An interface-condition substitution strategy for theoretical study of dissolution-timescale reactive infiltration instability in fluid-saturated porous rocks

A theoretical study of reactive infiltration instability is conducted on the dissolution timescale. In the present theoretical study, the transient behavior of a dissolution-timescale reactive infiltration system needs to be considered, so that the upstream region of the chemical dissolution front should be finite. In addition, the chemical dissolution front of finite thickness should be considered on the dissolution timescale. Owing to these different considerations, it is very difficult, even in some special cases, to derive the first-order perturbation solutions of the reactive infiltration system on the dissolution timescale. To overcome this difficulty, an interface-condition substitution strategy is proposed in this paper. The basic idea behind the proposed strategy is that although the first-order perturbation equations in the downstream region cannot be directly solved in a purely mathematical manner, they should hold at the planar reference front, which is the interface between the upstream region and the downstream region. This can lead to two new equations at the interface. The main advantage of using the proposed interface-condition substitution strategy is that through using the original interface conditions as a bridge, the perturbation solutions for the dimensionless acid concentration, dimensionless Darcy velocity, and their derivatives involved in the two new equations at the interface can be evaluated just by using the obtained analytical solutions in the upstream region. The proposed strategy has been successfully used to derive the dimensionless growth rate, which is the key issue associated with the theoretical study of dissolution-timescale reactive infiltration instability in fluid-saturated porous rocks.     

直-增-稳剖面设计问题的解析解

使用无量纲化方法对设计方程组进行了改写,新的无量纲化设计方程组有利于充分利用三角函数公式求解析解,所得到的解析解计算公式具有简洁的数学形式。将设计方程组求解问题分成两类,对于已知最大井斜角的第Ⅰ类问题,使用线性代数解方程组的克莱默法则直接就可以得出解析解。最大井斜角为未知数的第Ⅱ类问题,使用三角函数公式进行化简,得到形式简单、统一的解析解公式,避免了使用半角公式所带来的解析解计算公式的复杂性。所使用无量纲化方法具有一定的普适性,可以用于解决其他类型的二维剖面设计问题。     

Why asymptotic limit of the acid dissolution capacity can lead to a sharp dissolution front in chemical dissolution of porous rocks?

The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid‐saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems. However, there has been a debate in recent years that the asymptotic limit of the acid dissolution capacity (i.e., the acid dissolution capacity number approaching zero) alone cannot lead to a sharp dissolution front of the Stefan type in the acidization dissolution system, in which the dissolvable minerals of carbonate rocks are chemically dissolved by the injected acid flow. The acid dissolution capacity number is commonly defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid. In this paper, we use four different proof methods, including (i) direct use of the fundamental concepts; (ii) use of the mathematical governing equations of an acidization dissolution system; (iii) use of the different time scaling approach; and (iv) use of a moving coordinate system approach, to demonstrate that the asymptotic limit of the acid dissolution capacity can indeed lead to sharp dissolution fronts of the Stefan type in acidization dissolution systems on a much larger time scale (than the dissolution time scale). Our new finding is that on the reaction time scale, the condition of the conventional time derivative of porosity approaching zero alone can ensure that the acidization dissolution front has a sharp shape of the Stefan type. Copyright © 2017 John Wiley & Sons, Ltd.     

Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks

The chemical‐dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, pore‐fluid pressure and reactive chemical‐species transport in fluid‐saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re‐derived to correct this confusion in this paper. Owing to the morphological instability of a chemical‐dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical‐dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical‐dissolution front during its propagation within fluid‐saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical‐dissolution front instability problem within a fluid‐saturated porous medium. Copyright © 2007 John Wiley & Sons, Ltd.     

三峡地区碳酸盐岩化学组分与溶蚀速率的响应关系

文章通过室内静水溶蚀实验测定了三峡地区香溪河流域震旦-三叠系碳酸盐岩的化学溶蚀速率,探讨了碳酸盐岩的化学溶蚀速率对岩石化学组分的响应关系,为区域岩溶量化研究与地层含水性评价等提供了科学依据。研究结果表明:较纯碳酸盐岩的溶蚀速率受到CaO、SrO的促进作用和MgO的抑制作用共同控制,而这三者对纯灰岩的溶蚀速率影响较小;碳酸盐岩中的酸不溶物对化学溶蚀过程呈现出抑制的趋势。碳酸盐岩的化学溶蚀速率受到多化学组分的共同影响,综合决定了碳酸盐岩的可溶性。      

Computational simulation for the morphological evolution of nonaqueous phase liquid dissolution fronts in two-dimensional fluid-saturated porous media

This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described, a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front.     

