Development of a Theoretical Framework for Multi-Scale Modelling of Crude Oil Wax Deposition in Sub-Ambient Temperature Offshore Pipeline Systems in Nigeria

Wax deposition in offshore pipeline systems operating in the deep-water Niger Delta at sub-seabed temperatures represents one of the most technically complex flow assurance challenges confronting Nigerian petroleum production, yet available theoretical frameworks inadequately capture the coupled thermodynamic, rheological, and transport phenomena operating across molecular to pipeline scales. This study develops a multi-scale theoretical framework for wax deposition that integrates molecular dynamics simulation of wax crystallisation nucleation, mesoscale population balance modelling of wax crystal growth, and continuum-scale computational fluid dynamics simulation of coupled heat and mass transfer with deposition and aging in offshore pipeline geometries representative of deep-water Niger Delta fields. Molecular dynamics simulations using LAMMPS with a united-atom force field were used to determine wax crystal nucleation rates and surface energy parameters as functions of crude oil composition. These parameters informed a population balance model for crystal size distribution evolution, implemented in gPROMS. The continuum pipeline model incorporated the Matzain deposition sub-model modified with population balance-derived crystal parameters, implemented in OpenFOAM. The multi-scale framework was validated against experimental deposition data from a cold finger apparatus using two Niger Delta waxy crude oils. Predictions of deposition rate and deposit composition agreed with experimental measurements within 12% across all tested conditions. The study establishes a high-fidelity, theoretically grounded multi-scale wax deposition prediction tool with direct relevance to flow assurance engineering for Nigerian deep-water petroleum production. Keywords: wax deposition, multi-scale modelling, offshore pipeline, flow assurance, Niger Delta