Numerical methods for coupled processes in fractured porous media

Numerical simulations have become essential in the planning and execution of operations in the subsurface, whether this is geothermal energy production or storage, carbon sequestration, petroleum production, or wastewater disposal. As the computational power increases, more complex models become feasible, not only in the form of more complicated physics, but also in the details of geometric constraints such as fractures, faults and wells. These features are often of interest as they can have a profound effect on different physical processes in the porous medium. This thesis focuses on modeling and simulations of fluid flow, transport and deformation of fractured porous media. The physical processes are formulated in a mixed-dimensional discrete fracture matrix model, where the rock matrix, fractures, and fracture intersections form a hierarchy of subdomains of different dimensions that are coupled through interface laws. A new discretization scheme for solving the deformation of a poroelastic rock coupled to a Coulomb friction law governing fracture deformation is presented. The novelty of this scheme comes from combining an existing finite-volume discretization for poroelasticity with a hybrid formulation that adds Lagrange multipliers on the fracture surface. This allows us to formulate the inequalities as complementary functions and solve the corresponding non-linear system using a semi-smooth Newton method. The mixed-dimensional framework is used to investigate non-linear coupled flow and transport. Here, we study how highly permeable fractures affect the viscous fingering in a porous medium and show that there is a complex interplay between the unstable viscous fingers and the fractures. The computer code of the above contributions of the thesis work has been implemented in the open-source framework PorePy. The introduction of fractures is a challenge to the discretization and the implementation of the governing equations, and the aim of this framework is to enable researchers to overcome many of the technical difficulties inherent to fractures, allowing them to easily develop models for fractured porous media. One of the large challenges for the mixed-dimensional discrete fracture matrix models is to create meshes that conform to the fractures, and we present a novel algorithm for constructing conforming Voronoi meshes. The proposed algorithm creates a mesh hierarchy, where the faces of the rock matrix mesh conform to the cells of the fractures, and the faces of the fracture mesh conform to the cells of the fracture intersections. The flexibility of the mixed-dimensional framework is exemplified by the wide range of applications and models studied within this thesis. While these physical processes might be fairly well known in a porous medium without fractures, the results of this thesis improves our understanding as well as the models and solution strategies for fractured porous media

High performance scientific computing in applications with direct finite element simulation

