David F. Dominic

Improving Permeability Semivariograms with Transition Probability Models of Hierarchical Sedimentary Architecture Derived from Outcrop-Analog Studies

Received 21 July 2004; revised 22 February 2005; accepted 23 March 2005; published 30 July 2005. [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 ^

Comparing statistical models of physical heterogeneity in buried‐valley aquifers

The hypothesis that physical heterogeneity has similarities in separate aquifers created by similar depositional environments is tested by comparing statistical characteristics of facies assemblages. The comparisons are made for a number of data-rich sites in two buried-valley aquifers in the North American midcontinent: the White River aquifer in Indiana and the Miami Valley aquifer in Ohio. These were proglacial valleys that directed drainage away from Quaternary ice margins and were filled with glaciofluvial sediments: predominantly sand and gravel (s) lithofacies, with interbedded mud and diamicton (m) lithofacies. At scales encompassing assemblages of both lithofacies m and s, permeability is strongly bimodal. We find that it is useful to compare statistics that characterize the proportions, geometry, and spatial distribution of each facies. The results give rise to a general model for heterogeneity in valley-fill sediments along the proglacial sluiceway in both aquifers. The proportion of facies m is ∼15%. The mean thickness of facies m is 3.5 m and of the order of 10 m for facies s. The coefficient of variation in thickness for either facies is of the order of 1, with thickness ranging over orders of magnitude. Correspondingly, the vertical autotransition probabilities are exponential, and they are relatively symmetric with effective range of the order of 10 m. The lateral facies lengths are indicated to vary over orders of magnitude and to be multimodally distributed, with mean lengths of the order of 102 m, effective range in correlation structure of the order of 103 m, and lateral anisotropy ratio <2. There is some variation in how the facies m are vertically embedded within the facies s. The White River aquifer and areas in the Miami aquifer have facies proportions relatively stationary with elevation. In other areas of the Miami, there are near-horizontal zones having relatively higher or lower proportions. However, such variations on the general model give rise to similar statistics for mass transport within the context of a relevant remediation problem and thus would lead to a similar conclusion or decision. Thus one general model is applicable to both aquifers in this context. In a broader sense, we have illustrated a method by which other examples developed from data-rich sites can be compared.

Hydrofacies distribution and correlation in the Miami Valley Aquifer System

This study combines geostatistical analyses with geologic interpretations to further the quantitative understanding of physical heterogeneity within glaciofluvial aquifers. The stochastic simulation of aquifers requires quantitative measures of heterogeneity, including both cumulative distribution and spatial correlation functions. The heterogeneity in glaciofluvial aquifers is typified by low-permeability facies (e.g., till or lacustrine clay) juxtaposed with high-permeability facies (e.g., sand and gravel outwash). The Miami Valley aquifer system was examined at multiple sites for the spatial distribution and correlation of these two hydrofacies. Binary indicator geostatistics were used to quantitatively determine, at each site, the relative volume of each hydrofacies, their spatial distribution, the major principal direction of their spatial correlation, the minor principal direction, and the correlation range in these directions. The percent by volume of the system that is aquitard material decreases down the valley, from 31% to 12%. Each site has an elevation zone with more aquitard material relative to other elevations at that site. The percent aquitard material in these zones decreases down the valley from 45% to 22%. The maximum principal direction of spatial correlation in the aquitard zones generally is NE-SW, subparallel to the trend of the bedrock valley, with a range of the order of 0.75 km and minimum/maximum anisotropy ratio of 0.4. The locations exceeding 0.5 probability of aquitard occurrence generally occur on the valley margins. Thus, among the sites investigated, there is a trend down the valley in the ratio of aquitard volume to aquifer volume, and the spatial correlation and distribution of aquitard material are similar within the aquitard zones. Furthermore, these findings are consistent with aspects of the subglacial and proglacial depositional environments responsible for the facies assemblage and thus are likely to be applicable to other parts of the aquifer system and other aquifer systems where similar geologic processes are inferred to have existed.

Influence of small‐scale fluvial architecture on CO2 trapping processes in deep brine reservoirs

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.

The Influence of Streambed Heterogeneity on Hyporheic Flow in Gravelly Rivers

Deposits of open-framework gravel occurring in gravelly streambeds can exert a significant influence on hyporheic flow. The influence was quantified using a numerical model of the hyporheic zone. The model included open-framework gravel stratasets represented with commonly observed characteristics including a volume fraction of about one-third of the streambed sediment, a hydraulic conductivity two orders of magnitude greater than other strata present, and a spatial connectivity forming preferential-flow pathways. The influence of open-framework gravel stratasets on hyporheic flow was much greater than the influence of the channel morphology including meanders, point bars, dunes, and ripples. Seventy percent of the total hyporheic exchange occurred across 30% of the channel boundary at locations of open-framework gravel stratasets. The maximum local interfacial flux rates occurred at these locations, and were orders of magnitude greater than those at other locations. The local flux rates varied by six orders of magnitude over the channel boundary. The composite flow rate through the model with open-framework gravel stratsets was an order of magnitude greater than that through an equivalent but homogeneous model.

