Robert A. Schincariol

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.

Dispersive mixing dynamics of dense miscible plumes: natural perturbation initiation by local-scale heterogeneities

Abstract Two-dimensional, coupled variable-density flow and transport simulations with heterogeneous media advance understanding of how local-scale non-idealities create and control instabilities. Dense plumes (5000 mg l −1 NaCl) are introduced into a domain (1.50×0.56 m) with synthetically generated permeability fields. Simulations with the first set of realizations [mean permeability ( k )=5.7×10 −11 m 2 , ln( k ) variance=0.25, longitudinal correlation length ( τ x )=0.10 m, transverse correlation length ( τ z )=0.02 m] illustrate how the lower plume boundary is naturally perturbed by local-scale heterogeneities. Some of these perturbations are stable, some are highly bounded or pseudostable in certain portions of the field, while others rapidly destabilize the lower plume boundary. Even with similar macroscopic field statistics, widely varying degrees of density-induced mixing occur among different realizations. Unstable perturbations result in complex mixing features, such as coalescing of instability lobes as different portions of the plume sample various regions of the permeability field. Such mixing greatly enhances and controls the dispersion process. Based on the control that local field characteristics exhibit on instability growth and decay, the applicability of stability criteria to plume-type displacements in natural heterogeneous media is likely inappropriate. Additional simulations employing fields of lower variance and lower densities illustrate the delicate balance between these variables and the ability of the field to propagate unstable perturbations.

Impact of Groundwater Flow and Energy Load on Multiple Borehole Heat Exchangers

The effect of array configuration, that is, number, layout, and spacing, on the performance of multiple borehole heat exchangers (BHEs) is generally known under the assumption of fully conductive transport. The effect of groundwater flow on BHE performance is also well established, but most commonly for single BHEs. In multiple-BHE systems the effect of groundwater advection can be more complicated due to the induced thermal interference between the boreholes. To ascertain the influence of groundwater flow and borehole arrangement, this study investigates single- and multi-BHE systems of various configurations. Moreover, the influence of energy load balance is also examined. The results from corresponding cases with and without groundwater flow as well as balanced and unbalanced energy loads are cross-compared. The groundwater flux value, 10(-7) m/s, is chosen based on the findings of previous studies on groundwater flow interaction with BHEs and thermal response tests. It is observed that multi-BHE systems with balanced loads are less sensitive to array configuration attributes and groundwater flow, in the long-term. Conversely, multi-BHE systems with unbalanced loads are influenced by borehole array configuration as well as groundwater flow; these effects become more pronounced with time, unlike when the load is balanced. Groundwater flow has more influence on stabilizing loop temperatures, compared to array characteristics. Although borehole thermal energy storage (BTES) systems have a balanced energy load function, preliminary investigation on their efficiency shows a negative impact by groundwater which is due to their dependency on high temperature gradients between the boreholes and surroundings.

Geothermal Waste Heat Utilization from In Situ Thermal Bitumen Recovery Operations

In situ thermal methods for bitumen extraction introduce a tremendous amount of energy into the reservoirs raising ambient temperatures of 13 °C to as high as 200 °C at the steam chamber edge and 50 °C along the reservoir edge. In essence these operations have unintentionally acted as underground thermal energy storage systems which can be recovered after completion of bitumen extraction activities. Groundwater flow and heat transport models of the Cold Lake, Alberta, reservoir, coupled with a borehole heat exchanger (BHE) model, allowed for investigating the use of closed-loop geothermal systems for energy recovery. Three types of BHEs (single U-tube, double U-tube, coaxial) were tested and analyzed by comparing outlet temperatures and corresponding heat extraction rates. Initial one year continuous operation simulations show that the double U-tube configuration had the best performance producing an average temperature difference of 5.7 °C, and an average heat extraction of 41 W/m. Given the top of the reservoir is at a depth of 400 m, polyethylene piping provided for larger extraction gains over more thermally conductive steel piping. Thirty year operation simulations illustrate that allowing 6 month cyclic recovery periods only increases the loop temperature gain by a factor of 1.2 over continuous operation. Due to the wide spacing of existing boreholes and reservoir depth, only a small fraction of the energy is efficiently recovered. Drilling additional boreholes between existing wells would increase energy extraction. In areas with shallower bitumen deposits such as the Athabasca region, i.e. 65 to 115 m deep, BHE efficiencies should be larger.

A Synthesis of Three Decades of Eco-Hydrological Research at Scotty Creek, NWT, Canada

Scotty Creek, Northwest Territories (NWT), Canada, has been the focus of hydrological research for nearly three decades. Over this period, field and modelling studies have generated new insights into the thermal and physical mechanisms governing the flux and storage of water in the wetland-dominated regions of discontinuous permafrost that characterises much of the Canadian and circumpolar subarctic. Research at Scotty Creek has coincided with a period of unprecedented climate warming, permafrost thaw, and resulting land cover transformations including the expansion of wetland areas and loss of forests. This paper (1) synthesises field and modelling studies at Scotty Creek, (2) highlights the key insights of these studies on the major water flux and storage processes operating within and between the major land cover types, and (3) provides insights into the rate and pattern of the permafrost-thaw-induced land cover change and how such changes will affect the hydrology and water resources of the study region.

Fundamentals of Ground Water

The hydrologic sciences continue to grow in importance as issues of drought, population growth and pollution, and politics come together to raise water issues to new levels. While groundwater hydrology plays a central role in the hydrologic sciences, relatively few comprehensive textbooks cover this field. Between 1959 and 1979, Ground Water Hydrology (D.K.Todd) guided students and professionals. In 1979, Groundwater, (R.A. Freeze and J.A. Cherry) integrated geology and hydrology physics and chemistry and science and engineering. That text was followed in 1980 by Applied Hydrogeology (C.W. Fetter). Addressing a need for a new textbook, Physical and Chemical Hydrogeology (P.A. Domenico and F.W. Schwartz) was published in 1990.