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Fracture Evolution in Multi-mineral Systems: The Role of Mineral Composition, Flow Rate and Fracture Aperture Heterogeneity Hang Deng, Carl I. Steefel, Sergi Molins, and Donald DePaolo ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.7b00130 • Publication Date (Web): 29 Dec 2017 Downloaded from http://pubs.acs.org on December 31, 2017
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ACS Earth and Space Chemistry
Fracture Evolution in Multi-mineral Systems: The Role of Mineral Composition, Flow Rate and Fracture Aperture Heterogeneity Hang Deng1,*, Carl Steefel1, Sergi Molins1, Donald DePaolo1, 2 1. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 2. Earth and Planetary Science, University of California, Berkeley, Berkeley, CA, 94720 *email:
[email protected], cell: 609-937-9927
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Abstract
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Keywords: fracture evolution, mineral heterogeneity, reactive transport model, multi-reaction Damköhler number, geologic carbon storage, caprock integrity
Geochemical reactions add complexity to the characterization and prediction of fracture hydraulic properties because they depend on factors that are highly heterogeneous, such as mineral composition. But systematic analyses of fracture evolution in mineralogically heterogeneous systems are still limited. In this study, we investigated fracture evolution in multi-mineral systems using a reduced dimension reactive transport model. The model was developed and tested based on experimental studies and addresses the complex morphological and geochemical changes that arise from the presence of multiple minerals of different reactivity. Numerical experiments were performed using randomly generated initial fracture geometries based on representative geostatistics, different categories of mineral composition, and a range of flow rates that are relevant to geologic carbon storage systems. The simulation results showed distinct dissolution regimes at different flow rates, each of which produced characteristic dissolution patterns and temporal evolutions of chemical reactions and fracture hydraulic properties. Overall, as flow rate increases, fracture evolution shifts from compact dissolution to fracture channelization to uniform dissolution. The corresponding flow rate for a given dissolution regime, however, varies considerably with mineral composition. Fracture evolution, especially in the flow regime that induces fracture channelization, is also affected by initial fracture geometry. The numerical experiments were used to develop a multi-reaction Damköhler number () for the prediction of fracture evolution, and fracture channelization in particular, in multi-mineral systems. The multireaction Damköhler number also provides a useful framework for the evaluation of caprock integrity in geologic carbon storage systems.
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1. Introduction
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Fractures, natural and induced by anthropogenic activities, are abundant in various geological systems, including the weathered rock and soil layers and karst aquifers in the Earth’s critical zone and deep geological formations that are used for energy recovery and waste disposal 1-4. Fractures serve as preferential flow pathways in these geological systems, especially in otherwise impermeable rocks, and thus dominate gas and fluid flow and mass transfer in the geosphere 5-8. In fractured geological systems where corrosive fluids or non-native chemicals are introduced, such as in the injection of acidic fluids for geologic CO2 storage and hydraulic fracturing, geochemical reactions (e.g. mineral dissolution and precipitation) are promoted 9. As a result of these chemical reactions, fracture morphology and hydraulic properties (i.e. fracture hydraulic aperture and intrinsic fracture permeability) are subject to alteration. Quantification of flow and transport in fractured rocks, which is needed for reservoir-scale simulations and for interpreting field observations, may require explicit representation of discrete fractures 10, making fundamental understanding of the dynamic evolution of individual fractures critical.
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Previous studies have shown that flow rate plays an important role in controlling fracture alteration that is driven by mineral dissolution 11-15. The dissolution patterns show distinct features at different flow regimes. At a flow rate that is slow compared to the reaction rate, i.e. the residence time of the fluid is much longer than the time scale of reactions, local equilibrium is likely to be achieved. In this transport controlled regime, diffusion may become important, which tends to reduce local concentration gradient and suppress reactive instability 15-16. As a result, reactions and the resulting aperture change are limited to the inlet of the flow. This is also known as compact dissolution or face dissolution. At a flow rate that is fast in comparison to the reaction rate, the residence time of the fluid is short and local reactions become surface reaction controlled. In this case, highly reactive fluids persist throughout the length of the fracture, and dissolution is uniform throughout the fracture. At flow rates that are comparable to the reaction rate, the interplay between flow and reactions leads to the reactive infiltration instability (a form of geochemical self-organization phenomena), i.e. the perturbations due to geometric, flow and geochemical heterogeneity are amplified to create preferential flow channels in the fractures 17.
