The current streamline formulation is limited to single-porosity systems and is then not suitable for application to naturally fractured reservoirs. Describing the fluid transport in naturally fractured reservoirs has been recognized as a main challenge for simulation engineers due to the complicated physics involved. In this work, we generalized the streamline-based simulation to describe the fluid transport in naturally fractured reservoirs. We implemented three types of transfer function: the conventional transfer function (CTF), the diffusion transfer function (DTF), and the empirical transfer function (ETF). We showed that these transfer functions can be implemented easily in the current single-porosity streamline codes. These transfer functions have been added as a source term to the transport equation that describes the saturation evolution along the streamlines. We solved this equation numerically for all types of transfer functions. The numerical solution of the continuity equation with DTF and ETF requires discretizing a convolution term. We derived an analytical solution to the saturation equation with ETF in terms of streamline TOF to validate the numerical solution. We obtain an excellent match between the numerical and the analytical solution. The final stage of our study was to validate our work by comparing our dual-porosity streamline simulator (DPSS) to the commercial dual-porosity simulator, ECLIPSE. The dual-porosity ECLIPSE uses the CTF to describe the interaction between the matrix-blocks and the fracture system. The dual-porosity streamline simulator with CTF showed an excellent match with the dual-porosity ECLIPSE. On the other hand, dual-porosity streamline simulation with DTF and ETF showed a lower recovery than the recovery obtained from the dual-porosity ECLIPSE and the DPSS with CTF. This difference in oil recovery is not due to our formulation, but is related to the theoretical basis on which CTF, DTF, and ETF were derived in the literature. It was beyond the scope of this study to investigate the relative accuracy of each transfer function. We demonstrate that the DPSS is computationally efficient and ideal for large-scale field application. Also, we showed that the DPSS minimizes numerical smearing and grid orientation effects compared to the dual-porosity ECLIPSE.

The karst research community has known that traditional numerical groundwater flow codes ignore the non-Darcian, dual-permeability components of flow that can occur in karst aquifers. In this study, the potential limitations of using such tools are quantified by evaluating the relative performances of 3 groundwater flow models at a test-site near Weeki Wachee, Florida, in the dual-permeability Upper Floridan aquifer. MODFLOW-2005 and MODFLOW-2005 Conduit Flow Process (CFP), a Darcian/non-Darcian, dual-permeability groundwater flow code recently developed by the U.S. Geological Survey, are used in this study. A monitoring program consisting of discharge measurements and high frequency data from 2 springs and monitoring wells penetrating the matrix and conduit networks of a karst aquifer was initiated to characterize the test-site and constrain new parameters introduced with MODFLOW-2005 CFP. The monitoring program spanned conditions prior to, during, and following convective and tropical storm activity, and a drought. Analytical estimates for Reynolds numbers, ranging from 105 to 106, suggest that turbulent flow occurs in portions of the underlying conduit network. The direction and magnitude of fluid exchange observed between the matrix and conduit network indicate the conduit network underlying the test-site drains the matrix. Head differences and observed responses in monitoring wells penetrating the matrix and conduit network indicate that the hydraulic conductivities between the 2 networks do not significantly differ from each other. A conceptual model for the spatial distribution of preferential flow pathways using multiple data types, including shallow recession limbs observed in discharge hydrographs indicate a slow responding aquifer with a high storage capacity, and a poorly integrated conduit drainage network with little to no point recharge. Model performances were evaluated by comparing observed hydrographs for discharge and monitoring wells penetrating the matrix and conduit network following convective and tropical storm events, and drought conditions, to simulated values from transient simulations. Model statistics for 32 target wells and sensitivity analysis were included in the evaluation. The dual-permeability model using the MODFLOW-2005 CFP Mode 1 displayed the highest performance with improved matches ranging from 12 to 40% between simulated and observed discharges relative to the laminar and laminar/turbulent equivalent-continuum models.

