Flow in Channels and Fractures Analogies to Darcy’s Law

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# Flow in Channels and Fractures Analogies to Darcy’s Law - PowerPoint PPT Presentation

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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Presentation Transcript
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