A numerical study of two-phase flow with dynamic capillary pressure using an adaptive moving mesh method

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a travelling wave ansatz and efficient numerical methods. The travelling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is paid to the non-monotonic profiles. The travelling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach

Upscaling of Relative Permeability to Minimise Numerical Dispersion

Imperial Users onl

Pierce Field-Improved Oil Recovery by Water Flood Optimisation in a Turbidite Reservoir

Imperial Users onl

Upscaling Low Salinity Waterflooding in Heterogeneous Reservoirs

Imperial Users onl

Relevance of analytical Buckley-Leverett solution for immiscible oil displacement by various gases

In order to generate the valid numerical simulation model, the sufficient amount of gathered data from the oil field is required. However, it is not always possible to acquire such data at the initial stage of project development. Buckley and Leverett (1942) developed the analytical solution allowing to assess the oil displacement efficiency. One of the main assumptions of this model is incompressibility of oil and injected fluid. For slightly compressible water and oil such assumption is rational. However, that is not always the case when the gas is injected. This research aims to identify the conditions at which the usage of the incompressible gas model is appropriate. Likewise, the cases when the model of compressible gas is required are also evaluated. To accomplish the goals of this research, the comparative analysis between the injection of compressible and incompressible gases was undertaken using the numerical solution of the correspondent reservoir engineering problem. The validation of the numerical model was undertaken showing that it matches the analytical Buckley-Leverett solution. The findings of this research indicate that the relative and absolute density change with the pressure of the injected gas has the profound impact on the convergence between two models under consideration. With the increase in the injection pressure, the discrepancy between the models of compressible and incompressible gas raises for all the considered injection fluids (CO2, CH4 and N2). Due to a steep slope of 'density-pressure' curve for CO2 at low initial reservoir pressure, the incompressible model cannot accurately predict the oil displacement efficiency by this gas at any reasonable injection pressure. All 1D results are also representative for 2D simulation. However, the mismatch between two models increases considerably for 2D simulation scenarios.Comment: 16 pages, 8 figure

Mathematical analysis, scaling and simulation of flow and transport during immiscible two-phase flow

Fluid flow and transport in fractured geological formations is of fundamental socio-economic importance, with applications ranging from oil recovery from the largest remaining hydrocarbon reserves to bioremediation techniques. Two mechanisms are particularly relevant for flow and transport, namely spontaneous imbibition (SI) and hydrodynamic dispersion. This thesis investigates the influence of SI and dispersion on flow and transport during immiscible two-phase flow. We make four main contributions. Firstly, we derive general, exact analytic solutions for SI that are valid for arbitrary petrophysical properties. This should finalize the decades-long search for analytical solutions for SI. Secondly, we derive the first non-dimensional time for SI that incorporates the influence of all parameters present in the two-phase Darcy formulation - a problem that was open for more than 90 years. Thirdly, we show how the growth of the dispersive zone depends on the flow regime and on adsorption. To that end we derive the first known set of analytical solutions for transport that fully accounts for the effects of capillarity, viscous forces and dispersion. Finally, we provide numerical tools to investigate the influence of heterogeneity by extending the higher order finite-element finite-volume method on unstructured grids to the case of transport and two-phase flow

Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces