The alternating direction implicit (ADI) methods are computationally efficient and numerically effective tools for computing low-rank solutions of large-scale matrix equations. It is known in the literature that the low-rank ADI method for Lyapunov equations is a Petrov-Galerkin projection algorithm that implicitly performs model order reduction. It recursively enforces interpolation at the mirror images of the ADI shifts and places the poles of the reduced-order models at the ADI shifts. In this paper, we show that the low-rank ADI methods for Sylvester and Riccati equations are also Petrov-Galerkin projection algorithms that implicitly perform model order reduction. These methods likewise enforce interpolation at the mirror images of the ADI shifts; however, they do not place the poles at the mirror images of the interpolation points. Instead, their pole placement ensures that the projected Sylvester and Riccati equations they implicitly solve admit a unique solution.By observing that the ADI methods for Lyapunov, Sylvester, and Riccati equations differ only in pole placement and not in their interpolatory nature, we show that the shifted linear solves-which constitute the bulk of the computational cost-can be shared. The pole-placement step involves only small-scale operations and is therefore inexpensive. We propose a unified ADI framework that requires only two shifted linear solves per iteration to simultaneously solve six Lyapunov equations, one Sylvester equation, and ten Riccati equations, thus substantially increasing the return on investment for the computational cost spent on the linear solves. All operations needed to extract the individual solutions from these shared linear solves are small-scale and inexpensive.Since all ADI methods implicitly perform model order reduction when solving these matrix equations, we show that the resulting reduced-order models can be obtained as an additional byproduct. These models not only interpolate the original transfer function at the mirror images of the ADI shifts but also preserve important system properties such as stability, minimum-phase property, positive-realness, bounded-realness, and passivity. Consequently, the proposed unified ADI framework also serves as a recursive, interpolation-based model order reduction method, which can preserve several important properties of the original model in the reduced-order model.The accuracy and rapid convergence of ADI methods depend on the choice of ADI shifts. Two existing self-generating shift strategies, which do not require any precomputation of shifts, are also reviewed. We provide the theoretical justification for these two strategies, which was not given in the original work. In addition, we propose a computationally efficient, subspace-acceleration-based self-generating shift strategy that is theoretically well grounded and significantly outperforms the existing approaches. With this shift strategy, the unified ADI framework becomes a fully automatic toolbox capable of solving large-scale matrix equations, performing model order reduction, and designing controllers and observers for large-scale plant models without user intervention. Three numerical examples demonstrate the effectiveness of the proposed ADI framework and shift-generation strategy, confirming its advantages over existing methods.
Shale gas condensate reservoirs, characterized by high organic matter content and ultra-low permeability, exhibit complex fluid transport behavior governed by adsorption–desorption and molecular diffusion. Although CO2 huff-n-puff injection has shown promise for alleviating condensate blockage, enhancing hydrocarbon recovery, and enabling CO2 storage, the coupled adsorption–diffusion mechanisms remain poorly understood. In this study, a compositional numerical model was developed by coupling adsorption–diffusion processes with multiple CO2 trapping mechanisms to simulate the huff-n-puff process. The model was used to evaluate the effects of injection parameters, permeability, and total organic carbon (TOC) content on condensate mitigation, hydrocarbon recovery, and CO2 storage performance. Simulation results indicate that molecular diffusion promotes condensate re-vaporization, resulting in a modest increase in gas production but a slight decrease in oil recovery, with its impact diminishing as permeability decreases. Reservoirs with higher TOC exhibit improved methane recovery and greater CO2 sequestration potential due to competitive adsorption between CO2 and CH4. The overall CO2 storage efficiency ranges from 48% to 66%, with adsorption trapping identified as the dominant mechanism. These results highlight the critical role of adsorption in governing both hydrocarbon recovery and CO2 retention. The developed modeling framework provides new insights into optimizing CO2 huff-n-puff operations in shale gas condensate reservoirs, supporting the dual objectives of enhanced recovery and geological carbon storage.
