Numerical inverse interpretation of pneumatic tests in unsaturated fractured tuffs at the Apache Leap Research Site

Abstract

A three-dimensional stochastic numerical inverse model has been developed for characterizing the properties of unsaturated fractured medium through analysis of singleand cross-hole pneumatic tests. Over 270 single-hole [Guzman et al., 1996] and 44 cross-hole pneumatic tests [Illman et al., 1998; Inman, 1999] were conducted in 16 shallow vertical and slanted boreholes in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS), Arizona. The single-hole tests were interpreted through steady-state [Guzman et al., 1996] and transient [Illman and Neuman, 2000b] analytical methods. The cross-hole tests were interpreted by analytical type-curves [Illman and Neuman, 2000a]. I describe a geostatistical analysis of the steady-state single-hole data, and numerical inversion of transient single-hole and cross-hole data. The geostatistical analysis of single-hole steady-state data yields information about the spatial structure of air permeabilities on a nominal scale of 1 m. The numerical inverse analysis of transient pneumatic test data is based on the assumption of isothermal single-phase airflow through a locally isotropic, uniform or non-uniform continuum. The stochastic inverse model is based on the geostatistical pilot point method of parameterization [de Marsily, 1978], coupled with a maximum likelihood definition of the inverse problem [Carrera and Neuman, 1986a]. The model combines a finite-volume flow simulator, FEHM [Zyvoloski et al., 1997], an automatic mesh generator, X3D [Trease et al., 1996], a parallelized version of an automatic parameter estimator, PEST [Doherty et al., 1994], and a geostatistical code, GSTAT [Pebesma and Wesseling, 1998]. The model accounts directly for the ability of all borehole intervals to store and conduct air through the system; solves the airflow equations in their original nonlinear form accounting for the dependence of air compressibility on absolute air pressure; can, in principle, account for atmospheric pressure fluctuations at the soil surface; provides kriged estimates of spatial variations in air permeability and air-filled porosity throughout the tested fractured rock volume; and is applied simultaneously to pressure data from multiple borehole intervals as well as to multiple cross-hole tests. The latter amounts to three-dimensional stochastic imaging, or pneumatic tomography, of the rock as proposed by Neuman [1987] in connection with cross-hole hydraulic tests in fractured crystalline rocks near Oracle, Arizona. The model is run in parallel on a supercomputer using 32 processors. Numerical inversion of single-hole pneumatic tests allows interpreting multiple injection-step and recovery data simultaneously, and yields information about air permeability, air-filled porosity, and dimensionless borehole storage coefficient. Some of this cannot be accomplished with type-curves [Inman and Neuman, 2000b]. Air permeability values obtained by my inverse method agree well with those obtained by steady-state and type-curve analyses. Both stochastic inverse analysis of cross-hole data and geostatistical analysis of single-hole data, yield similar geometric mean and similar spatial pattern of air permeability. However, I observe a scale effect in both air permeability and air-filled porosity when I analyze cross-hole pressure records from individual monitoring intervals one by one, while treating the medium as being uniform; both pneumatic parameters have a geometric mean that is larger, and a variance that is smaller, than those obtained by simultaneous stochastic analysis of multiple pressure records. Overall, my analysis suggests that (a) pneumatic pressure behavior of unsaturated fractured tuffs at the ALRS can be interpreted by treating the rock as a continuum on scales ranging from meters to tens of meters; (b) this continuum is representative primarily of interconnected fractures; (c) its pneumatic properties nevertheless correlate poorly with fracture density; and (d) air permeability and air-filled porosity exhibit multiscale random variations in space.