Carrousel Extractor Operation Parameters

Reference ID: MET-DF9C | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

The carrousel extractor is a critical unit operation in the oilseed processing industry, designed for the continuous, countercurrent extraction of oil from solid flakes using a solvent, typically hexane. The system utilizes a rotating bed divided into discrete segments, allowing for a staged extraction process that maximizes mass transfer driving forces.

In process engineering, calculating the operational parameters of a carrousel extractor is essential to ensure that the solid residence time, solvent-to-solid ratio, and percolation rates remain within optimal bounds. Proper sizing prevents common operational failures such as bed flooding, insufficient extraction recovery, or mechanical stress due to improper rotation speeds. This reference sheet provides the mathematical framework for determining these parameters under steady-state, isothermal conditions.

Methodology & Formulas

The following formulas define the operational characteristics of the extractor based on mass balance and fluid dynamics principles.

1. Solid Throughput and Segment Volume
The segment volume V_seg is determined by the required solid mass flow rate ṁ_s, the bulk density of the solids ρ_bulk, the rotation speed N, and the total number of segments n_seg:

\[ V_{\text{seg}} = \frac{\dot{m}_{s}}{\rho_{\text{bulk}} \cdot \left(\frac{N}{60}\right) \cdot n_{\text{seg}}} \]

2. Solvent Flow and Percolation Velocity
The volumetric solvent flow rate Q_liq is derived from the mass flow of solvent ṁ_liq, which is calculated using the liquid-to-solid ratio (L/S). The percolation velocity v_perc is then determined by the cross-sectional area of the bed A_bed:

\[ Q_{\text{liq}} = \frac{\dot{m}_{s} \cdot (L/S)}{\rho_{\text{liq}}} \] \[ v_{\text{perc}} = \frac{Q_{\text{liq}}}{A_{\text{bed}}} \]

3. Pressure Drop and Hydrostatic Head
To prevent flooding, the pressure drop ΔP across the bed, calculated via Darcy's Law, must be less than the available hydrostatic head P_hydro provided by the liquid column of height h_bed:

\[ \Delta P = \frac{\mu \cdot v_{\text{perc}} \cdot h_{\text{bed}}}{K} \] \[ P_{\text{hydro}} = h_{\text{bed}} \cdot \rho_{\text{liq}} \cdot g \]

4. Extraction Recovery
The theoretical recovery R for a multi-stage extraction is estimated using the stage efficiency η and the total number of segments n_seg. Note that this simplified model assumes each stage contacts the solids with solvent of negligible solute concentration (cross-current approximation), providing a conservative estimate suitable for preliminary design:

\[ R = 1 - (1 - \eta)^{n_{\text{seg}}} \]

Operational Validity Criteria

Parameter	Constraint / Regime
Rotation Speed (N)	0.5 RPM ≤ N ≤ 5.0 RPM
Percolation Rate (v_perc)	5.0 m/h ≤ v_perc ≤ 40.0 m/h
Flooding Condition	ΔP < P_hydro
Recovery Target	R ≥ R_min

To maintain peak performance, process engineers should focus on the following key parameters:

Liquid-to-solid ratio to ensure complete extraction.
Cell rotation speed, which dictates the residence time of the material.
Bed permeability, monitored via pressure drop across the extraction bed.
Temperature profile of the solvent to maintain optimal viscosity and solubility.

If residual oil levels spike, perform the following diagnostic steps:

Verify the solvent flow rate to ensure it has not dropped below the setpoint.
Inspect the drainage screens for potential blinding or fouling.
Check the particle size distribution of the incoming feed, as excessive fines can impede solvent percolation.
Confirm that the solvent temperature is within the specified operating range to prevent channeling.

The bed height is critical for maintaining a consistent percolation rate. If the bed is too high, you risk excessive pressure drop and potential flooding. If the bed is too low, the solvent may bypass the material, leading to poor extraction efficiency and high solvent carryover. Always maintain the bed height within the design specifications to ensure uniform solvent distribution.

Worked Example: Carrousel Extractor Operation Parameters

A continuous carrousel extractor with 10 rotating segments is used to recover oil from soybean flakes using hexane at 60°C. The system operates under steady-state, isothermal conditions, with plug flow of solids and countercurrent liquid flow. The goal is to determine key operating parameters for a solid throughput of 1200 kg/h, using a rotation speed of 0.667 RPM, a bed area of 0.3 m², a bed height of 0.24 m, and a liquid-to-solid ratio of 1.0. Note that the recovery estimate uses a simplified cross-current stage model (see Methodology).

