Anisotropic dual-continuum representations for multiscale poroelastic materials:Development and numerical modelling

Dual-continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual-scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual-material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the dual-continuum model against fine-scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine-scale simulations show anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine-scale representations

Foundations and their practical implications for the constitutive coefficients of poromechanical dual-continuum models

A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.Comment: Transport in Porous Media (2019

Modelling of long-term along-fault flow of CO2 from a natural reservoir

Geological sequestration of CO2 requires the presence of at least one competent seal above the storage reservoir to ensure containment of the stored CO2. Most of the considered storage sites are overlain by low-permeability evaporites or mudrocks that form competent seals in the absence of defects. Potential defects are formed by man-made well penetrations (necessary for exploration and appraisal, and injection) as well as (for mudrocks) natural or injection-induced fracture systems through the caprock. These defects need to be de-risked during site selection and characterisation. A European ACT-sponsored research consortium, DETECT, developed an integrated characterisation and risk assessment toolkit for natural fault/fracture pathways. In this paper we describe the DETECT experimental-modelling workflow, which aims to be predictive for fault-related leakage quantification, and its application to a field case example for validation. The workflow combines laboratory experiments to obtain single-fracture stress-sensitive permeabilities; single-fracture modelling for stress-sensitive relative permeabilities and capillary pressures; fracture network characterisation and modelling for the caprock(s); upscaling of properties and constitutive functions in fracture networks; and full compositional flow modelling at field scale. We focus the paper on the application of the workflow to the Green River Site in Utah. This is a rare case of leakage from a natural CO2 reservoir, where CO2 (dissolved or gaseous) migrates along two fault zones to the surface. This site provides a unique opportunity to understand CO2 leakage mechanisms and volumes along faults, because of its extensive characterisation including a large dataset of present-day CO2 surface flux measurements as well as historical records of CO2 leakage in the form of travertine mounds. When applied to this site, our methodology predicts leakage locations accurately and, within an order of magnitude, leakage rates correctly without extensive history matching. Subsequent history matching achieves accurate leak rate matches within a-priori uncertainty ranges for model input parameters

EMSL Pore Scale Modeling Challenge/Workshop

Report covers the background for the workshop, objectives, important research directions, necessary capabilities and overall recommendations

The role of percolating and non-percolating phases in multiphaseflow in porous media

