A new method of mineral inversion based on error analysis and static response equation error: a case study of a shale gas reservoir in the wufeng-longmaxi formation

The accurate quantitative calculation of the volume fraction of mineral components is very important and basic work in formation evaluation. Using well log data to estimate the mineralogy, porosity, and total organic carbon (TOC) content is a mainstream method with core measurements often used. However, in shale reservoirs, there are many mineral components, such as organic matter and pyrite. Additionally, the pore structure is complex, and gas exists in the pores as free state, adsorbed state and dissolved state. These factors make the logging response characteristics of shale gas reservoirs more complex and thus the estimation of the mineral components more difficult. To address this problem, this paper proposes a mineral inversion method based on error analysis and response equation error. Based on the error analysis of the mineral inversion method, we first establish a technique to obtain interpretation parameters and the function of the response equation error combined with the core data. Then, based on the weighted total least square method (WTLS), we construct the objective function, and utilize the improved krill herd algorithm (OCKH) to solve the problem. Finally, we estimate the mineral component volume. The calculated results show that the method can accurately determine the clay, quartz + feldspar, carbonate contents, and porosity by using conventional logging data. Compared with the traditional mineral inversion method, the average relative error of the new method is reduced by 11.1%. In summary, the proposed method has high applicability to shale reservoirs and can supply the basic parameters for formation evaluation.

Effective Source Term Discretizations for Higher Accuracy Finite Volume Discretization of Parabolic Equations

A finite volume method is applied to develop space-time discretizations for parabolic equations based on an equation error method.A space-time expansion of the local equation error based on flux integral formulation of the equation is first designed using a desiredframework of neighboring quadrature points for the solution and local source terms. The quadrature weights are then determined through aminimization process for the error which constitutes all local compact fluxes about each centroid within the computational domain.In utilizing a local source term distribution to account for diffusive fluxes, the right minimizing quadrature weights and collocationpoints including subgrid points for the source terms may be determined and optimized for higher accuracies as well as robust higher-ordercomputational convergence. The resulting local residuals form a more complete description of the truncation errors which are then utilizedto assess the computational performances of the resulting schemes. The effectiveness of the discretization method is demonstrated by theresults and analysis of the schemes.

Active Noise Control System Based on the Improved Equation Error Model

This paper presents an algorithm structure for an active noise control (ANC) system based on an improved equation error (EE) model that employs the offline secondary path modeling method. The noise of a compressor in a gas station is taken as an example to verify the performance of the proposed ANC system. The results show that the proposed ANC system improves the noise reduction performance and convergence speed compared with other typical ANC systems. In particular, it achieves 28 dBA noise attenuation at a frequency of about 250 Hz and a mean square error (MSE) of about −20 dB.

A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method

In this paper, we present an ecient modication of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This -analytical method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.

Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.