The physical-based hydraulic constitutive model developed by fractal theory has received much attention, however, its performance in two-phase flows has not been fully evaluated. This study evaluates the ability of fractal-based hydraulic constitutive models to describe the two-phase flow combining mass and momentum conservation equations. After that, we investigate the injection and displacement characteristics of the amendment at NAPL (non-aqueous phase liquids)-contaminated low-permeability sites based on this fractal model. Points of interest are the effect of the location of hydraulic fracturing in layered soils on amendment injection and distribution and the corresponding key parameters. Comparison with experimental results reveals that the fractal model describes the two-phase flow behavior very well. Fractal dimension and intrinsic permeability of soils have significant effects on the two-phase flow. For layered soils, the lower part of the low-permeability layer is preferably recommended as the main fracturing and injection zone to obtain the optimal injection efficiency. Besides, due to the lower flow resistance, hydraulic fractures across layers can be treated as fractures in highly permeable layers. This work provides new insights into the application of fractal theory in describing two-phase flows.
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