Flow in Porous Media

Numerical Modeling of Fluid-Injection-Induced Shear Failure

Geothermal reservoir simulation represents a multi-physics problem involving for example fluid flow interacting with geomechanics. In this project, a numerical modeling framework is developed, which is suited to study induced seismicity due to reservoir operation. Both shear failure, due to fluid injection into fractured reservoirs [external pageDeb and Jenny 2017call_made], as well as the microseismic effect of fracture-aperture changes are modeled. The flow problem is solved for both fractures and porous damaged matrix. A grid- and timestep-independent numerical method was developed for flow and mechanical failure in fractured reservoirs [external pageDeb and Jenny 2017call_made and external page2020call_made]. Read more

Simulation of Fractured Geothermal Reservoirs

This is an interdisciplinary collaboration with various earth scientists from ETH Zürich. In the context of geothermal power production, Karvounis, Hajibeygi, and Jenny [external page2011call_made and external page2016call_made] have created a modeling framework for flow and transport in fractured porous media. It has proper interfaces which allow to interfere with rock mechanics and rock chemistry models. Moreover, everything is coupled with heat conduction in the rock. Due to the very large number of fractures, only the large ones are resolved. The cloud of small fractures is treated by effective permeabilities.

In a second collaborative effort involving Prof. Stephan Matthai (University of Melbourne), the uncertainty in the reservoir or more precisely the highly conductive fractures is addressed. To this end, we start from an ensemble of prior reservoir scenarios or realizations and update their parameters based on pressure and flow rate measurements becoming available over time during the stimulation-phase of a geothermal reservoir. For parameter updates, we use the ensemble Kalman filter (EnKF) methodology. After the initial stimulation phase, EnKF parameter updates are continued by using tracer measurements leading eventually to a posterior ensemble with significantly reduced parameter uncertainties [external pageLiem and Jenny 2020call_made].

Uncertainty Assessment of Flow and Transport in Porous Media

The transport of chemical substances in the subsurface is relevant in many different applications. For example, for the assessment of nuclear waste deposition sites or for the coordination of remediation actions after a contamination hazard, predictive simulation tools are required. These tools have to account for the uncertainty in the soil parameters, since measurements of the subsurface structure are typically very scarcely available. The main goal is to develop a simulation framework for tracer flow and transport that provides probabilistic information about local tracer concentration evolutions.

In this context, a probability density function (PDF) method was developed together with Prof. Hamdi Tchelepi (Stanford University) that is applicable for highly heterogeneous porous media [Meyer, Tchelepi, and Jenny external page2010acall_made, external page2010bcall_made, and external page2013call_made, external pageMeyer and Saggini 2016call_made, external pageDünser and Meyer 2016call_made, and Meyer external page2017call_made and external page2018call_made]. It accounts for advective transport, pore-scale dispersion, and can incorporate upscaled chemical fluid-phase reactions. Read more

Moreover, in a collaborative effort with Prof. Christoph Schwab and Prof. Siddhartha Mishra (both SAM, ETHZ), a multi-level Monte Carlo method has been developed, which allows to combine expensive high fidelity methods with cheap approximate solvers to achieve output statistics more efficiently [Müller, Jenny, and Meyer external page2013call_made, external page2014call_made, and external page2016call_made]. Furthermore, Müller, Jenny, and Meyer [external page2011call_made] have devised a combined polynomial-chaos/Monte Carlo method for transport uncertainty quantification.

Prediction of Non-Equilibrium Multi-Phase Flow

Currently, storing CO₂ in geological sub-surface formations seems to be one of the most promising feasible technologies to stabilize the CO₂ concentration in the Earth’s atmosphere. The prime objective of our research is to improve our understanding of how the physics and dynamics at the pore scales is linked to the macroscopic equations, which deal with average values. Therefore we have devised a new Lagrangian framework, which facilitates the formulation of models for sub-Darcy-scale physics [external pageTyagi et al. 2008call_made] and [Tyagi and Jenny external page2011acall_made and external page2011bcall_made].

At the pore scale, Khayrat and Jenny [external page2016call_made, external page2017acall_made, and external page2017bcall_made] have developed simulation capabilities and a sub-phase modeling approach both providing a better understanding of pore-scale multi-phase dynamics.

Multi-Scale Modeling

This is a collaboration with Dr. Seong Lee (Chevron). One of the major challenges in macroscopic simulations is the correct treatment of complex permeability distributions with strong variations and many length scales. To deal with this issue, various upscaling and multi-scale methods have been developed. In collaboration with the company Chevron we devised and developed a new multi-scale finite-volume (MSFV) algorithm, which has several advantageous properties compared with previous multi-scale methods [Jenny, Lee, and Tchelepi external page2003call_made and external page2006call_made], [external pageTchelepi et al. 2007call_made], [external pageLunati et al. 2011call_made] and [external pageHajibeygi and Jenny 2011call_made]. The MSFV method allows for very efficient studies of realistic multi-phase flow scenarios in heterogeneous porous media.

Cortinovis and Jenny [external page2014call_made] have investigated how the robustness with regard to permeability contrast/variance can be improved by an appropriate enrichment of the coarse space.