Principal Investigator

At a Glance

Theoretical and laboratory-scale models for the characterization of CO2-inspired flow in porous mediahave led to analytical formulae for ready modeling of leakage in sequestration projects.


Research Highlight

The Stone Group has investigated a variety of subsurface fluid flow problems inspired by carbon dioxide (CO2 ) sequestration. In these applications it is critical to characterize the rates at which two fluid phases (e.g. supercritical CO2 and water) rearrange in a porous medium. The fluid dynamics will be influenced by confinement of the flowing fluids, and it is critical to model processes such as fluid injection, buoyancy-driven spreading, and leakage. In particular, leakage could occur from an edge (or crack) in the porous medium, or along a porous boundary; such modeled processes may be very useful to characterize leakage from underground sequestration sites. The research program’s models are inspired by the various processes relevant to field studies, and are simplified representations of large-scale numerical simulations common to industrial-scale studies. That said, the model has been refined in collaboration with Michael Celia, to more accurately approximate a field situation. This collaboration has benefitted both research groups and has been made possible by the unique research partnerships afforded by the CMI initiative. Figure 2.2 summarizes research results for confined configurations without leakage, as a phase diagram that describes how the shape of the fluid-fluid interface during fluid injection can vary with time (T is a dimensionless time, defined as the real time rescaled by a characteristic time for the fluid flow in the porous medium) for different ratios M of the displaced fluid to the injected fluid.

The Stone Group has made several new modeling contributions to the field of fluid flow in porous media, in particular analytical descriptions that practitioners may use to rapidly estimate spreading and/or leakage rates for geometries typical of many underground environments. Analytical descriptions provide simple formulae for important physical processes such as fluid spreading during or after a fluid injection process. Such results allow the inclusion of important physical parameters such as the fluid density and viscosity, the porosity and permeability of the porous medium (which help to characterize the resistance of the medium to flow), and leakage paths for the fluid into the surrounding matrix. Also, laboratory experiments have been performed to test the basic premises of the different models and to check the analytical predictions for spreading and leakage rates. The laboratory studies also provide a convenient platform for visualizing the kinds of dynamics envisioned as relevant for subsurface flow. The focus on confinement effects for various flow regimes may be relevant for the transport of fluids (e.g. CO2 , H2 O) in pipelines.

Figure 2.2. Flow regimes for fluid injection into a confined porous medium. Five distinct dynamical regimes are identified, depending on two dimensionless groups: M, the viscosity ratio of the displaced fluid to the injected fluid, and T, the dimensionless time. The regime boundaries are indicated by symbols (numerical estimates) and dashed curves (analytical estimates). Typical shapes of the fluid-fluid interface are also shown in each of the individual regimes1.

The results of this research provide analytical formulae for easy modeling of flow in underground reservoirs. These results can readily inform policy and regulatory frameworks by providing first order estimates for the leakage rate and the horizontal span of a CO2 sequestration project. The Stone group is planning to use this approach of analytical and laboratory-scale models of geophysical scientists at the Geophysical Fluid Dynamics Laboratory (GFDL) who currently utilize complex numerical simulations to model climate change and the dynamics of ice flow relevant to the Arctic. It is anticipated this alternative approach to the problem will lead to a synergistic collaboration with the GFDL.



  1. Zheng, Z., B. Guo, I.C. Christov, M.A. Celia, and H.A. Stone, 2015. Flow regimes for fluid injection into a confined porous medium. J. Fluid Mech., 767: 881-909. doi:10.1017/jfm.2015.68.