Flow in Channels and Fractures Analogies to Darcy’s Law

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Presentation transcript:

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= 2.0428 x1010 d2 k in md d in inches Wormholes from acid stimulation Fractures Equivalent permeability, k=5.4476x1010 b2 b in inches Stimulation by hydraulic fracturing Naturally fractured reservoirs

Channels Darcy’s Equation: Poiseuille’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 A L

Fractures Darcy’s Equation: Buckingham’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 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 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