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Hydraulic properties of the fractures evolve according to the dissolution patterns. In the case of compact dissolution, fracture permeability does not increase significantly because of the lack of fracture opening at the downstream end. In the case of uniform dissolution, fracture permeability will increase substantially when no confining stress is present, and can decrease under confining stresses because of the removal of asperities, i.e. contact points 12, 18. Fracture channelization leads to rapid increase in fracture permeability, even under confining pressure, as asperities in nonchannelized regions in the fracture are preserved and can prevent the fracture from closing 18. The dimensionless Damköhler number, which is defined as the ratio between the reaction rate and flow rate, has been widely used to analyze dissolution patterns in fractures and porous media under different flow regimes 11, 13, 15, 19. The interplay between flow and reaction and the resulting dissolution patterns are scale dependent. The use of the Damköhler number provides a unified framework to analyze the evolution of fractures of different length and mineral dissolution rate. These analyses, however, focused on simple geochemical systems, where typically only a single mineral is present, as the choice of a single reaction rate in multimineral systems is less clear 20-21.
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As revealed by several experimental studies, however, heterogeneity in mineral composition can cause complex alteration of fracture morphology and hydraulic properties 22-31. When mineral grains of different reactivity are mixed, preferential dissolution of the fast-reacting mineral(s) leaves behind a porous layer that is composed of the remaining slow-/non-reacting minerals. This altered layer serves as a barrier that limits the contact between the fresh reactive fluid and the fast-reacting mineral, resulting in increasingly reduced dissolution of the fast-reacting mineral 25, 31. A similar phenomenon has been observed in the Earth’s critical zone, where weathering rinds coat unweathered cores of rocks 32. In fractures, the presence of the altered layer can limit the increase of fracture aperture and fracture permeability 22, 25, 33. In certain cases where the altered layer has a large porosity and is structurally weakened, the altered layer can detach from the fracture surface, or erode. If there is fracture wall erosion, the mobilized particles are transported downstream by the fluid, where they can accumulate at narrow points and reduce fracture hydraulic permeability 23, 30. In cases where a channel forms, the mobilized particles may be transported by the flow without clogging the fracture or leading to fracture permeability decrease 23, 34.
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These experimental studies have provided important insights regarding fracture alteration in multi-mineral systems, which are more common in the natural environment. For the same multi-mineral sample, the spatial patterns of fracture aperture change were observed to shift from compact dissolution to wormholing to uniform dissolution as flow rate increases 26. Péclet number, a measure of the relative magnitude of diffusion and advection rate, has been used to describe the flow regimes corresponding to different fracture dissolution patterns. It does not, however, include any information on the reaction rate, and therefore limits the ability to compare across mineral composition. It has been shown that the flow regime corresponding to a given spatial pattern can be different for a mineralogically heterogeneous sample from what would be expected if no mineral heterogeneity was present. For example, channelization was not observed in an argillaceous limestone even though flow conditions that favor channelization in a pure limestone fracture were used 23. In addition, development of the altered layer at a given flow rate was observed to vary with mineral composition 25. Most experimental studies, however, are performed under a limited range of conditions (e.g. length, flow rate) and include sample heterogeneity that is difficult to characterize, and thus do not allow systematic and quantitative analyses of fracture evolution as a function mineral composition.
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The objective of the current study is to develop an analytical framework for the investigation of fracture evolution, and fracture channelization in particular, in multi-mineral rock matrices such that comparison across mineral composition is possible. To this end, we first conduct a series of numerical experiments to examine fracture evolution in multi-mineral systems under different flow conditions and with different levels of geometric and mineralogical heterogeneity. This investigation is enabled by the recent development of a reduced dimension reactive transport model 34-35. Alternative 3D models would involve explicit discretization in the dimension of the fracture aperture, using either the pore-scale approach where the fracture surface is resolved explicitly or the dual-continuum approach 36. 3D models, however, are computationally demanding as fine meshing is typically required given the relatively small aperture size and altered layer thickness compared to fracture plane dimensions. In contrast, the reduced dimension model used in our study is computationally efficient. Further, the model can be viewed as conceptually similar to a dual-porosity model where the exchange between the fracture and the matrix is calculated with the rate model (eqns (4-6)). The model was developed and tested based on experimental studies, and captures the complex morphological and geochemical changes that arise from
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the coexistence of minerals of differing reactivity. The key features of the model are summarized in the Methods section, as flow conditions, initial fracture geometries, and geochemical conditions like mineral composition used for the numerical experiments. In the Results and Discussion section, we present the results of the numerical experiments and a multi-reaction Damköhler number () that can be used to predict and compare dissolution regimes of fractures across mineral composition. The multi-reaction Damköhler number provides a framework for the generalization of existing experimental studies and numerical simulations. We conclude the manuscript with a discussion of the implications for caprock integrity in geological carbon storage systems.
