Mohamad Reza Soltanian

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.

Multiscale Hyporheic Exchange Through Strongly Heterogeneous Sediments

Heterogeneity in hydraulic conductivity (K) and channel morphology both control surface water-groundwater exchange (hyporheic exchange), which influences stream ecosystem processes and biogeochemical cycles. Here we show that heterogeneity in K is the dominant control on exchange rates, residence times, and patterns in hyporheic zones with abrupt lithologic contrasts. We simulated hyporheic exchange in a representative low-gradient stream with 300 different bimodal K fields composed of sand and silt. Simulations span five sets of sand-silt ratios and two sets of low and high K contrasts (one and three orders of magnitude). Heterogeneity increases interfacial flux by an order of magnitude relative to homogeneous cases, drastically changes the shape of residence time distributions, and decreases median residence times. The positioning of highly permeable sand bodies controls patterns of interfacial flux and flow paths. These results are remarkably different from previous studies of smooth, continuous K fields that indicate only moderate effects on hyporheic exchange. Our results also show that hyporheic residence times are least predictable when sand body connectivity is low. As sand body connectivity increases, the expected residence time distribution (ensemble average for a given sand-silt ratio) remains approximately constant, but the uncertainty around the expectation decreases. Including strong heterogeneity in hyporheic models is imperative for understanding hyporheic fluxes and solute transport. In streams with strongly heterogeneous sediments, characterizing lithologic structure is more critical for predicting hyporheic exchange metrics than characterizing channel morphology. This article is protected by copyright. All rights reserved.

Critical Dynamics of Gravito-Convective Mixing in Geological Carbon Sequestration

When CO2 is injected in saline aquifers, dissolution causes a local increase in brine density that can cause Rayleigh-Taylor-type gravitational instabilities. Depending on the Rayleigh number, density-driven flow may mix dissolved CO2 throughout the aquifer at fast advective time-scales through convective mixing. Heterogeneity can impact density-driven flow to different degrees. Zones with low effective vertical permeability may suppress fingering and reduce vertical spreading, while potentially increasing transverse mixing. In more complex heterogeneity, arising from the spatial organization of sedimentary facies, finger propagation is reduced in low permeability facies, but may be enhanced through more permeable facies. The connectivity of facies is critical in determining the large-scale transport of CO2-rich brine. We perform high-resolution finite element simulations of advection-diffusion transport of CO2 with a focus on facies-based bimodal heterogeneity. Permeability fields are generated by a Markov Chain approach, which represent facies architecture by commonly observed characteristics such as volume fractions. CO2 dissolution and phase behavior are modeled with the cubic-plus-association equation-of-state. Our results show that the organization of high-permeability facies and their connectivity control the dynamics of gravitationally unstable flow. We discover new flow regimes in both homogeneous and heterogeneous media and present quantitative scaling relations for their temporal evolution.

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.

Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 1. Time-dependent effective retardation factor

This series of papers addresses the transport of reactive solutes in groundwater. In part 1, the time-dependent effective retardation factor, R∼eff(t), of reactive solutes undergoing equilibrium sorption is linked to hierarchical stratal architecture using a Lagrangian-based transport model. The model is based on hierarchical expressions of the spatial covariance of the log distribution coefficient, Ξ=ln⁡(Kd), and the spatial cross covariance between Ξ and the log permeability, Y=ln⁡(k). The spatial correlation structure in these covariance expressions is the probability of transitioning across strata types of different scales, and they are parameterized by independent and quantifiable physical attributes of sedimentary architecture including univariate statistics for Y, Ξ, and the proportions and lengths of facies. Nothing is assumed about Y- Ξ point correlation; it is allowed to differ by facies type. The duration of the time-dependent change in R∼eff(t) is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each scale of stratal architecture. The plume velocity and the effective retardation stabilize at a large-time limit after the plume centroid has traveled a distance that encompasses the effective ranges of these cross-transition probability structures. The well-documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the model. The model gives a viable explanation for the observed PCE plume deceleration, and thus the observed R∼eff(t) can be explained by the process of linear equilibrium sorption and the heterogeneity in k and Kd. In part 2 [Soltanian et al., 2015a], reactive plume dispersion, as quantified by the particle displacement variance is linked to stratal architecture using a Lagrangian-based transport model.

