Pneumatic fracturing is an in situ remediation enhancement technology developed to increase the permeability of contaminated geologic formations. This technology can also be used to deliver atomized liquid and particulate supplements to geologic formations, thereby enhancing in situ processes such as bioremediation and reactive dechlorination.
The main objective of this study was the development of a mathematical model that simulates the propagation of pneumatic fractures in soil and rock formations. Pneumatic fracture propagation differs from other fluid fracturing phenomena in the propagation velocity (1-3 m/sec) and the viscosity of the fracturing fluid (1.9E-05 Pa•sec). For the purposes of model development, the geologic formation was assumed to be homogenous with regard to composition, anisotropic with respect to pneumatic conductivity, and overconsolidated with respect to geostatic stress.
The propagation model was formulated by coupling equations describing the three physical processes controlling propagation: (i) pressure loss due to frictional effects; (ii) leak-off into the surrounding formation; and (iii) deflection of the overburden. Pressure dissipation was modeled based on Poiseuille\u27s law, and leak-off was modeled using two-dimensional Darcian flow. The deflection of the overlying formation was modeled as a circular plate clamped at its edges and subjected to logarithmically varying load.
The model was solved numerically and the solution was expressed as an algorithm. The algorithm seeks an equilibrium fracture radius and aperture that simultaneously satisfies flow continuity and stress equilibrium criteria at the fracture tip. Different methods of solution convergence were examined and the Bisection Method was found to be the most efficient.
Sensitivity analyses showed that model behavior was dominated by the pneumatic conductivity of the geologic formation since this parameter largely determines leak-off rate. The algorithm was calibrated with field data from six different pneumatic fracturing projects and regressed values of pneumatic conductivity and elastic modulus showed reasonable agreement with field measured values. The most important result of the calibration process was the coincidence between the regressed conductivity (1.1E-03 to 1.8E-05) and the post-fracture conductivities measured in the field (3.1E-03 to 1.7E-05). This result supported the fundamental thesis that final fracture radius is determined with the geologic formation in a disturbed state.
A separate pneumatic fracture propagation model was developed and solved based solely on the continuity criterion. The solution demonstrated reasonable correlation with field measured radii, although it tended to overestimate fracture radius in soil formations at shallow depths of injection (on an average 15 % more than field measured radius).
As a secondary objective of this study, a methodology to model the mechanism of particulate transport in a fluidized soil formation was proposed. The methodology was tested with field data from a recent case study
