Effective permeability of deformation bands in fault damage zones – Can deformation bands reduce the risk of fault leakage?

(1)

(2)

𝜃 𝑙, 𝜌

𝜌

𝛼.

𝑚

𝑏

𝑘 𝑘 𝒒

𝑝,

𝒒 = −𝑘∇𝑝, ∇ ⋅ 𝒒 = 0

𝑘 = 𝑘 𝑘 = 𝑘

(3)

𝐾 _,

𝛼 𝐾 _,

𝐾 ≥ 1

(1 − 𝜌 𝑎) +𝜌 𝑎𝐾 𝐾

≈ 1

1 +𝜌 𝑎𝐾 𝐾

. (1) 𝑎

𝛼.

𝜌 𝑎 ≪ 1.

𝑎 ≈ 1 𝜌 𝑎 ≪ 1

𝜌 𝑎𝐾 /𝐾 .

−𝐵

𝑎

𝑘

𝜎 𝐿 𝑅.

𝐹 = −𝑇 (𝑝 − 𝑝 )

𝑇 𝑝 𝑝

𝑇 = 𝑇 𝑇

𝑇 + 𝑇 , 𝑇 =𝑘 𝐴 𝒏 ⋅ 𝒅

𝒅 ⋅ 𝒅 , 𝑘 ∈ {𝐿, 𝑅}.

𝐴 𝒏

𝜎 𝑘 𝒅

𝑇 = 𝑇 𝑇

𝑇 + 𝑇 , 𝑇 = 𝑘 𝑇 𝑘 +𝑇 𝑎

2𝐴

, 𝑘 ∈ {𝐿, 𝑅}.

𝜌

𝑥

𝛼

𝐾 , =𝐾 _, 𝐴 _, + 𝐾 𝐴 _, 𝐴 , + 𝐴 ,

, (2)

𝐴 _, 𝐴 _,

𝐾 ,

(4)

𝐾 _,

𝐾 = 1

1 +𝐾 𝑎𝜌

𝐾 𝑐

. 𝑐

𝜃 = 𝒩(0, 𝜎),

𝑐 = 1, 𝑐 = sin (𝐸(|𝜃|)) 𝐸(|𝜃|)

𝐴 _, 𝐴 _,

𝑟 𝜌

𝑁, 𝑟

𝑃(𝑁 = 0) = exp −𝑙 𝜌 |sin(𝜃)| 𝑓(𝜃 + 𝜂)𝑓(𝜂)d𝜃d𝜂 ,

𝑓(𝜃)

2/𝜋 𝑁

𝐸(𝑁) = −log (𝑃(𝑁 = 0).

𝐸(𝑁)

𝑀

𝐸(𝑀) =1 − 𝑃(𝑁 = 0) 𝑃(𝑁 = 0) .

𝐴 _, = 𝑙 + 0.5 𝑙 𝐸(𝑀).

𝑁

(𝑎) = 10 (𝑏) = 10

(𝑐) ^𝐾^𝑏

𝑎𝐾𝑚

= 10⁰ (𝑑) = 10

𝑦

𝑥

𝑙

𝛼.

𝜎, ℛ = 𝒩(0, 𝜎 ), 𝜎 ≪ 1 𝑙 = 𝑙 cos ^√ 𝑙 = 𝑙 sin ^√ , 𝜌 = 𝜌𝑙

(5)

𝐴 _, = 1/𝜌 .

ℛ = 𝒩(0, (𝜋/12) )

𝜌 = 1 𝑙

𝜌 𝑙 = 1

𝑥 𝜌 (𝑥) = 𝐴 + 𝐵 ln ,

𝐴 𝐵

𝐵 = −8.33 m , 𝐴 = 13.33 ln 𝑊

1 m m − 5 ln 𝑊

1 m − 1 m , 𝑊

𝜌(𝑊 ) = 5 𝑇,

(𝑎) = 10 (𝑏) = 10

(𝑐) ^𝐾^𝑏

𝑎𝐾𝑚

= 10⁰ (𝑑) = 10

𝑦

𝑥

𝑊 = 1.74 𝑇 1 m

.

m,

𝑊₅

(6)

𝑊 = 1, 5, and 10

𝑦 𝑥 = 0

𝑦 𝑥

𝑥 𝑦

[𝑋, 𝑌].

𝑌,

𝑋,

𝜌 (𝑋) = 0.

= {10 , 10 , 10 , 10 } m

𝜃,

𝜎, ℛ = 𝒩(0, 𝜎 )

(𝑎) = 10 (𝑏) = 10

(𝑐) ^𝐾^𝑏

𝑎𝐾𝑚

= 10⁰ (𝑑) = 10

𝑊 = 5 𝜎 = 𝜋/ 12

𝑥 𝑦

𝑙 =

1 𝑊 = 5

𝜎,

𝜋/ 5

𝜎

(7)

(𝑎) = 10 (𝑏) = 10

(𝑐) = 10 (𝑑) = 10

𝑾_𝟓 𝑊

(𝑎) = 10 (𝑏) = 10

(𝑐) = 10 (𝑑) = 10

𝐴

(8)