Uncertainty Quantification for a Hydraulic Fracture Geometry: Application to Woodford Shale Data

Hydraulic fracturing enhances hydrocarbon production from low permeability reservoirs. Laboratory tests and direct field measurements do a decent job of predicting the response of the system but are expensive and not easily accessible, thus increasing the need for robust deterministic and numerical solutions. The reliability of these mathematical models hinges on the uncertainties in the input parameters because uncertainty propagates to the output solution resulting in incorrect interpretations. Here, I build a framework for uncertainty quantification for a 1D fracture geometry using Woodford shale data. The proposed framework uses Monte-Carlo-based statistical methods and is comprised of two parts: sensitivity analysis and the probability density functions. Results reveal the transient nature of the sensitivity analysis, showing that Young’s modulus controls the initial pore pressure, which after 1 hour depends on the hydraulic conductivity. Results also show that the leak-off is most sensitive to permeability and thermal expansion coefficient of the rock and that temperature evolution primarily depends on thermal conductivity and the overall heat capacity. Furthermore, the model shows that Young’s modulus controls the initial fracture width, which after 1 hour of injection depends on the thermal expansion coefficient. Finally, the probability density curve of the transient fracture width displays the range of possible fracture aperture and adequate proppant size. The good agreement between the statistical model and field observations shows that the probability density curve can provide a reliable insight into the optimal proppant size.

Design Optimization of Ship’s Bow Sailing in Kara Sea and Barents Sea

Ships performing their missions in the polar regions will inevitably suffer from sea ice collision, which will lead to structural safety problems. Therefore, ships should be designed according to the characteristics of polar sea ice to enable them to navigate safely in the polar regions. Based on the probability density curve of sea ice thickness and the occurrence frequency of sea ices of different sizes of the Kara Sea and the Barents Sea, this paper preliminarily designs ship’s bow sailing in the Kara Sea and the Barents Sea, establishes the ship’s bow-ice collision model and carries out numerical simulation to obtain the stress distribution. Then it optimizes the structure of the parts of the ship’s bow. After the optimization, the bow structure meets the strength requirements and the weight of the ship’s bow is relatively light.

Time difference of arrival estimation of microseismic signals based on alpha-stable distribution

Microseismic signals are generally considered to follow the Gauss distribution. A comparison of the dynamic characteristics of sample variance and the symmetry of microseismic signals with the signals which follow α-stable distribution reveals that the microseismic signals have obvious pulse characteristics and that the probability density curve of the microseismic signal is approximately symmetric. Thus, the hypothesis that microseismic signals follow the symmetric α-stable distribution is proposed. On the premise of this hypothesis, the characteristic exponent α of the microseismic signals is obtained by utilizing the fractional low-order statistics, and then a new method of time difference of arrival (TDOA) estimation of microseismic signals based on fractional low-order covariance (FLOC) is proposed. Upon applying this method to the TDOA estimation of Ricker wavelet simulation signals and real microseismic signals, experimental results show that the FLOC method, which is based on the assumption of the symmetric α-stable distribution, leads to enhanced spatial resolution of the TDOA estimation relative to the generalized cross correlation (GCC) method, which is based on the assumption of the Gaussian distribution.

Time difference of arrival estimation of microseismic signals based on alpha-stable distribution

Microseismic signals are generally considered to follow the Gauss distribution. A comparison of the dynamic characteristics of sample variance and the symmetry of microseismic signals with the signals which follows α-stable distribution, reveals that the pulse characteristics of the microseismic signal is outstanding and that the probability density curve of the microseismic signal is approximately symmetric. Thus, the hypothesis that microseismic signals follow the symmetric α-stable distribution is proposed. On the premise of this hypothesis, the characteristic exponent α of the seismic signals is obtained by utilizing the fractional low-order statistics, and then a new method of time difference of arrival (TDOA) estimation of microseismic signals based on fractional low-order covariance (FLOC) is proposed. Upon applying this method to the TDOA estimation of Ricker wavelet simulation signals and real microseismic signals, experimental results show that the FLOC method, which is based on the assumption of the symmetric α-stable distribution, leads to enhanced spatial resolution of the TDOA estimation relative to the generalized cross correlation (GCC) method, which is based on the assumption of the Gaussian distribution.

The Feature Description Method of Radar Signal Based on Improved Kernel Density Estimation

According to the problem that the existing radar signal feature cannot effectively express and analysis its characteristic, a description method of radar emitter signal feature based on improved kernel density estimation is proposed. This improved kernel density estimation algorithm combine the selection of fixed window and variable window's width to achieve the window's width automatic adjustment value between the different estimation points based on the sample distribution. Then the probability density curve using kernel density estimation algorithm as radar emitter signal parameters characteristics stored into database.

A New Recognition Method of Radar Emitter Signal

According to the problem that the existing radar signal recognition method cannot effectively identify the radar signal, a new recognition method based on kernel density estimation is proposed. First using kernel density estimation gets the probability density curve of radar emitter signal parameters, then storing the cures into database as the characteristics, in the end a radar emitter signal recognition algorithm based on template matching is proposed.

Demonstrating the Consequences of Violations of Assumptions in between-Subjects Analysis of Variance

This article describes how to use a personal computer to conduct a classroom demonstration of the effects of violations of the assumptions of analysis of variance (ANOVA) on the probability of Type I error. The demonstration is based on the idea that if many data sets of randomly selected numbers are submitted to an ANOVA, then the frequency distribution of empirical F values should approximate the probability density curve of the F statistic for the specified degrees of freedom. If violations of the assumptions do not impair the approximation, then the test is robust. Results obtained in various trials were consistent with the statistical literature in showing that violations of the assumptions of normality and homogeneity of variances have a measurable but small effect on the probability of Type I error, especially when all groups are the same size.