1,166 research outputs found
Flow Through a Porous Medium with Multiscale Log-Stable Permeability
We consider single-phase flow of an incompressible fluid through a random scaling porous medium. The joint multi-point probability distribution for the porosity and permeability is supposed to be log-stable and satisfy the conditions of the Kolmogorov's refined scaling hypothesis. A subgrid model is derived which is similar to Landau-Lifschitz formula. The similarity of the present method to the Wilson's renormalization group is noticed
Coarse graining equations for flow in porous media: a HaarWavelets and renormalization approach
Coarse graining of equations for flow in porous media is an important aspect in modelling permeable subsurface geological systems. In the study of hydrocarbon reservoirs as well as in hydrology, there is a need for reducing the size of the numerical models to make them computationally efficient, while preserving all the relevant information which is given at different scales.
In the first part, a new renormalization method for upscaling permeability in Darcy’s
equation based on Haar wavelets is presented, which differs from other wavelet based methods. The pressure field is expressed as a set of averages and differences, using a
one level Haar wavelet transform matrix. Applying this transform to the finite difference discretized form of Darcy’s law, one can deduce which permeability values on the
coarse scale would give rise to the average pressure field. Numerical simulations were
performed to test this technique on homogeneous and heterogeneous systems.
A generalization of the above method was developed designing a hierarchical transform
matrix inspired by a full Haar wavelet transform, which allows us to describe
pressure as an average and a set of progressively smaller scale differences. Using this transform the pressure solution can be performed at the required level of detail, allowing for different resolutions to be kept in different parts of the system.
A natural extension of the methods is the application to two-phase flow. Upscaling
mobility allows the saturation profile to be calculated on the fine or coarse scale while
based on coarse pressure values.
To conclude, an alternative approach to upscaling in multi-phase flow is to upscale
the saturation equation itself. Taking its Laplace transform, this equation can be reduced to a simple eigenvalue problem. The wavelet upscaling method can now be applied to
calculate the upscaled saturation profile, starting with fine scale velocity data
Recommended from our members
From multiscale modeling to metamodeling of geomechanics problems
In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework.
The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales.
To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing.
To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques
Image-based Modeling of Flow through Porous Media: Development of Multiscale Techniques for the Pore Level
Increasingly, imaging technology allows porous media problems to be modeled at microscopic and sub-microscopic levels with finer resolution. However, the physical domain size required to be representative of the media prohibits comprehensive micro-scale simulation. A hybrid or multiscale approach is necessary to overcome this challenge. In this work, a technique was developed for determining the characteristic scales of porous materials, and a multiscale modeling methodology was developed to better understand the interaction/dependence of phenomena occurring at different microscopic scales. The multiscale method couples microscopic simulations at the pore and sub-pore scales. Network modeling is a common pore-scale technique which employs severe assumptions, making it more computationally efficient than direct numerical simulation, enabling simulation over larger length scales. However, microscopic features of the medium are lost in the discretization of a material into a network of interconnected pores and throats. In contrast, detailed microstructure and flow patterns can be captured by modern meshing and direct numerical simulation techniques, but these models are computationally expensive. In this study, a data-driven multiscale technique has been developed that couples the two types of models, taking advantage of the benefits of each. Specifically, an image-based physically-representative pore network model is coupled to an FEM (finite element method) solver that operates on unstructured meshes capable of resolving details orders of magnitude smaller than the pore size. In addition to allowing simulation at multiple scales, the current implementation couples the models using a machine learning approach, where results from the FEM model are used to learn network model parameters. Examples of the model operating on real materials are given that demonstrate improvements in network modeling enabled by the multiscale framework. The framework enables more advanced multiscale and multiphysics modeling – an application to particle straining problems is shown. More realistic network filtration simulations are possible by incorporating information from the sub-pore-scale. New insights into the size exclusion mechanism of particulate filtration were gained in the process of generating data for machine learning of conductivity reduction due to particle trapping. Additional tests are required to validate the multiscale network filtration model, and compare with experimental findings in literature
Recommended from our members
An exploration of the IGA method for efficient reservoir simulation
Novel numerical methods present exciting opportunities to improve the efficiency of reservoir simulators. Because potentially significant gains to computational speed and
accuracy may be obtained, it is worthwhile explore alternative computational algorithms
for both general and case-by-case application to the discretization of the equations of porous media flow, fluid-structure interaction, and/or production. In the present
work, the fairly new concept of isogeometric analysis (IGA) is evaluated for its suitability
to reservoir simulation via direct comparison with the industry standard finite difference (FD) method and 1st order standard finite element method (SFEM). To this end, two main studies are carried out to observe IGA’s performance with regards to geometrical modeling and ability to capture steep saturation fronts. The first study explores IGA’s ability to model complex reservoir geometries, observing L2 error convergence rates under a variety of refinement schemes. The numerical experimental setup includes an 'S' shaped line sink of varying curvature from which water is produced in a 2D homogenous domain. The accompanying study simplifies the domain to 1D, but adds in multiphase physics that traditionally introduce difficulties associated with modeling of a moving saturation front. Results overall demonstrate promise for the IGA method to be a particularly effective tool in handling geometrically difficult features while also managing typically challenging numerical phenomena.Petroleum and Geosystems Engineerin
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
- …