On the essential spectrum of complete non-compact manifolds

In this paper, we prove that the $L^p$ essential spectra of the Laplacian on functions are $[0,+\infty)$ on a non-compact complete Riemannian manifold with non-negative Ricci curvature at infinity. The similar method applies to gradient shrinking Ricci soliton, which is similar to non-compact manifold with non-negative Ricci curvature in many ways.Comment: Minor modification

Training Images-Based Stochastic Simulation on Many-Core Architectures

In the past decades, multiple-point geostatistical methods (MPS) are increasing in popularity in various fields. Compared with the traditional techniques, MPS techniques have the ability to characterize geological reality that commonly has complex structures such as curvilinear and long-range channels by using high-order statistics for pattern reconstruction. As a result, the computational burden is heavy, and sometimes, the current algorithms are unable to be applied to large-scale simulations. With the continuous development of hardware architectures, the parallelism implementation of MPS methods is an alternative to improve the performance. In this chapter, we overview the basic elements for MPS methods and provide several parallel strategies on many-core architectures. The GPU-based parallel implementation of two efficient MPS methods known as SNESIM and Direct Sampling is detailed as examples

A study of correlation between permeability and pore space based on dilation operation

CO2 and fracturing liquid injection into tight and shale gas reservoirs induces reactivity between minerals and injected materials, which results in porosity change and thus permeability change. In this paper, the dilation operation is used to simulate the change of the porosity and the corresponding change of permeability based on Lattice-Boltzmann is studied. Firstly we obtain digital images of a real core from CT experiment. Secondly the pore space of digital cores is expanded by dilation operation which is one of basic mathematical morphologies. Thirdly, the distribution of pore bodies and pore throats is obtained from the pore network modeling extracted by maximal ball method. Finally, the correlation between network modeling parameters and permeabilities is analyzed. The result is that the throat change leads to exponential change of permeability and that the big throats significantly influence permeability.Cited as: Zha, W., Yan, S., Li, D., et al. A study of correlation between permeability and pore space based on dilation operation. Advances in Geo-Energy Research, 2017, 1(2): 93-99, doi: 10.26804/ager.2017.02.0

Study on the inter-porosity transfer rate and producing degree of matrix in fractured-porous gas reservoirs

The inter-porosity transfer is one of the decisive factors for gas development in fractured-porous gas reservoirs. In this article, we establish an analytical solution for the inter-porosity transfer rate and producing degree of matrix. Then, we study the law of inter-porosity transfer based on the solution. Through the Stehfest inversion transform, the typical curves of inter-porosity transfer rate and producing degree of matrix are plotted. It is found that the producing degree of matrix is close to zero in the initial period. Then, the inter-porosity transfer rate begins to increase, and the producing degree of matrix becomes larger. In the late period, the producing degree of matrix remains constant. In addition, the differences between the quasi-steady state model and the three kinds of unsteady state models are compared. It is found that the inter-porosity transfer occurs earlier in unsteady models. However, when pressure propagates to the external boundary, the transfer rate is equal between quasi-steady and unsteady models. It is also found that the inter-porosity transfer rate is slightly different in the three unsteady models, whereas in the spherical model it is largest at the intermediate period. Next, we discuss the influence of key parameters. The results reveal that gas reservoir radius, storage ratio, and inter-porosity flow factor can play an essential role in inter-porosity transfer. The findings of this study can improve our understanding of gas flow between fractures and matrix. Besides, it helps field engineers better understand the variation law of gas productivity in fractured-porous gas reservoirs, which can provide the scientific basis for making a development scheme

A Novel Method for Matching Reservoir Parameters Based on Particle Swarm Optimization and Support Vector Machine

When the reservoir physical properties are distributed very dispersedly, the matching precision of these reservoir parameters is not good. We propose a novel method for matching the reservoir physical properties based on particle swarm optimization (PSO) and support vector machine (SVM) algorithm. First, the data structure characteristics of the reservoir physical properties are analyzed. Then, the particle swarm differential perturbation evolution algorithm is used to cluster and characterize the reservoir physical properties. Finally, by using the SVM algorithm for feature reorganization and the least squares matching of the extracted reservoir physical properties, the feature quantity of the reservoir physical properties can be accurately mined and the pressure matching precision is improved. The experimental results show that employing the proposed method to analyze and sample the data characteristics of the physical properties of the reservoir is better. The extracted parameters can effectively reflect the physical characteristics of oil reservoirs. The proposed method has potential applications in guiding the exploration and development of oil reservoirs