1. Flow in Channels and Fractures Analogies to Darcy’s Law.

2. Channels and Fractures
Channels and Fractures can add significantly to flow capacity
Channels
Equivalent permeability, k= 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

3. 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

4. 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

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