API Oil-Water Separator

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 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:

$R$	3	6	10	15	20
$F$	1.28	1.37	1.52	1.64	1.74

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

Parameter	Default units	Description
Flow rate ( $Q$ )	m³/s	Wastewater volumetric flow rate through the separator.
Water viscosity ( $\mu$ )	Pa·s	Dynamic viscosity of the water phase (default $0.001$ Pa·s).
Water density ( $\rho_w$ )	kg/m³	Density of water (default $1000$ kg/m³).
Oil density ( $\rho_o$ )	kg/m³	Density of oil (default $900$ kg/m³).
Channel width ( $B$ )	ft	Width of each separator channel (default $10$ ft).

Outputs

Parameter	Default units	Description
Oil droplet rise rate ( $v_t$ )	ft/s	Terminal rise velocity of oil droplets.
Horizontal velocity ( $v_h$ )	ft/s	Adopted average horizontal flow velocity.
Cross-sectional area ( $A_c$ )	ft²	Required separator cross-sectional area.
Channel depth ( $d$ )	ft	Depth of each separator channel.
Separator length ( $L$ )	ft	Required separator length.
Number of channels ( $n$ )	–	Number of parallel separator channels.

Calculations

API Oil-Water Separator

Input data

Flow rate (Q)

Water viscosity

Water density

Oil density

Channel width (B)

Output data

Oil globules rise rate

Horizontal velocity

Cross-sectional area

Channel depth (d)

Separator length (L)

Number of separator channels