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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 FracturesAnalogies to Darcy’s Law

• 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

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

• 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

• 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

• 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