[pt] A presença de fraturas naturais em reservatórios de petróleo pode gerar grandes impactos no deslocamento de fluidos em seu interior. Os maiores problemas estão na irregularidade da área varrida pelo fluido injetado, por exemplo, a água, e a antecipação dos breakthroughs, ou seja, a chegada precoce da água aos poços produtores. De modo a analisar o efeito promovido pela presença de fraturas no meio, foram simulados os dois modelos de simulação de fluxo em reservatórios fraturados: o modelo de dupla-porosidade (DP) e o modelo de dupla-porosidade e dupla-permeabilidade (DPDK), bem como outros dois modelos derivados do modelo DP, o modelo de Subdomínios (SD) e o modelo MINC (Multiple Interacting Continua). Também foram realizadas análises paramétricas para compreender o impacto de propriedades, como as permeabilidades tanto da matriz quanto da fratura e o espaçamento das fraturas, no comportamento do fluxo em reservatórios fraturados. A presença de corredores de fraturas (fracture swarms) foi, igualmente, avaliada, assim como seu efeito associado à presença de camadas de altíssima permeabilidade (super-K). Por fim, foi simulado um modelo mais complexo, denominado GTEP, o qual foi construído a partir de uma seção aplicada à simulação de um reservatório carbonático gigante do Oriente Médio, com o intuito de exemplificar a irregularidade da área varrida em reservatórios naturalmente fraturados. / [en] The presence of natural fractures in oil reservoirs can generate major impacts on the fluid displacement inside them. The greatest problems are irregularity in the area swept by the injected fluid, e.g. water, and breakthroughs anticipation, or early arrival of water to the producing wells. In order to analyze the effect of the presence of fractures in the medium, two flow models of fractured reservoirs were constructed: the dual-porosity model (DP) and the dual-porosity and dual permeability model (DPDK), as well as two other models derived from the DP model, Subdomains model (SD) and MINC model (Multiple Interacting Continua). Parametric analyzes were also conducted to comprehend the impact of properties, such as the matrix permeability, the fracture permeability and the fracture spacing, on the flow behavior in fractured reservoirs. The presence of fracture corridors (fracture swarms) was also evaluated in three models, as well as its effect associated with the presence of layers of high permeability, denoted super-K. Finally, a more complex model, called GTEP Field, was simulated, which was constructed from a section applied to the simulation of a giant carbonate reservoir in the Middle East, in order to illustrate the irregularity of the swept area in natural fractured reservoirs.

[pt] Os reservatórios não convencionais de folhelho possuem permeabilidades muito baixas sendo necessário fraturar hidraulicamente a formação para aumentar a permeabilidade e conseguir um melhor desempenho do poço. O fraturamento hidráulico em vários estágios criado a partir de um poço horizontal gera uma complexa rede de fraturas, com variadas condutividades dentro do volume de reservatório estimulado. Neste trabalho realizamos análises paramétricas para avaliar os efeitos no desempenho do poço produtor causadas pela variação dos diferentes parâmetros dentro da complexa rede de fraturas criada. Estes parâmetros foram principalmente: os espaçamentos na rede de fraturas (sem propante), a condutividade na rede de fraturas (sem propante), a condutividade das fraturas primárias (preenchidas com propante), os espaçamentos das fraturas primárias (preenchidas com propante), a variação da permeabilidade ao longo das fraturas primárias e finalmente a variação das pressões do fundo do poço. Entender as relações entre o tamanho da rede de fraturas, os espaçamentos, a distribuição do propante e a condutividade das fraturas são parâmetros chaves para definir estratégias de estimulação e completação. Finalmente se fez uma simulação com injeção de água avaliando o impacto que causa na recuperação total de óleo e gás, e analisamos a possibilidade de aplicar este método de recuperação num reservatório fraturado hidraulicamente. / [en] The shale reservoirs have ultralow permeability requiring hydraulically