of this work might help to obtain a new transfer function for a dual-porosity model, which might improve the reliability of simulators for evaluation of naturally fractured reservoirs.
STARTING SOLUTION FOR SOME OSCILLATORY ROTATING FLOWS OF MAGNETOHYDRODYNAMIC SECOND-GRADE FLUID THROUGH POROUS SPACE
723-734
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
Tanzeela
Safdar
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
M.
Azram
Department of Science in Engineering, Faculty of Engineering, IIUM Kuala Lumpur 50727, Malaysia
This paper presents a starting solution for some oscillating flows of an incompressible and electrically conducting second-grade fluid through porous space in a rotating frame of reference. Modified Darcy’s law for a second-grade fluid has been utilized to discuss the flows through porous space. Exact analytical expressions for the velocity field are obtained in the presence of a transverse uniform magnetic field and Hall current using the Fourier sine transforms. The results are presented as a sum of steady-state and transient solutions. In the limiting case when α1 goes to zero, our solutions reduce to those for a Newtonian fluid. The obtained results are sketched for the variations of pertinent parameters and are analyzed through several graphs.
HODOGRAPHIC VISCOUS FLOWS IN POROUS MEDIUM
735-742
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
Tahira
Haroon
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Mohammad
Kahshan
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22010, Pakistan
Muhammad Raheel
Mohyuddin
COMSATS Institute of Information Technology, Abbottabad, Pakistan; Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195, Iran
Solutions for the equations of an incompressible viscous fluid flow in a porous medium are obtained by the hodograph transformation method. A suitable Legendre transform function is introduced, and the basic equations governing the flow are transformed in terms of this function. As applications, different flows and their corresponding velocity components are given.
FORCED CONVECTION IN A LENS-SHAPED DUCT FILLED WITH A POROUS MEDIUM
743-749
C .Y.
Wang
Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
The forced flow through a lens-shaped duct which is filled with a porous medium is studied. The Ritz method is well suited for obtaining the flow rate and the Nusselt number. The problem is governed by the aspect ratio and the porous medium parameters. Asymptotic formulas for large s are also obtained.