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PETE311_06A_Class11_(Maggard)

PETE311_06A_Class11_(Maggard) - – Flow in slots • A =...

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Flow in Channels and Fractures Analogies to Darcy’s Law
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Channels and Fractures Channels and Fractures can add significantly to flow capacity Channels Equivalent permeability, k = d 2 /32 in any consistent system (SI) Equivalent permeability, k = 2.0428 x10 10 d 2 k in md d in inches Wormholes from acid stimulation Fractures Equivalent permeability, k = b 2 /12 in any consistent system (SI) Equivalent permeability, k=5.4476x10 10 b 2 k in md b in inches Stimulation by hydraulic fracturing Naturally fractured reservoirs
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Channels Darcy’s Equation: Porous media Darcy units Poiseuille’s Equation: Flow in tubes (A = π r 2 ) Darcy units, EXCEPT μ in Poises Δ p in dyne/cm 2 Self Study - Derive the equivalent permeability shown previously Make units of all dimensions the same in both equations Cancel terms that are same dimension with same units Δ p L μ A k q = Δ p L μ 32 d A Δ p L μ 8 r π q 2 4 = = L A
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Fractures Darcy’s Equation: Porous media Darcy units Buckingham’s Equation: Flow in slots
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Unformatted text preview: – Flow in slots • A = b·h; vertical fractures – Darcy units, EXCEPT • μ in Poises • Δ p in dyne/cm 2 • Self Study - Derive the equivalent permeability shown previously – Make units of all dimensions the same in both equations – Cancel terms that are same dimension with same units Δ p L μ A k q = Δ p L μ 12 b A q 2 = b A Average Porosity • Bulk Volume Weighted, Integrated Average – For a discrete system with a specified number of channels/fractures • Note, φ c/f = 1 • V b,c/f can include multiple channels/fractures ∫ ∫ = b b V V dV dV total b, matrix b, matrix c/f b, c/f V V V + = Average Permeability • For channels or fractures of constant cross sectional area along flow path (parallel flow) – For discrete values of permeability (piecewise integration) • A c/f can include multiple channels/fractures ∫ ∫ = flow flow A A dA dA k k total matrix matrix c/f c/f A A k A k k + =...
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