Trajectory analysis and design optimization of a horizontal oil-water separator: Role of hydrodynamic and dimensional parameters

Melouka Bellil , Menouer Bennaoum , Ali Bellil

Abstract

The treatment of oil-contaminated industrial wastewater remains a critical environmental and economic challenge. This study presents a comprehensive hydrodynamic analysis and design optimization of a horizontal oil-water separator, integrating an automated control system with a theoretical trajectory model for oil droplets. This study develops a mathematical model based on force balance (buoyancy versus drag) under laminar flow conditions to predict droplet trajectories as functions of key hydrodynamic and dimensional parameters: droplet radius, inlet velocity, separator diameter, mass flow rate, and Reynolds number. The model yields explicit expressions for terminal rise velocity, rise time, residence time, and minimum required separator length. Parametric analysis reveals that smaller droplets (50 µm) dictate design requirements: at an inlet velocity of 0.005 m/s, a separator of radius 1.0 m requires a minimum length of 4.55 m to achieve complete separation, corresponding to a residence time of approximately 15 minutes. A critical mass flow rate of 0.5 kg/s is identified, below which buoyancy dominates and above which horizontal advection compromises efficiency. To maintain laminar conditions (Re < 2300), inlet velocity must not exceed 0.015 m/s for a 1.0 m diameter separator. The theoretical length-to-diameter ratio for the design droplet is approximately 2.3; applying a safety factor of 1.5–2.0 yields practical ratios of 3.4–4.6, aligning with industry standards (3:1 to 5:1). Quantitative design guidelines are summarized, including recommendations for separator diameter (≥1.0 m), maximum inlet velocity (≤0.015 m/s), and separator compartment sizing.

Key Words

hydrodynamic modeling; oil-water separator; parametric study; trajectory analysis; wastewater

Address

Melouka Bellil — Faculty of Nature and Life Sciences, Mustapha Stambouli University of Mascara, 305 Mamounia Road, Mascara, Algeria/ Faculty of Sciences and Technology, Mustapha Stambouli University of Mascara, 305 Mamounia Road, Mascara, Algeria
Menouer Bennaoum — Faculty of Sciences and Technology, Mustapha Stambouli University of Mascara, 305 Mamounia Road, Mascara, Algeria
Ali Bellil — Department of Chemical Engineering, Faculty of Chemistry, University of Sciences and Technology of Oran-MB, El Mnaouar, 1505, Bir ElDjir, Oran, Algeria

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