To improve the confidence of subsurface storage of fluids such as carbon-dioxide, acid-gas and hydrogen at various geological sites, a proper fluid dynamic understanding of flow phenomena occurring because of injecting these source fluids into a porous medium is necessary. While many advancements have been made in predicting the fluid flows in a uniform porous medium, the flow dynamics inside a non-uniform porous media remains less well understood. In this Thesis, we use theory, numerical simulations and experiments to clarify the fluid mechanics of injecting a source fluid into a saturated, multi-layered porous media in which each of the adjacent layers are separated by a sharp permeability jump. Throughout this study, we have considered small density differences between the source and ambient fluids (satisfying the Boussinesq approximation) and both these fluids are completely miscible with each other. The goal of the study is to inform three practical questions. The first research component is to predict the early-time spreading dynamics of plume fluid striking an inclined permeability jump, within porous media having upper- and lower-layers of comparable thicknesses. The plume fluid, upon striking a permeability jump, results in a pair of oppositely directed gravity currents propagating along slope in the up- and downdip directions. To address the flow dynamics along an inclined permeable boundary, we develop a theoretical model in which we derive coupled non-linear partial differential equations describing gravity currents propagating along slope and their draining into the lower layer. The model predicts flow dynamics at both transient- and steady-state conditions. We further validate this model with similitude laboratory experiments. Experimental images show that the interface of the flow front is blurred due to hydrodynamics dispersion, and hence is not especially sharp. The implications of this observation vis-{\` a}-vis theoretical model assumptions are discussed. The second research component is to study the effect of impermeable bottom and sidewall boundaries on the dynamics of the injected fluid. For this, we construct a two-layered porous medium inside a rectangular box and conduct experiments for various combinations of the source condition, permeability jump angle and layer depth. The experiments reveal the formation of two pairs of gravity currents, one in the upper layer (propagating along the permeability jump), and the second in the lower layer (propagating along the bottom boundary of the box). The dynamical influence of one gravity current upon the other, such as the occurrence of runout-override and remobilization from a state of runout, is investigated. At later instants in time, the gravity current flows are impeded due to the vertical sidewall boundaries which allows us to distinguish between two qualitatively different filling regimes, i.e.\,sequential vs.~simultaneous filling of the upper- and lower-layers. Furthermore, parameter combinations conducive to one or the other filling regime are also identified. The third research component regards to the flow pattern inside a more complicated multi-layered porous medium, i.e.~consisting of up to five layers. For this we derive steady analytical solutions for the gravity currents formed along each of the permeability jump boundaries. The model predicts the outer envelope of the flow pattern corresponding to steady flow conditions. Finite-element based COMSOL simulations are also performed for different combinations of layer permeabilities and also by changing the permeability jump angles. The comparison of outer envelope with the theory shows good agreement. Also, the impact of adding intermediate layers of different permeabilities on the maximum span of runout and storage areas are investigated.

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