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Two different mathematical schemes for solving chemical dissolution-front instability problems in fluid-saturated rocks

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Science China(Technological Sciences) 2022年第1期65卷 147-156页

作者： zhao chongbin HOBBS Bruce ORD Alison Computational Geosciences Research Centre Central South UniversityChangsha 410083China Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of EducationCentral South UniversityChangsha 410083China School of Earth and Environment The University of Western AustraliaCrawleyWA 6009Australia

Chemical dissolution-front instability(CDFI)problems usually involve multiple temporal and spatial scales,as well as multiple processes.A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion,which can be used to judge the instability of a chemical dissolution-front(CDF)propagating in the fluidsaturated rock.This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner,rather than in a numerical simulation manner.The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme,a curved surface coordinate system is used,while in the second mathematical scheme,a planar surface coordinate system is employed.In particular,all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail.The main theoretical outcomes of this study have demonstrated that(1)two different mathematical schemes under consideration can produce exactly the same theoretical criterion;(2)the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically;(3)the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner.

关键词： chemical dissolution theoretical analysis mathematical scheme front instability fluid-saturated rocks

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Near-field performance of chemical dissolution-front instability around a circular acid-injection-well in fluid-saturated porous media

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Science China(Technological Sciences) 2023年第7期66卷 2025-2035页

作者： zhao chongbin HOBBS Bruce ORD Alison Computational Geosciences Research Centre Central South UniversityChangsha 410083China Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of EducationCentral South UniversityChangsha 410083China School of Earth and Environment University of Western AustraliaCrawleyWA 6009Australia

This paper investigates the near-field performance of chemical dissolution-front instability(CDFI) around a circular acidinjection-well in fluid-saturated porous media(FSPM) through using purely mathematical deductions.After the mathematical governing equations of the CDFI problem involving radially divergent flow are briefly described,both analytical base solutions and perturbation solutions for the considered problem are mathematically derived.These analytical solutions lead to the theoretical expression of the perturbation induced dimensionless growth-rate and the following two new findings.The first new finding is that the critical Peclet number of a chemical dissolution system(CDS) associated with radially divergent flow in FSPM is not only a function of the permeability ratio between the undissolved and dissolved regions as well as the dimensionless wavenumber,but also a function of the circular chemical dissolution-front location relative to the circular acid-injection-well in FSPM.The second new finding is that as the direct result of considering a nonzero radius of the circular acid-injection-well,there exits a critical closeness number,which may be used to assess where the circular chemical dissolution-front starts becoming unstable in the CDS associated with radially divergent flow.Based on these two new findings,a theoretical criterion of two parts has been established.The first part of the established theoretical criterion answers the scientific question when a circular chemical dissolution-front can become unstable,while the second part of the established theoretical criterion answers the scientific question where a circular chemical dissolution-front can become unstable.Through applying the established theoretical criterion,a long-term existing mystery why the wormhole pattern of fractal nature and the compact pattern of fingering nature are formed at different locations away from the circular acid-injection-well circumference in fluid-saturated carbonate rocks has been successfully revealed.

关键词： near-field performance circular injection well radially divergent flow analytical solutions dissolution-front instability porous media

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并网变流器全工况阻抗模型的黑箱辨识方法

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电力系统保护与控制 2024年第4期52卷 48-55页

作者：赵崇滨姜齐荣电力系统及发电设备控制与仿真国家重点实验室(清华大学电机工程与应用电子技术系) 北京100084

阻抗分析法因适用于并网变流器控制结构和参数均未知的黑箱系统,已成为工程中评估宽频振荡风险的重要选择。以跟网型三相两电平变流器为例,首先,使用谐波线性化方法,严格推导了计及直流侧耦合的交流侧全工况开/闭环理论阻抗模型,实现了... 详细信息

阻抗分析法因适用于并网变流器控制结构和参数均未知的黑箱系统,已成为工程中评估宽频振荡风险的重要选择。以跟网型三相两电平变流器为例,首先,使用谐波线性化方法,严格推导了计及直流侧耦合的交流侧全工况开/闭环理论阻抗模型,实现了模型参数与工作点高阶项的完全解耦。其次,依据理论模型特征,明确了黑箱辨识方法的基本原理,分析了辨识单一开/闭环阻抗模型频率响应所需的工况数量。使用辨识得到的全工况阻抗模型,实现了不同短路比条件下系统安全运行域的快速评估,并通过时域仿真验证了其准确性。此外,讨论了所提方法的合理性、普适性以及相对于深度学习方法的优越性,为阻抗分析法的实际应用提供了参考。

