# Souders-Brown Equation

on . Posted in Fluid Dynamics

The Souders-Brown equation is an empirical equation used in chemical engineering to estimate the maximum vapor flow rate in a vertical two-phase flow system.  The equation is commonly used to determine the flooding point in distillation columns, which is the point at which the liquid and vapor phases can no longer be properly separated, leading to reduced column efficiency.  By calculating the maximum vapor flowrate at the flooding point, engineers can design and operate distillation columns more effectively.

The equation takes into account the density difference between the liquid and vapor phases.  When the vapor flow rate exceeds the maximum value predicted by the equation, the liquid phase will be entrained with the vapor phase, leading to flooding.  It's worth noting that the Souders-Brown equation is a simplified correlation and provides a conservative estimate of the flooding point.  In practice, engineers may apply safety factors or use more advanced models to refine the design and operation of distillation columns.

### Souders-Brown Equation

$$v = K \; \sqrt{ \rho_l - \rho_v \;/\; \rho_v }$$     (Souders-Brown Equation)

$$K = v \;/\; \sqrt{ \rho_l - \rho_v \;/\; \rho_v }$$

$$\rho_l = V^2 \; ( \rho_v \;/\; K^2 ) + \rho_v$$

$$\rho_v = \rho_l \;/\; ( v \;/\; K )^2 + 1$$

### Solve for v

 vapor velocity factor, K liquid density, ρl vapor density, ρv

### Solve for K

 max allowable vapor velocity, v liquid density, ρl liquid density, ρv

### Solve for ρl

 max allowable vapor velocity, v vapor density, ρv vapor velocity factor, K

### Solve for ρv

 liquid density, ρl max allowable vapor velocity, v vapor velocity factor, K

Symbol English Metric
$$v$$ = maximum allowable vapor velocity $$ft \;/\; sec$$ $$m \;/\; s$$
$$K$$ = vapor velocity factor $$dimensionless$$
$$\rho_l$$   (Greek symbol rho) = liquid density $$lbm \;/\; ft^3$$ $$kg \;/\; m^3$$
$$\rho_v$$   (Greek symbol rho) = vapor density $$lbm \;/\; ft^3$$ $$kg \;/\;m^3$$

K Factors for maximum allowable superficial velocity (API Spec 12J)

• Vertical separator  -  5 ft. high  -  K = 0.12 to 0.24
• Vertical separator  -  10 ft. high  -  K = 0.18 to 0.35
• Horizontal separator  -  10 ft. long  -  K = 0.40 to 0.50
• Horizontal separator  -  Other lengths L ft. long  -  K = 0.40 to 0.50 $$\left( \frac{L}{10}\right)^{0.56}$$
• Spherical separator  -  All  -  K = 0.2 to 0.35
$$dimensionless$$