tailieunhanh - Reservoir Formation Damage Episode 1 Part 8

Tham khảo tài liệu 'reservoir formation damage episode 1 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Particulate Processes in Porous Media 157 subject to eo t 0 8-32 Tcr is the critical shear stress and ke is an erosion rate constant given by Khilar and Fogler 1987 ke 0 when Tw Tcr 8-33 and ke 0 otherwise 8-34 There are several alternative ways of expressing the hydraulic force. The Rabinowitsch-Mooney equation for non-Newtonian fluid wall shearstress Tw in pipes is given by Metzner and Reed 1955 4 dx J V D J 8-35 The non-Darcy equation can be modified by applying the capillary tubes analogy and the procedure by Ikoku and Ramey Jr. 1979 un vộ NndK I dp dx 8-36 where iie is the effective viscosity given by Nnd2 2 3n 8-37 k and n are some empirical parameters which assume k p and rí 1 for Newtonian fluids. The critical shear stress Tcr is a function of the particle stickiness to the surface characterized by the kx constant and the particle concentration at pore surface Civan 1990 1996 T k ca Lcr KxLp 8-38 where a is an empirical constant. 158 Reservoir Formation Damage Based on Eqs. 8-35 and 8-36 the excess shear stress can be correlated for one-dimensional horizontal flow t - T v w cr Un eD cr 8-39 The previous studies are mostly limited to one-dimensional Newtonian fluid flow and they typically used Civan et al. 1989 Khilar and Folger 1987 Gruesbeck and Collins 1982 Cernansky and Siroky 1985 Ohen and Civan 1989 1990 K - r - dp dx - - 3p 3x cr 41 tf - p 7C cr u - ucr 8-40 In general for multi-dimensional flow Civan 1996 tw - Tcr 8 -1 4 pD Vy - Tcr s 8-41 where y is the flow potential and D is the hydraulic tube diameter tensor for anisotropic media. 8 is a unit vector. Particle Transfer Across Fluid-Fluid Interfaces The driving force for particle transfer between two fluid phases is the wettability of the fluid phases relative to the wettability of the particles. Particles prefer to be in the phase that wets them Muecke 1979 see Figure 8-9 by Civan 1994 . But mixed-wet particles tend to remain on the interface where they are most stable Ivanov et al. 1986 see .