621 research outputs found
A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs
Representing the reservoir as a network of discrete compartments with
neighbor and non-neighbor connections is a fast, yet accurate method for
analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale
compartments with distinct static and dynamic properties is an integral part of
such high-level reservoir analysis. In this work, we present a hybrid framework
specific to reservoir analysis for an automatic detection of clusters in space
using spatial and temporal field data, coupled with a physics-based multiscale
modeling approach. In this work a novel hybrid approach is presented in which
we couple a physics-based non-local modeling framework with data-driven
clustering techniques to provide a fast and accurate multiscale modeling of
compartmentalized reservoirs. This research also adds to the literature by
presenting a comprehensive work on spatio-temporal clustering for reservoir
studies applications that well considers the clustering complexities, the
intrinsic sparse and noisy nature of the data, and the interpretability of the
outcome.
Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal
Clustering; Physics-Based Data-Driven Formulation; Multiscale Modelin
Solution strategies for nonlinear conservation laws
Nonlinear conservation laws form the basis for models for a wide range of physical phenomena. Finding an optimal strategy for solving these problems can be challenging, and a good strategy for one problem may fail spectacularly for others. As different problems have different challenging features, exploiting knowledge about the problem structure is a key factor in achieving an efficient solution strategy. Most strategies found in literature for solving nonlinear problems involve a linearization step, usually using Newton's method, which replaces the original nonlinear problem by an iteration process consisting of a series of linear problems. A large effort is then spent on finding a good strategy for solving these linear problems. This involves choosing suitable preconditioners and linear solvers. This approach is in many cases a good choice and a multitude of different methods have been developed. However, the linearization step to some degree involves a loss of information about the original problem. This is not necessarily critical, but in many cases the structure of the nonlinear problem can be exploited to a larger extent than what is possible when working solely on the linearized problem. This may involve knowledge about dominating physical processes and specifically on whether a process is near equilibrium. By using nonlinear preconditioning techniques developed in recent years, certain attractive features such as automatic localization of computations to parts of the problem domain with the highest degree of nonlinearities arise. In the present work, these methods are further refined to obtain a framework for nonlinear preconditioning that also takes into account equilibrium information. This framework is developed mainly in the context of porous media, but in a general manner, allowing for application to a wide range of problems. A scalability study shows that the method is scalable for challenging two-phase flow problems. It is also demonstrated for nonlinear elasticity problems. Some models arising from nonlinear conservation laws are best solved using completely different strategies than the approach outlined above. One such example can be found in the field of surface gravity waves. For special types of nonlinear waves, such as solitary waves and undular bores, the well-known Korteweg-de Vries (KdV) equation has been shown to be a suitable model. This equation has many interesting properties not typical of nonlinear equations which may be exploited in the solver, and strategies usually reserved to linear problems may be applied. In this work includes a comparative study of two discretization methods with highly different properties for this equation
Nonlinear nonlocal multicontinua upscaling framework and its applications
In this paper, we discuss multiscale methods for nonlinear problems. The main
idea of these approaches is to use local constraints and solve problems in
oversampled regions for constructing macroscopic equations. These techniques
are intended for problems without scale separation and high contrast, which
often occur in applications. For linear problems, the local solutions with
constraints are used as basis functions. This technique is called Constraint
Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM).
GMsFEM identifies macroscopic quantities based on rigorous analysis. In
corresponding upscaling methods, the multiscale basis functions are selected
such that the degrees of freedom have physical meanings, such as averages of
the solution on each continuum.
This paper extends the linear concepts to nonlinear problems, where the local
problems are nonlinear. The main concept consists of: (1) identifying
macroscopic quantities; (2) constructing appropriate oversampled local problems
with coarse-grid constraints; (3) formulating macroscopic equations. We
consider two types of approaches. In the first approach, the solutions of local
problems are used as basis functions (in a linear fashion) to solve nonlinear
problems. This approach is simple to implement; however, it lacks the nonlinear
interpolation, which we present in our second approach. In this approach, the
local solutions are used as a nonlinear forward map from local averages
(constraints) of the solution in oversampling region. This local fine-grid
solution is further used to formulate the coarse-grid problem. Both approaches
are discussed on several examples and applied to single-phase and two-phase
flow problems, which are challenging because of convection-dominated nature of
the concentration equation
Application of M3GM in a Petroleum Reservoir Simulation
Reservoir formations exhibit a wide range of heterogeneity from micro to macro scales. A simulation that involves all of these data is highly time consuming or almost impossible; hence, a new method is needed to meet the computational cost. Moreover, the deformations of the reservoir are important not only to protect the uppermost equipment but also to simulate fluid pattern and petroleum production strategy. In this regard, multiscale multiphysic mixed geomechanical model (M3GM) is recently developed. However, applications of petroleum reservoirs through gas or water injection in the depleted reservoir are in concern. In the present paper, a multiscale finite volume framework and a finite element method are employed to simulate fluid flow and rock deformation respectively. The interactions of solid and fluid phases are instated through the M3GM framework. Then, its application in the petroleum reservoir through injection process is validated. The numerical results are compared with the fine scale simulations and reasonable agreement with high computational efficiency is obtained
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