Daniel R. Lester

Stochastic relationships for periodic responses in randomly heterogeneous aquifers

[1]xa0The aim of this work is to develop a theoretical framework for the analysis of groundwater head oscillations commonly observed in bores near boundaries of surface water bodies that are subject to periodic variations in stage height. Restricting attention to the linear groundwater flow equation, the dynamics of head variations induced by periodic modes acting at boundaries are governed by a complex-valued time-independent equation parameterized by the modal frequency of interest. For randomly heterogeneous aquifers the hydraulic conductivity field may be regarded as a spatial random variable. Stochastic relationships between the conductivity spectrum and the induced head oscillation spectrum are generated from a stochastic perturbation approach. Spatial correlative relationships are derived for several stochastic models incorporating up to three spatial dimensions. Explicit calculations of head oscillation autocovariances and spectral densities are parameterized by conductivity statistics, including integral scale and variance, and by modal frequency. The results show that time domain head responses to periodic boundary forcing are strongly dependent on multidimensional effects and on spatial correlation structure. Computational simulations show that the stochastic variance estimators match simulated head fluctuation variances for a range of modal frequencies and aquifer diffusivities and that joint inversion of conductivity integral scale and variance is possible with moderate numbers of sampling points.

Toward enhanced subsurface intervention methods using chaotic advection.

Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media. These scalars can be targeted by pump-and-treat methods or by amendment technologies. Application examples include in-situ leaching for metals, recovery of dissolved contaminant plumes, or utilizing heat energy in geothermal reservoirs. While conventional pumping methods work reasonably well, costs associated with maintaining pumping schedules are high and improvements in efficiency would be welcome. In this paper we discuss how transient switching of the pressure at different wells can intimately control subsurface flow, generating a range of programmed flows with various beneficial characteristics. Some programs produce chaotic flows which accelerate mixing, while others create encapsulating flows which can isolate fluid zones for lengthy periods. In a simplified model of an aquifer subject to balanced pumping, chaotic flow topologies have been predicted theoretically and verified experimentally using Hele-Shaw cells. Here, a survey of the key characteristics of chaotic advection is presented. Mathematical methods are used to show how these characteristics may translate into practical situations involving regional flows and heterogeneity. The results are robust to perturbations, and withstand significant aquifer heterogeneity. It is proposed that chaotic advection may form the basis of new efficient technologies for groundwater interventions.

Global parametric solutions of scalar transport

Passive scalar transport involves complex interactions between advection and diffusion, where the global transport rate depends upon scalar diffusivity and the values of the (possibly large) set of parameters controlling the advective flow. Although computation of a single solution of the advection-diffusion equation (ADE) is simple, in general it is prohibitively expensive to compute the parametric variation of solutions over the full parameter space Q, even though this is crucial for, e.g. optimization, parameter estimation, and elucidating the global structure of transport. By decomposing the flows within Q so as to exploit symmetries, we derive a spectral method that solves the ADE over Q three orders of magnitude faster than other methods of similar accuracy. Solutions are expressed in terms of the exponentially decaying natural periodic patterns of the ADE, sometimes called strange eigenmodes. We apply the method to the experimentally realisable rotated arc mixer chaotic flow, both to establish numerical properties and to calculate the fine-scale structure of the global solution space for transport in this chaotic flow. Over 10^5 solutions within Q are resolved, and spatial pattern locking, a symmetry breaking transition to disordered spatial patterns, and fractally distributed optima in transport rate are observed. The method exhibits exponential convergence, and efficiency increases with resolution of Q.

On oscillating flows in randomly heterogeneous porous media

The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties.

Transport in a partially open porous media flow

In nature dissipative fluxes of fluid, heat, and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flow and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring.

