Average permeability in a radial systems (such as those encountered in reservoirs around a wellbore) is a parameter for understanding fluid flow through porous media. Permeability is a measure of the ability of a porous material (like a reservoir rock) to allow fluids (oil, gas, or water) to pass through it.
For radial flow systems, which are common in well-reservoir models, the average permeability depends on how permeability varies spatially within the reservoir. In a homogeneous radial system, permeability is assumed to be constant. However, in real reservoirs, permeability often varies with radius (due to heterogeneity, layering, or damage near the wellbore, such as skin effects). The average permeability in such cases is typically calculated using an appropriate averaging method, depending on the flow geometry and reservoir properties.
Key Points about Radial Systems
Radial Flow - Fluid flows toward or away from a well in a cylindrical pattern, with the well at the center.
Permeability Variation - Permeability can vary radially (decreasing near the well due to formation damage or increasing outward).
Averaging Methods - The effective or average permeability in radial systems is often derived from Darcy’s law applied to radial flow.
Average Permeability in a Radial Systems Formula |
||
| \( k_{avg} \;=\; \dfrac{ k_a \cdot k_e \cdot ln \left( \dfrac{ r_d }{ r_w } \right) }{ k_a \cdot ln \left( \dfrac{ r_d }{ r_l } \right) + k_e \cdot ln \left( \dfrac{ r_l }{ r_w } \right) }\) | ||
| Symbol | English | Metric |
| \( k_{avg} \) = Average Permeability in a Radial Systems | \(mD\) | - |
| \( k_a \) = Permeability Between r_w and r_l | \(mD\) | - |
| \( k_e \) = Permeability Between r_d and r_l | \(mD\) | - |
| \( r_d \) = Drainage Radius | \(ft\) | - |
| \( r_w \) = Well Bore Radius | \(ft\) | - |
| \( r_l \) = Radius Lesser than r_d | \(ft\) | - |
