The storage of carbon dioxide plays a fundamental role in our global effort to reduce the atmospheric concentration of greenhouse gases (GHG) and achieve our long-term climate goals. The pore space in sedimentary rocks could suffice to store all the CO2 removed from the air, making geological sequestration a promising carbon storage technology. Geological sequestration involves the injection of CO2 in either (dissolved) gas, liquid, or supercritical phase, into the pore space of subsurface rock formations, such as abandoned oil and gas reservoirs and saline aquifers. Once there, CO2 can become trapped due to a series of physical and/or chemical mechanisms, some relating directly to the pore scale, such as structural, residual, and mineral storage. To study these storage mechanisms, both a robust framework for the simulation of fluid flow at the pore scale and an accurate description of the pore scale geometry of the host rock, are required. In this work, we present the application of a cloud-based, pore-scale flow simulator to the study of CO2 storage in geological formations. The prototype technology comprises a cloud storage space that stores the high-resolution X-ray microtomography images of suitable rocks, a REST API that allows the submission of data processing and flow simulation jobs, and a web-based graphical user interface that facilitates the interaction with all the other components. We have used the tool to transform the rock pore space geometry into network of connected capillaries with spatially varying radii. This fined-grained capillary network representation of the rock is then used to perform single-phase flow simulations, which served accurately estimate the permeability of several sedimentary rocks with a range of morphologies as measured experimentally. Single phase simulation results have also been validated experimentally using a Si/SiO2-based microfluidic chip, fluorescent microbeads and high-speed optical imaging. We have then extended such simulation tool to account for multi-phase flow phenomena that is relevant for the study of the physical mechanisms behind residual storage and can be used for analyzing the infiltration and retention of CO2 inside a capillary network under varying fluid and rock parameters.