Average Permeability for Linear Flow in Series Beds Formula |
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| \( k_{avg} \;=\; \dfrac{ L_1 + L_2 + L_3 }{ \dfrac{ L_1 }{ k_1 } + \dfrac{ L_2 }{ k_2 } + \dfrac{ L_3 }{ k_3 } }\) | ||
| Symbol | English | Metric |
| \( k_{avg} \) = Average Permeability for Linear Flow in Series Beds | \(mD\) | - |
| \( L_1 \) = Length of Layer 1 | \(ft\) | - |
| \( L_2 \) = Length of Layer 2 | \(ft\) | - |
| \( L_3 \) = Length of Layer 3 | \(ft\) | - |
| \( k_1 \) = Permeability for Layer 1 | \(mD\) | - |
| \( k_2 \) = Permeability for Layer 2 | \(mD\) | - |
| \( k_3 \) = Permeability for Layer 3 | \(mD\) | - |
Average permeability for linear flow in series beds within a petroleum reservoir can be derived from the principles of fluid flow through porous media, as described by Darcy's Law. In a series configuration, the beds are arranged such that the fluid flows sequentially through each layer, one after another, with the same flow rate passing through all beds. The total pressure drop across the system is the sum of the pressure drops across each individual bed. For linear flow in series beds, the average permeability is calculated as the harmonic mean of the permeabilities of the individual beds. This reflects the fact that the layer with the lowest permeability tends to dominate the resistance to flow in a series arrangement.
Average Permeability for Linear Flow in Series Beds Formula
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| \( k_{avg} \;=\; \dfrac{ L_t }{ \sum_{i=1}^n \left( \dfrac{ L_i }{ k_i } \right) }\) | ||
| Symbol | English | Metric |
| \( k_{avg} \) = Average Permeability for Linear Flow in Series Beds | \(mD\) | - |
| \( L_t \) = Total Length (or Thickness) of all Beds Combined) | \(ft\) | - |
| \( L_i \) = Length (or thickness) of the i-th Beds | \(ft\) | - |
| \( k_1 \) = Permeability of the i-th Beds | \(mD\) | - |