Carl A. Mendoza

On the generation of instabilities in variable density flow

Interfacial or fingering instabilities have been studied recently in relation to contamination problems where a more dense plume is enclosed by and is moving along in a body of less dense fluid. Instabilities can play an important role in the mixing or dispersion process. Through the use of a variable density flow and transport code, we were able to study how the style of interfacial perturbation controls the pattern of instability development. Whether initial perturbations grow or decay depends mainly on the wavelength of the perturbing function. A critical perturbation wavelength must be exceeded for a perturbation to grow; otherwise the perturbation simply decays. Our work confirms earlier analyses that suggest that all stratified systems are inherently unstable, given some spectrum of the perturbing waves that exceed the critical wavelength. By implication, Rayleigh number stability criteria are inappropriate for evaluating the dense plume problem. Our study also demonstrates how numerical errors in a mass transport code can serve as a perturbing function and lead to the development of instabilities. However, these instabilities are not physically realistic and are essentially uncontrollable because their character depends on the extent to which numerical errors develop, as evidenced by the grid Peclet and Courant numbers.

Instabilities in variable density flows: Stability and sensitivity analyses for homogeneous and heterogeneous media

This study improves our understanding of instability phenomena that may accompany the transport of dense plumes of dissolved contaminants. One major objective is to test how well analytic stability theory developed by List [1965] applies to the transport of dense plumes in both homogeneous and heterogeneous media. The data to test the prediction come from numerical model experiments in which instability growth is generated by perturbing the interface between fluids of differing density. Stability criteria, as determined by the transverse Rayleigh number, the ratio of transverse to longitudinal Rayleigh numbers, and the nondimensional wave number, compare very well with results observed in the numerical experiments for isotropic media. Comparisons involving correlated random fields were much less successful because plume stability is determined on a local basis as a function of the changing permeability field. Instabilities tend to dissipate in zones of lower permeability and grow in zones of higher permeability. Another objective of the study is to determine the factors that contribute to stability and instability in homogeneous and heterogeneous systems. Sensitivity analyses using a transport model within the framework of Lists stability theory show that stability is promoted by low medium permeability, small density differences, and significant dispersion. In heterogeneous media, stability is promoted by increased correlation length scales and increased log permeability variance. Furthermore, the simulations illustrate the intimate relationship that exists between instability growth and decay and the heterogeneous nature of the permeability field. Thus stability criteria that do not incorporate characteristics of the permeability field will not be suitable for natural or field-scale porous media.

Assessing the anisotropic permeability of Glossifungites surfaces

The potential permeability enhancement of a substrate that has been burrowed by a suite of fauna that inhabit geological firmgrounds (i.e. the Glossifungites ichnofacies) is investigated by using computer simulations, laboratory and field measurements to assess the effective permeability of a Pleistocene Glossifungites surface. All the testing methods indicate that the effective permeability of a substrate is markedly enhanced by the presence of sand-filled Glossifungites burrows in the low-permeability substrate. Furthermore, the permeability of these burrowed horizons can be well approximated by using a modified arithmetic mean that accounts for the degree of interconnectivity between burrows. These formulae are robust and, conceptually at least, can be applied to a variety of geological media and burrow configurations.

Fossilized worm burrows influence the resource quality of porous media

Burrow-associated, selective dolomitization in the Yeoman Formation limestone (Ordovician, Williston basin) is characterized by distinct textural heterogeneity. Physical parameters such as permeability, porosity, tortuosity, and dispersivity are therefore difficult to assess. This study compares the relative dispersivities of three geologic media: homogeneous sandstone, fractured limestone, and burrowed dolomitic limestone. Results show that the flow paths present in burrow-associated dolomite are tortuous, and that the interaction between the flow paths and the matrix is extensive. Such rocks act as dual-permeability systems in the subsurface. Hydrocarbon production from such deposits will be strongly influenced by burrow-related heterogeneity, and its influence should be carefully considered before secondary recovery schemes are implemented.

Surface fluid convection during Cordilleran extension and the generation of metamorphic CO2 contributions to Cenozoic atmospheres

Modeling of hydrogeological regimes associated with crustal extension indicate that flux values for deeply convected meteoric water are on the order of 10 −3 m 3 ċ m −2 ċ yr −1 . Calculated CO 2 fluxes produced by infiltration-driven, metamorphic decarbonation reactions along the circulation path are 2.4 × 10 −4 m 3 ċ m −2 ċ yr −1 . Appication of the model to Cenozoic extension in the North American Cordillera demonstrates that CO 2 generated in this manner may have been a major contributor to elevated CO 2 contents of Cenozoic atmospheres and the resulting global warming due to CO 2 greenhouse effect.

Simulation of dense vapor migration in discretely fractured geologic media

Density-induced advection of organic vapors has been demonstrated to be a significant transport process in granular porous media if the permeability is sufficiently high such that density-induced advection dominates over vapor diffusion. In the context of partially saturated fractured media, the presence of a network of open fractures may lead to rapid rates of density-induced advection of the vapors in the fractures, even though the matrix may have low permeability. To investigate the various factors which affect vapor migration in discretely fractured porous media, a two-dimensional finite element model has been developed whereby the porous matrix is represented by rectangular elements and the fractures are represented as one-dimensional line elements which are superimposed onto the rectangular grid. The cross-sectional model includes the processes of advection due to density and pressure gradients, and vapor and aqueous diffusion in both the fractures and the porous matrix. Phase partitioning between the vapor and aqueous phases and the aqueous and solid phases is assumed to be at equilibrium. Results from simulations involving a single vertical fracture indicate that density-induced advection decreases in importance as the fracture aperture decreases. In this case, there appears to be a critical fracture aperture, above which density-induced advection is the dominant process, and below which vapor diffusion dominates. Simulations that include a network of horizontal and vertical fractures show the importance of matrix properties such as air porosity and water content. An increase in the matrix air porosity results in a higher storage capacity for vapor-phase contaminants and allows more diffusion to occur from the fractures to the matrix, whereas a higher matrix water content results in an increase in the degree of phase partitioning between the vapor and the water phases. Although these two processes act to retard the migration of the vapor plume, they can be problematic in the context of vapor extraction in fractured porous media. The reason for this is that these processes tend to increase the amount of contaminant mass that exists in the low-permeability matrix. As a result, vapor extraction in fractured porous media can be very difficult.