Knowns (Input Parameters and Units):

Number of segments: \( n_{\text{seg}} = 10 \)
Bulk density of solids: \( \rho_{b} = 550.0\ \text{kg}\cdot\text{m}^{-3} \)
Liquid density: \( \rho_{l} = 650.0\ \text{kg}\cdot\text{m}^{-3} \)
Dynamic viscosity: \( \mu = 3.0 \times 10^{-4}\ \text{Pa}\cdot\text{s} \)
Permeability: \( K = 1.0 \times 10^{-10}\ \text{m}^{2} \)
Gravitational acceleration: \( g = 9.81\ \text{m}\cdot\text{s}^{-2} \)
Stage efficiency: \( \eta = 0.3 \)
Solid throughput: \( \dot{m}_{s,\text{in}} = 1200\ \text{kg}\cdot\text{h}^{-1} \)
Rotation speed: \( N = 0.667\ \text{RPM} \)
Bed cross-section area: \( A_{b} = 0.3\ \text{m}^{2} \)
Bed height: \( h_{b} = 0.24\ \text{m} \)
Liquid-to-solid ratio: \( L/S = 1.0 \)

Step-by-Step Calculation:

Convert solid throughput to consistent SI units:
\[ \dot{m}_{s} = \frac{\dot{m}_{s,\text{in}}}{3600} = \frac{1200}{3600} = 0.333\ \text{kg}\cdot\text{s}^{-1} \]
Determine segment volume: The segment volume is the active volume occupied by solids in one cell. Using the throughput, rotation speed, and number of segments:
\[ V_{\text{seg}} = \frac{\dot{m}_{s}}{\rho_{b} \cdot \left(\frac{N}{60}\right) \cdot n_{\text{seg}}} = \frac{0.333\ \text{kg}\cdot\text{s}^{-1}}{550\ \text{kg}\cdot\text{m}^{-3} \cdot \left(0.667\ \text{RPM} / 60\right) \cdot 10} = 5.452 \times 10^{-3}\ \text{m}^{3} \] Rounded to three decimal places: \( V_{\text{seg}} = 0.005\ \text{m}^{3} \).
Compute solvent mass flow: With an overall liquid-to-solid ratio of 1.0,
\[ \dot{m}_{l} = \dot{m}_{s} \cdot \frac{L}{S} = 0.333\ \text{kg}\cdot\text{s}^{-1} \cdot 1.0 = 0.333\ \text{kg}\cdot\text{s}^{-1} \]
Convert solvent mass flow to volumetric flow:
\[ Q_{l} = \frac{\dot{m}_{l}}{\rho_{l}} = \frac{0.333\ \text{kg}\cdot\text{s}^{-1}}{650\ \text{kg}\cdot\text{m}^{-3}} = 5.128 \times 10^{-4}\ \text{m}^{3}\cdot\text{s}^{-1} \]
Calculate percolation velocity: The superficial velocity of liquid percolating through the bed is
\[ v_{\text{perc}} = \frac{Q_{l}}{A_{b}} = \frac{5.128 \times 10^{-4}\ \text{m}^{3}\cdot\text{s}^{-1}}{0.3\ \text{m}^{2}} = 1.709 \times 10^{-3}\ \text{m}\cdot\text{s}^{-1} \] Express in metres per hour for empirical comparison:
\[ v_{\text{perc},h} = v_{\text{perc}} \cdot 3600 = 6.154\ \text{m}\cdot\text{h}^{-1} \]
Determine pressure drop across the bed (Darcy's law):
\[ \Delta P = \frac{\mu \cdot v_{\text{perc}} \cdot h_{b}}{K} = \frac{(3.0 \times 10^{-4}\ \text{Pa}\cdot\text{s}) \cdot (1.709 \times 10^{-3}\ \text{m}\cdot\text{s}^{-1}) \cdot 0.24\ \text{m}}{1.0 \times 10^{-10}\ \text{m}^{2}} = 1230.769\ \text{Pa} \]
Compute hydrostatic head of the liquid bed:
\[ P_{\text{hyd}} = h_{b} \cdot \rho_{l} \cdot g = 0.24\ \text{m} \cdot 650\ \text{kg}\cdot\text{m}^{-3} \cdot 9.81\ \text{m}\cdot\text{s}^{-2} = 1530.360\ \text{Pa} \]
Estimate overall recovery (simplified cross-current stage model): Using an empirical stage efficiency of 30%, the recovery after 10 stages is
\[ R = 1 - (1 - \eta)^{n_{\text{seg}}} = 1 - (0.7)^{10} = 1 - 0.028 = 0.972 \] (Displayed as 0.972, from exact value 0.971752)

Final Answer:

The calculated operating parameters for the carrousel extractor, using the given inputs, are:

Segment volume: \( V_{\text{seg}} = 0.005\ \text{m}^{3} \)
Solvent mass flow: \( \dot{m}_{l} = 0.333\ \text{kg}\cdot\text{s}^{-1} \)
Volumetric solvent flow: \( Q_{l} = 5.128 \times 10^{-4}\ \text{m}^{3}\cdot\text{s}^{-1} \)
Percolation velocity: \( v_{\text{perc}} = 1.709 \times 10^{-3}\ \text{m}\cdot\text{s}^{-1} \) (equivalent to \( 6.154\ \text{m}\cdot\text{h}^{-1} \))
Pressure drop: \( \Delta P = 1230.769\ \text{Pa} \) (below the hydrostatic head of \( 1530.360\ \text{Pa} \), ensuring no flooding)
Expected oil recovery: \( R = 0.972 \) (97.2%)

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle

Carrousel Extractor Operation Parameters

Introduction & Context

🚀 Skip the Manual Math!

Methodology & Formulas

Operational Validity Criteria

Worked Example: Carrousel Extractor Operation Parameters