Theoretical analyses of acidization dissolution front instability in fluid‐saturated carbonate rocks

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid‐saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.     

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical analyses of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper mainly deals with the theoretical aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved‐mineral equilibrium concentration in the pore fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid‐saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when temperature variation effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. The related theoretical and numerical results have demonstrated that: (i) a temperature increase in a non‐isothermal chemical dissolution system can have some influence on the propagation speed of the planar chemical dissolution front in the system. Generally, the chemical dissolution front in the non‐isothermal chemical dissolution system propagates slower than that in the counterpart isothermal chemical dissolution system when the temperature of the non‐isothermal chemical dissolution system is higher than that of the counterpart isothermal chemical dissolution system; (ii) a temperature increase in the non‐isothermal chemical dissolution system can stabilize the chemical dissolution front propagating in the system, because it can cause a decrease in the Zhao number of the system but does not affect the critical Zhao number of the system; and (iii) the temperature gradient in the upstream direction of a chemical dissolution front is smaller than that in the downstream direction of the chemical dissolution front when the non‐isothermal chemical dissolution system is supercritical. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of medium and pore‐fluid compressibility on chemical‐dissolution front instability in fluid‐saturated porous media

Theoretical analysis and computational simulations have been carried out to investigate how medium and pore‐fluid compressibility affects the chemical‐dissolution front propagation, which is associated with a fully‐coupled nonlinear problem between porosity, pore‐fluid pressure, pore‐fluid density and reactive chemical‐species transport within a deformable and fluid‐saturated porous medium. When the fully‐coupled nonlinear system is in a subcritical state, some analytical solutions have been derived for a special case, in which the ratio of the equilibrium concentration to the solid molar density of the chemical species is approaching zero. To investigate the effect of either medium compressibility or pore‐fluid compressibility on the evolutions of chemical dissolution fronts in supercritical chemical dissolution systems, numerical algorithms and procedures have been also proposed. The related theoretical and numerical results have demonstrated that: (i) not only can pore‐fluid compressibility affect the propagating speeds of chemical dissolution fronts in both subcritical and supercritical systems, but also it can affect the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; (ii) medium compressibility may have a little influence on the propagating speeds of chemical dissolution fronts, but it can have significant effects on the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; and (iii) both medium and pore‐fluid compressibility may stabilize irregular chemical‐dissolution‐fronts in supercritical chemical dissolution systems. Copyright © 2011 John Wiley & Sons, Ltd.     

动水压力作用下碳酸盐岩溶蚀作用模拟实验研究

为研究岩溶地区水库蓄水不同条件下动水压力驱动下的碳酸盐岩溶蚀作用机制。以乌江流域某水电站坝前地区碳酸盐岩为研究对象,利用自行研制的开放体系压力溶蚀实验系统,对不同动水压力（0～2.0 MPa）条件下CO2水溶液溶蚀碳酸盐岩的过程进行实验模拟,其结果显示,动水压力增大会引起碳酸盐岩的溶蚀作用加剧,溶解速率曲线随动水压力的变化而发生显著改变;随动水压力的增大,岩石的化学溶解量和机械破坏量同时增大,两者的比值随着压力增大逐渐趋于1：1,两者之间存在耦合关系。采用扫描电镜与压汞试验相结合的方法进行微观研究发现,动水压力对碳酸盐岩的溶蚀作用不仅发生于岩石表面,使表面溶孔增大并加深,产生次生孔隙和次生矿物,同时还改变着岩石的内部孔隙结构,降低其渗透性并弱化结构面的连接。     

Hydrothermal mixing,carbonate dissolution and sulfide precipitation in Mississippi Valley-type deposits