fracturing the formation to improve permeability and get a better well performance. The multistage hydraulic fractures system created from a horizontal well generates a complex fracture network with different conductivities within the stimulated reservoir volume. In this work we made parametric analyzes to assess the effects on producer well performance caused by the variation of different parameters within the complex network fractures created. These parameters were mainly: spacing in the un-propped fracture network, the conductivity in the unpropped fracture network, primary fracture conductivity, primary fracture spacing, the variation of permeability along the primary fractures and finally the variation of downhole pressures. Understanding the relationship between fracture network size, fracture spacing, proppant distribution, and fracture conductivity is critical to stimulation and completion design. Finally a simulation with water injection evaluating its impact on recovering oil and gas was carried out, and the possibility of applying this method of recovery in a fractured reservoir was evaluated.The shale reservoirs have ultralow permeability requiring hydraulically fracturing the formation to improve permeability and get a better well performance. The multistage hydraulic fractures system created from a horizontal well generates a complex fracture network with different conductivities within the stimulated reservoir volume. In this work we made parametric analyzes to assess the effects on producer well performance caused by the variation of different parameters within the complex network fractures created. These parameters were mainly: spacing in the un-propped fracture network, the conductivity in the unpropped fracture network, primary fracture conductivity, primary fracture spacing, the variation of permeability along the primary fractures and finally the variation of downhole pressures. Understanding the relationship between fracture network size, fracture spacing, proppant distribution, and fracture conductivity is critical to stimulation and completion design. Finally a simulation with water injection evaluating its impact on recovering oil and gas was carried out, and the possibility of applying this method of recovery in a fractured reservoir was evaluated.

[pt] Os reservatórios de petróleo do pré-sal brasileiro são encontrados em rochas carbonáticas localizadas em ambiente offshore na borda da plataforma continental. Com o fim de explorar essas jazidas de forma mais segura e rentável, é essencial representá-las corretamente nos modelos de simulação de escoamento. Entretanto, esta não é uma tarefa simples. Essas rochas carbonáticas recorrentemente apresentam fraturas e carstes nos quais o escoamento se comporta de forma diferente da simulação tradicional utilizando porosidade única. Para solucionar o problema, existem técnicas que representam o escoamento através dos diversos meios porosos. No entanto, essas modelagens inserem diversas complexidades para a correta caracterização das formações geológicas e da previsão da produção. Nesse trabalho são analisados os impactos que algumas das características das fraturas, da matriz e da malha de poços têm no resultado das simulações com dupla porosidade e permeabilidade. / [en] Petroleum reservoirs of the Brazilian pre-salt are found in carbonate rocks located offshore at the edge of the continental shelf. To optimize the exploitation of these reservoirs, it is of paramount importance to properly represent them in the flow simulation models. Nevertheless, this is not a straightforward task. Carbonate rocks usually present fractures and karsts, where flow differs from what is traditionally represented by single porosity reservoir simulators. With the purpose of better modelling the fluid flow behavior through multiple media, alternative techniques exist. However, these alternatives require additional complexities and variables for the adequate characterization of the geologic formations and production forecast. In this work, the impact that some of the fracture and matrix characteristics and the well positioning have on the results of dual-porosity and dual-permeability simulations is addressed.

