Reactive Infiltration Instability Research Articles

Some fundamental issues associated with theoretical analyses of reactive infiltration instability in fluid‐saturated porous media

AbstractThis paper deals with three fundamental issues associated with theoretical analyses of reactive infiltration instability (RII) problems in fluid‐saturated porous media. The first fundamental issue is to determine the spatial shapes of chemical dissolution‐fronts in the limit case of the mineral dissolution ratio approaching zero in both conventional time (daily life time) and unconventional time (abstract time) domains. The chemical dissolution‐front is commonly represented by the spatial shape of the porosity profile. The second fundamental issue is to conduct theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through directly solving dimensional mathematical governing equations in the conventional time domain. The third fundamental issue is to carry out theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through solving dimensionless mathematical governing equations in the unconventional time domain. Through purely mathematical deductions, it has been proven that: (1) the spatially sharp shape of a chemical dissolution‐front, which is theoretically predicted either at a much smaller timescale than the dissolution timescale associated with the daily life time or at a much larger timescale than the dissolution timescale associated with the daily life time, can be observed in the daily life time domain; (2) the theoretical instability criterion of an RII problem can be established directly at three different length‐scales in the daily life time domain; and (3) although the spatial shape of a chemical dissolution‐front at the dissolution timescale associated with the daily life time cannot be observed in the daily life time domain, the theoretical instability criterion of an RII problem at the dissolution timescale associated with the daily life time can be established when a physically consistent mathematical transform is used in the theoretical analysis.

Reactive-infiltration instability in a Hele-Shaw cell influenced by initial aperture and flow rate

We experimentally investigate dissolution morphologies in a radial Hele-Shaw cell. We observe a unique phenomenon where the dissolution front shifts from stable to unstable and uncover the role of buoyancy-driven convection in forming radial stripes (dissolution ``flower'') on the solid surface. We propose a phase diagram to predict the transitions of dissolution patterns.

Evidence of Volatile‐Induced Melting in the Northeast Asian Upper Mantle

AbstractA seismic low velocity layer (LVL) above the mantle transition zone (MTZ), often thought to be caused by volatile‐induced melting, can significantly modulate planetary volatile cycles. In this work, we show that an LVL observed beneath northeast Asia is characterized by small, 0.8 0.5 vol%, average degrees of partial melting. Seismically derived P‐T conditions of the LVL indicate that slab‐derived , possibly combined with small amounts of O, is necessary to induce melting. Modeling the reactive infiltration instability of the melt in a stationary mantle above a stalled slab, we demonstrate that the volatile‐rich melt slowly rises above the stalled slab in the MTZ, with percolation velocities of 200–500 m/yr. The melt remains stable within the LVL for this geologically significant period of time, potentially transferring up to 52 Mt/yr of from the subducting slab to the mantle for an LVL similar in areal extent () to the northeast Asian LVL. Reaction between the melt channels and the LVL mantle precipitates up to 200 ppmw solid C in localized zones. Using the inferred small melt volume fraction to model trace element abundances and isotopic signatures, we show that interaction between this melt and the surrounding mantle can over the long‐term produce rocks bearing a HIMU like geochemical signature.

Geological Carbon Sequestration by Reactive Infiltration Instability

We study carbon capture and sequestration (CCS) over time scales of 2000 years by implementing a numerical model of reactive infiltration instability caused by reactive porous flow. Our model focuses on the mineralization of CO2 dissolved in the pore water—the geological carbon sequestration phase of a CCS operation—starting 10–100 years after the injection of CO2 in the subsurface. We test the influence of three parameters: porosity, mass fraction of the Ca-rich feldspar mineral anorthite in the solid, and the chemical reaction rate, on the mode of fluid flow and efficiency of CaCO3 precipitation during geological carbon sequestration. We demonstrate that the mode of porous flow switches from propagation of a planar front at low porosities to propagation of channels at porosities exceeding 10%. The channels develop earlier for more porous aquifers. Both high anorthite mass fraction in the solid phase and high reaction rates aid greater amounts of carbonate precipitation, with the reaction rate exerting the stronger influence of the two. Our calculations indicate that an aquifer with dimensions 500 m × 2 km × 2 km can sequester over 350 Mt solid CaCO3 after 2000 years. To precipitate 50 Mt CaCO3 after 2000 years in this aquifer, we suggest selecting a target aquifer with more than 10 wt% of reactive minerals. We recommend that the aquifer porosity, abundance of reactive aluminosilicate minerals such as anorthite, and reaction rates are taken into consideration while selecting future CCS sites.

