Simulation of subsurface heterogeneity is important for modeling subsurface flow and transport processes. Previous studies have indicated that subsurface property variations can often be characterized by fractional Brownian motion (fBm) or (truncated) fractional Levy motion (fLm). Because Levy-stable distributions have many novel and often unfamiliar properties, studies on generating fLm distributions are rare in the literature. In this study, we generalize a relatively simple and computationally efficient successive random additions (SRA) algorithm, originally developed for generating Gaussian fractals, to simulate fLm distributions. We also propose an additional important step in response to continued observations that the traditional SRA algorithm often generates fractal distributions having poor scaling and correlation properties. Finally, the generalized and modified SRA algorithm is validated through numerical tests.

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, Dem, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for study, based on data availability and quality. Field-scale Dem values were calculated, either directly using data reported in the literature or by reanalyzing the corresponding field tracer tests. Surveyed data indicate that the effective-matrix-diffusion-coefficient factor FD (defined as the ratio of Dem to the lab-scale matrix diffusion coefficient [Dem] of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value could be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems. Furthermore, we observed a moderate trend toward systematic increase in the emDFmDDF value with observation scale, indicating that the effective matrix diffusion coefficient is likely to be statistically scale dependent. The FD value ranges from 1 to 10,000 for observation scales from 5 to 2,000 m. At a given scale, the FD value varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.