xiii, 133 p.La predicción del flujo separado, incluida la pérdida de un avión completo mediantela dinámica de fluidos computacional (CFD) se considera uno de los grandes desaf¿¿os que seresolverán en 2030, según NASA. Las ecuaciones no lineales de Navier-Stokes proporcionan laformulación matemática para flujo de fluidos en espacios tridimensionales. Sin embargo, todaviafaltan soluciones clásicas, existencia y singularidad. Ya que el cálculo de la fuerza bruta esintratable para realizar simulación predictiva para un avión completo, uno puede usar la simulaciónnumérica directa (DNS); sin embargo, prohibitivamente caro ya que necesita resolver laturbulencia a escala de magnitud Re power (9/4). Considerando otros métodos como el estad¿¿sticopromedio Reynolds¿s Average Navier Stokes (RANS), spatial average Large Eddy Simulation(LES), y Hybrid Detached Eddy Simulation (DES), que requieren menos cantidad de grados delibertad. Todos estos métodos deben ajustarse a los problemas de referencia y, además, cerca las paredes, la malla tieneque ser muy fina para resolver las capas l¿¿mite (lo cual significa que el costo computacional es muycostoso). Por encima de todo, los resultados son sensibles a, por ejemplo, parámetros expl¿¿citos enel método, la malla, etc.Como una solución al desaf¿¿o, aqu¿¿ presentamos la adaptación Metodolog¿¿a de solución directa deFEM (DFS) con resolución numérica disparo, como una familia predictiva, libre de parámetros demétodos para flujo turbulento. Resolvimos el modelo de avión JAXA Standard Model (JSM) ennúmero realista de Reynolds, presentado como parte del High Lift Taller de predicción 3.Predijimos un aumento de Cl dentro de un error de 5 % vs experimento, arrastre Cd dentro de 10 %error y detenga 1 ¿ dentro del ángulo de ataque.El taller identificó un probable experimento error depedido 10 % para los resultados de arrastre. La simulación es 10 veces más rápido y más barato encomparación con CFD tradicional o existente enfoques. La eficiencia proviene principalmente dell¿¿mite de deslizamiento condición que permite mallas gruesas cerca de las paredes, orientada aobjetivos control de error adaptativo que refina la malla solo donde es necesario y grandes pasos detiempo utilizando un método de iteración de punto fijo tipo Schur, sin comprometer la precisión delos resultados de la simulación.También presentamos una generalización de DFS a densidad variable y validado contra el problemade referencia MARIN bien establecido. los Los resultados muestran un buen acuerdo con losresultados experimentales en forma de sensores de presión. Más tarde, usamos esta metodolog¿¿apara resolver dos aplicaciones en problemas de flujo multifásico. Uno tiene que ver con un flashtanque de almacenamiento de agua de lluvia (consorcio de agua de Bilbao), y el segundo es sobre eldiseño de una boquilla para impresión 3D. En el agua de lluvia tanque de almacenamiento,predijimos que la altura del agua en el tanque tiene un influencia significativa sobre cómo secomporta el flujo aguas abajo de la puerta del tanque (válvula). Para la impresión 3D,desarrollamos un diseño eficiente con El flujo de chorro enfocado para evitar la oxidación y elcalentamiento en la punta del boquilla durante un proceso de fusión.Finalmente, presentamos aqu¿¿ el paralelismo en múltiples GPU y el incrustado sistema dearquitectura Kalray. Casi todas las supercomputadoras de hoy tienen arquitecturas heterogéneas,1 See the UNESCO Internacional Standard nomenclature for fields of Science and Technologyacomo CPU+GPU u otros aceleradores, y, por lo tanto, es esencial desarrollar marcoscomputacionales para aprovecha de ellos. Como lo hemos visto antes, se comienza a desarrollar eseCFD más tarde en la década de 1060 cuando podemos tener poder computacional, por lo tanto, Esesencial utilizar y probar estos aceleradores para los cálculos de CFD. Las GPU tienen unaarquitectura diferente en comparación con las CPU tradicionales. Técnicamente, la GPU tienemuchos núcleos en comparación con las CPU que hacen de la GPU una buena opción para elcómputo paralelo.Para múltiples GPU, desarrollamos un cálculo de plantilla, aplicado a simulación depliegues geológicos. Exploramos la computación de halo y utilizamos Secuencias CUDA paraoptimizar el tiempo de computación y comunicación. La ganancia de rendimiento resultante fue de23 % para cuatro GPU con arquitectura Fermi, y la mejora correspondiente obtenida en cuatro LasGPU Kepler fueron de 47 %.This research was carried out at the Basque Center for Applied Mathematics (BCAM) within the CFD Computational Technology (CFDCT) and also at the School of Electrical Engineering and Computer Science(Royal Institue of Technology, Stockholm, Sweden). Which is suported by Fundacion Obra Social “la Caixa“, Severo Ochoa Excellence research centre 2014-2018 SEV-2013-0323, Severo Ochoa Excellence research centre 2018-2022 SEV-2017-0718, BERC program 2014-2017, BERC program 2018-2021, MSO4SC European project, Elkartek. This work has been performed using the computing infrastructure from SNIC (Swedish National Infrastructure for Computing)

High Performance Scientific Computing in Applications with Direct Finite Element Simulation

To predict separated flow including stall of a full aircraft with Computational Fluid Dynamics (CFD) is considered one of the problems of the grand challenges to be solved by 2030, according to NASA [1]. The nonlinear Navier- Stokes equations provide the mathematical formulation for fluid flow in 3- dimensional spaces. However, classical solutions, existence, and uniqueness are still missing. Since brute-force computation is intractable, to perform predictive simulation for a full aircraft, one can use Direct Numerical Simulation (DNS); however, it is prohibitively expensive as it needs to resolve the turbulent scales of order Re4 . Considering other methods such as statistical average Reynolds’s Average Navier Stokes (RANS), spatial average Large Eddy Simulation (LES), and hybrid Detached Eddy Simulation (DES), which require less number of degrees of freedom. All of these methods have to be tuned to benchmark problems, and moreover, near the walls, the mesh has to be very fine to resolve boundary layers (which means the computational cost is very expensive). Above all, the results are sensitive to, e.g. explicit parameters in the method, the mesh, etc. As a resolution to the challenge, here we present the adaptive time- resolved Direct FEM Solution (DFS) methodology with numerical tripping, as a predictive, parameter-free family of methods for turbulent flow. We solved the JAXA Standard Model (JSM) aircraft model at realistic Reynolds number, presented as part of the High Lift Prediction Workshop 3. We predicted lift Cl within 5% error vs. experiment, drag Cd within 10% error and stall 1◦ within the angle of attack. The workshop identified a likely experimental error of order 10% for the drag results. The simulation is 10 times faster and cheaper when compared to traditional or existing CFD approaches. The efficiency mainly comes from the slip boundary condition that allows coarse meshes near walls, goal-oriented adaptive error control that refines the mesh only where needed and large time steps using a Schur-type fixed-point iteration method, without compromising the accuracy of the simulation results. As a follow-up, we were invited to the Fifth High Order CFD Workshop, where the approach was validated for a tandem sphere problem (low Reynolds number turbulent flow) wherein a second sphere is placed a certain distance downstream from a first sphere. The results capture the expected slipstream phenomenon, with appx. 2% error. A comparison with the higher-order frameworks Nek500 and PyFR was done. The PyFR framework has demonstrated high effectiveness for GPUs with an unstructured mesh, which is a hard problem in this field. This is achieved by an explicit time-stepping approach. Our study showed that our large time step approach enabled appx. 3 orders of magnitude larger time steps than the explicit time steps in PyFR, which made our method more effective for solving the whole problem. We also presented a generalization of DFS to variable density and validated against the well-established MARIN benchmark problem. The results show good agreement with experimental results in the form of pressure sensors. Later, we used this methodology to solve two applications in multiphase flow problems. One has to do with a flash rainwater storage tank (Bilbao water consortium), and the second is about designing a nozzle for 3D printing. In the flash rainwater storage tank, we predicted that the water height in the tank has a significant influence on how the flow behaves downstream of the tank door (valve). For the 3D printing, we developed an efficient design with the focused jet flow to prevent oxidation and heating at the tip of the nozzle during a melting process. Finally, we presented here the parallelism on multiple GPUs and the embedded system Kalray architecture. Almost all supercomputers today have heterogeneous architectures, such as CPU+GPU or other accelerators, and it is, therefore, essential to develop computational frameworks to take advantage of them. For multiple GPUs, we developed a stencil computation, applied to geological folds simulation. We explored halo computation and used CUDA streams to optimize computation and communication time. The resulting performance gain was 23% for four GPUs with Fermi architecture, and the corresponding improvement obtained on four Kepler GPUs were 47%. The Kalray architecture is designed to have low energy consumption. Here we tested the Jacobi method with different communication strategies. Additionally, visualization is a crucial area when we do scientific simulations. We developed an automated visualization framework, where we could see that task parallelization is more than 10 times faster than data parallelization. We have also used our DFS in the cloud computing setting to validate the simulation against the local cluster simulation. Finally, we recommend the easy pre-processing tool to support DFS simulation.La Caixa 201