A semianalytical approach for solving first‐order perturbation equations of dissolution‐timescale reactive infiltration instability problems in fluid‐saturated rocks

SummaryThis paper presents a semianalytical approach for solving first‐order perturbation (FOP) equations, which are used to describe dissolution‐timescale reactive infiltration instability (RII) problems in fluid‐saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface‐condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element‐by‐element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution‐timescale RII problems in fluid‐saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution‐timescale RII system.

Three‐Dimensional Hydrochemical Model for Dissolutional Growth of Fractures in Karst Aquifers

AbstractThis paper is intended to present a newly developed, comprehensive model to understand hydrochemical behaviors related to dissolutional growth of complex fractures underground. Under a fully implicit solution framework, the finite volume approach is employed to solve the reactive‐convective‐dispersive system. Based on the embedded discrete fracture model, a novel modeling approach is proposed to describe dissolutional fractures with various apertures in three dimensions (3‐D). This model is verified against preexisting numerical models. Then, a 3‐D field case study regarding hypogene speleogenesis in a deep‐seated, artesian setting is carried out, based on field data concerning karst terrain compiled from Western Ukraine. Finally, we perform a case study to elucidate the finger‐like dissolution process related to a synthetic 3‐D fracture network in gypsum and limestone with heterogeneous aperture fields. Simulation results suggest that (a) the combination of the kinetic trigger mechanism and the transverse speleogenesis concept favors the generation of hierarchical caves in homogeneous fractures; (b) the mechanism of reactive infiltration instabilities determines dissolutional propagation in gypsum with rough fractures; and (c) in limestone, nonlinear kinetics matters for both uniform‐ and variable‐aperture fractures.

Reactive instabilities in linear acidizing on carbonates

Acid injection, reactive instabilities and wormholing in carbonate reservoirs is investigated through the analysis of the linear acidizing problem theoretically and experimentally. Theoretically acidizing was analyzed by formulating the problem as a reactive moving boundary Stefan type problem. Wormholing is viewed as a reactive infiltration instability to the trivial solution of uniform dissolution. A linear stability analysis from the equilibrium state is performed and the critical wavenumber below which instabilities have a positive growth rate is identified. When applied to the scale of the experiment, an optimum injection velocity is identified for a given formation and injection concentration, for the growth for a single wormhole. This optimum injection velocity scales with the inverse of the specimen diameter. Experimentally, linear acidizing tests were performed in Mons chalk, a high porosity analogue of North Sea reservoir chalk. In the experiments the critical injection velocity for wormhole formation at minimum acid injection was obtained and the results were compared with the theoretical predictions.

Reactive-infiltration instability in radial geometry: From dissolution fingers to star patterns.

We consider the process of chemical erosion of a porous medium infiltrated by a reactive fluid in a thin-front limit, in which the width of the reactive front is negligible with respect to the diffusive length. We show that in the radial geometry the advancing front becomes unstable only if the flow rate in the system is sufficiently high. The existence of such a stable region in parameter space is in contrast to the Saffman-Taylor instability in radial geometry, where for a given flow rate the front always eventually becomes unstable, after reaching a certain critical radius. We also examine the similarities between the reactive-infiltration instability and the similar instability in the heat transfer, which is driving the formation of star-like patterns on frozen lakes.

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

SummaryA 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.

Microfluidic measurement of the dissolution rate of gypsum in water using the reactive infiltration-instability

We present an original method for measuring the intrinsic dissolution rate of gypsum. We use a simple microfluidic setup, with a gypsum block inserted between two polycarbonate plates, which is dissolved by water. By changing the flow rate and the distance between the plates, we can scan a wide range of Péclet and Damköhler numbers, characterizing the relative magnitude of advection, diffusion and reaction in the system. We find the dissolution to be unstable, with a formation of a characteristic fingering pattern. The dissolution rate can then be calculated from the initial wavelength of this pattern. Alternatively, it can also be estimated from the time it takes for the gypsum chip to get completely dissolved near the inlet channel. The method presented here is general and can be used to assess the dissolution rates of other minerals.

