Heterogeneous Reservoir Characterization Utilizing Efficient Geology Preserving Reservoir Parameterization through Higher Order Singular Value Decomposition (HOSVD)

Petroleum reservoir parameter inference is a challenging problem to many of the reservoir simulation work flows, especially when it comes to real reservoirs with high degree of complexity and non-linearity, and high dimensionality. In fact, the process of estimating a large number of unknowns in an inverse problem lead to a very costly computational effort. Moreover, it is very important to perform geologically consistent reservoir parameter adjustments as data is being assimilated in the history matching process, i.e., the process of adjusting the parameters of reservoir system in order to match the output of the reservoir model with the previous reservoir production data. As a matter of fact, it is of great interest to approximate reservoir petrophysical properties like permeability and porosity while reparameterizing these parameters through reduced-order models. As we will show, petroleum reservoir models are commonly described by in general complex, nonlinear, and large-scale, i.e., large number of states and unknown parameters. Thus, having a practical approach to reduce the number of reservoir parameters in order to reconstruct the reservoir model with a lower dimensionality is of high interest. Furthermore, de-correlating system parameters in all history matching and reservoir characterization problems keeping the geological description intact is paramount to control the ill-posedness of the system. In the first part of the present work, we will introduce the advantages of a novel parameterization method by means of higher order singular value decomposition analysis (HOSVD). We will show that HOSVD outperforms classical parameterization techniques with respect to computational and implementation cost. It also, provides more reliable and accurate predictions in the petroleum reservoir history matching problem due to its capability to preserve geological features of the reservoir parameter like permeability. The promising power of HOSVD is investigated through several synthetic and real petroleum reservoir benchmarks and all results are compared to that of classic SVD. In addition to the parameterization problem, we also addressed the ability of HOSVD in producing accurate production data comparing to those of original reservoir system. To generate the results of the present work, we employ a commercial reservoir simulator known as ECLIPSE. In the second part of the work, we will address the inverse modeling, i.e., the reservoir history matching problem. We employed the ensemble Kalman filter (EnKF) which is an ensemble-based characterization approach to solve the inverse problem. We also, integrate our new parameterization technique into the EnKF algorithm to study the suitability of HOSVD based parameterization for reducing the dimensionality of parameter space and for estimating geologically consistence permeability distributions. The results of the present work illustrates the characteristics of the proposed parameterization method by several numerical examples in the second part including synthetic and real reservoir benchmarks. Moreover, the HOSVD advantages are discussed by comparing its performance to the classic SVD (PCA) parameterization approach. In the first part of the present work, we will introduce the advantages of a novel parameterization method by means of higher order singular value decomposition analysis (HOSVD). We will show that HOSVD outperforms classical parameterization techniques with respect to computational and implementation cost. It also, provides more reliable and accurate predictions in the petroleum reservoir history matching problem due to its capability to preserve geological features of the reservoir parameter like permeability. The promising power of HOSVD is investigated through several synthetic and real petroleum reservoir benchmarks and all results are compared to that of classic SVD. In addition to the parameterization problem, we also addressed the ability of HOSVD in producing accurate production data comparing to those of original reservoir system. To generate the results of the present work, we employ a commercial reservoir simulator known as ECLIPSE. In the second part of the work, we will address the inverse modeling, i.e., the reservoir history matching problem. We employed the ensemble Kalman filter (EnKF) which is an ensemble-based characterization approach to solve the inverse problem. We also, integrate our new parameterization technique into the EnKF algorithm to study the suitability of HOSVD based parameterization for reducing the dimensionality of parameter space and for estimating geologically consistence permeability distributions. The results of the present work illustrate the characteristics of the proposed parameterization method by several numerical examples in the second part including synthetic and real reservoir benchmarks. Moreover, the HOSVD advantages are discussed by comparing its performance to the classic SVD (PCA) parameterization approach

Discovery of Hidden Structures in Microseismic Data Using Tensor Decompositions and Multiway Component Analysis

