Correlation analysis of statistical facies fault models

Doklady Earth Sciences - This paper addresses seismic imaging of fault zones and analysis of the seismic data with the use of the fault facies model developed at Uni Research CIPR. Simulated and...     

Sensitivity Analysis of Discrete Fracture Network Connectivity Characteristics

Mathematical Geosciences - This paper presents the results of a sensitivity analysis of the characteristics of discrete fracture network (DFN) connectivity. The sizes of the maximum and mean...     

Power-Law Testing for Fault Attributes Distributions

This paper is devoted to statistical analysis of faults’ attributes. The distributions of lengths, widths of damage zones, displacements and thicknesses of fault cores are studied. Truncated power-law (TPL) is considered in comparison with commonly used simple power-law (PL) (or Pareto) distribution. The maximal likelihood and the confidence interval of the exponent for both PL and TPL are estimated by appropriate statistical methods. The Kolmogorov–Smirnov (KS) test and the likelihood ratio test with alternative non-nested hypothesis for exponential distribution are used to verify the statistical approximation. Furthermore, the advantage of TPL is proved by Bayesian information criterion. Our results suggest that a TPL is more suitable for describing fault attributes, and that its condition is satisfied for a wide range of fault scales. We propose that using truncated power laws in general might eliminate or relax the bias related to sampling strategy and the resolution of measurements (such as censoring, truncation, and cut effect) and; therefore, the most reliable range of data can be considered for the statistical approximation of fault attributes.     

Analysis of fault scaling relations using fault seismic attributes

We have studied three‐dimensional fault geometries through a geologically integrated analysis of fault seismic attribute volumes. We used a series of coherence (semblance) and filtered coherence attribute volumes with parameters optimised for imaging faults in the studied seismic volumes. Fault geometric attributes such as along strike segment length and displacement were measured on fault seismic attributes. The scaling relationships of fault geometric attributes were studied using statistical methods such as the Bayesian information criterion, the likelihood ratio test, and the bootstrap method. Univariate distributions of fault segment length and maximum displacement show a truncated power law for most of the fault data. The statistical results indicate a piecewise‐linear relation with two slopes between depth and fault segments lengths: depth and mean displacement. For these relations, we observe consistent increases in fault segment lengths and mean displacements from the lower tip of the fault at depth toward a point of inflection at shallower depth at the vertical section. From that point, a reduction in fault segment lengths and mean displacements toward the upper tip of the fault at the shallower depth occurs. Fault segmentation along strike increases toward the lower and upper tips of the fault, but the maximum number of segments are located near the lower tip of the fault in two of the studied faults. The fault segment length is maximum, where the number of segments (along strike) is least close to the middle of the fault in the vertical section.     

Modified adaptive local–global upscaling method for discontinuous permeability distribution

The paper is devoted to the upscaling method appropriate for single-phase flow in media with discontinuous permeability distribution. The suggested algorithm is a modification of the iterative adaptive local–global upscaling developed by Chen and coauthors. The key feature of this method is a consistency between local and coarse global calculated characteristics. In this work, we apply a modified procedure to determine the boundary conditions used in the local fine-scale computation. To increase the accuracy of these boundary conditions on each iteration, we involve an additional preliminary step based on the results of coarse scale calculations from the previous iteration. Numerical tests show an essential improvement of the accuracy of upscaled flow rates for most of the realizations of statistical permeability distribution. Although the developed method is universal, its efficiency increases with increasing of permeability contrast.     

Deformation band populations in fault damage zone—impact on fluid flow

Fault damage zones in highly porous reservoirs are dominated by deformation bands that generally have permeability-reducing properties. Due to an absence of sufficiently detailed measurements and the irregular distribution of deformation bands, a statistical approach is applied to study their influence on flow. A stochastic model of their distribution is constructed, and band density, distribution, orientation, and flow properties are chosen based on available field observations. The sensitivity of these different parameters on the upscaled flow is analyzed. The influence of a heterogeneous permeability distribution was also studied by assuming the presence of high permeability holes within bands. The fragmentation and position of these holes affect significantly the block-effective permeability. Results of local upscaling with a diagonal and full upscaled permeability tensor are compared, and qualitatively similar results for the flow characteristics are obtained. Further, the procedure of iterative local–global upscaling is applied to the problem.     

Statistical Analysis of Fracture-Length Distribution Sampled Under the Truncation and Censoring Effects

The present paper addresses statistical analysis and estimation of fracture-length distributions at scales influenced by the truncation and censoring effects. The computational method employed here uses fracture-length distributions of a given set of measurements and information about observational constraints (i.e., window of observation) to estimate the probability density of the truncated and censored parts of fracture data sets. The results are benchmarked against power-law based maximal likelihood estimations commonly used for the same purpose. The relationship between the accuracy of estimates and size of the window of observation is studied. The utility of employing statistical models with arbitrary probability distributions of fracture lengths in order to provide a valid statistical model approximation is also considered. A verification of the suggested approximation using the Kolmogorov–Smirnov test applied to truncated and censored data is proposed. Numerical computations show that the proposed method can represent an essential improvement compared to other commonly employed techniques.