[1] Cross-stratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the crosstransition probabilities of unit types having the greatest contrast in permeability. The shape of those cross-transition probabilities can be, in turn, largely determined by the variance of the lengths of those unit types. A sufficient condition for an exponential-like semivariogram is the repeated occurrence of unit types having both a contrast in permeability and a large length variance. These relationships are shown through writing the identities for spatial correlation of permeability in a hierarchical and multimodal form and as a function of the transition probabilities for the sedimentary unit types. These relationships are also illustrated through analyzing data representing cross-stratified sediments within a point bar deposit.

Porosity in sediments that contain a mix of coarser- and finer-grained components varies as a function of the porosity and volume fraction of each component. We considered sediment mixtures representing poorly sorted sands and gravely sands. We expanded an existing fractional-packing model for porosity to represent mixtures in which finer grains approach the size of the pores that would exist among the coarser grains alone. The model well represents the porosity measured in laboratory experiments in which grain sizes and volume fractions were systematically changed within sediment mixtures. Permeability values were determined for these sediment mixtures using a model based on grain-size statistics and the expanded fractional-packing porosity model. The permeability model well represents permeability measured in laboratory experiments using air- and water-based permeametry on the model sediment mixtures.

In the paper "Bed lead grain velocities and sediment transport rates" by J. S. Bridge and D. F. Dominic (Water Resources Research, 20(4), 476-490, 1984) we have discovered a relatively minor error, but believe that the implications of the correction are interesting enough to present here. Equation (13) should be revised to read U• --a [U, -U,c (tan s/tan %)•/2]where tan •c is the value of tan • at the threshold of bed grain movement. The importance of this correction is that it allows the second term on the right-hand side of equation (13a) to approach zero toward the point of true suspension as tan • tends to zero. In its original form, (13) predicts that the grain velocity is always less than the fluid velocity by the amount aU,c, which is clearly not the case at the point of true suspension.However, this modification has a very minor influence on predicted bed lead transport rates, because at low transport stages tan • • tan •c, and at high transport stages U, is much larger than U,, (tan s/tan %)•/:. It is therefore not recommended that this modified version of (13) be incorporated in the bedload transport equations (15) and (16). For clarity, (18) should also be rewritten as tan % = (aU,½ /Vg)2; however, it has already been stated clearly in Tables 4 and 5 that the tan • values obtained using (18) and (11) are those at the threshold of grain motion. It is interesting that these values of tan •c are very similar to Hanes and lnman's [1985] experimentally determined values of the critical dynamic friction coefficient (defined as the ratio of grain shear stress to normal stress required to maintain grains moving over an immobile boundary). REFERENCE Hanes, D. M., and D. L. Inman, Experimental evaluation of a dynamic yield criterion for granular fluid flows, J. Geephys. Res., 90, 3670-3674, 1985.

[1] As analogs for aquifers, outcrops of sedimentary deposits allow sedimentary units to be mapped, permeability to be measured with high resolution, and sedimentary architecture to be related to the univariate and spatial bivariate statistics of permeability. Sedimentary deposits typically can be organized into hierarchies of unit types and associated permeability modes. The types of units and the number of hierarchical levels defined on an outcrop might vary depending upon the focus of the study. Regardless of how the outcrop sediments are subdivided, a composite bivariate statistic like the permeability semivariogram is a linear summation of the autosemivariograms and cross semivariograms for the unit types defined, weighted by the proportions and transition probabilities associated with the unit types. The composite sample semivariogram will not be representative unless data locations adequately define these transition probabilities. Data reflecting the stratal architecture can often be much more numerous than permeability measurements. These lithologic data can be used to better define transition probabilities and thus improve the estimates of the composite permeability semivariogram. In doing so, bias created from the incomplete exposure of units can be reduced by a Bayesian approach for estimating unit proportions and mean lengths. We illustrate this methodology with field data from an outcrop in the Española Basin, New Mexico.Citation: Dai, Z., R. W. Ritzi Jr., and D. F. Dominic (2005), Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies, Water Resour. Res., 41, W07032,

A number of important candidate CO2 reservoirs exhibit sedimentary architecture reflecting fluvial deposition. Recent studies have led to new conceptual and quantitative models for sedimentary architecture in fluvial deposits over a range of scales that are relevant to CO2 injection and storage. We used a geocellular modeling approach to represent this multiscaled and hierarchical sedimentary architecture. With this model, we investigated the dynamics of CO2 plumes, during and after injection, in such reservoirs. The physical mechanism of CO2 trapping by capillary trapping incorporates a number of related processes, i.e., residual trapping, trapping due to hysteresis of the relative permeability, and trapping due to hysteresis of the capillary pressure. Additionally, CO2 may be trapped due to differences in capillary entry pressure for different textural sedimentary facies (e.g., coarser‐grained versus finer‐grained cross sets). The amount of CO2 trapped by these processes depends upon a complex system of nonlinear and hysteretic characteristic relationships including how relative permeability and capillary pressure vary with brine and CO2 saturation. The results strongly suggest that representing small‐scale features (decimeter to meter), including their organization within a hierarchy of larger‐scale features, and representing their differences in characteristic relationships can all be critical to understanding trapping processes in some important candidate CO2 reservoirs.