Flow in channels and fractures analogies to darcy s law
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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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Flow in channels and fractures analogies to darcy s law

Flow in Channels and FracturesAnalogies to Darcy’s Law


Channels and fractures

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


Channels

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


Fractures

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


Average porosity

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


Average permeability

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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