Evolution of planar fractures in limestone: The role of flow rate, mineral heterogeneity and local transport processes

The processes that affect the evolution of fracture geometry and reactive transport in limestone fractures were evaluated using an integrated experimental and modeling approach. Flow-through experiments were performed to investigate the alteration of three artificially made planar limestone fractures, which were exposed to HCl-acidified water flow (pH 3.8 ± 0.1) at three different rates. Reactive infiltration instability developed in the fractures because of small fracture aperture variations and naturally occurring heterogeneity in the rock, i.e., the presence of clay spots of higher porosity. The dissolution regime changed from conical to dominant and ramified wormhole with increasing flow rate, i.e., Péclet number. Maps of fracture aperture obtained from X-ray micro-tomography imaging, together with measurements of permeability and analyses of fluid chemistry, provided experimental constraints for modeling. Numerical simulations were performed using a 2.5D continuum reactive transport model to examine the development of flow patterns and the reactivity and permeability evolution over time, and to interrogate the impacts of fluid reactivity, mineral heterogeneity and diffusive boundary layer. The modeling results showed that fracture alteration is very sensitive to initial fluid reactivity and mineralogical heterogeneity, in addition to flow rate. The changes of local transport processes during fracture opening also affected the reactivity of the fractured samples.

Reply to comment on “validity of using large-density asymptotics for studying reaction-infiltration instability in fluid-saturated rocks”

In this reply we further demonstrate and confirm that the main conclusion (namely, that the asymptotic limit of the acid dissolution capacity can lead to sharp dissolution fronts) in our recent publication in this journal is correct and valid. The basis of the incorrect critique in the comment is whether or not a physically-consistent velocity scale should be used in deriving the dimensionless partial differential equations of the reactive infiltration instability problem in fluid-saturated rocks. In addition, there is confusion in the comment between the conclusions drawn from results obtained using different time scales (such as a dissolution time scale and a much larger time scale than the dissolution time scale) in the process of describing the reactive infiltration instability problem, and using different mathematical transforms (such as a physically-consistent mathematical transform and a physically-inconsistent one) in the nondimensionalization of dimensional partial differential equations.

Impact of microstructure evolution on the difference between geometric and reactive surface areas in natural chalk

Reactive infiltration instability (RII) drives the development of many natural and engineered flow systems. These are encountered e.g. in hydraulic fracturing, geologic carbon storage and well stimulation in enhanced oil recovery. The surface area of the rocks changes as the pore structure evolves. We combined a reactor network model with grey scale tomography to seek the morphological interpretation for differences among geometric, reactive and apparent surface areas of dissolving natural porous materials. The approach allowed us to delineate the experimentally convoluted variables and study independently the effects of initial geometry and macroscopic flowrate. Simulations based on North Sea chalk microstructure showed that geometric surface not only serves as the interface for water-rock interactions but also represents the regional transport heterogeneities that can be amplified indefinitely by dissolutive percolation. Hence, RII leads to channelization of the solid matrix, which results in fluid focusing and an increase in geometric surface area. Fluid focusing reduces the reactive surface area and the residence time of reactants, both of which amplify the differences in question, i.e. they are self-supporting. Our results also suggested that the growing and merging of microchannels near the fluid entrance leads to the macroscopic "fast initial dissolution" of chemically homogeneous materials.

Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix

AbstractA reactive fluid dissolving a uniform porous material triggers an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. The concentration field within the dissolving region contains two different length scales, upstream (no reaction) and downstream of the front position. Previous investigations of the reactive-infiltration instability have considered one or other of the scales to be dominant, leading to rather different conclusions. Here we describe a more general linear stability analysis which includes both length scales simultaneously. We show how previous work corresponds to special cases of our more general analysis and obtain closed-form solutions for small permeability gradients.

Pore Scale Processes Associated with Subsurface CO2 Injection and Sequestration

The injection of CO2 into the Earth’s subsurface drives the fluid-rock system into “far-from- equilibrium” conditions, which means that the fluxes that return the system to equilibrium are nonlinearly related to the generalized driving forces (e.g., chemical affinities and gradients in the fluid pressures and chemical potentials). The nonlinear response results in emergent structures and self-organization (Prigogine 1968, 1980; Ortoleva 1994; Lasaga 1998; Jamtveit and Meakin 1999), of which the reactive infiltration instability is a well-known example in the Earth Sciences that is directly applicable to CO2 injection and caprock integrity (Ortoleva et al. 1987; Hoefner and Fogler 1988; Steefel and Lasaga 1994; Steefel and Maher 2009). Flow, solute transport, colloid transport, mineral dissolution and mineral precipitation combine within the mechanical framework of the porous medium to generate precipitate structures in individual pores correlated over many thousands to millions of pores, and immiscible fluid structures with fractal geometry over scales from millimeters to kilometers (Feder 1988). The focus in this chapter is on processes, emergent and otherwise, taking place at the pore scale, defined here as the scale where individual grains and fluid interfaces can be resolved. The chief focus of research in recent years has been to improve the understanding of the nonlinear dynamics specifically associated with biogeochemical and microbially induced processes coupled to physical processes such as flow and diffusion at the pore scale. When coupled, whether in field-scale applications, bench-scale experiments, or in models, emergent behavior may result, including changes in permeability, diffusivity, and reactivity. The pore scale is an important scale to analyze these emergent behaviors given that it provides the architecture within which the smaller scale (nano and molecular scale) processes occur. For the individual processes to interact, transport is typically necessary and the resulting behavior …

Reactive-infiltration instabilities in rocks. Fracture dissolution

AbstractA reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport-limited dissolution, nonlinear kinetics, and a finite-length system.

