Wide Range Of Peclet Research Articles

Reactive transport modeling for assessing coupled hydrogeochemical processes at interfaces in deep geological repositories: from the laboratory to the real world

Abstract. Deep geological repositories with a multi-barrier concept are foreseen by various countries for the disposal of high-level radioactive waste. Simulation tools for a close-to-reality description of repository evolution scenarios are required, especially to resolve the challenging task of comparing and assessing the long-term safety of different repository concepts in different host rocks within the German site-selection process. Chemical, thermal, and pressure gradients at the interfaces of the different barriers in a repository can lead to mineral dissolution and precipitation, generating non-linear responses in transport and mechanical properties of barrier materials and host rocks. Reactive transport modeling (RTM) can be applied to investigate these perturbations and processes across temporal and spatial scales to assess subsurface evolution. Nevertheless, implementing RTM at the continuum scale while accounting for pore-scale heterogeneities and geometry evolution remains a challenge. Pore-scale simulations offer the potential to capture the complex evolution of porous media over a broad range of Peclet and Damköhler numbers, and they can be utilized to improve the RTM by using upscaling methods (Prasianakis et al., 2020). In this context, we developed “lab-on-a-chip” experiments, combining time-lapse high-resolution optical microscopy and confocal Raman spectroscopy to test extended constitutive equations to classically employed Archie's law to improve the description of changes in transport properties (e.g., diffusivity) in evolving porous media in RTM. The 3D Raman tomography of the porous media combined with pore-scale modeling enabled the derivation of upscaled transport parameters. Our results highlight the importance of calibrating pore-scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers, whose results can be further used for the derivation of upscaled modeling parameters. The derived and parameterized constitutive equations based on simple systems have been tested in reactive transport models as a sensitivity case study to evaluate uncertainties in the predictions of the evolution of real subsurface systems such as clay–cement interfaces in deep geological repositories.

A Lab on a Chip Experiment for Upscaling Diffusivity of Evolving Porous Media

Reactive transport modelling is a powerful tool to assess subsurface evolution in various energy-related applications. Upscaling, i.e., accounting for pore scale heterogeneities into larger scale analyses, remains one of the biggest challenges of reactive transport modelling. Pore scale simulations capturing the evolutions of the porous media over a wide range of Peclet and Damköhler number in combination with machine learning are foreseen as an efficient methodology for upscaling. However, the accuracy of these pore scale models needs to be tested against experiments. In this work, we developed a lab on a chip experiment with a novel micromodel design combined with operando confocal Raman spectroscopy, to monitor the evolution of porous media undergoing coupled mineral dissolution and precipitation processes due to diffusive reactive fluxes. The 3D-imaging of the porous media combined with pore scale modelling enabled the derivation of upscaled transport parameters. The chemical reaction tested involved the replacement of celestine by strontianite, whereby a net porosity increase is expected because of the smaller molar volume of strontianite. However, under our experimental conditions, the accessible porosity and consequently diffusivity decreased. We propose a transferability of the concepts behind the Verma and Pruess relationship to be applied to also describe changes of diffusivity for evolving porous media. Our results highlight the importance of calibrating pore scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers of which results can be further used for the derivation of upscaled parameters.

A multiscale finite element method for the solution of transport equations

A multiscale Galerkin finite element scheme based on the residual free bubble function method is proposed to generate stable and accurate solutions for the transport equations namely diffusion-reaction (DR), convection-diffusion (CD) and convection-diffusion-reaction (CDR) equations. These equations show multiscale behavior in reaction or convection dominated situations. The idea is based on the approximation of the definite integral of the interpolation function within the element, instead of the function approximation. The numerical experiments are performed using the bilinear Lagrangian elements. To validate the approach, the numerical results obtained for a benchmark problem are compared with the analytical solution in a wide range of Peclet and Damköhler numbers. The results show that the developed method is capable of generating stable and accurate solutions.

The Design of a Heat Transfer Liquid Metal MHD Experiment for ALEX

An experiment to study heat transfer in liquid metal MHD flow, under conditions relevant to coolant channels for tokamak first wall and high heat flux devices, is described. The experimental configuration is a rectangular duct in a transverse magnetic field, heated on one wall parallel to the field. The specific objective of the experiment is to resolve important issues related to the presence and heat transfer characteristics of wall jets and flow instabilities in MHD flows in rectangular ducts with electrically conducting walls. Available analytical tools for MHD thermal hydraulics have been used in the design of the test article and its instrumentation. Proposed tests will cover a wide range of Peclet and Hartmann numbers and interaction parameters.

On finite and semi-infinite steady state tubular reactor models.

Two contrasting models of one-dimensional axial dispersion tubular reactors are studied. One is a finite reactor model with zero concentration gradient at the exit and the other is a semi-infinite reactor model with its solution truncated at the exit. The comparison of concentration profiles and conversions between the two models for first-oder reactions shows that, for a reasonably wide range of Peclet and Damkohler numbers, the profiles as well as the conversions agree quite well and the choice of model is of little consequence. It is within the intermediate range of Damkohler numbers and low Peclet numbers that the two models give rise to considerably different profiles and conversions.