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Flow in Channels and Fractures Analogies to Darcy’s Law

Flow in Channels and Fractures Analogies to Darcy’s Law. 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

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Flow in Channels and Fractures Analogies to Darcy’s Law

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  1. Flow in Channels and FracturesAnalogies to Darcy’s Law

  2. Channels and Fractures • Channels and Fractures can add significantly to flow capacity • Channels • Equivalent permeability, k = d2/32 in any consistent system (SI) • Equivalent permeability, k = 2.0428 x1010 d2 • k in md • d in inches • Wormholes from acid stimulation • Fractures • Equivalent permeability, k = b2/12 in any consistent system (SI) • Equivalent permeability, k=5.4476x1010 b2 • k in md • b in inches • Stimulation by hydraulic fracturing • Naturally fractured reservoirs

  3. Channels A L • Darcy’s Equation: • Porous media • Darcy units • Poiseuille’s Equation: • Flow in tubes (A = r2 ) • Darcy units, EXCEPT •  in Poises • p in dyne/cm2 • 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

  4. Fractures • Darcy’s Equation: • Porous media • Darcy units • Buckingham’s Equation: • Flow in slots • A = b·h; vertical fractures • Darcy units, EXCEPT •  in Poises • p in dyne/cm2 • 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 A b

  5. Average Porosity • Bulk Volume Weighted, Integrated Average • For a discrete system with a specified number of channels/fractures • Note, c/f = 1 • Vb,c/f can include multiple channels/fractures

  6. Average Permeability • For channels or fractures of constant cross sectional area along flow path (parallel flow) • For discrete values of permeability (piecewise integration) • Ac/f can include multiple channels/fractures

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