Power-law decay in rate of solute removal from ground water with various exponents associated with matrix diffusion in granular packed bed

Power-law decay of pollutant concentration in flushing gas is often observed during the remediation of contaminated groundwater. However, the underlying mechanisms that cause the power law are not clear in many cases and the variations of the exponent of the power law can not be explained by the existing models with a solid physical basis. In order to obtain a variety of the values of exponent, we propose a simple two-fluid cubic lattice model. We first created a complex interfacial geometry between gas and liquid in a granular packed bed using a percolation model, and then calculated the removal rate of solute with matrix diffusion by performing the random walk of solute particles in the invaded liquid phase until the random walkers of solute reach to the gas/liquid interface. A significant power law was observed in the dissipation rate of solute particles with the proposed model. As the saturation of the invading gas in the matrix increases, the absolute value of exponent increased from 0.5, up to approximately 1.0, which cannot be reproduced by the previous analytical models. We successfully showed that the matrix diffusion with a complicated gas/liquid interface causes the power-law behavior with various exponents.