L’objectif général de ma thèse est de développer une modélisation spatialisée à l’échelle d’un versant, afin de mieux rendre compte des principales voies de transfert des pesticides dans les terrains agricoles. Je cherche à adopter une approche simplifiée, mais qui permet néanmoins de représenter les discontinuités existantes (parcelles, fossés, talus … etc). En effet, on souhaite pouvoir quantifier les mécanismes du transfert des pesticides en prenant en compte l’influence des éléments du paysage (parcelles, fossés, bandes enherbées …etc) sur la partition des transferts d’eau et de pesticides en surface et en subsurface. On s’appuie pour ce développement sur les données acquises sur le bassin versant expérimental de la Morcille (69), qui servent à fournir des ordres de grandeur et un cadre pour tester la pertinence des développements effectués. Une synthèse bibliographique sur les processus en jeu et les modèles existants a conduit au choix de la plateforme de modélisation hydrologique CMF, développée à l’université de Giessen (Kraft, 2012). Cette dernière permet une modélisation orientée objet d’un système hydrologique (colonne de sol, versant, bassin versant ...etc) et propose une grande variété d’équations physiques pour la représentation des processus hydrologiques. Le travail est mené sur trois étapes, une première consiste à l’évaluation du comportement de la plateforme et la validation de sa réponse via la comparaison dans un premier temps via un modèle 1D suite à une comparaison avec Hydrus1D. Dans un second temps, nous avons mené des simulations en 2D en comparant avec le modèle Cathy en se basant sur les travaux de Sulis et al. (2010) et avec Hydrus2D (Simunek et al., 1999 & Simunek et al., 2001) sur un versant inspiré du versant expérimental de la Morcille. La deuxième étape consiste à la prise en compte des écoulements préférentiels dans certains types de sol structurés, nous paraît nécessaire pour une meilleure représentation des processus en jeu. La représentation du transfert préférentiel des produits phytosanitaires via les macropores vers la ressource en eau représente encore un défi pour la recherche. L’approche à double perméabilité (DP) choisie contient le développant d’une nouvelle fonction d’infiltration dans les macropores. Notre modèle DP contient également deux fonctions alternatives d’échange matrice-macropores ; la première est proportionnelle à la différence des teneurs en eau des deux compartiments du sol (Philip, 1968). La deuxième fonction d’échange est une onde diffusante basée sur l’approche présentée par van Genuchten (1993). La dernière partie de la thèse consiste en la modélisation des solutés suivant successivement les deux approches : simple porosité et double perméabilité, en considérant le transport des solutés par convection et une adsorption linéaire. La validation de notre approche de modélisation est menée en comparant avec les simulations d’Hydrus1D/2D. / The aim of my thesis is to develop a spatial scale modeling of a catchment, to better reflect the main pathways of pesticides in agricultural lands. We are looking to adopt a simplified approach, yet it allows to represent the existing discontinuities (plots, ditches, embankments ... etc). Indeed, we wish to quantify the mechanisms of transfer of pesticides taking into account the influence of landscape features (patches, ditches, grass strips ... etc) on the partition of water transfers and pesticides in surface and subsurface. It relies for this development on the acquired data on the experimental watershed Morcille (69), which serve to provide orders of magnitude and a framework to test the relevance of business developments. A literature review on the processes involved and the existing models led to the choice of hydrological modeling framework CMF, developed at the University of Giessen (Kraft, 2012). CMF allows for object oriented modeling of a hydrologic system (soil column, slope, watershed etc.) and offers a wide variety of physical equations for the representation of hydrological processes. The work is conducted in three steps, the first involves assessing the behavior of CMF and validating its response via the comparison initially via a 1D model following a comparison with Hydrus1D. Secondly, we conducted 2D simulations comparing with the Cathy model based on the work of Sulis et al. (2010) and Hydrus2D (Simunek et al., 1999 & Simunek et al., 2001) on a hillslope inspired from the experimental slope of Morcille. The second step is to take account of preferential flow in certain types of structured soil, seems necessary for better representation of the processes. The representation of the preferential transfer of pesticides through macropores to water resources is still a research challenge. The dual permeability approach (DP) contains selected developing the infiltration of a new function in the macropores. Our DP model also contains two alternative exchange functions matrix-macropores; the first one is proportional to the difference of the water contents of the two compartments of the soil (Philip, 1968). The second exchange function is a diffusing wave based on the approach outlined by van Genuchten (1993). The last part of the thesis consists in the modeling of solutes successively following two approaches: single dual porosity and permeability, considering the convective transport of solutes and a linear adsorption. The validation of our modeling approach is conducted by comparing with the Hydrus1D / 2D simulations.

