In the oil and gas industry, it is crucial that the transport of hydrocarbons through long pipelines occurs in the most efficient and safest way. These pipelines can cover up to several tens to hundreds of kilometres. Hydrocarbons are not the only fluids present within the pipelines, often they are filled with a mixture of oil, gas, water and even sand particles. The flow phenomena associated with this multiphase mixture complicate the transport operations of the industry. The operations covered in the present study are: flushing, batch transport and hydrate inhibition.% in which is focussed on the physical challenges on.

Simulation techniques exist to reproduce the multiphase flow phenomena. However, three-dimensional Computational Fluid Dynamics (CFD) models require very much computational power and the one-dimensional two-fluid models, such as OLGA and COMPAS, are not capable of capturing all involved flow phenomena. The goal of the present study is to develop a one-dimensional model of high accuracy to reproduce miscible fluid-fluid displacements in long pipelines, in which the focus is on the displacement within the aqueous phase of a multiphase mixture. The model must be able to reproduce slip velocities and gravity currents within this aqueous phase without solving the momentum equations. Furthermore, the model must account for turbulent dispersion, mass transfer, pipeline inclination and differences in thermodynamic properties of the fluids.

Two virtual regions are created in the model in which both fluids can be present. The upper region is associated with the less dense fluid and the lower region is related to the denser fluid. The mass of the regions is tracked by a mass conservation equation. To account for the changes in the concentrations of the fluids in the regions two advection-diffusion equations are solved. These three equations are coupled by exchange terms. The velocity variables are solved by a slip relation between the regions and by a velocity equation derived from the incompressibility condition. All equations are cross-sectionally averaged to ensure the one-dimensionality of the model. To reproduce the appropriate slip interface between the regions several slip relation functions are derived. An empirical relation for the turbulent axial dispersion is implemented in the advection-diffusion equations of the two regions.

The one-dimensional miscible fluid-fluid displacement model is discretised by employing a finite volume method on a staggered grid, by using the Crank-Nicolson time integration and different schemes for the advective terms. The diffusion terms are discretised by the central approximation method. The flow variables are solved by a coupled approach using Picard's method to linearise the nonlinear terms. Moreover, the possibilities of applying Newton's method for linearisation have also been studied. The model is validated by comparing the flow solution of a single-phase advection-diffusion equation to the analytical solution of a turbulent diffusion equation. Even the flow solutions obtained on relatively coarse grids turn out to be of high accuracy.

By simulating miscible fluid-fluid displacement cases it is shown that the model is able to reproduce slip velocities and gravity currents under different circumstances. A linear empirical relation for the volumetric transfer terms is derived by matching the numerical simulation results to experimental results and to CFD results of a specific miscible fluid-fluid displacement case. The CFD results were also obtained as a part of this study; thereto the Fluent CFD package was applied. The CFD results were also used to obtain the exchange terms in the one-dimensional flow model.