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Mass Transfer in Multiphase Systems and its Applications Part 2

Tham khảo tài liệu 'mass transfer in multiphase systems and its applications part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media 29 different fluids it also depends on the internal geometrical structure of the porous medium. A second consequence of the continuum hypothesis is an uncertainty in the boundary conditions to be used in conjunction with the resulting macroscopic equations for motion and heat and mass transfer Salama van Geel 2008b . A third consequence is the fact that the derived macroscopic point equations contain terms at the lower scale. These terms makes the macroscopic equations unclosed. Therefore they need to be represented in terms of macroscopic field variables though parameters that me be identified and measured. 5. Single-phase flow modeling 5.1 Conservation laws Following the constraints introduced earlier to properly upscale equations of motion of fluid continuum to be adapted to the upscaled continuum of porous medium researchers and scientists were able to suggest the governing laws at the new continuum. They may be written for incompressible fluids as Continuity V- Vp 0 5 Momentum d vp 1 pp dt Pp Pp V vp p p p vp V vpỳ -V ppỳH Pp w - v - v4Kv 6 Energy 3 fa y a dt P 21 p yvpỳ V Tpỳ kV Tp Q 7 Solute transport p cp p p M-v Cp V D -v Cp S 8 dt I I p p where v p and Pp epresent the intrinsic average velocity and pressure respectively and v is the superficial average velocity v Vu2 v2 a pCp m pCp f k kM pCp f is the thermal diffusivity. From now on we will drop the averaging operator 0 to simplify notations. The energy equation is written assuming thermal equilibrium between the solid matrix and the moving fluid. The generic terms Q and S in the energy and solute equations represent energy added or taken from the system per unit volume of the fluid per unit time and the mass of solute added or depleted per unit volume of the fluid per unit time due to some source e.g. chemical reaction which depends on the chemistry the surface properties of the fluid solid interfaces etc. . .