BISQ理论模型与声波测井响应研究

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1 * BISQ, 133 BISQ BISQ BISQ BISQ BISQ : PACC: 43, 665, [1], * (:4743) cuizwjlu@sina.com; kexiew@public.cc.jl.cn

2 [] [3 4] Dvorkin Nur [5 6] - BISQ [7-13] [7-9], [1] BISQ [11 1] BISQ BISQ BISQ BISQ BISQ [13] [14] [15] [, 16]

3 BISQ Dvorkin Nur 1993 [5] BISQ ( ) BISQ BISQ M M M M S ( ω, R) 1 S ( ω, R) 1 J ( R) λrj ( λr) 1 λ λ ω ρ ~ ω R ( ) M Dvorkin [6] ρ ~ ( ω ) ρ ~ ( ω ) iη ωκ ( ω ) 3 ( ) κ ω ) 1 [ F iω ρ α ηφ] ( ω ) κ ( ω ) κ κ 4 α κ η ρ φ F(ω [ 17] BISQ [18] BISQ H u + ω ρu + C C u + ω ρ u + M w + ω ρ w + ω w ρ ~ w 5a 5b ρ ρ φρ + 1+ φ ρ ρ s ( ) w φ( U u U C αm H K + 4G / 3 + α ) s b M α 1 K b / K s b K, K s 3

4 kˆ u ( r t ) u kˆ, i e ( k r ωt ) w ( r ) k ˆ i( k r ωt ) t w e 6, 5a b w Y u ( ) ( ~ ) ~ H M C Y H + M ρ C ρ Y + ρρ ρ ρ 7 k 1, ω Y1, P ( k ) Re( Y ) V ω Re 1 Q 1 Im( k) Re( k ) 8 3 [18], ωρ κ ηφ << 1 7 ( K + 4G / α ) Y 1 ρ b 3 + M [ ωκ ( 1 α M H ) M ] iη ωκ M Y 9 iη / 4 J ( x) xj ( x) 1+ x L 1 x S ( ω, R) ( iηωr κ M ) 8 + ( ηωr κ M ) 48, x λr 1 S( ω ) V P ω κ / η Im( S ) S Re( S ) 11a M 1 Q P [ Im( S ) Re( S )] 11b ω, 1 VP 3 M κ ηr Q P 4M κ ηr ω 1 1,, V ω M ( 1 α M / ) κ / η Q P H P 4

5 BISQ BISQ 8 4 φ m κ K b η.1pa.s Pa Pa K s G 9 Pa 65Kg/m ρ s α (U / u ) a b 1 1 1a 1b BISQ a b 5

6 BISQ BISQ BISQ [11] 3 3 3a 3b R <1Hz / π π 4 4 4a 4b BISQ 1 BISQ 6

7 1Hz R 3mm BISQ [13] a,5b BISQ [15] Pride [] 5 η ~ ρ α ρ / φ 1 M λ ω α ρ Mφ M ( ω ) n n λ j M R j 7

8 J ( j n ) n 1,,3L J ( λr) J J 1 M j n M M > H u M 1 λr < j.45 J1( λr) λrj ( λr) 13 λr BISQ w BISQ 5a 5b u u + ω ρ u C u + ω ρ u 14 u k ω ρ / ω ρ C 15 H / BISQ C H 15 M ( ω ) ( 1 / K ) K b s K ( b + 4G / 3 ρ / ρ + K b / K 1) s BISQ [16] 6, 8

9 BISQ BISQ BISQ A BISQ 1993 Dvorkin Nur z P P C u + M w M ( w + α u) C αm α 1 K / K A-1 b s r 9

10 u r, w r A- u η w P ρ A-3 t κ ( ω) t A- A-3 P r η κ w ( ω ) t r A-4 w ( z, r, t ) w ( r ) r r i e ( lz ωt ) ω ) P ( z, r, t ) P ( r i( lz t ) e A-5 A-5 A-4 w ( r r ) ω ~ ρ 1 P ( r) ( ω) r A-6 ( ω) κ ρ (ω ) [16] A-6 A-4 [5] Dvorkin z P ( r ) w ( r r ) r u w z u ( z, t) D 1 i e ( lz t ω ) i( lz ωt ) w z ( z, t) D e A-8 D A-8A-1 θ A-6 D1 r d dr P 1 dp ~ ω ρ( ω) + + P ( ) ~ il D + αd1 ω ρ( ω) A-9 r dr M r R P R A-9 1

