tailieunhanh - Reservoir Formation Damage Episode 1 Part 5

Tham khảo tài liệu 'reservoir formation damage episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 82 Reservoir Formation Damage Ap g L _nDb A p q - n r H 128p Lh 5-8 5-9 K is the intrinsic permeability of porous media. The cross-sectional area of porous media open for flow can be expressed by Ap Ab nnDb 4 t5 10 Therefore equating Eqs. 5-9 and 10 and substituting Eqs. 5-1 and 10 results in the following relationship for the mean hydraulic tube diameter 472x7 5-11 Equating Eqs. 5-6 and 11 leads to the following Carman-Kozeny equation 1938 f Ộ i ỵộ TĩĩeẬi-ộ 5-12 Two alternative forms can also be derived. Substitution of Eq. 5-7 into 12 yields 5-13 or substituting Eq. 5-5 into Eq. 5-12 and then rearranging yields a power law type relationship given as Kozeny 1927 K 1 Ộ3 5-14 Based on the analysis of data by Jacquin 1964 Adler et al. 1990 suggested a power low coưelation of permeability with respect to porosity as 5-15 Permeability Relationships 83 Bourbie et al. 1986 determined that n 7 for Ộ and n 3 for ộ . In view of this evidence and Eq. 5-14 the Carman-Kozeny equation appears to be valid for the Ị fractional porosity range. Reis and Acock 1994 warn that these exponents may be low because the permeabilities were not corrected for the Klinkenberg effect. The Modified Carman-Kozeny Equation Incorporating the Flow Units Concept The derivation of the Carman-Kozeny equation presented in the preceding section inherently assumed uniform diameter cyclindrical flow tubes analogy. Therefore for applications to nonuniform diameter flow tubes the Carman-Kozeny equation has been modified by inserting a geometric shape factor Fs Amaefule et al. 1993 as ÍÃ i u 1lụ-ộ 5-16 Hearn et al. 1984 1986 introduced the flow units concept and Amaefule et al. 1993 defined a lumped parameter as following called the flow zone indicator to combine the three unknown parameters Fs T and s into one unknown parameter 1 V s g FZI 5-17 Therefore a plot of experimental data based on the logarithmic form of Eq. 5-16 Amaefule et al. 1993 Hog FZI2 21ogM-j- 5-18 should yield a