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Wang, Qiqi

Publications and source records attributed to Wang, Qiqi.

9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Aperture size distribution, length, and preferential location of bed-parallel veins in shale

Bed-parallel, calcite-filled veins (BPVs) are common in shale formations, and although they have been widely described in other studies, little is known about their population aperture size distribution. To address this knowledge gap, we analyzed BPV sizes in outcrops and cores from the Vaca Muerta Formation, Neuquén Basin, Argentina; in two cores from the Marcellus Formation, Appalachian Basin, northeast Pennsylvania; and in one core from the Wolfcamp Shale, Delaware Basin, West Texas. Nine out of ten aperture size populations follow a negative exponential distribution, with one following a weak power law. Bed-parallel vein size distribution and intensity vary among formations and within the same shale. We define three groups of distributions: (1) Vaca Muerta outcrops, with the highest BPV intensity and the largest BPVs (cumulative frequency of 4.9 BPVs per meter [BPVs/m] for apertures 0.265 mm to 8.7 cm); (2) Vaca Muerta cores with a similar BPV intensity overall but with no apertures wider than 1.2 cm; and (3) Vaca Muerta, Wolfcamp, and Marcellus cores with the fewest BPVs (cumulative frequency up to 0.63 BPVs/m) and very few wider than 1 cm. Aperture and length in two outcrop data sets are weakly positively correlated and follow power laws with exponents of 0.44 and 0.49. Mechanical interfaces at boundaries between different lithologies exert a strong control on BPV location, with 65–75% of observed interfaces having BPVs along them. Only 25–30% of the BPVs occur at observed material interfaces, however, and unless subtle, unobserved mechanical layering is present, other factors must also control location. BPV intensity and organic richness (TOC) from Vaca Muerta well logs are correlated in some instances but not in others, indicating TOC is not always a good proxy for BPV location or intensity. Furthermore, these findings provide useful information for modeling of hydraulic fracture treatments where BPVs may influence development of the stimulated fracture network, for example by limiting height growth.

58 GEOSCIENCES↗
DOE OSTI2022

Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds

Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Trajectory-Driven Algorithm for Differentiating SRB Measures on Unstable Manifolds

Sinai-Ruelle-Bowen (SRB) measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on unstable manifolds are critical in the sensitivity analysis of hyperbolic chaos. These derivatives, known as the SRB density gradients, are by-products of the regularization of Lebesgue integrals appearing in the original linear response expression. In this paper, we propose a novel trajectory- driven algorithm for computing the SRB density gradient defined for systems with high-dimensional unstable manifolds. We apply the concept of measure preservation together with the chain rule on smooth manifolds. Due to the recursive one-step nature of our derivations, the proposed procedure is memory-efficient and can be naturally integrated with existing Monte Carlo schemes widely used in computational chaotic dynamics. Here, we numerically show the exponential convergence of our scheme, analyze the computational cost, and present its use in the context of Monte Carlo integration.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Blonigan, Patrick J.↗
NASA NTRS2016

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Blonigan, Patrick J.↗