11 J P ( z, r, t) ( λr) wz u z M 1 + α λ ω ~ ρ M A-1 λrj ( λr) z z P () r r P av 1 πr ( z, t) R J π rp ( z, r, t)dr 1( λr) wz u z M 1 + α A-11 λrj ( λr) z z A-11 A-1 M J 1( λr) M 1 λrj ( λr) A-1 ( ) 1 F ω Dvorkin Nur 1993 [1] Qiao W X, Wu W Q, Wang Y J 1996 Progress in Physics (in Chinese)[ ] [] M A J. Acoust. Soc. Am [3] Wang K X, Dong Q D1986 Acta Petrolei Sinica 7 59 (in Chinese)[,, ] [4] Zhou Y F, Wang Y J, Ma L et al Acta Phys.Sin (in Chinese)[ 49 48] [5] Dvorkin J., and Nur A Geophysics [6] Dvorkin J., R. Nolen-Hoeksema, and Nur A Geophysics [7] J.O. Parra Geophysics 65 [8] Yang D H, Zhang Z J Chinese. Science.Bulletin (in Chinese)[,, ] 11

12 [9] Yang D H, Zhang Z J Wave Motion 35 3 [1] Cheng Y F, Yang D H, and Yang H Z Chin.Phy.Lett [11] Yang K D, Yang D H, Wang S Q Chinese J Geophysics (in Chinese) [ ] [1] Meng Q S, He Q D, Zhu J W et al 3, Journal o Jinlin University(Earth Science Edition)33 17(in Chinese)[,, 3 ( ) 33 17] [13] Cui Z W and Wang K X, 3, Int.J.Eng.Sci [14] Wang K X, J. E. White, Wu X Y 1996 Acta Geophysica Sinica (in Chinese) [ J. E. White, ] [15] Hu H S 3 Acta Phys.Sin (in Chinese) [ ] [16] Hu H S, Wang K X, Liu J Q Chinese J.Comput.Phys(in Chinese)19 3(in Chinese) [,, 19 3] [17] Hu H S, Wang K X 1 Chinese J Geophysics (in Chinese)[, ] [18] Cao Z L, Wang K X 1 Annual J Chin. Geophys.Soc.31[ 1 31] [19] Dutta N C. and Odé H Geophysics [] Pride S.R Phys.Rev.B

13 Slow waves propagation in BISQ poroelastic model * Cui Zhi Wen Wang Ke Xie Cao Zheng Liang Hu Heng Shan (Department o Acoustics & Microwaves, School o Physics, Jilin University, Changchun, 133, China) Abstract The slow compressional wave (P-wave) in Porous media based on BISQ model is investigated. The low requency approximate expression or velocity and attenuation o P-wave is given. Comparing with model, BISQ model predicts that: the attenuation o P waves is very large at low requency and decrease with characteristic uirt low length (R) increasing, velocity dispersion are weaken and the velocity low requency limit is not zero and decrease with R increasing, the ratio o pore luid-displacement and bulk-displacement is similar to attenuation and phase is dierent obviously; The seepage low induced by P wave at the luid-porous media interace is more large than that o model, which can be induced larger accompanying electric ield. For the sake o contrast, the properties o the ast compressional wave are also presented. Two conclusions are induced rom BISQ model: there is no uirt mechanism in in-viscid luid-saturated porous media and there is no dynamic compatibility phenomenon in viscid luid-saturated porous media. Keywords: Porous medium, Squirt low, Slow compressional waves, Dynamic compatibility PACC: 43..Jr, 6.65, 91.3 *Project supported by the National Natural Science Foundation(Grant No.4743) 13

14 41 45 (1a) Vp1(m/s) k 1k 1k 1M Vp(m/s) (1b) R(mm) k 1k 1k 1M 1 14

15 .5 (a).4 Q p k 1k 1k 1M Q p -1 1M 1k 1k 1k 1 (b) R(mm) m 1 1 1k 1k 1k 1M 15

16 5 4 3 R(mm) (3a) 1 1 1k 1k 1k 1M (3b) 1 1 1k 1k 1k 1M 3 16

17 1. U p1 /u p (4a) 1 1 1k 1k 1k 1M U p /u p 1M 1k 1k 1k 1 1 (4b) 1 1 1k 1k 1k 1M R(mm)

18 .1 1E-3 (5a) 1E-4 Wp1/Ui 1E-5 1E-6 1E-7 1E k 1k 1k 1M.1 (5b) Wp/Ui.1 1E-3 1E-4 R1mm 3mm 6mm 1mm 1 1 1k 1k 1k 1M 5 18

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