Fairness in same-day delivery (SDD) becomes increasingly important as customers demand equitable service pledge, yet cost-driven merchants’ preferences for nearby customers create service disparities across regions. Drone fleet resupply presents a fast and traffic-free solution capable of navigating complex terrains, while truck-based delivery complements it by overcoming the drone’s limitations in endurance and operational range. Previous studies mainly address single-drone, single-truck problems, with limited attention to the potential of drone fleet resupply with multi-truck systems to solve fairness issues. This research fills this gap by originally proposing a drone fleet resupply system for stochastic requests, where drones perform multiple trips to replenish any truck as needed, with consideration of drone endurance limitations. This problem is formulated as a sequential decision process (SDP) and solved through a deep Q-learning (DQL) approach to maximize service rates while ensuring fairness. A piecewise linear reward function is designed to improve convergence. Comparative results against benchmark policies demonstrate DQL’s potential to manage highly stochastic logistics operations. Key findings include: (1) Drone fleet resupply enhances regional fairness and overall service rates, demonstrating strong robustness in serving long-distance and time-sensitive deliveries; (2) An appropriate reward function significantly facilitates fairness, while penalties further improve it but are ineffective alone; (3) An optimal drone-truck fleet mix exists to balance service rates and associated costs, while adding more trucks alone substantially improves service rates but incurs larger costs; (4) The proposed approach remains effective across drone capacities, while extended drone endurance yields limited gains in service rate but significantly lowers delivery costs.
The physical triggers for carbon isotope reversal (e.g., delta C-13(1) > delta C-13(2)) in deep shale gas have long been obscured by free gas and remain controversial. To decouple the physical isotope fractionation mechanisms within extremely confined spaces and quantify their impact on gas reservoir evaluation, this study establishes a cross-scale framework integrating dynamic displacement experiments, a Continuous Stirred-Tank Reactor (CSTR) model, and Zero-Point Energy (ZPE) modified Molecular Dynamics (MD) simulations, using 13X zeolite with uniform channels as the physical end-member. The results show that after stripping the free gas background interference via the CSTR model, the intrinsic desorption fractionation extremum of methane reaches -90.3 parts per thousand. Microscopic simulations further confirm that this fractionation process is governed by the kinetic differentiation of Knudsen diffusion and the thermodynamic retention effect driven by ZPE. Possessing a lower zero-point energy, C-13 faces a higher desorption energy barrier (Delta E-a,(C)13 > Delta E-a,(C)12) leading to its delayed release during the late stage of displacement, which directly drives the "V-shaped" rollover of the isotopic trajectory. This study clarifies for the first time that the deep coupling of strong pore confinement and gas composition drying is the underlying physical trigger for isotope reversal, avoiding the severe overestimation of reservoir thermal maturity caused by the blind application of conventional geochemical empirical formulas. Meanwhile, this paper proposes using the "V-shaped" rollover point of produced gas isotopes as a novel, non-intrusive engineering indicator to accurately identify the reservoir depletion state (matrix residual gas <20%) and define the optimal time window for CO2-Enhanced Gas Recovery.
In-situ hydrogen (H2) generation accompanying carbon dioxide (CO2) mineralization in basalt offers a promising dual pathway for renewable energy generation and geological carbon storage. Currently, the interactive effects of thermodynamics, hydrochemistry, and reservoir parameters on CO2 sequestration and H2 generation mechanisms remain unclear. Therefore, a two-dimensional multiphysics reactive transport model, combined with an L25(56) orthogonal design, is developed to assess the sensitivity of six key factors (porosity, horizontal permeability, permeability anisotropy ratio, temperature, pressure, and pH) on the coupled CO2 mineralization-H2 production process. Simulations reveal that the injected CO2 induces the dissolution and redox reactions of Fe-rich minerals (e.g., olivine), generating substantial in-situ H2 while converting CO2 into stable carbonate minerals (e.g., magnesite and siderite). The spatial distribution of these reactions is controlled by the acidic fluid migration. Sensitivity analysis indicates that reservoir temperature is the primary controlling factor for both CO2 mineralization efficiency and total H2 production, with statistical significance far exceeding other factors. pH serves as a critical secondary factor for H2 output, where acidic environments significantly enhance H2 generation. Reservoir pressure determines the H2 phase transition behavior by regulating the solubility threshold. Furthermore, porosity exhibits distinct control effects: it correlates negatively with CO2 mineralization, while adequate porosity is a prerequisite for the formation of free-phase H2 gas caps. This study demonstrates that the optimal geological conditions for CO2 mineralization and H2 production do not fully overlap, providing a differentiated scientific basis for engineering site selection to balance carbon reduction and energy production.
