Publication Date


Document Type


Committee Members

David F. Dominic (Committee Member), Mark N. Goltz (Committee Member), Chaocheng Huang (Committee Member), Robert W. Ritzi (Advisor), Thaddeus Tarpey (Committee Member)

Degree Name

Doctor of Philosophy (PhD)


A new form of the Lagrangian-based model for macrodispersion of inert (non-reactive) solutes is presented. The model is based on a hierarchical expression of the spatial covariance of log-permeability representing a hierarchy of stratal unit types with a corresponding hierarchy of permeability subpopulations. The covariance expression representing the hierarchy of unit types is a linear sum of terms corresponding to the probability of transitioning across stratal unit types of different scales, and these terms are directly related to quantifiable geometric attributes of the hierarchical stratal architecture. The new macrodispersion model is also a linear sum of terms, with different integral scales defined by the hierarchy of cross-transition probabilities and computed from the proportions and length statistics of the stratal unit types. The model allows the study of the contribution of each term to the composite particle displacement variance, and thus the study of how the hierarchical stratal architecture influences plume spreading. The method was applied using data from the well-studied Borden research site and synthetic data representing a channel-belt deposit. The data from the Borden site included permeability data, and geologic data occurring in much greater abundance than the permeability data. The model parameters governing time-dependent behavior are the proportions and mean lengths of strata as determined from the geologic data. The other model parameters required were the univariate statistics (mean and variance) for permeability within the smallest-scale strata. The univariate statistics for permeability were computed with a much smaller number of data than Sudicky (1986) required for the conventional approach based on fitting models to the sample bivariate statistics. The dispersion model developed from these data with the new method represents the field-measured particle displacement variance that occurred in the natural gradient tracer test well. The contributions to time-dependent macrodispersion by strata at each scale were computed and analyzed independently. This analysis revealed that macrodispersion at the Borden site is primarily controlled by the proportions and the mean length of larger-scale strata of medium sand (M) and strata of fine sand and silt (FZ), with secondary contributions by smaller-scale strata types occurring within the larger scale units. The plume has to cross about 12 contacts between M and FZ units (about 6 couplets, which each are about 10 m in length on average) before reaching the time-constant macrodispersivity, which occurs after about 700 days. Synthetic (permeability and integer-indicator) data were created by sampling a digital model to study the spatial correlation structure of log-permeability. The analysis showed that the correlation structure of log permeability was controlled by the structures of auto- and cross transition probabilities. The structure of the autotransition probability was controlled by the proportions, and the mean and the variance in lengths of cross stratasets. The structures of the cross transition probabilities were controlled also by those of compound bar deposits and major channel fills. Using the new method, the correlation could be represented well by modeling the hierarchy of transition probabilities from the geologic data and combing them with the univariate statistics of log permeability within the cross stratasets.

Page Count


Department or Program

Department of Earth and Environmental Sciences

Year Degree Awarded