Dissolution Trapping of Carbon Dioxide in Heterogeneous Aquifers.

The geologic architecture in sedimentary reservoirs affects the behavior of density-driven flow and the dispersion of CO2-rich brine. The spatial organization and connectivity of facies types play an important role. Low-permeability facies may suppress fingering and reduce vertical spreading, but may also increase transverse mixing. This is more pronounced when geologic structures create preferential flow pathways through connected facies types. We perform high-resolution simulations of three-dimensional (3D) heterogeneous formations whose connectivity cannot be represented in two-dimensional models consistent with percolation theory. This work focuses on the importance of 3D facies-based heterogeneity and connectivity on advection-diffusion transport of dissolved CO2. Because the dissolution of CO2 and the subsequent density increase of brine are the driving force for gravitational instabilities, we model the phase behavior with the accurate cubic-plus-association equation-of-state, which accounts for the self-association of polar water molecules and the cross-association between CO2 and water. Our results elucidate how the spatial organization of facies affects the dynamics of CO2 convective mixing. Scaling relations for the evolution of a global dispersion-width provide insights that can be universally applied. The results suggest that the long-term evolution and scaling of dispersion are surprisingly similar for homogeneous and (binary and multiscale) heterogeneous porous media.

Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: the Lagrangian approach.

Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion.

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.

The Kozeny-Carman equation with a percolation threshold.

A procedure has been developed for calculating permeability (k) from the Kozeny-Carman equation, a procedure that links ideas from percolation theory with the ideas of Koltermann and Gorelick (1995) and Esselburn et al. (2011). The approach focuses on the proportion of coarser pores that are occupied by finer sediments relative to a percolation threshold proportion (ω(c)). If the proportion occupied is below ω(c), then the unoccupied coarser pores percolate. Otherwise they do not percolate. Following the ideas of Koltermann and Gorelick (1995), the effective grain-size term in the Kozeny-Carman equation is calculated using the geometric mean if the unoccupied coarse pores percolate, and using the harmonic mean if otherwise. Following ideas of Esselburn et al. (2011), this approach is implemented by evaluating the potential for grains in each size category to occupy pores among sediment of each larger-size category. Application of these ideas to physical sediment models for sands and gravels, which have known k, indicates that a threshold does indeed exist. Results also suggest that the Kozeny-Carman equation is robust and gives representative values for k, even though ω(c) is not precisely known.

Conservative models: parametric entropy vs. temporal entropy in outcomes.

The geologic architecture in aquifer systems affects the behavior of fluid flow and the dispersion of mass. The spatial distribution and connectivity of higher-permeability facies play an important role. Models that represent this geologic structure have reduced entropy in the spatial distribution of permeability relative to models without structure. The literature shows that the stochastic model with the greatest variance in the distribution of predictions (i.e., the most conservative model) will not simply be the model representing maximum disorder in the permeability field. This principle is further explored using the Shannon entropy as a single metric to quantify and compare model parametric spatial disorder to the temporal distribution of mass residence times in model predictions. The principle is most pronounced when geologic structure manifests as preferential-flow pathways through the system via connected high-permeability sediments. As per percolation theory, at certain volume fractions the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly underrepresent the entropy in the real, three-dimensional, aquifer system. Thus to be conservative, stochastic models must be three-dimensional and include geologic structure.

Porosity and permeability in ternary sediment mixtures.

Permeability, k, and porosity, φ, were measured in mixtures of fine, medium, and coarse sand, where the volume fraction of each of the three components was systematically varied. The k was modeled well by the Kozeny-Carman equation for three-component mixtures by using a representative grain size parameter, d, computed by averaging the grain diameters of components recursively, with averaging methods based on whether finer components exist in sufficient volume to fill the pores within coarser components. The φ was modeled well by using linear interpolation with piecewise-planar models. We explored the use of differing numbers of piecewise-planar elements in the model, and illustrate the trade-off between the increased accuracy and the increased data requirements that both come from adding more elements. The k model is a function of both d and φ, but more sensitive to d. The k model gave results consistent with measured values when computed using either measured φ values, or values from any of the φ models.

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.

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.

Porosity and permeability in sediment mixtures.

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.

Modeling multiscale heterogeneity and aquifer interconnectivity.

A number of methods involving indicator geostatistics were combined in a methodology for characterizing and modeling multiscale heterogeneity. The methodology circumvents sources of bias common in data from borehole logs. We applied this methodology to the complex heterogeneity within a regional system of buried valley aquifers, which occurs in the western glaciated plains of North America and includes the Spiritwood Aquifer. The region is conceptualized as having a hierarchical organization with three facies assemblage types (large-scale heterogeneity) and two facies types within each assemblage (small-scale heterogeneity). We statistically characterized the sedimentary architecture at both scales, formulated indicator correlation models from those characterizations, and used the models to simulate the architecture in a multiscale realization. We focused on the interconnectivity of units creating higher-permeability pathways. Higher-permeability pathways span the realization even though the proportion of higher-permeability facies is less than the percolation threshold. Thus, geologic structures as represented in the indicator correlation models create interconnectivity above that which would occur if the higher-permeability facies were randomly placed. This amount of interconnection among higher-permeability facies within the multiscale realization is consistent with that suggested in prior hydraulic and geochemical studies of the regional system.