Groundwater Cooling of a Supercomputer in Perth, Western Australia: Hydrogeological Simulations and Thermal Sustainability

Groundwater cooling (GWC) is a sustainable alternative to conventional cooling technologies for supercomputers. A GWC system has been implemented for the Pawsey Supercomputing Centre in Perth, Western Australia. Groundwater is extracted from the Mullaloo Aquifer at 20.8xa0°C and passes through a heat exchanger before returning to the same aquifer. Hydrogeological simulations of the GWC system were used to assess its performance and sustainability. Simulations were run with cooling capacities of 0.5 or 2.5 Mega Watts thermal (MWth), with scenarios representing various combinations of pumping rate, injection temperature and hydrogeological parameter values. The simulated system generates a thermal plume in the Mullaloo Aquifer and overlying Superficial Aquifer. Thermal breakthrough (transfer of heat from injection to production wells) occurred in 2.7–4.3xa0years for a 2.5 MWth system. Shielding (reinjection of cool groundwater between the injection and production wells) resulted in earlier thermal breakthrough but reduced the rate of temperature increase after breakthrough, such that shielding was beneficial after approximately 5 years pumping. Increasing injection temperature was preferable to increasing flow rate for maintaining cooling capacity after thermal breakthrough. Thermal impacts on existing wells were small, with up to 10 wells experiencing a temperature increaseu2009≥u20090.1xa0°C (largest increase 6xa0°C).RésuméLe refroidissement par eaux souterraines (RES) est une alternative durable aux technologies conventionnelles de refroidissement pour les superordinateurs. Un système RES a été mis en œuvre pour le Centre de Supercalcul de Pawsey à Perth en Australie occidentale. L’eau souterraine est extraite de l’aquifère Mullaloo à une température de 20.8xa0°C et circule à travers un échangeur à chaleur avant d’être réinjectée dans le même aquifère. Des simulations hydrogéologiques du système RES ont été utilisées pour évaluer sa performance et durabilité. Les simulations ont été effectuées en considérant des capacités de refroidissement de 0.5 ou 2.5 Mega Watts thermique (MWth), avec des scénarios représentant différentes combinaisons de débit de pompage, de température d’injection et de valeurs de paramètres hydrogéologiques. Le système simulé génère un panache thermique dans l’aquifère de Mullaloo et dans l’aquifère superficiel sus jacent. La percée thermique (transfert de chaleur à partir de l’injection vers les puits de production) s’est produite après 2.7–4.3 ans pour le système 2.5 MWth. Un blindage (réinjection d’eau souterraine froide entre les puits d’injection et de production) a entraîné une percée thermique plus tôt, mais a réduit le taux d’augmentation de la température après la percée, de telle sorte que ce blindage a été bénéfique après environ 5 ans de pompage. L’augmentation de la température d’injection était préférable à l’augmentation du débit pour maintenir la capacité de refroidissement après la percée thermique. Les impacts thermiques sur les puits existants étaient faibles, avec un maximum de 10 puits connaissant une augmentation de températureu2009≥u20090.1xa0°C (la plus grande augmentation est de 6xa0°C).ResumenEl enfriamiento por agua subterránea (GWC) es una alternativa sustentable para las tecnologías convencionales de enfriamiento de supercomputadoras. Se implementó un sistema GWC para el Pawsey Supercomputing Centre en Perth, Australia occidental. El agua subterránea se extrae del acuífero Mullaloo a 20.8xa0°C y pasa a través de un intercambiador de calor antes de retornar al mismo acuífero. Las simulaciones hidrogeológicas del sistema GWC se usaron para evaluar su rendimiento y sustentabilidad. Las simulaciones se corrieron con capacidades de enfriamiento de 0.5 o 2.5 Mega Watts térmicos (MWth), con escenarios que representan varias combinaciones de caudales de bombeo, temperaturas de inyección y valores de parámetros hidrogeológicos. El sistema simulado genera una pluma térmica en el acuífero Mullaloo y en el acuífero superficial suprayacente. La ruptura térmica (transferencia de calor a partir de la inyección a los pozos de producción) ocurrió en 2.7–4.3 años para una sistema de 2.5 MWth. El blindaje (reinyección de agua subterránea fría entre los pozos de inyección y los pozos de producción) dio lugar a una ruptura térmica más temprana, pero redujo la tasa de aumento de la temperatura después de la ruptura, de tal manera que el blindaje fue beneficioso después de aproximadamente 5 años de bombeo. El aumento de temperatura de inyección fue preferible al aumento de la tasa de flujo para mantener la capacidad de enfriamiento después de la ruptura térmica. Los impactos térmicos en los pozos existentes fueron pequeños, con hasta 10 pozos experimentando un aumento de la temperaturau2009≥u20090.1xa0° C (el incremento mayor fue de 6xa0° C).摘要对于超级计算机常规冷却技术来说,地下水冷却一个可持续的可替代选择。西澳大利亚珀斯Pawsey超级计算中心应用了地下水冷却系统。20.8 °C的地下水从Mullaloo含水层抽取,在返回含水层前经过热交换器。利用地下水冷却系统的水文地质模拟评价其性能和可持续性。模拟时冷却能力为0.5或2.5 百万瓦热量,展现抽水量、注入温度和水文地质参数值各种组合方案。模拟系统在Mullaloo含水层及上覆的表层含水层产生了热卷流。一个2.5 百万瓦热量系统2.7–4.3 年后出现了热突围 (从注入井到生产井的热传递)。屏蔽 (注入井和生产井之间的冷却地下水再注入) 导致较早的热突围,但降低了突围后温度增加的速度,这样,大约抽水5年后,屏蔽是非常有益的。对突围后保持冷却能力来说,增加注入温度比增加流速更好。对现有井的热影响非常小, 有10口井温度升高了u2009≥u20090.1xa0°C (升高最多的为6 °C)。ResumoO resfriamento por águas subterrâneas (RPAS) é uma alternativa sustentável às tecnologias de resfriamento convencional para supercomputadores. Um sistema de RPAS foi implementado para o Centro de Supercomputação de Pawsey em Perth, Austrália Ocidental. A água subterrânea é extraída a partir do Aquífero Mullaloo à 20.8xa0°C e passa através de um trocador de calor antes de retornar ao mesmo aquífero. Simulações hidrogeológicas do sistema de RPAS foram usadas para avaliar seu desempenho e sustentabilidade. Simulações foram executadas com capacidades de resfriamento de 0.5 ou 2.5 Mega Watts termais (MWt), com cenários representando várias combinações de taxas de bombeamento, temperatura de injeção e valores de parâmetros hidrogeológicos. O sistema simulado gera uma pluma termal no Aquífero Mullaloo e no Aquífero Superficial sobrejacente. Colapso termal (transferência de calor da injeção ao poço de produção) ocorreu de 2.7–4.3 anos para um sistema de 2.5 MWt. A proteção (reinjeção da água fria entre os poços de injeção e produção) resultou em um colapso termal anterior mas reduziu a taxa de aumento da temperatura despois do colapso, tal que a proteção foi benéfica depois de aproximadamente 5 anos de bombeamento. O aumento da temperatura de injeção foi preferido à aumentar a taxa de fluxo na manutenção da capacidade de resfriamento após o colapso termal. Impactos termais nos poços existentes foram pequenos, com um total de 10 poços apresentando um aumento de temperaturau2009≥u20090.1xa0°C (maior aumento 6xa0°C).

