Abstract
Solute transport under single-phase flow conditions in porous micromodels was studied using high-resolution optical imaging. Experiments examined loading (injection of ink-water solution into a clear water-filled micromodel) and unloading (injection of clear water into an ink-water filled micromodel). Statistically homogeneous and fine-coarse porous micromodels patterns were used. It is shown that the transport time scale during unloading is larger than that under loading, even in a micromodel with a homogeneous structure, so that larger values of the dispersion coefficient were obtained for transport during unloading. The difference between the dispersion values for unloading and loading cases decreased with an increase in the flow rate. This implies that diffusion is the key factor controlling the degree of difference between loading and unloading transport time scales, in the cases considered here. Moreover, the patterned heterogeneity micromodel, containing distinct sections of fine and coarse porous media, increased the difference between the transport time scales during loading and unloading processes. These results raise the question of whether this discrepancy in transport time scales for the same hydrodynamic conditions is observable at larger length and time scales.
Highlights
Solute transport in porous media is relevant to a wide range of applications in contaminant hydrogeology, geothermal engineering, petroleum engineering, and a variety of chemical engineering systems (Whitaker 1967; Fried and Combarnous 1971; Balakotaiah et al 1995; Coats and Smith 1964; Erfani et al 2019, 2020, 2021)
Advection is the transport of a solute with the pore velocity (v) of the carrier fluid, and diffusion mechanism is due to the concentration gradient given by Fick’s law
This experiment focused on quantifying, at a small pore scale, possible differences between the time scales of loading and unloading processes, characterized in terms of DL and DL ) and unloading ( (DUL)
Summary
Solute transport in porous media is relevant to a wide range of applications in contaminant hydrogeology, geothermal engineering, petroleum engineering, and a variety of chemical engineering systems (Whitaker 1967; Fried and Combarnous 1971; Balakotaiah et al 1995; Coats and Smith 1964; Erfani et al 2019, 2020, 2021). Transport in porous materials is controlled by two physical processes: advection and diffusion. Advection is the transport of a solute with the pore velocity (v) of the carrier fluid, and diffusion mechanism is due to the concentration gradient given by Fick’s law. Where L denotes the characteristic transport length and Dm is the molecular diffusion coefficient. Due to the presence of the no-slip boundary on solid surfaces, tortuosity of the porous material and preferential pathways, a solute will spread along the flow direction via fluctuations from the average velocity. These fluctuations can be quantified by the dispersion coefficient (D), which is defined statistically as
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