关键词：阻抗分析法黑箱系统模型辨识全工况稳定性分析

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Advances in numerical algorithms and methods in computational geosciences with modeling characteristics of multiple physical and chemical processes

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Science China(Technological Sciences) 2015年第5期58卷 783-795页

作者： zhao chongbin Computational Geosciences Research Centre Central South University CSIRO Earth Science and Resource Engineering

This paper aims to provide a brief introduction to recent advances in numerical algorithms and methods in the emerging computational geoscience filed with general simulation characteristics of modeling multiple chemical and physical processes that take place in ore-generating systems within the Earth's crust. Due to significant differences between Earth systems and engineering systems, the existing numerical algorithms and methods, which are designed for simulating realistic problems in the engineering fields, may not be straightforwardly used to simulate ore-generating problems without significant improvements. Thus, extensive and systematic studies have been conducted, in recent years, to develop new numerical algorithms and methods for simulating different aspects of ore-generating problems. Not only can the outcomes of these studies provide new simulation tools for better understanding the controlled dynamic mechanisms that take place in ore-generating systems, but also they have enriched the research contents of computational mechanics in the broad sense.

关键词：系统物理过程数值算法计算力学地球科学化学过程模拟工具模特工程系统

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Computational simulation of wave propagation problems in infinite domains

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Science China(Physics,Mechanics & Astronomy) 2010年第8期53卷 1397-1407页

作者： zhao chongbin Computational Geosciences Research Centre Central South UniversityChangsha 410083China CSIRO Division of Exploration and Mining P.O.Box 1130BentleyWA 6102Australia

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.

关键词： wave absorbing boundary dynamic infinite element wave propagation infinite domain computational simulation

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Transient-state instability analysis of dissolution-timescale reactive infiltration in fluid-saturated porous rocks: Purely mathematical approach

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Science China(Technological Sciences) 2020年第2期63卷 319-328页

This paper deals with how the purely mathematical approach can be used to solve transient-state instability problems of dissolution-timescale reactive infiltration(DTRI) in fluid-saturated porous rocks. Three key steps involved in such an approach are:(1) to mathematically derive an analytical solution(known as the base solution or conventional solution) for a quasi-steady state problem of the dissolution timescale, which is viewed as a frozen state of the original transient-state instability problem;(2)to mathematically deduce a group of first-order perturbation partial-differential equations(PDEs) for the quasi-steady state problem;(3) to mathematically derive an analytical solution(known as the perturbation solution or unconventional solution) for this group of first-order perturbation PDEs. Because of difficulty in mathematically solving a transient-state instability problem of DTRI in general cases, only a special case, in which some nonlinear coupling between governing PDEs of the problem can be decoupled, is considered to illustrate these three key steps in this study. The related theoretical results demonstrated that the transient chemical dissolution front can become unstable in the DTRI system of large Zh numbers when the long wavelength perturbations are applied to the system. This new finding may lay the theoretical foundation for developing innovative technique to exploit shale gas resources in the deep Earth.

关键词： mathematical study dissolution timescale reactive infiltration instability chemical dissolution perturbation solution porous rocks

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A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated carbonate rocks

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Science China(Technological Sciences) 2017年第8期60卷 1197-1210页

作者： zhao chongbin HOBBS Bruce ORD Alison Computational Geosciences Research Centre Central South University School of Earth and Environment The University of Western Australia