Chapter 27 – Porosity and Permeability in Bioturbated Sediments

Owing to the textural contrast that commonly exists between matrix and trace fossils, biogenic flow media are common in the rock record. Broadly speaking, the permeability contrast between the matrix and the trace-fossil-affected zones constitutes the most important parameter for characterizing biogenically influenced flow media. Biogenic permeability is separated into two categories: (1) highly contrasting permeability fields (dual-permeability networks) and (2) comparably diffuse and lowly contrasting permeability fields (dual-porosity networks). Dual-permeability flow media normally display poor reservoir characteristics in that only the permeable conduits (i.e., trace fossils) effectively transmit fluids, and resources may be absent in the tighter matrix. Also, a large number of tortuous, tubular flow paths constitute the flow medium. Dual porosity may also reduce the resource quality of a sedimentary rock by introducing nearly unpredictable heterogeneities and often presenting a gradient of permeability fields between the burrowed and matrix end-members. The assessment of bulk permeability, which in practical terms is the upscaled permeability from trace-fossil versus matrix-scale to bed- and bedset scales, is in need of research and refinement. At the present, a few studies have shown that the bulk permeability of strata containing isolated burrows dominantly follows the harmonic mean of burrow/matrix permeabilities. As burrow connectivity increases, the geometric and the arithmetic means of permeability can be applied. A gradation exists between the three methods that we are not yet able to characterize. Recent research has shown that the geometric and harmonic means can be applied to media that are > 20% bioturbated. Factors other than connectivity influence bulk permeability, including burrow diameter and burrow architecture. The influence of these parameters is not yet quantified.

Regionalization of Runoff Variability of Alberta, Canada, by Wavelet, Independent Component, Empirical Orthogonal Function, and Geographical Information System Analyses

Statistical methods of wavelet, independent component analysis (ICA), and empirical orthogonal function (EOF) analysis were used together with geographical information systems (GIS) to regionalize runoff variability, establish baseline predisturbance hydrologic regimes, and account for runoff heterogeneity across Alberta, Canada as part of an effort to develop future adaptive forest management practices for Alberta. Both ICA and EOF identified three hydrologic clusters from 59 stations of catchment runoff data. However, ICA identified hydrologic clusters that agree better with the five ecoregions of Alberta than that of EOF. These are the Rocky Mountains and foothills, where runoff was characterized by a fairly consistent temporal variability and dominated by a strong annual cycle, southern Alberta/central Alberta, where temporal heterogeneity and a weak annual cycle dominated the runoff variability, and in southwestern Alberta, where the runoff variability was characterized by annual, 4–7, and 11-year cy...

The impact of gravel extraction on groundwater dependent wetlands and lakes in the Boreal Plains, Canada

The impact of gravel excavation on a groundwater dependent ecosystem (GDE) in a glacial outwash plain was determined using a combination of time-series stable isotopic measurements (δ2H and δ18O) and a numerical flow model of lake–groundwater interaction. Isotopic analyses of the lake and groundwater indicated a shift from a dominance of evaporative enrichment to more meteoric conditions, confirming the hypothesis of increased recharge following forest clearing and gravel extraction from an esker on the outwash plain. The effect of these land-use changes on source water for the GDE was quantified by simulating the lake water budget, seepage, and groundwater conditions for a period spanning pre- and post-mining activity. Enhanced cycling of shallow groundwater, driven by increased recharge in the gravel excavation area, was predicted to cause annual groundwater discharge pulses greater than baseline conditions for the groundwater-fed lake. The additional groundwater discharge represents approximately 4% of the annual lake budget, increasing the flushing rate of the lake. The influence of regional groundwater conditions, represented by variation of water table gradient and outwash hydraulic conductivity, and an alternative excavation location were investigated in a sensitivity analysis. Simulation results illustrate that a simple groundwater capture zone analysis for the GDE could be used to determine a location for gravel excavation that would reduce impact on GDE water source.

Low Evapotranspiration Enhances the Resilience of Peatland Carbon Stocks to Fire

Boreal peatlands may be vulnerable to projected changes in the wildfire regime under future climates. Extreme drying during the sensitive post-fire period may exceed peatland ecohydrological resilience, triggering long-term degradation of these globally significant carbon stocks. Despite these concerns, we show low peatland evapotranspiration at both the plot and landscape scale post-fire, in water-limited peatlands dominated by feather moss that are ubiquitous across continental western Canada. Low post-fire evapotranspiration enhance the resilience of carbon stocks in such peatlands to wildfire disturbance and reinforces their function as a regional source or water. Near-surface water repellency may provide an important, previously unexplored, regulator of peatland evapotranspiration that can induce low evapotranspiration in the initial post-fire years by restricting the supply of water to the peat surface.