Three-dimensional numerical inversion of pneumatic cross-hole tests in unsaturated fractured tuff 2. Equivalent parameters, high-resolution stochastic imaging and scale effects

In paper 1 of this two-part series we described a three-dimensional numerical inverse model for the interpretation of cross-hole pneumatic tests in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS) near Superior, Arizona. Our model is designed to analyze these data in two ways: (1) by considering pressure records from individual borehole monitoring intervals one at a time, while treating the rock as being spatially uniform, and (2) by considering pressure records from multiple tests and borehole monitoring intervals simultaneously, while treating the rock as being randomly heterogeneous. The first approach yields a series of equivalent air permeabilities and air-filled porosities for rock volumes having length scales ranging from meters to tens of meters, represented nominally by radius vectors extending from injection to monitoring intervals. The second approach yields a high-resolution geostatistical estimate of how air permeability and air-filled porosity, defined on grid blocks having a length scale of 1 m, vary spatially throughout the tested rock volume. It amounts to three-dimensional pneumatic "tomography" or stochastic imaging of the rock. Paper 1 described the field data, the model, and the effect of boreholes on pressure propagation through the rock. This second paper implements our inverse model on pressure data from five cross-hole tests at ALRS. We compare our cross-hole test interpretations by means of the two approaches with earlier interpretations by means of type curves and with geostatistical interpretations of single-hole test data. The comparisons show internal consistency between all pneumatic test interpretations and reveal a very pronounced scale effect in permeability and porosity at ALRS.