A large number of Mississippi Valley-Type (MVT) deposits are located within dissolution zones in carbonate host rocks. Some genetic models propose the existence of cavities generated by an earlier event such as a shallow karstification, that were subsequently filled with hydrothermal minerals. Alternative models propose carbonate dissolution caused by the simultaneous precipitation of sulfides. These models fail to explain either the deep geological setting of the cavities, or the observational features which suggest that the dissolution of carbonates and the precipitation of minerals filling the cavities are not strictly coeval. We present a genetic model inspired by the textural characteristics of MVT deposits that accounts for both the dissolution of carbonate and precipitation of sulfides and later carbonates in variable volumes. The model is based on the mixing of two hydrothermal fluids with a different chemistry. Depending on the proportion of the end members, the mixture dissolves and precipitates carbonates even though the two mixing solutions are both independently saturated in carbonates. We perform reactive transport simulations of mixing of a regional groundwater and brine ascending through a fracture, both saturated in calcite, but with different overall chemistries (Ca and carbonate concentrations, pH, etc). As a result of the intrinsic effects of chemical mixing, a carbonate dissolution zone, which is enhanced by acid brines, appears above the fracture, and another zone of calcite precipitation builds up between the cavity and the surrounding rock. Sulfide forms near the fracture and occupies a volume smaller than the cavity. A decline of the fluid flux in the fracture would cause the precipitation of calcite within the previously formed cavities. Therefore, dissolution of carbonate host rock, sulfide precipitation within the forming cavity, and later filling by carbonates may be part of the same overall process of mixing of fluids in the carbonate host rock.Editorial handling: C. Everett     

The effect of Fe-oxidizing bacteria on Fe-silicate mineral dissolution

Acidithiobacillus ferrooxidans are commonly present in acid mine drainage (AMD). A. ferrooxidans derive metabolic energy from oxidation of Fe²⁺ present in natural acid solutions and also may be able to utilize Fe²⁺ released by dissolution of silicate minerals during acid neutralization reactions. Natural and synthetic fayalites were reacted in solutions with initial pH values of 2.0, 3.0 and 4.0 in the presence of A. ferrooxidans and in abiotic solutions in order to determine whether these chemolithotrophic bacteria can be sustained by acid-promoted fayalite dissolution and to measure the impact of their metabolism on acid neutralization rates. The production of almost the maximum Fe³⁺ from the available Fe in solution in microbial experiments (compared to no production of Fe³⁺ in abiotic controls) confirms A. ferrooxidans metabolism. Furthermore, cell division was detected and the total cell numbers increased over the duration of experiments. Thus, over the pH range 2–4, fayalite dissolution can sustain growth of A. ferrooxidans. However, ferric iron released by A. ferrooxidans metabolism dramatically inhibited dissolution rates by 50–98% compared to the abiotic controls.

Two sets of abiotic experiments were conducted to determine why microbial iron oxidation suppressed fayalite dissolution. Firstly, fayalite was dissolved at pH 2 in fully oxygenated and anoxic solutions. No significant difference was observed between rates in these experiments, as expected, due to extremely slow inorganic ferrous iron oxidation rates at pH 2. Experiments were also carried out to determine the effects of the concentrations of Fe²⁺, Mg²⁺ and Fe³⁺ on fayalite dissolution. Neither Fe²⁺ nor Mg²⁺ had an effect on the dissolution reaction. However, Fe³⁺, in the solution, inhibited both silica and iron release in the control, very similar to the biologically mediated fayalite dissolution reaction. Because ferric iron produced in microbial experiments was partitioned into nanocrystalline goethite (with very low Si) that was loosely associated with fayalite surfaces or coated the A. ferrooxidans cells, the decreased rates of accumulation of Fe and Si in solution cannot be attributed to diffusion inhibition by goethite or to precipitation of Fe–Si-rich minerals. The magnitude of the effect of Fe³⁺ addition (or enzymatic iron oxidation) on fayalite dissolution rates, especially at low extents of fayalite reaction, is most consistent with suppression of dissolution by interaction between Fe³⁺ and surface sites. These results suggest that microorganisms can significantly reduce the rate at which silicate hydrolysis reactions can neutralize acidic solutions in the environment.     

