Solute transport is relevant to several applications such as groundwater remediation and CO₂ storage in the subsurface as well as drug delivery in microfluidic devices. We have developed pore network models that can simulate transport in the presence or absence of chemical reactions. Network models are a class of microscale models that are approximate in nature. Their approximation is reflected in a simplified representation of the microstructure and the physics. As a result, network computations are very fast, often by orders of magnitude compared to higher fidelity methods (e.g., CFD). However, they are not always reliable as they cannot estimate or control prediction errors. Traditional network models of solute transport can incur large errors, which tend to be highest when molecular diffusion is weak. Our networks overcome such limitations through a mathematical reformulation of the governing equations and a more accurate geometric representation of the microstructure. While the ability to estimate or control errors remains elusive (inherent to all pore networks), we have established empirical error bounds that ensure reliable application of the networks to new problems. Compared to high-fidelity CFD, our network models yield predictions within 10% error at O(10^3-4) times the speed, openning the door to rapid engineering and control of solute transport in porous media.

References: Mehmani & Tchelepi (2017), Oostrom, Mehmani, et al. (2016), Mehmani & Balhoff (2015a), Mehmani & Balhoff (2015b), Yang, Mehmani, et al. (2015), Mehmani & Balhoff (2014)

Simulation of mechanical deformation in a fractured domain (Mehmani et al, 2021a)

Contacts are ubiquitous in porous materials. At large scales, contacts appear as internal surfaces of discontinuity, or fractures, within a porous medium often described as a continuum. At small scales, contacts take the form of microcracks or fissures between individual grains or minerals making up the porous medium. In subsurface applications, contacts provide preferential flow paths for in-situ fluids, which can either boost energy recovery (e.g., geothermal) or pose leakage risks for sequestered waste (e.g., nuclear, CO₂). In batteries, contacts or cracks reduce the device lifespan by inhibiting the flow of charge through the electrodes. Computational models provide a reliable way to engineer these systems, but the underlying mathematical equations pose significant numerical challenges. Our goal is to design new discretization schemes and linear/nonlinear solvers that can rapidly and robustly solve these equations. The implications extend to a wide range of problems and scales where contacts and fractures are important.

References: Mehmani et al. (2021a), Mehmani et al. (2021b)

Ostwald ripening is the process by which isolated, partially miscible bubbles exchange mass with each other via molecular diffusion through the surrounding wetting phase. The force that drives this diffusion is the gradient in the capillary pressure of bubbles. In a bulk fluid, wherein bubbles are spherical, all bubbles merge into one big bubble due to ripening. Whereas in a porous medium, bubbles evolve towards a new distribution with different bubble shapes and sizes than their initial distribution. Such evolution dynamics become even more complicated when the initial bubble population exhibits a heterogeneous composition (e.g., CO₂ and H₂ in underground hydrogen storage). Our goal is to develop computational models and macroscopic theories, validated against experiments conducted by our collaborators, to understand multi-componenet Ostwald ripening and the effects it has on the hydraulic properties and storage capacity of a porous material. The implications are relevant to subsurface CO₂ sequestration, underground H₂ storage, and the optimal design of electrolizers and fuel cells where oxygen/water management are important design and operational considerations.

References: Xu, Mehmani et al. (2019), Wang, Mehmani, Xu (2021), Mehmani & Xu (2022), Mehmani & Xu (2022), Yu et al. (2022), Bueno, Ayala, Mehmani (2023)

Hybrid computing for understanding the implications of CO₂ leakage [center image courtesy of Petroleum Technology Research Centre’s Aquistore project].

Flow and transport in porous media occur at the microscale but have macroscopic manifestations that are of practical importance in a several engineering applications. In CO₂ storage, for example, geochemical reactions can lead to mineral dissolution or precipitation that alter the microstructure of a rock and ultimately enhance or reduce its permeability. Quite often, it is desirable to model such systems purely at the macroscale without ever resolving the microscale dynamics. When this is possible, one says that scales are separated. A purely macroscale description can then be constructed and used in practice. For many practical problems, including strong mineral dissolution and precipitation, scales are not separated and the dynamics of the microscale remain coupled to those of the macroscale. In this case, a purely macroscopic description does not exist and microscale computations must be, somehow, incorporated into macroscale modeling. Such models, that establish a two-way coupling between a macroscale and a microscale model are called hybrid, and various techniques have been proposed in the literature targeting different aspects of the problem. We focus on hybrid mortar domain decomposition methods, which allow parts of a domain to be represented with a macroscale model and other parts with a microscale model. The two parts are coupled by exchanging information at the interface. The framework has the advantage of coupling fundamentally different model types, with potentially different physics, and being scalable on parallel platforms. They can also be used to simply solve very large, purely microscale problems. Together with our collaborators, we have developed and applied such techniques to passive and reactive transport in CO₂ sequestration and leakage, non-Newtonian flow, and near-well as well as far-field upscaling of permeability.

References: Mehmani et al. (2014), Mehmani et al. (2012), Sun, Mehmani, Balhoff (2012), Sun, Mehmani, et al. (2012)