PhD Thesis Defence by Rima Benhammadi

The predoctoral researcher Rima Benhammadi, from the Groundwater and Hydrogeochemistry group, will defend her thesis on 25th November at 11:00h in ETSECCPB, UPC, Campus Nord Building C1. Classroom: 002.

Directors: Juan J. Hidalgo and Marco Dentz

Tutor: Maartin Saaltink

Thesis Committee: Verónica Morales, Luis Cueto-Felgueroso and Daniel Fernández García

Abstract:
This thesis seeks to advance the understanding of convective mixing in heterogeneous porous media, a topic that remains comparatively underexplored compared to its homogeneous counterpart. Through the combination of high-resolution numerical simulations and laboratory experiments, we explore how spatial variability in permeability influences the onset, development, and efficiency of convective mixing processes, with applications to thermal convection, CO2 dissolution and reactive transport.
First, we begin by investigating thermal convection in the classic Horton-Rogers-Lapwood (HRL) configuration, where permeability fields are modeled as two-dimensional, log-normally distributed random fields with varying variance and correlation lengths. These serve as quantitative measures of the underlying heterogeneity. Our conducted parametric study shows that increasing the variance and/or the correlation length of the log-permeability field enhances segregation, sharpens thermal interfaces, and leads to more irregular flow structures. While the dissolution flux decreases with Rayleigh number in both homogeneous and heterogeneous systems, its sensitivity to permeability variance becomes more pronounced at longer correlation lengths. In highly heterogeneous cases, high-permeability zones near boundaries coincide with stagnation points that influence the formation of temperature plumes and localised strain rates, while the interface width decreases, indicating enhanced stretching and deformation due to the underlying structure.
Next, we study CO2 convective dissolution in heterogeneous Hele-Shaw cells, via a combined experimental-numerical approach. Heterogeneity is introduced through variations in the cell gap width, corresponding to a log-normal distribution of permeability with fixed variance and correlation lengths. Results show that heterogeneity advances the onset of instability, increases the amplitude and growth rate of convective fingers, and causes more distorted and dispersive flow patterns. However, the dimensionless wavenumber of the instability remains similar to that in homogeneous cells. A comparison of the autocorrelation functions of the fingering patterns and the permeability field shows that heterogeneity increases the dimensionless correlation length of the fingering pattern, which in turn slows down its growth once the finger size becomes comparable to the heterogeneity scale.
Finally, we investigate reactive convective dissolution involving the bimolecular chemical reaction ( A + B > C ), across four permeability configurations: homogeneous, horizontally layered, vertically layered, and multi-Gaussian log-normally distributed fields. Key metrics such as product mass, reaction rate, front position and width and mixing length are all substantially affected by the structure of the permeability field. Vertically layered and log-normal configurations promote more efficient mixing and faster front progression. Overall, when horizontal correlation length is small relative to the vertical, convective transport and mixing efficiency are maximised.
Collectively, these findings demonstrate that it is not simply the presence of heterogeneity, but the specific structure of the permeability, particularly its variance and spatial correlation, that fundamentally governs convective behaviour. The insights gained show the necessity of incorporating geologically realistic heterogeneity into the predictive models.