Description

Design an API 421 oil–water separator (rectangular gravity separator) by estimating the oil droplet rise velocity (Stokes’ law), defining a conservative horizontal velocity, and sizing the cross-sectional area, number of channels, channel depth, and separator length, according to API 421 hydraulic and geometric recommendations.

API 421 oil–water separator

Calculation basis

Oil droplet rise (terminal) velocity (Stokes regime):

$$ v_t = \frac{g}{18\mu}(\rho_w - \rho_o)D^2 $$

Where:

• $g$ is gravity
• $\mu$ is the water dynamic viscosity
• $\rho_w$ is water density
• $\rho_o$ is oil density
• $D$ is the oil droplet diameter

The calculation assumes a fixed design droplet diameter:

$$ D = 150\mu\text{m} = 0.015 \times 10^{-2}\text{m} $$

Horizontal velocity selection

A preliminary horizontal velocity is defined as:

$$ v_h^* = 15 v_t $$

This velocity is then limited to a maximum of 3 ft/min, following API-style conservative practice. The resulting value $v_h$ is used for all subsequent calculations.

Geometry sizing

Cross-sectional flow area:

$$ A_c = \frac{Q}{v_h} $$

Number of channels (each channel limited to 160 ft²):

$$ n = \left\lceil \frac{A_c(\text{ft}^2)}{160} \right\rceil $$

Channel depth:

$$ d = \frac{A_c}{Bn} $$

Separator length:

• Velocity ratio: $$ R = \frac{v_h}{v_t} $$

• Turbulence factor $F$ obtained by linear interpolation from API 421:

• Separator length: $$ L = F \cdot R \cdot d $$

API 421 recommendation checks (warnings)

Warnings are issued when values fall outside API 421 typical guidance:

• Channel width: $6 \le B \le 20$ ft
• Channel depth: $3 \le d \le 8$ ft
• Depth/width ratio: $0.3 \le d/B \le 0.5$
• Length/width ratio: $L/B > 5$
• Velocity ratio range: if $R$ is outside $[3,20]$, adopt $F = 1.28$ or $F = 1.74$

Inputs

Outputs