Worldwide there is considerable concern over the effects of human activities on the quantity and quality of freshwater. Measurement of infiltration behaviour will be important for improving freshwater management. This study identifies that New Zealand has a sporadic history of measuring soil water movement attributes on a limited number of soil types, although the current practical demand should be large for management of irrigation, dairy farm effluent disposal, as well as municipal / domestic waste- and storm-water disposal. Previous research has demonstrated that infiltration behaviour is governed by the interplay between numerous mechanisms including hydrophobicity and preferential flow, the latter being an important mechanism of contaminant leaching for many NZ soils. Future characterisation will need to recognise the dynamic nature of these interactions, and be able to reliably characterise the key infiltration mechanisms. Since macropores are responsible for preferential flow, it is critical that infiltration studies use a representative sample of the macropore network. The aim of this project was to study the mechanisms governing the infiltration behaviour of a layered soil in large (50 x 70 cm) monolith lysimeters, where the connectivity of the macropore network remains undisturbed. Four lysimeters of the Gorge silt loam were collected, a structured soil with four distinct layers. On each lysimeter there were four separate infiltration experiments, with water applied under suctions of 0, 0.5, 1, and 1.5 kPa by a custom-built tension infiltrometer. Each lysimeter was instrumented with 30 tensiometers, located in arrays at the layer boundaries. There was also a field experiment using ponded dye infiltration to visually define preferential flowpaths. Analysis of dye patterns, temporal variability in soil matric potential (Ψm), and solute breakthrough curves all show that preferential flow is an important infiltration mechanism. Preferential flowpaths were activated when Ψm was above -1.5 kPa. During saturated infiltration, at least 97% of drainage was through the ‘mobile’ pore volume of the lysimeter (θm), estimated among the lysimeters at 5.4 – 8.7 % of the lysimeter volume. Early-time infiltration behaviour did not show the classical square-root of time behaviour, indicating sorptivity was not the governing mechanism. This was consistent across the four lysimeters, and during infiltration under different surface imposed suctions. The most likely mechanism restricting sorptivity is weak hydrophobicity, which appears to restrict infiltration for the first 5 – 10 mm of infiltration. Overall, the Gorge soil’s early-time infiltration behaviour is governed by the dynamic interaction between sorptivity, hydrophobicity, the network of air-filled pores, preferential flow and air encapsulation. Long-time infiltration behaviour was intimately linked to the temporal dynamics of Ψm, which was in turn controlled by preferential flow and soil layer interactions. Preferential flowpaths created strong inter-layer connectivity by allowing an irregular wetting front to reach lower layers within 2 – 15 mm of infiltration. Thereafter, layer interactions dominate infiltration for long-time periods, as Ψm in soil layers with different K(Ψm) relationships self-adjusts to try to maintain a constant Darcy velocity. An important finding was that Ψm rarely attained the value set by the tension infiltrometer during unsaturated infiltration. The results show that ‘true’ steady-state infiltration is unlikely to occur in layered soils. A quasi-steady state was identified once the whole column had fully wet and layer interactions had settled to where Ψm changes occurred in unison through each soil layer. Quasi-steady state was difficult to identify from just the cumulative infiltration curve, but more robustly identified as when infiltration matched drainage, and Ψm measurements showed each layer had a stable hydraulic gradient. I conclude that the in-situ hydraulic conductivity, K(Ψm), of individual soil layers can be accurately and meaningfully determined from lysimeter-scale infiltration experiments. My results show that K(Ψm) is different for each soil layer, and that differences are consistent among the four lysimeters. Under saturated flow the subsoil had the lowest conductivity, and was the restricting layer. Most interestingly this pattern reversed during unsaturated flow. As Ψm decreased below -0.5 to -1 kPa, the subsoil was markedly more conductive, and the topsoil layers became the restricting layers. All four soil layers demonstrate a sharp decline in K(Ψm) as Ψm decreases, with a break in slope at ~ -1 kPa indicating the dual-permeability nature of all layers.