Simulation of 2D Riser Regenerator

Riser regenerators are regenerating vessels used for removing the coke deposited on the catalyst and provide heat of reaction for the cracking process. Coke formation is unavoidable in the catalytic cracking process, which is probably formed by the dehydrogenation and condensation of poly-aromatic and olefins. Fast deactivation by blocking the active pores of the catalyst is a consequence of coke deposition. Riser regenerators are used for regenerating spent FCC catalyst by burning the coke deposited on the catalyst body. These are better compared to the conventional turbulent fluidised beds due to large capacities, higher gas-solid contact efficiency, high heat and mass transfer rates and low solids inventory. These regenerators also offer advantages over conventional scale reactors such as reaction speed, greater combustion of coke, reliability, cost effective, scalability and better safety and control. The present work is aimed to study the behaviour of regeneration reaction of coke inside riser regenerator. The advantages of multiple air inlet riser regenerator have been found out by studying the phenomenon inside the regenerator. The transient simulation has been carried out. The transient solution shows the species concentration and temperature profile inside the riser regenerators. The result reveals that the temperature of the gas increases with axial length and species concentration decreases. It has been found that multiple air inlet regenerator provide a better combustion than the single inlet regenerator

Available CFD models assessment

ABSTRACT: The partial differential equations that govern fluid flow and heat transfer are not usually amenable to analytical solutions, except for very simple cases. Therefore, in order to analyze fluid flows, flow domains are split into smaller subdomains (made up of geometric primitives like hexahedron and tetrahedron in 3D and quadrilaterals and triangles in 2D). The governing equations are then discretized and solved inside each of these subdomains. In the present situation, a finite volume method will be used to solve the approximate representation of the equations’ system. Care must be taken to ensure proper continuity of solution across the common interfaces between two subdomains, so that the approximate solutions inside various portions can be put together to give a complete picture of fluid flow in the entire domain. The subdomains are often called elements or cells and the collection of all elements or cells is called a mesh or grid. The origin of the term mesh (or grid) goes back to early days of CFD when most analyses were 2D in nature. For 2D analyses, a domain split into elements resembles a wire mesh, hence the name.N/

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts.publishedVersio

Numerical simulation of flooding from multiple sources using adaptive anisotropic unstructured meshes and machine learning methods