Reactive infiltration instability of a granitization front during the generation and development of granite-gneiss domes

The origin of granite-gneiss domes is traditionally attributed to gravity tectonics, the ascent of granite-gneiss diapirs in a gravitational field owing to a relative decrease in the density of granitized rocks compared with their protolith. This is usually considered by the example of a two-layer medium with a lower layer of granitized rocks overlain by a denser protolith layer; the development of gravitational instability in the system results in the ascent of a granite-gneiss diapir. However, the diapiric process can be initiated only if Archimedes’ buoyancy forces at the roof of the granite-gneiss layer will overcome the resistance of the protolith rocks related to their long-term strength. Under the conditions of plastic deformations, this requires the existence of a large-scale irregularity in the relief of the layer boundary, namely, an antiform cusp in the roof of the granite-gneiss layer. The model is based on the assumption that such antiforms appear owing to the reactive infiltration instability of the morphology of the granitization front caused by an increase in the fluid permeability of granitized rocks compared with that of the protolith. The results of computer modeling support the geological feasibility of the reactive infiltration mechanism of the generation and development of the protodiapiric forms of the granitization front triggering the development of the diapiric process of the gravitational upwelling of granite-gneiss domes. The model of a protodiapir stage allows us to consider dome formation as a result of the development of two sequential instabilities: the reactive infiltration instability of the granitization front related to an increase in the permeability of the transformed rock followed by the gravitational instability related to a relative decrease in rock density.

Numerical Investigation of Melt Segregation Using FEM Coding Environment Escript

Understanding of melt segregation and extraction is one of the major outstanding problems of melting processes in Earth's mantle. The volcanoes that lie along the Earth's tectonic boundaries are fed by melt that is generated in the mantle. However, it still remains unclear how this melt is extracted and finds its way towards the volcanoes. Two important mechanisms in melt segregation and migration are reactive fluid flow and mechanical shear. Reactive fluid flow describes the formation and segregation/migration of melt significantly affected by chemical interaction between melt and rock. This reactive-infiltration instability results in melt fingering which eases the transition from porous to channelized flow and provides a key element in some of the geological phenomena on earth. The second important mechanism in melt migration is localization due to mechanical shear. Recent studies have shown that when partially molten rock is subjected to simple shear, bands of high and low porosity are formed at a particular angle to the direction of maximum extension. Thus melt distribution is also influenced by stresses in partially molten rock [2,3]. The main aim of this paper is to identify the main mechanisms inducing melt segregation and effective flow. More specifically we investigate the melt reaction instability and melt band formation in this study. Here, in addition to providing a better understanding of melting phenomena in the mantle, we also develop a numerically validated model which can be used as an active and open source for future more complicated studies. For the melt bands problem, we employ the equations of magma migration in viscous materials which was originally derived by McKenzie (1984), and for the fingering instability problem we refer to the well known equations of reactive transport [4]. We write two different numerical codes using the FEM environment “escript”. We test the codes for a set of well-understood case problems which have been studied previously by other researchers.

Modelling melting rates in upwelling mantle

Upwelling regions of the mantle can undergo partial melting as a result of decompression. Many models for the dynamics of these regions have largely ignored the actual melting process or have prescribed a uniform melting rate proportional to the upwelling velocity. This paper uses a simple model for an upwelling column to calculate the melting rate from conservation principles. The model rock comprises two chemical components, and is assumed to be in thermodynamic equilibrium. For idealized linear phase constraints the melting rate can be calculated analytically, and is found to be proportional to the average upwelling velocity of both the matrix and melt. A secondary aim is to discuss reactive instabilities; the model predicts that the one dimensional state will be linearly stable, whereas previous models have suggested that reactive infiltration instability should occur. This is argued to be a result of the ‘background’ melting rate which has not usually been fully accounted for, but which has a stabilizing effect. The model here can also be applied to a column in which some melt is already present, and in that case it does exhibit a channeling instability. It is concluded that accounting for melt production consistently in mid-ocean ridge models is important when assessing the likely modes of melt transport.

Effect of Reactive Surface Areas Associated with Different Particle Shapes on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Rocks

In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.