Worldwide there is considerable concern over the effects of human activities on the quantity and quality of freshwater. Measurement of infiltration behaviour will be important for improving freshwater management. This study identifies that New Zealand has a sporadic history of measuring soil water movement attributes on a limited number of soil types, although the current practical demand should be large for management of irrigation, dairy farm effluent disposal, as well as municipal / domestic waste- and storm-water disposal. Previous research has demonstrated that infiltration behaviour is governed by the interplay between numerous mechanisms including hydrophobicity and preferential flow, the latter being an important mechanism of contaminant leaching for many NZ soils. Future characterisation will need to recognise the dynamic nature of these interactions, and be able to reliably characterise the key infiltration mechanisms. Since macropores are responsible for preferential flow, it is critical that infiltration studies use a representative sample of the macropore network. The aim of this project was to study the mechanisms governing the infiltration behaviour of a layered soil in large (50 x 70 cm) monolith lysimeters, where the connectivity of the macropore network remains undisturbed. Four lysimeters of the Gorge silt loam were collected, a structured soil with four distinct layers. On each lysimeter there were four separate infiltration experiments, with water applied under suctions of 0, 0.5, 1, and 1.5 kPa by a custom-built tension infiltrometer. Each lysimeter was instrumented with 30 tensiometers, located in arrays at the layer boundaries. There was also a field experiment using ponded dye infiltration to visually define preferential flowpaths. Analysis of dye patterns, temporal variability in soil matric potential (Ψm), and solute breakthrough curves all show that preferential flow is an important infiltration mechanism. Preferential flowpaths were activated when Ψm was above -1.5 kPa. During saturated infiltration, at least 97% of drainage was through the ‘mobile’ pore volume of the lysimeter (θm), estimated among the lysimeters at 5.4 – 8.7 % of the lysimeter volume. Early-time infiltration behaviour did not show the classical square-root of time behaviour, indicating sorptivity was not the governing mechanism. This was consistent across the four lysimeters, and during infiltration under different surface imposed suctions. The most likely mechanism restricting sorptivity is weak hydrophobicity, which appears to restrict infiltration for the first 5 – 10 mm of infiltration. Overall, the Gorge soil’s early-time infiltration behaviour is governed by the dynamic interaction between sorptivity, hydrophobicity, the network of air-filled pores, preferential flow and air encapsulation. Long-time infiltration behaviour was intimately linked to the temporal dynamics of Ψm, which was in turn controlled by preferential flow and soil layer interactions. Preferential flowpaths created strong inter-layer connectivity by allowing an irregular wetting front to reach lower layers within 2 – 15 mm of infiltration. Thereafter, layer interactions dominate infiltration for long-time periods, as Ψm in soil layers with different K(Ψm) relationships self-adjusts to try to maintain a constant Darcy velocity. An important finding was that Ψm rarely attained the value set by the tension infiltrometer during unsaturated infiltration. The results show that ‘true’ steady-state infiltration is unlikely to occur in layered soils. A quasi-steady state was identified once the whole column had fully wet and layer interactions had settled to where Ψm changes occurred in unison through each soil layer. Quasi-steady state was difficult to identify from just the cumulative infiltration curve, but more robustly identified as when infiltration matched drainage, and Ψm measurements showed each layer had a stable hydraulic gradient. I conclude that the in-situ hydraulic conductivity, K(Ψm), of individual soil layers can be accurately and meaningfully determined from lysimeter-scale infiltration experiments. My results show that K(Ψm) is different for each soil layer, and that differences are consistent among the four lysimeters. Under saturated flow the subsoil had the lowest conductivity, and was the restricting layer. Most interestingly this pattern reversed during unsaturated flow. As Ψm decreased below -0.5 to -1 kPa, the subsoil was markedly more conductive, and the topsoil layers became the restricting layers. All four soil layers demonstrate a sharp decline in K(Ψm) as Ψm decreases, with a break in slope at ~ -1 kPa indicating the dual-permeability nature of all layers.