Microseismic data is used by companies to analyze and check numerous processes, including horizontal well performance, directional drilling and, most recently, hydraulic fracturing. The microseismic data analysis approach is important and there is a lot more to discover within microseismic technology with an application of the correct data analysis approach. For example, different visualization methods could potentially contain hidden structures, not visible by traditional methods. This work proposes a new methodology to access those hidden structures. In particular, machine learning tools, such as Tensor Decomposition (TD) and Multiway Component Analysis (MWCA), were utilized to gain more information from a previously existing pool of microseismic data. The extracted hidden structures can be used to learn more about source location, from which the information about fracture propagation could be inferred within the reservoir. This potentially gives a fast and cost-effective technique to analyze hydraulic fracturing processes. The work further illustrates applicability to a real microseismic study of the noise reduction and model reduction methods, based on the same machine learning techniques. A special case of TD, Higher-Order Singular Value Decomposition (HOSVD) is used to decompose the data, while MWCA is used to show the relationship between the decomposed structure and hidden structures within the dataset. Finally, possible steps to improve the technology are outlined. Since the applications of MWCA and TD are still emerging, future enhancements to this methodology are expected

Model Order Reduction in Porous Media Flow Simulation and Optimization

Subsurface flow modeling and simulation is ubiquitous in many energy related processes, including oil and gas production. These models are usually large scale and simulating them can be very computationally demanding, particularly in work-flows that require hundreds, if not thousands, runs of a model to achieve the optimal production solution. The primary objective of this study is to reduce the complexity of reservoir simulation, and to accelerate production optimization via model order reduction (MOR) by proposing two novel strategies, Proper Orthogonal Decomposition with Discrete Empirical Interpolation Method (POD-DEIM), and Quadratic Bilinear Formulation (QBLF). While the former is a training-based approach whereby one runs several reservoir models for different input strategies before reducing the model, the latter is a training-free approach. Model order reduction by POD has been shown to be a viable way to reduce the computational cost of flow simulation. However, in the case of porous media flow models, this type of MOR scheme does not immediately yield a computationally efficient reduced system. The main difficulty arises in evaluating nonlinear terms on a reduced subspace. One way to overcome this difficulty is to apply DEIM onto the nonlinear functions (fractional flow, for instance) and to select a small set of grid blocks based on a greedy algorithm. The nonlinear terms are evaluated at these few grid blocks and interpolation based on projection is used for the rest of them. Furthermore, to reduce the number of POD-DEIM basis and the error, a new approach is integrated in this study to update the basis online. In the regular POD-DEIM work flow all the snapshots are used to find one single reduced subspace, whereas in the new technique, namely the localized POD-DEIM, the snapshots are clustered into different groups by means of clustering techniques (k-means), and the reduced subspaces are computed for each cluster in the online (pre-processing) phase. In the online phase, at each time step, the reduced states are used in a classifier to find the most representative basis and to update the reduced subspace. In the second approach in order to overcome the issue of nonlinearity, the QBLF of the original nonlinear porous media flow system is introduced, yielding a system that is linear in the input and linear in the state, but not in both input and state jointly. Primarily, a new set of variables is used to change the problem into QBLF. To highlight the superiority of this approach, the new formulation is compared with a Taylor's series expansion of the system. At this initial phase of development, a POD-based model reduction is integrated with the QBLF in this study in order to reduce the computational costs. This new reduced model has the same form as the original high fidelity model and thus preserves the properties such as stability and passivity. This new form also facilitates the investigation of systematic MOR, where no training or snapshot is required. We test these MOR algorithms on the SPE10 and the results suggest twofold runtime speedups for a case study with more than 60,000 grid blocks. In the case of the QBLF, the results suggests moderate speedups, but more investigation is needed to accommodate an efficient implementation. Finally, MOR is integrated in the optimization work flow for accelerating it. The gradient based optimization framework is used due to its efficiency and fast convergence. This work flow is modified to include the reduced order model and consequently to reduce the computational cost. The water flooding optimization is applied to an offshore reservoir benchmark model, UNISIM-I-D, which has around 38,000 active grid blocks and 25 wells. The numerical solutions demonstrate that the POD-based model order reduction can reproduce accurate optimization results while providing reasonable speedups

Desenvolvimento de um simulador substituto de reservatório multiescala acoplado com geomecânica

