Multiphase Flow in Fractures: Co-Current and Counter-Current Flow in a Fracture

Abstract

Abstract Multiphase flow through fractures is important not only for naturally fractured petroleum reservoirs but also for underground disposal of radioactive waste and geothermal hydrotransport, cap rock integrity, as well as underground water and aquifer flow. For instance, naturally fractured reservoirs located in Northern Alberta contain large quantities of heavy oil and bitumen. It still remains unclear how multiple phases flow in fractures and how to determine the relative permeability of each phase that can be used in reservoir simulators. In typical practice, simulation of fractured reservoirs uses, in general, very crude and unproven hypotheses such as linear relative permeability curves. However, by using inaccurate relative permeability curves, large errors of the predicted oil recovery can result. In this work, a relatively simple flow model is derived to determine analytic functions for the relative permeability curves versus phase saturation in a single fracture. The results show that relative permeability is not just a function of the fluid saturations but also of the fluid properties and flow pattern within the fracture itself. The analysis reveals that at certain viscosity ratios and flow pattern conditions, the relative permeability of one phase can exceed unity owing to lubrication effects. The available experimental data confirms the validity of the proposed model. Introduction Fracture-dominated flow is not only important for naturally fractured petroleum reservoirs but also for underground disposal of radioactive waste, geothermal hydrotransport, cap rock integrity, and underground water and aquifer flow. In naturally fractured reservoirs, fractures are highly conductive flow pathways that dominate fluid transport throughout the reservoir. To examine flow of multiphase flow in fractures, many different experimental(1-12), theoretical(13-18) and numerical studies(19-26) have been done. However, flow structure and momentum transfer between flowing phases in fractures are not yet well understood(4, 27, 28). Transport parameters such as relative flow rates of phases and the relationship between fracture geometry and flow remain unclear. The relative permeability concept can be used to describe behaviour of multiple phases flowing together through porous media, interfering and aiding each other to move under the action of a pressure gradient. Despite the importance of relative permeability in fracture flows, still there is no unique and consistent theory which provides an easy, yet computationally inexpensive, method to calculate relative permeability curves in fractures.