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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

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

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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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

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 *** 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 *** 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 *** particular,all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great *** 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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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 aeidization 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： acidization dissolution front propagation critical length alternative approach critical time carbonate 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 *** 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 *** analytical solutions lead to the theoretical expression of the perturbation induced dimensionless growth-rate and the following two new *** 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 *** 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 *** on these two new findings,a theoretical criterion of two parts has been *** 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 *** 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 carbo

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

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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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Finite element modeling of convective pore-fluid flow in fluid-saturated porous rocks within upper crust:An overview

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Journal of Central South University 2019年第3期26卷 501-514页

作者： ZHAO Chong-bin Bruce HOBBS alison ord Computational Geosciences Research Centre Central South University School of Earth and Environment the University of Western Australia

Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process that triggers and controls the CPFF are extremely important for the exploration of new mineral deposits and underground oil resources. From the viewpoint of science, the CPFF within the upper crust can be treated as a kind of thermodynamic instability problem of pore-fluid in fluid-saturated porous media. The key issue of dealing with this kind of problem is to assess whether a nonlinear thermodynamic system under consideration is supercritical. To overcome limitations of using theoretical analysis and experimental methods in dealing with the CPFF problems within the upper crust, finite element modeling has been broadly employed for solving this kind of problem over the past two decades. The main purpose of this paper is to overview recent developments and applications of finite element modeling associated with solving the CPFF problems in large length-scale geological systems of complicated geometries and complex material distributions. In particular, two kinds of commonly-used finite element modeling approaches, namely the steady-state and transient-state approaches, and their advantages/disadvantages are thoroughly presented and discussed.

关键词： convective flow steady-state approach transient-state approach numerical modeling upper crust porous rock

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Effects of different numerical algorithms on simulation of chemical dissolution-front instability in fluid-saturated porous rocks

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Journal of Central South University 2018年第8期25卷 1966-1975页

作者： ZHAO Chong-bin Bruce HOBBS alison ord Computational Geosciences Research Centre Central South UniversityChangsha 410083China School of Earth and Environment The University of Western AustraliaCrawleyWA 6009Australia

Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for *** chemical dissolution-front instability problem in fluid-saturated porous rocks is no *** this kind of instability problem has both the conventional(***)and the unconventional(***)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous *** this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this *** the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic *** particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous *** related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.

关键词： numerical algorithm chemical dissolution front instability computational simulation porous rocks

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辽东半岛海城-大石桥菱镁矿矿床成因探讨

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地质学报 2022年第4期96卷 1340-1355页

作者：胡古月孙新胜郑军余旭辉王东波李延河赵悦陈翰徐莺 alison ord 中国地质科学院矿产资源研究所自然资源部成矿作用与资源评价重点实验室北京100037 辽宁省第五地质大队有限公司辽宁营口115100 成都理工大学地球科学学院四川成都610059 四川省地质矿产勘查开发局区域地质调查队四川成都610213 中国地质科学院矿产综合利用研究所四川成都610041 西澳大学地球科学学院勘查靶区中心珀斯6009澳大利亚

辽东半岛古元古界辽河群大石桥组三段地层中赋存有全球最大工业储量的菱镁矿矿床。在总结和整理已发表的辽东半岛晶质菱镁矿床地质和地球化学数据的基础上,本次研究进行了Mg和B同位素测试及研究工作,获得以下认识:①菱镁矿矿体呈北东东... 详细信息

辽东半岛古元古界辽河群大石桥组三段地层中赋存有全球最大工业储量的菱镁矿矿床。在总结和整理已发表的辽东半岛晶质菱镁矿床地质和地球化学数据的基础上,本次研究进行了Mg和B同位素测试及研究工作,获得以下认识:①菱镁矿矿体呈北东东走向,产于大石桥组三段,但不同矿床的矿体厚度差异较大(30~300 m),菱镁矿矿体与顶、底板高镁白云岩之间以断层接触为主,常可见到绿泥石化板岩和碳质千枚岩产于大型菱镁矿矿体的内部韧性剪切面上,说明地层经历了强烈构造形变作用;②围岩白云岩与晶质菱镁矿矿石的地球化学特征基本一致,均表现为大离子亲石性元素(K、Rb、Ba、Sr等)亏损和氧同位素负漂移(δ^(18)O:-24.9‰~-11.0‰);③在经历构造形变和角闪岩相变质作用后,菱镁矿矿石仍继承有海相蒸发沉积岩的稳定同位素地球化学特征(δ^(13)C:-2.7‰~+1.6‰;δ^(34)S:+15.6‰~+23.7‰;δ^(26)Mg:-1.53‰~-0.49‰;δ^(11)B:+9.8‰~+13.4‰);④后期裂控型滑石具有相对较高的δ^(26)Mg值(-0.32‰~-0.15‰),发生滑石矿化的菱镁矿(δ^(11)B:+7.7‰~+8.4‰)和围岩变粒岩(δ^(11)B:+4.3‰)显示较低的δ^(11)B值,这反映了变质热液作用所引发的Mg和B同位素分馏现象。因此,辽东半岛海城-大石桥地区菱镁矿矿床镁质富集的根本原因可能为湖相沉积碳酸盐岩经准同生阶段的富镁卤水交代所致,非后期变质热液交代作用的结果。