The natural phenomenon associated with the chemical dissolution of dissolvable minerals of rocks can be employed to develop innovative technology in mining and oil extracting engineering.This paper presents a new alternative approach for theoretically dealing with chemical dissolution front(CDF) propagation in fluid-saturated carbonate rocks.Note that the CDF is represented by the porosity front in this study.In this new approach,the porosity,pore-fluid velocity and acid concentration are directly used as independent variables.To illustrate how to use the present new approach,an acidization dissolution system(ADS) consisting of carbonate rocks,which belongs to one of the many general chemical dissolution systems(CDSs),is taken as an application example.When the acid dissolution capacity(ADC) number(that is defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid) approaches zero,the present new approach can be used to obtain analytical solutions for the stable ADS.However,if the ADC number is a nonzero finite number,then numerical solutions can be only obtained for the ADS,especially when the ADS is in an unstable state.The related theoretical results have demonstrated that:(1) When the ADS is in a stable state and in the case of the ADC number approaching zero,the present new approach is mathematically equivalent to the previous approach,in which the porosity,pore-fluid pressure and acid concentration are used as independent variables.However,when the ADS is in an unstable state,the use of the present new approach leads to a free parameter that needs to be determined by some other ways.(2) The existence of a non-step-type dissolution front within a transient region should at least satisfy that none of the ADC number,injected acid velocity and reciprocal of the dissolution reaction rate is equal to zero in the stable ADS.

关键词：化学溶解碳酸盐岩流体饱和传播不稳定状态酸化孔隙流体压力流体速度

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A unified theory for sharp dissolution front propagation inchemical dissolution of fluid-saturated porous rocks

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Science China(Technological Sciences) 2019年第1期62卷 163-174页

作者： zhao chongbin HOBBS Bruce ORD Alison Computational Geosciences Research Centre Central South University School of Earth and Environment The University of Western Australia

This paper presents a unified theory to deal with when, why and how a sharp acidization dissolution front(ADF), which is represented by the porosity distribution curve, can take place in an acidization dissolution system composed of fluid-saturated porous rocks. The theory contains the following main points:(1) A reaction rate of infinity alone can lead to a sharp ADF of the Stefan-type in the acidization dissolution system. This sharp front is unstable when permeability in the downstream region is smaller than that in the upstream region.(2) For a finite reaction rate, when the acid dissolution capacity number approaches zero,the ADF can have a sharp profile of the Stefan-type either on a much smaller time scale or on a much larger time scale than the dissolution time scale. In the former case, the ADF may become unstable on a much larger time scale than the transport time scale, while in the latter case, it may become unstable if the growth rate of a small perturbation is greater than zero.(3) On the dissolution time scale, even if both the reaction rate is finite and the acid dissolution capacity number approaches zero, the profile of an ADF may not be sharp because it is in a transient state. In this case, not only can an ADF change its profile with time, but also its morphology can grow if the growth rate of a small perturbation is greater than zero. Due to the involvement of both the change rate and the growth rate of the ADF profile, it is necessary to conduct a transient linear stability analysis for determining whether or not a time-dependent ADF is stable in the acidization dissolution system.

关键词： sharp dissolution front stationary/steady state transient state acid dissolution capacity acidization dissolution porous rocks

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An efficient time-integration method for nonlinear dynamic analysis of solids and structures

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Science China(Physics,Mechanics & Astronomy) 2013年第4期56卷 798-804页

作者： LIU TianYun LI QingBin zhao chongbin State Key Laboratory of Hydro-Science and Engineering Tsinghua University Computational Geosciences Research Centre Central South University

This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration differentiation formula and the trapezoidal rule, resulting in a self-starting, single step, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.

关键词：非线性动力分析动态结构集成方法二阶非线性固体拉格朗日乘子计算软件非线性分析

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Flexible Power Supply System of AC Electric Arc Furnace

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Journal of Modern Power Systems and Clean Energy 2023年第2期11卷 622-633页

作者： chongbin zhao Qirong Jiang Dong Liu Department of Electrical Engineering Tsinghua UniversityBeijing 100084China Capital Engineering&Research Incorporation Ltd. Beijing 100176China

The AC electric arc furnace(EAF)is becoming a core apparatus of the modern steel industry.Nevertheless,it used to be a major threat of power quality in the traditional power supply system.In this paper,a flexible power supply system of the AC EAF is proposed,which is expected to completely alter its inherent cognition of impact load in the power grid.The basics of the power supply for EAF are first reviewed and the novel techniques to enhance the operation flexibility of EAF are introduced.The power circuit and the control structure are then presented,followed by the detailed strategies of various operations fully considering the features of EAF.A large disturbance stability criterion based on the mixed potential theory is also established for the practical application.Both electromagnetic transient simulations using PSCAD and benefit analyses verify the feasibility of the proposed system.

关键词： Electric arc furnace(EAF) power electronics control power quality power supply system stability analysis

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