The combined influence of gravity, flow rate and small scale heterogeneity on core-scale multiphase flow of CO₂ and brine [electronic resource]
Keywords: Energy Resources Engineering

The purpose of the research is to understand and predict the combined influences of viscous, gravity and capillary forces in heterogeneous rocks over the range of conditions relevant to storage of CO2 in deep underground geological formations. The study begins by quantifying the separate and combined influences of flow rate, gravity, and sub-core capillary heterogeneity on brine displacement using the 3-D simulator TOUGH2 (Kuo et al. 2010). These studies demonstrate that the average saturation depends on the capillary and gravity numbers in a predictable way. Based on the insight gained from numerical simulation, this work develops an approximate semi-analytical solution for predicting the average steady-state saturation during multiphase core flood experiments over a wide range of capillary and gravity numbers as well as a wide range of heterogeneity. Although computational technology has improved greatly, running high-resolution 3D models including capillarity, gravity, and capillary heterogeneity still takes a significant amount of computational effort. The new solution provided here is a quick and easy way to estimate the flow regimes for horizontal core floods. A two dimensional analysis of the governing equations for the multiphase flow system at steady-state is used to develop the approximate semi-analytical solution. We have developed a new criterion to identify the viscous-dominated regime at the core scale where the average saturation is independent of flow rate. Variations of interfacial tension, core permeability, length of the core, and the effects of buoyancy, capillary and viscous forces are all accounted for in the semi-analytical solutions. We have also shown that three dimensionless numbers (NB, Ngv, Rl) and two critical gravity numbers (Ngv, c1, Ngv, c2) are required to properly capture the balance of viscous, gravity, and capillary forces. There is good agreement between the average saturations calculated from the 3-D simulations and the analytical model. This new model can be used to design and interpret multiphase flow core-flood experiments, gain better understanding of multiphase flow displacement efficiency over a wide range of conditions and for different fluid pairs, and perhaps even provide a tool for studying the influence of sub-grid scale multiphase flow phenomena on reservoir-scale simulations. One practical application for the new semi-analytical solution is to help design and interpret core flood experiments, including assuring that relative permeability measurements are made in the viscous dominated regime, evaluating potential flow rate dependence, influence of core-dimension on a multiphase flow experiments, and influence of fluid properties on the experiments. New guidelines and suggestions for making relative permeability measurements are presented. Results are based on a combination of high resolution of 3D simulations and core-flooding experiments with X-ray CT scanning of saturation distributions. Effects of flow rate, permeability, surface tension, core length, boundary conditions, sub-core scale heterogeneity, and gravity over a range of fractional flows of CO2 are systematically investigated. Synthetic "data sets" are generated using TOUGH2 and subsequently used to calculate relative permeability curves. A comparison between the input relative permeability curves and "calculated" relative permeability is used to assess the accuracy of the "measured" values. Results show that for a modified capillary number (Ncv=kLpc*A/H2[mu]CO2qt) smaller than 15, flows are viscous dominated. Under these conditions, saturation depends only on the fractional flow and is independent of flow rate, gravity, permeability, core length and interfacial tension. For modified capillary numbers less than 15, accurate whole-core relative permeability measurements can be obtained regardless of the orientation of the core and for a high degree of heterogeneity under a range of relevant and practical conditions. Importantly, the transition from the viscous to gravity/capillary dominated flow regimes occurs at much higher flow rates for heterogeneous rocks. For modified capillary numbers larger than 15, saturation gradients develop along the length of the core and accurate relative permeability measurements are not obtained using traditional steady state methods. However, if capillary pressure measurements at the end of the core are available, or can be estimated from independently measured capillary pressure curves and the measured saturation at the inlet and outlet of the core, accurate relative permeability measurements can be obtained even when there is a small saturation gradient across the core.