On the Importance of Gravity in DNAPL Invasion of Saturated Horizontal Fractures
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Invasion percolation (IP) models of dense non-aqueous phase liquid (DNAPL) invasion into saturated horizontal fractures typically neglect viscous and gravity forces, as it is assumed that capillarity dominates in many situations. An IP model simulating DNAPL invasion into saturated horizontal fractures was modified to include gravity as a local effect. The model was optimized using a genetic algorithm, and demonstrated that the inclusion of gravity is important for replicating the architecture of the DNAPL invasion pattern. The optimized gravity-included simulation showed the DNAPL invasion pattern to be significantly more representative of the experimentally observed pattern (80% accuracy) than did the optimized gravity-neglected simulation (70% accuracy). Additional simulations of DNAPL invasion in 360 randomly generated fractures were compared with and without gravity forces. These simulations showed that with increasing fracture roughness, the minimum difference between simulations with and without gravity increases to 35% for a standard deviation of the mid-aperture elevation field (SDz ) of 10 mm. Even for low roughness (SDz = 0.1 mm), the difference was as high as 30%. Furthermore, a scaled Bond Number is defined which includes data regarding DNAPL type, media type and statistical characteristics of the fracture. The value of this scaled Bond Number can be used to determine the conditions under which gravity should be considered when simulating DNAPL invasion in a macroscopically horizontal fracture. Finally, a set of equations defining the minimum and maximum absolute percentage difference between gravity-included and gravity-neglected simulations is presented based on the fracture and DNAPL characteristics.
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