By Alexander N Golubiatnikov, Margarita Eglit, Dewey H Hodges
This quantity is meant to aid graduate-level scholars of Continuum Mechanics turn into more adept in its functions throughout the answer of analytical difficulties. released as separate books — half I on idea and issues of half II offering suggestions to the issues — professors can also locate it fairly worthy in getting ready their lectures and examinations. half I features a short theoretical remedy for every of the most important components of Continuum Mechanics (fluid mechanics, thermodynamics, elastic and inelastic solids, electrical energy, dimensional research, and so on), in addition to the references for extra interpreting. the majority of half II contains approximately one thousand solved difficulties. The ebook comprises bibliographical references and index.
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Furthermore, heat conduction may also occur between the coexisting fluid phases. For simplicity in the exposition, we may invoke local thermal equilibrium in the fluid and assume that the temperature is the same in all fluid phases. In addition, some variables such as porosity, density, and viscosity may depend on temperature. We start by defining the internal energy of the composite system, consisting of the flowing multiphase mixture and the solid matrix, as ρα Sα Uα + (1 − φ)ρ R C R T, φρU = φ (23) α where Uα , C R , and T are the specific internal energy of phase α, the heat capacity of the rock, and the common temperature, respectively.
Using relations (53), introducing the following definitions: n U = ck Uk , (64) pk , (65) k=1 n p= k=1 Hk = Uk + pk , ρck (66) n kT = k T,k , (67) k=1 for the total specific energy, the total pressure, the specific enthalpy of species k, and the total heat conductivity, respectively, summing up Eqs. (57) and (63) over all components, and combining the resulting equations, we obtain the temperature equation for the multicomponent fluid 20 φρC L. Di G. Sigalotti et al. ∂T +ρCv·∇T = −∇ · ∂t n Hk dk −∇ ·( pv)+∇ ·(φk T ∇T )−εr σ S B T 4 + Q, k=1 (68) where C is the multicomponent fluid heat capacity, defined as C= 1 ρ n ρk Ck .
Part 1. Physical mechanisms and simulator formulation. Oil Gas Sci Technol - Rev IFP 65(2):239–262 Lemonnier P, Bourbiaux B (2010b) Simulation of naturally fracture reservoirs. State of the art. Part 2. Matrix-fracture transfers and typical features of numerical studies. Oil Gas Sci Technol - Rev IFP 65(2):263–286 Lichtner PC (1988) The quasi-stationary state approximation to coupled mass transport and fluidrock interaction in a porous media. Geochimica et Cosmochimica Acta 52:143–165 Liu HH, Ahlers CF, Cushey MA (2000) Analysis of hydrologic properties.
Continuum mechanics via problems and exercises by Alexander N Golubiatnikov, Margarita Eglit, Dewey H Hodges