热液矿床成矿作用研究新途径:数值模拟

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.

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

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.

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

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.

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

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.

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

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.

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

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.