Flow in Channels and Fractures Analogies to Darcy’s Law

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Flow in Channels and Fractures Analogies to Darcy’s Law

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Flow in Channels and Fractures Analogies to Darcy’s Law

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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

- Flow in slots
- 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 a discrete system with a specified number of 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

- For discrete values of permeability (piecewise integration)