Brownell-Katz Number formula |
||
|
\( N_{BK} \;=\; N_c \cdot N_B \) (Brownell-Katz Number) \( N_c \;=\; \dfrac{ N_{BK} }{ N_B }\) \( N_B \;=\; \dfrac{ N_{BK} }{ N_c }\) |
||
| Symbol | English | Metric |
| \( N_{BK} \) = Brownell-Katz Numbe | \( dimensionless \) | \( dimensionless \) |
| \( N_c \) = Capillary Number | \( dimensionless \) | \( dimensionless \) |
| \( N_B \) = Bond Number | \( dimensionless \) | \( dimensionless \) |
Brownell-Katz Number, abbreviated as \(N_{BK}\), a dimensionless number, used in fluid dynamics and related fields, particularly in the study of multiphase flow through porous media. It is a combination of two other dimensionless numbers: the Capillary Number and the Bond Number. This number helps characterize the relative importance of viscous forces, capillary forces, and gravitational forces in a system. The Brownell-Katz Number increases directly with flow velocity, dynamic viscosity, and fluid density. It is typically used in contexts like oil reservoir engineering or soil science to analyze how fluids (such as oil, water, or gas) move through porous materials under the influence of these forces.
Brownell-Katz Number provides insight into the balance between the forces driving fluid flow and those resisting it, aiding in the design and analysis of processes like enhanced oil recovery or groundwater flow. While a precise mathematical definition can vary depending on the specific application, it generally takes the form of a product or ratio involving the Capillary Number (which compares viscous forces to surface tension) and the Bond Number (which compares gravitational forces to surface tension).
The Brownell-Katz Number is a tool to interpret the competition between forces in porous media flow. Its value guides expectations about fluid behavior, with low values emphasizing capillary trapping and high values highlighting viscous or gravitational dominance.
Brownell-Katz Number Interpretation
- Low Brownell-Katz Number (N_{BK} << 1) - Capillary forces dominate over both viscous and gravitational forces. Fluid flow is strongly influenced by surface tension and the geometry of the porous medium (pore size). This scenario is common in slow flow regimes or systems with high interfacial tension, where fluids tend to remain trapped or move minimally due to capillary resistance.
- Moderate Brownell-Katz Number (N_{BK} ≈ 1) - Indicates a balance between viscous, capillary, and gravitational forces. All three forces play a significant role, and the flow behavior depends on the specific conditions of the system (fluid properties, flow rate, and medium characteristics). This is often a transitional regime where small changes in parameters (like velocity or viscosity) can shift the dominant force.
- .High Brownell-Katz Number (N_{BK} >> 1) - Viscous and/or gravitational forces dominate over capillary forces. Fluid displacement is driven primarily by the flow velocity (viscous effects) or density differences (gravitational effects), with less resistance from capillary effects.
Brownell-Katz Number Applications
- Petroleum Engineering - Understanding oil and water flow in reservoir rocks, predicting residual oil saturation after secondary recovery processes, and designing enhanced oil recovery techniques. The balance between viscous, gravitational, and capillary forces determines the displacement of one fluid by another in the porous rock.
- Hydrogeology = Analyzing groundwater flow and the movement of contaminants in aquifers.
- Chemical Engineering - Designing and optimizing processes involving flow through packed beds, filtration, and separation.
- Soil Science - Studying water infiltration and retention in soils.
