SPH modelling and validation of multi-phase flows and sediment transport: application to the oil and gas industry

Abstract

Multi-phase flows are common in various industrial contexts, in particular in the oil and gas industry. In extraction and injection of oil and gas, multi-phase mixtures of oil, natural gas and water are piped between the reservoir and the surface. The complexity of these flows in gas pipelines increases with the presence of solid particles which can lead to losses in production due to equipment downtime or reduced inflow. A good understanding of fluid and flow mechanics and distribution may help to minimise this problem, restoring production to an economically sustainable level. High-fidelity predictive computational multi-phase methods have shown to be helpful both for understanding these complex phenomena and for optimising operational conditions in processes involving fluid-particle systems. Smoothed Particle Hydrodynamics (SPH) has been successfully extended to a variety of fluid-dynamic systems, overcoming the obstacles met by Eulerian Computational Fluid Dynamics (CFD) when dealing with a large range of length scales, coupling between phases, complex small scale physics and less than effective averaging techniques. Conventional SPH is a total Lagrangian meshless technique that tracks field variables (such as density, velocity and acceleration) obtained through approximating the governing equations discretised by a set of particles in the fluid domain. It features a remarkable flexibility in handling complex flow fields and in including physical effects (such as surface tension, multi-phase flows with density differences between the considered media and free-surface flows). The main objective of this project is to investigate numerical solutions for the specific context of oil and gas industry, purely through SPH, by implementing and validating multi-phase flow and advection models. The adopted solution for the first model is the implementation of Colagrossi and Landrin's (2003) multi-phase model and of a surface tension model based on the Continuum Surface Force (CSF) model first presented by Brackbill (1992) and adapted to SPH by Hu and Adams (2006). The major novelty concerning the present work is to be found within the second model, in which the sediment is modelled using a generalized advection equation between the fluid SPH particles for each considered granulometric category, following the general formulation presented by Krištof et al. (2009). For validation purposes, a number of multi-phase fluid flow and sediment transport test-cases is used together with analytical and other benchmark numerical solutions. The test cases include a theoretical surface tension case, the rising of an air bubble in water and the non-Boussinesq lock-exchange for the fluid-fluid system, ensuring that relevant multi-phase phenomena are correctly modelled. A set of sand dumping cases is considered for the validation of the proposed advection model (solid-fluid system). The results show that both models are accurate and capable of treating complex flow conditions found in oil and gas applications, such as interface phenomena related with multi-phase flows and sediment transport in fluid media. The implemented SPH formulation is yet extended to cases exploring other variables of the code within a similar context, using materials typically found in oil and gas systems, namely, a wet water-oil dam break, settling of sand in a water column and dam break with sand sediments. The considered applications adequately predict scenarios different from the ones considered in the validation process involving multi-phase systems, sediment motion and drift within a column of water.