Over the past few decades, urban floods have been gaining more attention due to their increase in frequency. To provide reliable flooding predictions in urban areas, various numerical models have been developed to perform high-resolution flood simulations. However, the use of high-resolution meshes across the whole computational domain causes a high computational burden. In this thesis, a 2D control-volume and finite-element (DCV-FEM) flood model using adaptive unstructured mesh technology has been developed. This adaptive unstructured mesh technique enables meshes to be adapted optimally in time and space in response to the evolving flow features, thus providing sufficient mesh resolution where and when it is required. It has the advantage of capturing the details of local flows and wetting and drying front while reducing the computational cost. Complex topographic features are represented accurately during the flooding process. This adaptive unstructured mesh technique can dynamically modify (both, coarsening and refining the mesh) and adapt the mesh to achieve a desired precision, thus better capturing transient and complex flow dynamics as the flow evolves. A flooding event that happened in 2002 in Glasgow, Scotland, United Kingdom has been simulated to demonstrate the capability of the adaptive unstructured mesh flooding model. The simulations have been performed using both fixed and adaptive unstructured meshes, and then results have been compared with those published 2D and 3D results. The presented method shows that the 2D adaptive mesh model provides accurate results while having a low computational cost. The above adaptive mesh flooding model (named as Floodity) has been further developed by introducing (1) an anisotropic dynamic mesh optimization technique (anisotropic-DMO); (2) multiple flooding sources (extreme rainfall and sea-level events); and (3) a unique combination of anisotropic-DMO and high-resolution Digital Terrain Model (DTM) data. It has been applied to a densely urbanized area within Greve, Denmark. Results from MIKE 21 FM are utilized to validate our model. To assess uncertainties in model predictions, sensitivity of flooding results to extreme sea levels, rainfall and mesh resolution has been undertaken. The use of anisotropic-DMO enables us to capture high resolution topographic features (buildings, rivers and streets) only where and when is needed, thus providing improved accurate flooding prediction while reducing the computational cost. It also allows us to better capture the evolving flow features (wetting-drying fronts). To provide real-time spatio-temporal flood predictions, an integrated long short-term memory (LSTM) and reduced order model (ROM) framework has been developed. This integrated LSTM-ROM has the capability of representing the spatio-temporal distribution of floods since it takes advantage of both ROM and LSTM. To reduce the dimensional size of large spatial datasets in LSTM, the proper orthogonal decomposition (POD) and singular value decomposition (SVD) approaches are introduced. The performance of the LSTM-ROM developed here has been evaluated using Okushiri tsunami as test cases. The results obtained from the LSTM-ROM have been compared with those from the full model (Fluidity). Promising results indicate that the use of LSTM-ROM can provide the flood prediction in seconds, enabling us to provide real-time flood prediction and inform the public in a timely manner, reducing injuries and fatalities. Additionally, data-driven optimal sensing for reconstruction (DOSR) and data assimilation (DA) have been further introduced to LSTM-ROM. This linkage between modelling and experimental data/observations allows us to minimize model errors and determine uncertainties, thus improving the accuracy of modelling. It should be noting that after we introduced the DA approach, the prediction errors are significantly reduced at time levels when an assimilation procedure is conducted, which illustrates the ability of DOSR-LSTM-DA to significantly improve the model performance. By using DOSR-LSTM-DA, the predictive horizon can be extended by 3 times of the initial horizon. More importantly, the online CPU cost of using DOSR-LSTM-DA is only 1/3 of the cost required by running the full model.Open Acces

Grid Generation and CFD Analysis of Variable Geometry Screw Machines

This thesis describes the development of grid generation and numerical methods for predicting the flow in variable geometry, positive displacement screw machines. It has been shown, from a review of available literature, that the two main approaches available to generate deforming grids for the CFD analysis of 3D transient flow in screw machines are algebraic and differential. Grids that maintain the cell count and connectivity, during solution, provide the highest accuracy and customised grid generation tools have the capability to accommodate large mesh deformations. For the analysis of screw rotors with a variable lead or varying profile, these techniques are suitable but are required to be developed further with new procedures that can define the three dimensional variation of geometry of the rotors onto the computational grid. An algebraic grid generation method was used for deforming grid generation of variable lead and varying profile rotors. Functions were developed for correlating a specified lead variation along the rotor axis with the grid spacing. These can be used to build a continuously variable lead with linear, quadratic or higher order functions. For variable profile rotors, a novel approach has been developed for three dimensional grid structuring. This can be used to specify a continuously variable rotor profile, a variable lead, and both internal and external rotor engagement, thus making it possible to generate rotor domains with conical and variable lead geometries. New grid distribution techniques were developed to distribute boundary points on the rotors from the fixed points on the rack and the casing. These can refine the grid in the region of interlobe leakage gaps between the rotors, produce a one to one connected interface between them and improve the cell quality. Inflation layers were applied and tested for mesh refinement near the rotor boundaries. Case studies have been presented to validate the proposed grid generation techniques and the results have been compared with experimental data. Simulated results agreed well with measured data and highlighted the conditions where deviations are highest. Results with variable geometry rotors showed that they achieve steeper internal pressure rise and a larger discharge port area could be used. With variable lead rotors the volumetric efficiency could be improved by reducing the sealing line length in the high pressure zone. Calculations with inflation layers showed that local velocities were better predicted but there was no substantial influence on the integral performance parameters