Multiscale Upscaling Procedure of Carbon Dioxide Injection with Capillary Heterogeneity Effects

Advisor

Sally M. Benson

Abstract

In the context of CO₂ storage and sequestration, several studies have observed variations in the saturation distributions during multiphase flow from the sub-core to the meter scale, attributed to capillary heterogeneities. These heterogeneities consist of spatial variations in porosity and permeability, or, due to the Leverett J-function scaling, spatial variation of the capillary pressure-saturation relationship. Usually ignored in viscous dominated flow, they play a critical role in CO₂-brine flow where capillary and gravity effects dominate, due to the low flow rates that characterize these processes, and the low viscosity of CO₂. Our objective is to develop an analytical and numerical framework that accounts for the effect of capillary heterogeneities at sub core scale to further include them in large-scale simulations of carbon dioxide injection into deep saline aquifer. We demonstrate the ability of the Stanford General Purpose Research Simulator (GPRS) to accurately model immiscible two-phase flow in the presence of capillary heterogeneity. The results from GPRS are compared to existing semi-analytical solutions.

Because reservoir scale simulations that include fine-scale capillary heterogeneity effects are computationally expensive, the use of upscaling technique to reduce the computational cost appears natural. However, a one-stage upscaling that includes global information on the flow requires a fine-scale global simulation, which is not a tractable problem. For this reason, we develop in this work a multistage upscaling procedure for two-phase flow with strong capillary heterogeneity effects. This procedure is applicable to the carbon dioxide injection phase of a storage project, which is a drainage process where initially water-filled pores become partially filled with CO₂. The first stage consists of a local steady-state upscaling method that averages properties from the fine-scale to the core scale. The second stage is a global dynamic upscaling procedure that proceeds from the core scale to the reservoir scale. The method involves the calculation of upscaled capillary pressure in the capillary limit along with dynamically upscaled relative permeability functions. In the second stage, upscaled single phase flow functions, such as transmissibility and well index, are also computed using a global upscaling method.

This multistage procedure is applied to a two-dimensional heterogeneous system where CO₂ is injected into a brine-filled reservoir at different injection rates. The accuracy of the upscaling procedure is assessed by comparing intermediate-scale simulation results with coarse-scale results generated using both the dynamic upscaling procedure and a simpler approach with no capillary pressure and fine-scale relative permeability curves. The dynamic global upscaling method for the second stage is shown to give better results, that is to say closer to the fine-scale simulation results and hence more accurate than the simpler method. It manages to capture the capillary heterogeneity effects in terms of the fractional flow at the producer, and the velocity and shape of the front displacement. In addition, the robustness of the procedure is evaluated by conducting simulations with and without gravity effects. It is shown that reasonably accurate coarse models, in terms of speed and shape of the front displacement, could be generated for gravity examples by computing upscaled properties from fine-scale simulations without gravity effects.