HIGH ORDER BOUND-PRESERVING DISCONTINUOUS GALERKIN METHODS AND THEIR APPLICATIONS IN PETROLEUM ENGINEERING

This report contains researches in the theory of high-order bound-preserving (BP) discontinuous Galerkin (DG) method and their applications in petroleum engineering. It contains both theoretical analysis and numerical experiments. The compressible miscible displacements and wormhole propagation problem, arising in petroleum engineering, is used to describe the evolution of the pressure and concentrations of different components of fluid in porous media. The important physical features of concentration and porosity include their boundedness between 0 and 1, as well as the monotone increasing for porosity in wormhole propagation model. How to keep these properties in the simulation is crucial to the robustness of the numerical algorithm. In the first project, we develop high-order bound-preserving discontinuous Galerkin methods for the coupled system of compressible miscible displacements on triangular meshes. We consider the problem with multi-component fluid mixture and the (volumetric) concentration of the jth component,cj, should be between 0 and 1. The main idea is stated as follows. First, we apply the second-order positivity-preserving techniques to all concentrations c′ js and enforce P jcj= 1 simultaneously to obtain physically relevant boundedness for every components. Then, based on the second-order BP schemes, we use the second-order numerical fluxes as the lower order one to combine with high-order numerical fluxes to achieve the high-order accuracy. Finally, since the classical slope limiter cannot be applied to polynomial upper bounds, we introduce a new limiter to our algorithm. Numerical experiments are given to demonstrate the high-order accuracy and good performance of the numerical technique. In our second project, we propose high-order bound-preserving discontinuous Galerkin methods to keep the boundedness for the porosity and concentration of acid, as well as the monotone increasing for porosity. The main technique is to introduce a new variable r to replace the original acid concentration and use a consistent flux pair to deduce a ghost equation such that the positive-preserving technique can be applied on both original and deduced equations. A high-order slope limiter is used to keep a polynomial upper bound which changes over time for r. Moreover, the high-order accuracy is attained by the flux limiter. Numerical examples are given to demonstrate the high-order accuracy and bound-preserving property of the numerical technique

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Modelamiento numérico de la producción masiva de arena durante la producción en frío de crudo pesado

ilustraciones, diagramasCold heavy oil production with sand (CHOPS) is a single well technology that involves the deliberate initiation and sustaining of sand inflow into the wells using progressive cavity pumps (PCP) to produce at oil high rates with a subsequent high-pressure drawdown around the wellbore and improvement in oil well productivity. CHOPS is a primary recovery method extensively used in the world as a profitable and simple technology. Foamy-oil flow and wormhole formation are the main mechanisms of CHOPS, where aggressive sand production is a consequence of geomechanical issues such as elastoplastic behavior, stress redistribution, failure criteria, pressure gradient, erosion, and sand liquefaction. The general objective of this thesis is to build a numerical model to predict and explain massive sand production during cold heavy oil production by coupling fluid flow with geomechanics and considering stress redistribution and erosional processes. This research also identifies the relevant phenomena of massive sand production and describes the interaction between geomechanical and erosional processes. A methodology is proposed to model the initiation and propagation of wormholes based on geomechanical behavior. A 3D-single well model is built to understand the cold heavy oil production with sand, considering relevant dynamics such as stress redistribution and the interaction between geomechanical and erosional processes, by coupling fluid flow with geomechanics. This model couples a three-phase fluid flow model and an elastoplastic model and integrates other models: a sand production model, a foamy-oil module, and a conceptual model for wormhole formation. This coupled model is verified and validated firstly by components and lately integrating step by step the different components using commercial software such as ABAQUS® and CMG®. Field cases are run to calibrate the parameters of the sand production model resulting in low sand levels, a case with the main characteristics of a CHOPS well is run and its results are analyzed, and a sensitive study is performed to evaluate the impact of variables such as pressure drawdown, cohesion, internal friction angle, and stress regime. Finally, a special case is built combing all variables and looking to promote sand production with successful results.Ea producción en frío de crudo pesado con arena (CHOPS) es una tecnología de un solo pozo que involucra el inicio deliberado y el mantenimiento del flujo arena a los pozos utilizando bombas de cavidad progresiva (PCP) para producir petróleo a altas tasas con un subsiguiente alto gradiente de presión alrededor del pozo. y mejora en la productividad de los pozos de petróleo. CHOPS es un método de recuperación primaria ampliamente utilizado en el mundo como una tecnología rentable y sencilla. El flujo de crudo espumoso y la formación de agujeros de gusano son los principales mecanismos de CHOPS, donde la producción agresiva de arena es consecuencia de problemas geomecánicos como el comportamiento elastoplástico, la redistribución de esfuerzos, los criterios de falla, el gradiente de presión, la erosión y la licuefacción de la arena. El objetivo general de esta tesis es construir un modelo numérico para predecir y explicar la producción masiva de arena durante la producción en frío de crudo pesado acoplando el flujo de fluidos con la geomecánica y considerando la redistribución de esfuerzos y los procesos de erosión. Esta investigación también identifica los fenómenos relevantes de producción masiva de arena y describe la interacción entre los procesos geomecánicos y erosivos. Se propone una metodología para modelar la iniciación y propagación de agujeros de gusano basada en el comportamiento geomecánico. Se construye un modelo de pozo único en 3D para comprender la producción en frío de crudo pesado con arena, considerando dinámicas relevantes como la redistribución de esfuerzos y la interacción entre los procesos geomecánicos y erosivos, al acoplar el flujo de fluidos con la geomecánica. Este modelo combina un modelo de flujo de fluido trifásico y un modelo elastoplástico e integra otros modelos: un modelo de producción de arena, un módulo de crudo espumoso y un modelo conceptual para la formación de agujeros de gusano. Este modelo acoplado es verificado y validado primeramente por componentes y posteriormente integrando paso a paso los diferentes componentes utilizando software comerciales como ABAQUS® y CMG®. Se corren casos de campo para calibrar los parámetros del modelo de producción de arena resultando en bajos niveles de arena, se corre un caso con las principales características de un pozo CHOPS y se analizan sus resultados, y se realiza un estudio de sensibilidad para evaluar el impacto de variables como como el gradiente de presión, la cohesión, el ángulo de fricción interna y el régimen de esfuerzos. Finalmente, se construye un caso especial combinando todas las variables y buscando promover la producción de arena con resultados exitosos. (Texto tomado de la fuente)DoctoradoDoctor en IngenieríaGeomecánica aplicada a la ingeniería de yacimientosÁrea curricular de Ingeniería Química e Ingeniería de Petróleo

ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in the areas of (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving Langley facilities and scientists; and (4) computer science

Analysis of Flow Behavior for Acid Fracturing Wells in Fractured-Vuggy Carbonate Reservoirs

This study develops a mathematical model for transient flow analysis of acid fracturing wells in fractured-vuggy carbonate reservoirs. This model considers a composite system with the inner region containing finite number of artificial fractures and wormholes and the outer region showing a triple-porosity medium. Both analytical and numerical solutions are derived in this work, and the comparison between two solutions verifies the model accurately. Flow behavior is analyzed thoroughly by examining the standard log-log type curves. Flow in this composite system can be divided into six or eight main flow regimes comprehensively. Three or two characteristic V-shaped segments can be observed on pressure derivative curves. Each V-shaped segment corresponds to a specific flow regime. One or two of the V-shaped segments may be absent in particular cases. Effects of interregional diffusivity ratio and interregional conductivity ratio on transient responses are strong in the early-flow period. The shape and position of type curves are also influenced by interporosity coefficients, storativity ratios, and reservoir radius significantly. Finally, we show the differences between our model and the similar model with single fracture or without acid fracturing and further investigate the pseudo-skin factor caused by acid fracturing

A general poro-elasto-plastic model for poorly consolidated sands

Sand failure and production are likely to occur during oil and gas production, especially in poorly consolidated formations. Most past research focuses on either experimental work to understand sanding mechanisms or simple sand production models to estimate the onset of sand production. Such models are usually not enough to capture sanding behavior in complex situations in the field. In this dissertation, a numerical 3D sand production prediction model is developed based on a general poro-elasto-plastic model for multi-phase fluid flow, which can predict both the onset of sanding and the volume of sand produced. The model is thoroughly validated with multiple analytical solutions. It is also validated with experiment data for the onset of sanding, sand production volume, and cavity shape caused by sand production. The model results are shown to agree well with all these experimentally measured quantities and for the first time predict sanding behavior in complex geometries over a wide range of conditions. From extensive sand production experiments, four distinct cavity shapes have been frequently observed: spiral shear band cavity, V-shape cavity, dog-ear cavity, and slit mode cavity. However, the reasons and the sanding mechanisms responsible for this behavior have not been fully articulated. Results presented here show that the model is capable of capturing all the complicated cavity shapes, and provide qualitative guidelines to define the conditions under which each type of cavity will be formed. The effect of different well completions on sand failure and production have been investigated with the model. Results show the potential advantage of using frac-packs for reducing the fluid pressure gradients and redistributing stresses. In addition, the impact of rock and fluid properties on sanding behavior has been studied to show the importance of mechanical failure and fluid erosion on sanding. Wells with multiple oriented perforations are analyzed to study the effect of perforation design on sand production. The application of the model has been further extended to quantitatively explain some field observations, including: delayed sanding in gas wells, sanding caused by water breakthrough, and water hammer effects. Simulation results suggest that rock strengthening by water evaporation and non-Darcy effects in gas flow can delay sand production. On the other hand, sanding after water breakthrough can be explained by accelerating sand failure and fluid erosion due to an increase in the water saturation. The impact of water hammer on sand failure has been investigated to optimize subsurface valve location and shut-in procedure. Finally, the sand production model is applied to a field case for HPHT wells to study sanding mechanisms for different sanding behavior observed in two wells in similar locations in the field. Simulation results show that rock heterogeneity and natural fractures are the most likely reasons for sand production in this field. The difference in onset of sanding from the two wells can be explained by different in-situ stresses, while the difference in severity of sanding can be explained by differences in pressure drawdown and the orientation of perforations. The critical drawdown during reservoir depletion are determined under different conditions from the model to guide drawdown management so as to prevent sanding issues.Petroleum and Geosystems Engineerin