Delineation of shallow stratigraphy using ground penetrating radar

Abstract Ground penetrating radar surveys were conducted at four sites to investigate the shallow stratigraphy and to determine the applicability and performance of the radar technique. A basic analog-recording radar system with a single 80 MHz antenna was used for all of the surveys. Good stratigraphic control existed at all of the sites so that the effectiveness of the radar could be evaluated. The four sites were distinctly different in composition and extent. At an upland farm site in the glaciated region of southwestern Ohio a clay-rich soil covers shallow bedrock. Some soil horizons were identifiable on the radar profiles, but only to a depth of 1.4 m. At a sand and gravel quarry in southwestern Ohio the depositional patterns of the unsaturated deposits were clearly imaged to a depth greater than 4 m. At a hydraulic fill dam in western Ohio the changes in the internal composition of the earthen fill were observed on the radar records to depths of 4 m. On San Salvador in the Bahamas radar profiles over partially consolidated carbonate sand revealed an extensive series of buried beach ridges to depths of 4 m. These data were useful in understanding the depositional history of the area, which could not be determined from surface and pit sampling alone. These studies show that ground penetrating radar is an important tool for studying shallow stratigraphy where the ground conductivity is low enough to permit radar reflections from depths of interest.

Understanding the impact of open-framework conglomerates on water–oil displacements: the Victor interval of the Ivishak Reservoir, Prudhoe Bay Field, Alaska

The Victor Unit of the Ivishak Formation in the Prudhoe Bay Oilfield is characterized by high net-to-gross fluvial sandstones and conglomerates. The highest permeability is found within sets of cross-strata of open-framework conglomerate (OFC). These cross-strata are preserved within unit-bar deposits and assemblages of unit-bar deposits within compound (braid)-bar deposits, and may form thief zones limiting enhanced oil recovery. We incorporate recent research that has quantified important attributes of preserved sedimentary architecture into high-resolution models. Waterflooding experiments using these models demonstrate the control that such architecture has on oil production rate, water breakthrough time, and spatial and temporal distribution of residual oil saturation. We found that when the pressure gradient is orientated perpendicular to the palaeoflow direction, the total oil production and the water breakthrough time are larger, and the remaining oil saturation is smaller, than when it is orientated parallel to palaeoflow. The pressure difference between production and injection wells does not affect sweep efficiency, although the spatial distribution of oil remaining in the reservoir critically depends on this value. Oil sweep efficiency decreases slightly with increase in the proportion of OFC cross-strata. Whether or not clusters of connected OFC span the domain does not visibly affect sweep efficiency.

Air‐Based Measurements of Permeability in Pebbly Sands

We considered small-scale measurement of permeability in pebbly sands having coarser grains supported in a finer grained matrix (fine packing). Our central question was whether air-based measurements are representative if made with a permeameter tip seal pressed in the sand matrix. We created pebbly sands and variably sorted sands, with systematic variation in aspects of their fine packing. We made permeability measurements by inserting the tip seal of an air permeameter in the matrix of these samples and compared them to the permeability of the composite sample determined by both water-based methods and theory. The air-permeameter measurements made in this way represent the permeability of the composite mixtures of coarser and finer grains and allow for the discernment of permeability between samples with different matrix compositions, ranging from fine to coarse sand. Furthermore, the collective results show that permeability differences in the pebbly sands and variably sorted sands with fine packing, however measured, are primarily due to differences in matrix permeability and not due to differences in the size or the percentage of the coarser grains.

Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales

Solute transport in subsurface environments is controlled by geological heterogeneity over multiple scales. In reactive transport characterized by a low Damköhler number, it is also controlled by the rate of kinetic mass transfer. A theory for addressing the impact of sedimentary texture on the transport of kinetically sorbing solutes in heterogeneous porous formations is derived using the Lagrangian-based stochastic methodology. The resulting model represents the hierarchical organization of sedimentary textures and associated modes of log conductivity (K) for sedimentary units through a hierarchical Markov Chain. The model characterizes kinetic sorption using a spatially uniform linear reversible rate expression. Our main interest is to investigate the effect of sorption kinetics relative to the effects of K heterogeneity on the dispersion of a reactive plume. We study the contribution of each scale of stratal architecture to the dispersion of kinetically sorbing solutes in the case of a low Damköhler number. Examples are used to demonstrate the time evolution and relative contributions of the auto- and cross-transition probability terms to dispersion. Our analysis is focused on the model sensitivity to the parameters defined at each hierarchical level (scale) including the integral scales of K spatial correlation, the anisotropy ratio, the indicator correlation scales, and the contrast in mean K between facies defined at different scales. The results show that the anisotropy ratio and integral scales of K have negligible effect upon the longitudinal dispersion of sorbing solutes. Furthermore, dispersion of sorbing solutes depends mostly on indicator correlation scales, and the contrast of the mean conductivity between units at different scales.

MEASURING THE PERMEABILITY OF OPEN-FRAMEWORK GRAVEL

Open-framework gravel has permeability, k, above the measurement range of most laboratory constant-head permeameters because the head difference across the length of conventional permeameters is too small to be measured. Here we addressed the challenge of measuring the high k by using a 3 m long permeameter. The head difference over this length was of the order of 10(-2) to 10(-3) m, which we could measure to the nearest 10(-5) m. We collected data over the range of linear, laminar flow to nonlinear, laminar flow to verify that k was measured using data collected within the Darcian regime. We measured k between 4000 and 100,000 Darcies among experiments using different sediments.