Similitude analysis of DNAPL breakthrough times in single fractures

In this study, similitude and mass storage analyses are performed to determine time scale factors for the scenario of DNAPL flow in single, one-dimensional parallel plate and variable aperture fractures. The obtained time scale factors are compared to the breakthrough times generated by a validated numerical model which is based on the partial differential equations governing isothermal multiphase flow in a single, one-dimensional fracture. Matrix effects are initially ignored, but the validity of this simplification is later explored for cases of interest. An inspectional analysis breakthrough time is derived from Darcy's equation for multiphase flow and is found to agree closely with numerically modelled breakthrough times when matrix effects are ignored. To include matrix effects, an inspectional analysis of the partial differential equation for macroscopic mass balance is performed but is not found to improve the results found using Darcy's equation. Instead, a mass storage analysis is used to combine the relative potential storage capacities of the fracture and matrix with the inspectional analysis breakthrough time, resulting in a mass storage potential ratio (Mm:Mf). Preliminary results suggest that the condition Mm:Mf > 1 is a better indicator of scenarios likely to have significantly increased breakthrough times due to matrix effects compared to other approaches. The methods employed in this study go some way to explaining the effects of different DNAPL, fracture and matrix properties on breakthrough times through heterogeneous fractures so that order-of-magnitude estimates of breakthrough times can be calculated without the need to employ a complex numerical multiphase flow model. This work will then form the basis of an examination of aqueous phase DNAPL back-diffusion from the matrix into the fracture for much larger field- and time-scale scenarios.