Dissolution kinetics of natural magnesite in lactic acid solutions

In this study, the dissolution of magnesite particles in aqueous lactic acid solutions was investigated in a batch reactor employing the parameters of stirring speed, particle size, temperature and acid concentration. The shrinking core model was evaluated to determine the effect of particle size, temperature and concentration. It was also found that the stirring speed did not change the dissolution. Consequently, it was determined that the dissolution rate is controlled by surface chemical reaction. The activation energy of the process was determined to be 50.3 kJ mol^− 1.     

基于除镉作用机理探讨的碳羟磷灰石溶解特性研究

碳羟磷灰石（CHap）在含镉溶液和空白溶液中溶解特性的对比实验结果表明：介质pH值是影响CHap溶解的重要因素,强酸务件下,溶解度最大;溶钙量和溶磷量的摩尔比均不是1、67;溶解初期阶段反应速度快,动力学过程复杂,后期阶段符合一级反应动力学特征,说明CHap溶解机理符合氢催化模型、非化学计量比溶解模型、多核模型,在含镉溶液中溶解时,还包括离子交换模型,即溶液中的镉离子与CHap中的钙离子发生交换作用。从溶解特性的角度推测：CHap除镉过程中存在有离子交换作用机理。     

频域内饱和多孔介质的参数反演分析

基于Biot理论,假定固体颗粒和孔隙内流体均不可压缩,建立了以固体骨架位移表示的的控制方程.考虑单层饱和多孔介质在竖向简谐荷载作用下一维动力响应,通过理论推导获得了骨架位移、应力以及孔隙流体压力等物理量的解析表达式.基于饱和土的简谐动力模型试验数据,与所得到的理论解答相结合,将饱和多孔介质材料参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了遗传算法和模拟退火算法,并通过试验和数值算例验证了所得材料参数的正确性.     

Double Diffusion-Driven Convective Instability of Three-Dimensional Fluid-Saturated Geological Fault Zones Heated from Below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.     

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 John Wiley & Sons, Ltd.     

On Garg's solution of Biot's equations for wave propagation in a one-dimensional fluid-saturated elastic porous solid

Garg's approximate analytical solutions of Biot's equations for wave propagation in a fluid-saturated elastic porous solid of infinite extent subjected to a velocity boundary condition of a Heaviside function at one end are examined for small and large drag. Garg's approximations were apparently introduced to facilitate exact inversion of Laplace transforms of certain quantities. The approximate solutions are compared with carefully evaluated numerical inverses of the Laplace transform solutions for different soils with widely varying properties. It is seen that for most soils (clays, silts and, sands) the error in Garg's approximate solutions in insignificant, and the solutions can be used as benchmarks for verifying numerical analysis procedures such as finite element codes.     

Geochemistry of a spring-dense karst watershed located in a complex structural setting, Appalachian Great Valley, West Virginia, USA

The distribution and chemistry of the springs in the Tuscarora Creek watershed is controlled by both geologic structure and karst dissolution. The watershed is located in eastern West Virginia in the structurally complex Great Valley of the Appalachian Valley and Ridge province. The upper portion of the stream parallels strike along a mapped fault zone and is bordered by clastic rocks that comprise North Mountain. The lower reaches of the stream flow cross-strike through Cambro-Ordovician carbonates. The controlling chemical signature in the spring water is carbonate dissolution. Little evidence was seen for the recharge from adjacent clastic rocks although differences in the Ca/Mg molar ratio between springs indicated the presence of localized spring basins in headwater reaches. Na, Cl and Ca generally increased from upstream to downstream in the cross-strike reaches. Comparison of stream and cumulative spring discharge was consistent with significant groundwater base-flow contribution directly to the creek, particularly in the strike-parallel region. The largest spring in the watershed (>162 L/s) was sampled during and after a large storm event along with the adjacent creek. The creek displayed a typical dilution response with each flood pulse, whereas the spring had only a limited or delayed response. The overall chemical and thermal stability of the spring, relative to the creek, indicated the lack of significant direct hydraulic connection between the two. The conceptual model for the area includes localized flowpaths in the headwater region where the stream flow is parallel to strike and a thrust fault. In addition to the shallow localized flowpaths, a deeper, more regional flowpath likely exists for a large spring further downstream.