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2. Methods
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2.1 Reduced Dimension Reactive Transport Model To simulate dissolution-driven fracture alteration, we adopt a reduced dimension model that was developed and tested based on experimental observations. Details of the model can be found in previous publications 34-35, and only the key features of the model are summarized here.
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The reduced dimension model is implemented in CrunchFlow, a multi-component reactive transport code 37. It includes three modules. The core module provides the fundamental framework, in which the fracture is discretized into a 2D mesh within the fracture plane. Each grid cell is a continuum, i.e. fracture and rock matrix co-exist. The governing advection-diffusion-reaction equation (eqn(1)) is discretized using the integrated finite difference method following the 2D mesh and solved for the total concentration of each component ( ). The Darcian flux () is solved using Darcy’s law and permeability that is calculated from local fracture aperture (, ) using the cubic law 38. The isotropic tensor ( ) includes molecular diffusion. The reaction term ( ) accounts for the contribution from dissolution (negative) and precipitation (positive) reactions of minerals. Porosity of each grid cell is calculated based on local fracture aperture, and updated over time.
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While the configuration of the core module allows the consideration of fracture aperture variations and therefore fracture geometry heterogeneity, the dimension across the fracture aperture is not treated explicitly, i.e., it is not discretized. Two additional modules were developed to account for the processes across the fracture aperture, specifically the development of an altered layer on the fracture surface and its erosion due to the detachment of the altered rock matrix. It is assumed that the two fracture halves are symmetric.
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In the altered layer module, the reaction front for each individual mineral is tracked based on its respective reaction rate and volume fraction. As a result of differential dissolution, mineral fronts retreat into the rock matrix at different rates. The aperture of a given mineral (, , ) is the distance between the dissolution fronts of this mineral ( ) on both sides of the fracture, i.e. the thickness of the region where this mineral is depleted, including the fracture aperture itself and a portion of the matrix. The mineral-specific aperture is calculated using eqn(2) from the volume fraction of that mineral in the intact rock matrix ( , , ) and the volume fraction of the mineral in the grid ( , , ), which is controlled by the reaction rate of the mineral.
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, , =
= −∇ ∙ + ∇ ∙ ∇ −
! 1
−
#,$,%
&' ,$,%
eqn(1)
eqn(2)
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ACS Earth and Space Chemistry
where ! is the thickness of the simulated domain in the third dimension perpendicular to the fracture plane. The mineral front that retreats the slowest defines the fracture surface, and the distance between the two fracture surfaces is the fracture aperture, also referred to as the flow aperture or geometric aperture in this study (, ) (eqn(3)).
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, = min+, ,, , … , , , .
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The distance between the fracture surface and the mineral front that retreats the fastest is the thickness of the altered layer (/). Following previous observations 23, 39, only diffusion and no flow is considered in the altered layer. Given that the dissolution products of the fast-reacting mineral have to diffuse through the altered layer, the dissolution of the fast-reacting mineral is increasingly subject to a diffusive transport limitation as the altered layer develops. This diffusion limitation, as quantified by the diffusion controlled reaction rate ( 0&& ), is proportional to the ratio between the effective diffusion coefficient of the porous altered layer (1&& ) and its thickness (eqn(4)). The effective reaction rate ( 1&& ) (eqn(5)) is determined by the lower value of 0&& and the surface reaction rate 23 & , which is calculated using Transition State Theory type rate laws in this study. In eqn(6), 4 5 is the kinetic coefficient, 6 5 denotes the reactive surface area, 768 represents the ion activity product and 91: is the equilibrium constant. The exponents ;< and ;= here are assumed to be one.
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0&& ∝
eqn(3)
?@AA B
eqn(4)