Complete parametric scalar dispersion

Complex interactions between advection and diffusion give rise to enhanced scalar transport in cases where the advective field generates Lagrangian chaos. As the dispersion rate is a complex function of scalar diffusivity and parameters controlling the flow field, resolution of scalar dispersion over this parameter space is useful for better understanding interactions between advection and diffusion. In this paper we resolve the fine-scale structure asymptotic transport over the flow parameter space for Peclet numbers from 100 to 105 for a physically realizable flow, yielding a 50-fold acceleration of scalar dispersion at Pe = 105. These results generate considerable insight into the global structure of transport and facilitate identification of mechanisms governing scalar dispersion; features include fractal distributions of dispersion rate, solution mode-locking, an order-disorder transition and localisation of transport optima.

Lagrangian topology of reoriented potential flows

Scalar transport in closed potential flows is investigated for the specific case of a periodically reoriented dipole flow. For scalar advection, Lagrangian chaos can be achieved with breakdown of the regular Hamiltonian structure, which is governed by symmetry conditions imposed by the dipole flow. Instability envelopes associated with period-doubling bifurcations of fixed points govern which regions of the flow control parameter space admits global chaos. These are further refined via calculation of Lyapunov exponents. These results suggest significant scalar transport enhancement is possible within potential flows, given appropriate programming of stirring protocols.