scholarly journals Fundamentals of the Finite Element Method for Heat and Fluid Flow

2004 ◽  
Author(s):  
Roland W. Lewis ◽  
Perumal Nithiarasu ◽  
Kankanhalli N. Seetharamu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
The Finite Element Method ◽  
Heat And Fluid Flow ◽  
Element Method

Finite-Element Analysis of Temperature and Thermal Stresses Induced by Hot Water Injection

1978 ◽  
Vol 18 (06) ◽  
pp. 457-469 ◽  
Author(s):  
T. Aktan ◽  
S.M. Farouq Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Fluid Flow ◽  
Thermal Stresses ◽  
Water Injection ◽  
Hot Water ◽  
The Finite Element Method ◽  
Heat And Fluid Flow ◽  
Element Method

Abstract Results of an experimental study of the temperature and pressure dependence of rock elastic moduli were used in a numerical mathematical model that describes the unsteady-state, two-dimensional flow of a single-phase, single-component, slightly compressible hot fluid and that calculates the state of stress in porous media. The numerical formulation was conducted using the finite-element method of triangular elements to discretize the space domain and backward differencing for discretizing the time domain. Sections of the model dealing with the flow of mass and heat, and stress calculations were tested separately then, the complete model was used to investigate the effect of temperature-dependent Young's moduli and Poisson's ratios on the state of stress and the propagation of thermal and pore stresses with an advancing hot water front in porous media. porous media Introduction The finite-element method forms the basis for a versatile analysis procedure applicable to problems in several different fields. Essentially, the finite-element idealization replaces the continuum with a finite number of discrete elements. Geometry of the elements is defined by a set of spatial points (called nodal points) of the system. Heat and fluid-flow problems are analyzed by using interpolation functions for the unknown temperatures and pressures. Thus, the variables within elements are pressures. Thus, the variables within elements are defined completely in terms of the values at nodal points. The isoparametric element concept, where points. The isoparametric element concept, where the geometry and displacements of the element are described in terms of the same parameters and are of the same order, is particularly useful for stress analysis in continuous bodies. The investigation of thermal stresses may be found helpful when answering questions associated with heated reservoir rocks. Creation of microfactures in formations subjected to elevated temperatures often results in increased permeabilities. A correlation between the thermal stresses induced by these high temperatures and the degree of microfracturing affecting the rock absolute permeability could be useful in understanding fluid flow permeability could be useful in understanding fluid flow in heated reservoirs. It also would be interesting to see if thermal stresses have any effect on the casing failures in steam injection or geothermal wells. The analysis under consideration involves the determination of pressures, temperatures, and stresses in a porous medium undergoing hot-water injection. The study is complicated further by the transient nature of the variables. Background The finite-element method has been used widely for studying stresses in various kinds of structures. The basic concepts of the method, first laid down by Turner et al, essentially are composed of the idealization of continuous bodies by a set of interconnected finite elements with known behavioral characteristics. Recently, this versatile method was applied to diverse kinds of engineering problems, mainly in heat and fluid-flow areas. Desai problems, mainly in heat and fluid-flow areas. Desai and Abel list the fields where the method may be applied. Visser solved the unsteady-state heat conduction equations, using a variational approach. He solved for temperature distribution, also calculating the associated stresses by determining the displacements occurring in the body due to this temperature field. Later, Zienkiewicz and Parekh used two- and three-dimensional curved isoparametric elements to solve the same equation by using the Galerkin principle. SPEJ P. 457

scholarly journals Finite element modeling of fluid flow in fractured porous media using unified approach

2020 ◽  
Vol 43 (1) ◽  
pp. 13-22
Author(s):  
Hai-Bang Ly ◽  
Hoang-Long Nguyen ◽  
Minh-Ngoc Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Fractured Porous Media ◽  
Flow In Porous Media ◽  
Soil Science ◽  
The Finite Element Method ◽  
Element Method

Understanding fluid flow in fractured porous media is of great importance in the fields of civil engineering in general or in soil science particular. This study is devoted to the development and validation of a numerical tool based on the use of the finite element method. To this aim, the problem of fluid flow in fractured porous media is considered as a problem of coupling free fluid and fluid flow in porous media or coupling of the Stokes and Darcy equations. The strong formulation of the problem is constructed, highlighting the condition at the free surface between the Stokes and Darcy regions, following by the variational formulation and numerical integration using the finite element method. Besides, the analytical solutions of the problem are constructed and compared with the numerical solutions given by the finite element approach. Both local properties and macroscopic responses of the two solutions are in excellent agreement, on condition that the porous media are sufficiently discretized by a certain level of finesse. The developed finite element tool of this study could pave the way to investigate many interesting flow problems in the field of soil science.

scholarly journals THERMO-HYDRAULIC FINITE ELEMENT MODELLING OF DISTRICT HEATING NETWORK BY THE UNCOUPLED APPROACH

2003 ◽  
Vol 9 (3) ◽  
pp. 153-162 ◽  
Author(s):  
Irena Gabrielaitienė ◽  
Rimantas Kačianauskas ◽  
Bengt Sunden
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
District Heating ◽  
Multilayered Structure ◽  
The Finite Element Method ◽  
Flow And Heat Transfer ◽  
Transfer Problems ◽  
Element Method

The modelling of uncoupled fluid flow and heat transfer problems of a district heating network using the finite element method (FEM) is presented. Since the standard thermo-hydraulic pipe elements cannot be directly used for modelling insulation, the main attention was paid to discretisation of multilayered structure of pipes and surrounding by one-dimensional thermal elements. In addition, validity of the finite element method was verified numerically by solving fluid flow and heat transfer problems in district heating pipelines. Verification analysis involves standard single pipe problems and simulation of fragment of district heating in Vilnius. Pressure and temperature results obtained by finite element method are compared with those by other approaches.

Simulation of upscaling effects due to wave-induced fluid flow in Biot media using the finite-element method

2007 ◽  
Vol 62 (3) ◽  
pp. 193-203 ◽  
Author(s):  
J. Germán Rubino ◽  
Juan E. Santos ◽  
Stefano Picotti ◽  
José M. Carcione
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
The Finite Element Method ◽  
Wave Induced ◽  
Element Method
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