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

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

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

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Three-dimensional Modeling of Acid Transport and Etching in a Fracture

Acid fracture stimulation generates higher well production but requires engineering design for treatment optimization. To quantify the cost and benefit of a particular acid fracture treatment an engineer must predict the resulting fracture’s conductivity, which is based on the etched width created by the injected acid. Etching occurs along the fracture surface but is based on acid flowing through the fracture, so an evaluation tool should describe three-dimensional physics and chemistry. Current practice is to estimate conductivity utilizing two-dimensional models. Unfortunately, these models necessarily assume how acid is distributed in the fracture and often misrepresent the amount of acid etching upon which the conductivity is based. A fully three-dimensional modeling tool to evaluate and predict acid fracture performance across the wide range of carbonate field properties has been developed. The model simulates acid transport and fracture face dissolution. The acid transport model includes the solution of the three-dimensional velocity and pressure fields, the non-Newtonian characteristics of most acid fracturing fluids, and diffusion of acid toward the fracture surface. The model numerically solves the equations describing the three-dimensional acid transport and reaction within a fracture to yield the etched width created by acid along the fracture. The conductivity is calculated with the simulator derived acid-etched width, using correlations recently developed that reflect the small scale heterogeneity of carbonate rock as it creates etching along the fracture surface. The performance of an acid fracture treatment is quantified with conductivity, which is strongly dependent on the etched width created by the acid. This robust new tool more accurately models the impact of design decisions on the acid-etched width and provides a rational path for treatment optimization. Cases typical of industry practice are presented that demonstrate the model capabilities