关键词：辽东半岛古元古代辽河群菱镁矿矿床潟湖相富镁卤水交代变质重结晶

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热液矿床成矿作用研究新途径:数值模拟

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地质科学 2019年第3期54卷 678-690页

作者：袁峰李晓晖胡训宇李跃贾蔡 ord alison 张明明戴文强李贺合肥工业大学资源与环境工程学院合肥230009 矿床成因与勘查技术研究中心合肥工业大学合肥230009 安徽省矿产资源与矿山环境工程技术研究中心合肥230009 西澳大利亚大学澳大利亚珀斯6009

热液矿床是最具有工业价值的矿床类型之一,传统矿床学研究在成岩成矿作用、成矿机制和成矿规律等方面已有丰硕成果.但仍存在一些尚无法有效回答的科学问题。近年来,数值模拟方法逐步应用于热液矿床的研究,已成为成矿过程定量研究的新手... 详细信息

热液矿床是最具有工业价值的矿床类型之一,传统矿床学研究在成岩成矿作用、成矿机制和成矿规律等方面已有丰硕成果.但仍存在一些尚无法有效回答的科学问题。近年来,数值模拟方法逐步应用于热液矿床的研究,已成为成矿过程定量研究的新手段。本文系统总结了近年来热液矿床成矿过程数值模拟研究的成果和进展,并对存在问题和发展趋势进行了分析和展望,以期进一步推动这一交叉学科领域的研究.

关键词：热液矿床数值模拟研究现状未来发展

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基于地表数据及产状数据的交切断层建模方法研究

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大地构造与成矿学 2023年第6期47卷 1256-1266页

作者：赵义来 alison ord 汤静如胡荣国杨启军汪劲草王本达桂林理工大学地球科学学院广西隐伏金属矿产勘查重点实验室广西桂林541004 桂林理工大学有色金属矿产勘查与资源高效利用协同创新中心广西桂林541004 Centre for Exploration Targeting School of Earth SciencesUniversity of Western AustraliaPerthWA 6009Australia 中国有色集团(广西)平桂飞碟股份有限公司广西贺州542800

三维地质建模是地质研究的有力工具,断层的三维建模比其他地质体建模具有更大的难度,其中一个主要难题是交切断层切割关系的处理。本文以广西珊瑚矿田为例,探讨了基于地表数据和产状数据的交切断层建模方法,采用地表断层线-剖面断层轨迹... 详细信息

三维地质建模是地质研究的有力工具,断层的三维建模比其他地质体建模具有更大的难度,其中一个主要难题是交切断层切割关系的处理。本文以广西珊瑚矿田为例,探讨了基于地表数据和产状数据的交切断层建模方法,采用地表断层线-剖面断层轨迹-系列断层线-断层面的技术路线进行切割断层建模,采用初始断层面-断后约束条件-交切处理-约束插值的技术路线进行被切割断层的建模,并与其他建模方法的建模效果进行对比和讨论。最终形成了如下建模方法:(1)以旋转法求取部分切割断层的错开部位约束,以平移法求取完全切割断层的错开部位约束;以断层错开部位约束、地表断层线约束及断层面边界约束为控制条件,进行断层面DSI插值,实现断层错动;(2)局部法建模、分段断层线的平移连接及过度追求完全切割关系建模可能分别引起断层面延展可控性差、断面整体偏移误差及沿走向过度延伸问题,与地质事实相悖,故本文优选采用了整体法建模、顺延连接分段断层线及遵从原有切割关系的处理方法,获得了较好的建模效果。

关键词：三维地质建模交切断层部分切割约束插值珊瑚矿田

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