Das Verständnis makroskopischer Phänomene bei Mehrphasenströmungen in porösen Medien ist sowohl von wissenschaftlicher Seite als auch für Anwendungen von großem Interesse. Obwohl seit über einem Jahrhundert intensiv daran geforscht wird und die Phänomene auf der Porenskala durch die Gleichungen der klassischen Hydrodynamik beschrieben werden, ist bis heute keine Theorie vorhanden, die auf Labor- und Feldskala Hysterese und residuale Fluidkonfigurationen bei Mehrphasenströmungen umfassend und physikalisch richtig beschreibt. Die Berücksichtigung der unterschiedlichen hydrodynamischen Eigenschaften von perkolierenden und nichtperkolierenden Fluidanteilen auf makroskopischen Skalen könnte der Schlüssel zu einem besseren Modell sein. Hilfer schlägt ein Modell vor (Phys. Rev. E. 73, 016307 (2006)), in welchem diese Unterschiede nicht ignoriert werden. Erste quasistationäre Lösungen dieses Modells geben Hoffnung, dass durch das Einbeziehen dieser Unterschiede in der Modellbildung Schwachpunkte traditioneller Ansätze behoben werden können. Weitergehende Untersuchungen dieses Modells und seiner Gleichungen bilden die Aufgabenstellung dieser Dissertation. Um die Gleichungen zu studieren, wurden Umformungen und Näherungen formuliert, die analytische Lösungen ermöglichen. Außerdem wurden Schließbedingungen formuliert, die die Lösung zeitabhängiger Fragestellungen erlauben. Vier Anfangs- und Randwertprobleme wurden analytisch bzw. quasianalytisch gelöst. Sie sind Verallgemeinerungen des Buckley-Leverett-Problems, der schwerkraftgetriebenen Umverteilung, des McWhorter-Sunada-Problems und des Philip-Problems. Ferner wurden vier numerische Algorithmen entwickelt, die Anfangs- und Randwertprobleme für unterschiedliche mathematische Formulierungen und physikalische Näherungen des Modells lösen. Mit diesen Algorithmen wurden Laborexperimente simuliert. Die Experimente können drei Klassen zugeordnet werden. Die erste Klasse bilden Experimente mit einer geschlossenen porösen Säule. In diesen Experimenten bewirken allein die Schwerkraft und Kapillar- und Grenzflächenkräfte eine Umverteilung der Fluide. Die Ergebnisse zeigen, dass das Modell hysteretisches Verhalten in Sättigungsverteilungen beschreiben kann. Sie illustrieren außerdem Gemeinsamkeiten und Unterschiede zu bestehenden Modellen. Die gewonnenen Aussagen können im Labor überprüft werden. Die zweite Klasse bilden Experimente, bei denen eine poröse Säule von einem von außen aufgeprägten Fluss durchströmt wird. Die Simulationen zeigen, dass die Beschreibung der Dynamik residualer Sättigungen mit diesem Modell möglich ist. Die dritte Klasse bilden Experimente mit Druckrandbedingungen. Solche Experimente werden im Labor zur Bestimmung und Überprüfung von Kapillardrucksättigungsbeziehungen durchgeführt. Die Simulation eines solchen Experiments stimmt gut mit Messwerten aus der Literatur überein. Die Ergebnisse dieser Dissertation zeigen, dass zumindest einige Schwächen traditioneller Ansätze durch die Berücksichtigung der unterschiedlichen hydrodynamischen Eigenschaften von perkolierenden und nichtperkolierenden Fluidanteilen behoben werden können. Für das neue Modell wurden analytische und quasianalytische Lösungen bestimmt und Verfahren entwickelt, numerische Lösungen zu berechnen. Einige der numerischen Lösungen wurden mit experimentellen Daten verglichen. Es konnte eine gute Übereinstimmung der Ergebnisse gezeigt werden. Die übrigen Lösungen dienen als Vorschlag für Experimentatoren. Eine Durchführung dieser Experimente im Labor würde wichtige Erkenntnisse zur Qualität des Modells liefern.Understanding macroscopic phenomena of multiphase flow in porous media is of great interest for applications but from a scientific perspective as well. Although it has been a focus of research for more than a century and the dynamics of the fluids on pore-scale are governed by the classical hydrodynamic equations, until now, a theory which predicts comprehensively and physically sound hysteretic phenomena and residual fluid configurations on the laboratory and field scale has not been available. Percolating and nonpercolating fluid parts show fundamentally different hydrodynamic behavior and taking into account these differences on macroscopic scales might be the key to a better model. Hilfer proposes a model (Phys. Rev. E. 73, 016307 (2006)) which treats microscopically percolating fluid regions and nonpercolating regions as distinct phases on a macroscopic scale. In a quasi-stationary limit, the results indicate that the model may solve deficiencies of traditional approaches. Further studies of the proposed model form the objective of this thesis. The model is investigated by using different strategies including analytical, numerical and modeling techniques. The underlying set of nonlinear, coupled, partial differential equations has been reformulated and approximations have been made to render analytical solutions possible. Closure conditions permitting time-dependent solutions have been proposed. Four initial and boundary value problems have been set and solved analytically and quasi analytically respectively. The problems are generalizations of the Buckley-Leverett problem, the gravity driven redistribution, the McWhorter-Sunada problem and the Philip problem for traditional approaches. Further, four different numerical algorithms have been developed to solve initial and boundary value problems for different mathematical formulations and physical approximations of the model. These algorithms have been used to simulate laboratory experiments. Considered are three different categories of experiments. The first category covers experiments with a closed porous column. In these experiments, gravity as well as capillary and interfacial forces exclusively induce a redistribution of the fluids. The results show that the model predicts hysteresis in the dynamics of the fluids. They illustrate further the similarities and differences to existing models. The results may be checked in the laboratory. The second category covers experiments with a porous column which is streamed by an externally applied flux. The simulations show that residual saturation dynamics are described by the model. The third category covers experiments in which the pressure at the boundaries of the porous column is controlled. Such experiments are usually conducted to measure capillary pressure saturation relations. A comparison of simulations and experimental data shows good agreement. In this thesis, it has been shown that at least some of the deficiencies of traditional approaches are solved by taking into account the distinct hydrodynamic properties of percolating and nonpercolating fluid parts. Analytical and quasi analytical solutions have been found and numerical methods and algorithms have been developed. Some numerical solutions have been compared to experimental data with good agreement. The other solutions suggest experiments to further validate the model