Orientador: Philippe Remy Bernard DevlooTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de GeociênciasResumo: Os softwares de simulação de reservatórios são utilizados como ferramentas para o entendimento dos reservatórios de petróleo e eventualmente, para diagnosticar anomalias operacionais. O aumento da potência computacional permite aos engenheiros de reservatórios desenvolver modelos geológicos mais realistas, refinados e com uma grande quantidade de dados de entrada. Alguns exemplos são os modelos multi-físicos que acoplam efeitos geomecânicos, térmicos, geoquímicos e modelos que incluem múltiplas escalas inerentes aos modelos de campo completo. Estes modelos são geralmente caros, porque o cálculo direto de um modelo geocelular refinado gera enormes sistemas lineares de equações. Quando é considerado o efeito da deformação geomecânica com o fluxo de fluido através de meios porosos, um sistema muito grande de equações associado com a elasticidade é acoplado a um sistema igualmente grande de equações, associadas ao fluxo de fluido e ao transporte de massa. Portanto, a maioria das simulações são realizadas sem considerar o acoplamento geomecânico. Essas simulações ignoram fenômenos físicos que podem ter sérios impactos ambientais, como ativação de falhas, subsidência e outros. Neste trabalho desenvolve-se um inovador método multiescala que permite diretamente simular um modelo geocelular fino em uma maneira econômica. Um modelo substituto também foi desenvolvido para simular a deformação geomecânica acoplada ao modelo de fluido. O objetivo é obter aproximações do problema multifísico não linear descrito pelas equações multifásicas poroelásticas. Para atingir esse objetivo, diferentes tecnologias de elementos finitos são integradas dentro de um simulador de reservatórios, resolvendo problemas que incluem um modelo geocelular com diferentes escalas, acoplado a um modelo substituto de deformação geomecânica. O modelo matemático é escrito em uma forma adequada para a estrutura de elementos finitos do NeoPZ. Em cada passo de tempo, a aproximação é obtida como uma sequência de problemas elásticos, de Darcy e de transporte. Cada componente nesta sequência é tratado por um esquema numérico diferente e / ou espaço de aproximação; em primeiro lugar, um modelo substituto, inspirado na teoria das inclusões poroelásticas, é usado para o cálculo da deformação geomecânica das rochas; em segundo lugar, utiliza-se um método multi-escala baseado na aproximação mista de equações multifásicas; em terceiro lugar, para a convecção das fases, uma aproximação mista multi-escala do campo de velocidade de Darcy é usada, em conjunto com um esquema de upwind de primeira ordem. O potencial da abordagem numérica é demonstrado através de vários exemplos bidimensionais e tridimensionais, em que os reservatórios são simulados usando malhas não estruturadas. Todas as simulações foram executadas usando estruturas computacionais de baixo custoAbstract: Reservoir simulation softwares are used as a tool to understand the behavior of petroleum reservoirs and, eventually, to diagnose operating anomalies. The increased computational power allows reservoir engineers to develop more realistic geological models, that are very refined and have a large amount of input data. As an example, multi-physics models couple geomechanical, thermal, geochemical effects and include multiple scales inherent to full field models. These models are generally costly, because the direct calculation of a refined geocellular model, generates huge linear systems of equations. When coupling the geomechanical deformation with fluid flow through porous media, a very large system of equations associated with elasticity, is coupled to an equally large system of equations, which is associated with fluid flow and mass transport. Therefore, most simulations are performed without considering the geomechanical coupling. These simulations ignore physical phenomena that can have serious environmental impacts such as fault activation, land subsidence and others. In this work an innovative multiscale method is developed, allowing the direct simulation of a fine geocellular model in a cost-effective way. A surrogate model has also been developed for simulating the geomechanical deformation coupled to the fluid model. The goal is obtain approximations for the nolinear multiphysic problem decribed by the multiphase poroelastic equations. In order to attain this goal, different finite element technologies are integrated within a reservoir simulator, solving problems that include a geocellular model with different scales, coupled with a surrogate model of geomechanical deformation. The mathematical model is written in a form suitable for the NeoPZ finite element framework. At each timestep, the approximation is obtained as a sequence of elastic, Darcy's and transport problems. Each component in this sequence is treated by a different numerical scheme and/or approximation space; first, a surrogate model, inspired on the theory of poroelastic inclusions, is used for the calculation of the geomechanical deformation of rocks; second, a multiscale method based on mixed approximation of multiphase equations is used; third, for the convection of the phases, a mixed multiscale approximation of the Darcy's velocity field is used together with a first-order upwind scheme. The potential of the numerical approach is demonstrated through several bi-dimensional and three-dimensional examples, in which reservoirs are simulated using unstructured meshes. All simulations have been executed using low cost computational structuresDoutoradoExplotaçãoDoutor em Ciências e Engenharia de Petróle

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios