TAILIEUCHUNG - Reservoir Formation Damage Episode 1 Part 7

Tham khảo tài liệu 'reservoir formation damage episode 1 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 132 Reservoir Formation Damage v ơ .v . 7-21 Several other relationships which may be convenient to use in the formulation of the transport phenomena in porous media are given in the following The volume flux My and the velocity Vj of a phase j are related by e7 7-22 where e-r is the volume fraction of the irreducible phase j in porous media. When an irreducible residual fluid saturation Sjr exists in porous media Eq. 7-22 should be substituted into Eq. 7-15 for the flowing phase volume flux as 7-23 In deforming porous media the volumetric flux of the solid phase can be expressed in terms of the velocity according to the following equation M. V 7-24 where es and Vj denote the solid phase volume fraction and velocity respectively. Substituting Eq. 7-14 Eq. 7-24 becomes w5 l- v5 7-25 Accounting for the immobile fluid fraction yr in deforming porous media the volumetric flux of the fluid relative to the deforming solid phase is given by Civan 1994 1996 7-26 The volume fraction of species i of phase j in the bulk system is given by v Gj ơớ 7-27 Multi-Phase and Multi-Species Transport in Porous Media 133 or by Pi j kj cikj 7-28 The mass concentration of species Ỉ in phase j is given by Cij P ij 7-29 The molar concentration of species i in phase j is given by Cij cij Mi 7-30 The volume flux of species i in phase j is given by ưij 5ijUrj 7-31 where urj is the volume flux of phase j. The mass flux of species i in phase j is given by mij cijurj ẽỉkjUrkj 7-32 Multi-Species and Multi-Phase Macroscopic Transport Equations The macroscopic description of transport in porous media is obtained by elemental volume averaging Slattery 1972 . The formulations of the macroscopic equations of conservations in porous media have been carried out by many researchers. A detailed review of these efforts is presented by Whitaker 1999 . The mass balances of various phases are given by Civan 1996 1998 3 3í eý pj V- pà ỹ-k i7 33 where urj is the fluid flux relative to the solid phase t is the .