Implicit finite volume and discontinuous Galerkin methods for multicomponent flow in unstructured 3D fractured porous media

Abstract We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstructured triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete fractures. A lowest-order implicit finite volume (FV) transport update is also developed for the same grid types. The implicit methods are compared to an Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains, the unconditionally stable implicit transport update is shown to increase computational efficiency by orders of magnitude as compared to IMPEC, which has a time-step constraint proportional to the pore volume of discrete fracture grid cells. However, when lowest-order Euler time-discretizations are used, numerical errors increase linearly with the larger implicit time-steps, resulting in high numerical dispersion. Second-order Crank–Nicolson implicit MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show twice the convergence rate for the DG methods as compared to FV, resulting in two to three orders of magnitude higher computational efficiency. Numerical experiments demonstrate the efficiency and robustness in modeling compressible multicomponent flow on irregular and fractured 2D and 3D grids, even in the presence of fingering instabilities.

Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian‐based transport model: 2. Particle displacement variance

This series of papers addresses the transport of sorbing solutes in groundwater. In part 2, plume dispersion, as quantified by the particle displacement variance, X11R(t), is linked to hierarchical sedimentary architecture using a Lagrangian-based transport model. This allows for a fundamental understanding of how dispersion arises from the hierarchical architecture of sedimentary facies, and allows for a quantitative decomposition of dispersion into facies-related contributions at different scales within the hierarchy. As in part 1, the plume behavior is assumed to be controlled by linear-equilibrium sorption and the heterogeneity in both the log permeability, Y=ln⁡(k), and the log distribution coefficient, Ξ=ln⁡(Kd). Heterogeneity in Y and Ξ arises from sedimentary processes and is structured by the consequent sedimentary architecture. Our goal is to understand the basic science of the dispersion process at this very fundamental level. The spatial auto and cross covariances for the relevant attributes are linear sums of terms corresponding to the probability of transitioning across stratal facies types defined at different scales. Unlike previous studies that used empirical relationships for the spatial covariances, here the model parameters are developed from independent measurements of physically quantifiable attributes of the stratal architecture (i.e., proportions and lengths of facies types, and univariate statistics for Y and Ξ). Nothing is assumed about Y- Ξ point correlation; it is allowed to differ by facies type. However, it is assumed that Y and Ξ variance is small but meaningful, and that pore-scale dispersion is negligible. The time-dependent spreading rate is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each relevant scale of stratal hierarchy. As in part 1, the well-documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the model. The model was parameterized with univariate statistics for Y, Ξ of (PCE), and proportions and lengths of lithologic facies types defined at two scales within a two-level hierarchical classification, as given by Ritzi et al. (2013). The model gives a viable explanation for the observed PCE plume dispersion, and thus X11R(t) can be explained by the process of linear equilibrium sorption and the heterogeneity in k and Kd. The results quantitatively show that the k- Kd cross correlation, though small, and varied by facies type, can significantly impact the particle displacement variance. Furthermore, by quantitatively decomposing the dispersion into facies-related contributions, we gain the fundamental insight that that the time-dependent rate of spreading is mostly defined by the cross-transition probability correlation structure imparted by the proportions and sizes of the larger-scale facies types.

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.

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.

A new method for analysis of variance of the hydraulic and reactive attributes of aquifers as linked to hierarchical and multiscaled sedimentary architecture

This technical note presents a useful methodology for studying how the variance of hydraulic and/or reactive attributes of an aquifer are linked to the multiscaled and hierarchical sedimentary architecture of the aquifer. A new recursive equation is derived which quantitatively describes how the variance is related to sedimentary facies defined at all scales across an entire stratal hierarchy. As compared to prior published equations that emphasize differences in means among facies populations within a hierarchical level, it emphasizes differences across levels. Because of the hierarchical relationships among the terms of the equation, we find it to be useful for conducting a holistic analysis of the relative contributions to the variance arising from all facies types defined across all scales. The methodology is demonstrated using appropriate field data, and is shown to be useful in defining parsimonious classification systems.