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1.
Krzaczek  M.  Nitka  M.  Kozicki  J.  Tejchman  J. 《Acta Geotechnica》2020,15(2):297-324

The paper deals with two-dimensional (2D) numerical modelling of hydro-fracking (hydraulic fracturing) in rocks at the meso-scale. A numerical model was developed to characterize the properties of fluid-driven fractures in rocks by combining the discrete element method (DEM) with computational fluid dynamics (CFD). The mechanical behaviour of the rock matrix was simulated with DEM and the behaviour of the fracturing fluid flow in newly developed and pre-existing fractures with CFD. The changes in the void geometry in the rock matrix were taken into account. The initial 2D hydro-fracking simulation tests were carried out for a rock segment under biaxial compression with one injection slot in order to validate the numerical model. The qualitative effect of several parameters on the propagation of a hydraulic fracture was studied: initial porosity of the rock matrix, dynamic viscosity of the fracking fluid, rock strength and pre-existing fracture. The characteristic features of a fractured rock mass due to a high-pressure injection of fluid were realistically modelled by the proposed coupled approach.

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2.
Yan  Chengzeng  Fan  Hongwei  Huang  Duruo  Wang  Gang 《Acta Geotechnica》2021,16(10):3061-3086

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

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3.

Fracture interaction mechanisms and reactivation of natural discontinuities under fluid pressurization conditions can represent critical issues in risk assessment of caprock integrity. A field injection test, carried out in a damage fault zone at the decameter scale, i.e., mesoscale, has been studied using a distinct element model. Given the complex structural nature of the damage fault zone hydraulically loaded, the contribution of fracture sets on the bulk permeability has been investigated. It has been shown that their orientation for a given in situ stress field plays a major role. Based on these results, a simpler model with a fluid-driven fracture intersecting a second fracture has been set up to perform a sensitivity analysis. It is in presence of a minimum differential stress value with a minimum angle with the maximum principal stress that the second fracture could be both, hydraulically and mechanically reactivated. Results also showed that in the vicinity of the fluid-driven fracture, a natural fracture will offer contrasted hydromechanical responses on each side of the intersection depending on the stress conditions and its orientation with respect to the stress field. In this case, we show that a hydromechanical decoupling can occur along the same plane. These results provide insights into fracture-controlled permeability of fault zones depending on the properties of the fractures and their hydromechanical interactions for a given in situ stress field.

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4.
Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ v  ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ h  ≤ 6 MPa and simple transverse fracture for Δσ h  ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ h from 6 MPa to 12 MPa.  相似文献   

5.
On the basis of Navier-Stokes equation, a digital analogue of crossing flow is carried out by means of finiteelement analysis performed through penalty function formulation. The results of the digital analogue are ingood agreement with that of the previous hydraulic physical simulation. They both demonstrate the effect of"deflection flow" occurring at the fracture intersection that the fracture-water crossing flow deflects △q intothe wide fracture.  相似文献   

6.
We present an extended finite element framework to numerically study competing hydraulic fracture propagation. The framework is capable of modeling fully coupled hydraulic fracturing processes including fracture propagation, elastoplastic bulk deformation and fluid flow inside both fractures and the wellbore. In particular, the framework incorporates the classical orifice equation to capture fluid pressure loss across perforation clusters linking the wellbore with fractures. Dynamic fluid partitioning among fractures during propagation is solved together with other coupled factors, such as wellbore pressure loss (\(\Delta p_w\)), perforation pressure loss (\(\Delta p\)), interaction stress (\(\sigma _\mathrm{int}\)) and fracture propagation. By numerical examples, we study the effects of perforation pressure loss and wellbore pressure loss on competing fracture propagation under plane-strain conditions. Two dimensionless parameters \(\Gamma = \sigma _\mathrm{int}/\Delta p\) and \(\Lambda = \Delta p_w/\Delta p\) are used to describe the transition from uniform fracture propagation to preferential fracture propagation. The numerical examples demonstrate the dimensionless parameter \(\Gamma \) also works in the elastoplastic media.  相似文献   

7.
In this paper, we investigate the fractal properties of binary maps of rock fractures at different scales and different geological types, as well as different families of fracture patterns obtained from a two-dimensional Laplacian growth model (LGM). From these analyses we figure out which families of the LGM patterns match the structural properties of the fracture binary maps. The LGM is defined in terms of a nonlinear map that depends on two parameters, λ and \mathfraka\mathfrak{a}, that respectively define the area and shape of the elements of the aggregate that conforms the patterns. The fractal dimension and roughness exponent of the LGM patterns are found to depend on \mathfraka\mathfrak{a}, with 0 < \mathfrak a < 10<\mathfrak {a}<1. From a detailed statistical analysis of these patterns we found that the fractal dimensions of capacity, correlation and information decrease monotonically as \mathfraka\mathfrak{a} increases. We also found that the values of these three fractal dimensions tend to collapse on top of each other as \mathfraka\lessapprox1\mathfrak{a}\lessapprox1. Remarkably, the fractal properties of rock fractures in the scales from millimeters up to a few meters appear to be well represented by the fractal structure of the LGM families of patterns with \mathfraka=0.15\mathfrak{a}=0.15 and 0.30, while the fractal properties of rock fractures in the scale of kilometers seems to be well represented by the LGM family with \mathfraka=0.90\mathfrak{a}=0.90. In addition, the three fractal dimension values of fracture binary maps in the scales from millimeters up to meters were found to be different between them. Nonetheless, for fractures in the scale of kilometers, the values of the three fractal dimensions are very close to each other as an indication of self-similar behavior. Analysis of the corrections to the scaling of the roughness exponent, ζ, suggests that they are negligible for the LGM family of fracture patterns with \mathfraka=0.9\mathfrak{a}=0.9. This finding points to a self-affine structure for this family of patterns. In fact, the calculated roughness exponent results are in the range of values characteristic of rock fractures.  相似文献   

8.
We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

9.
Zeng  Qingdong  Yao  Jun  Shao  Jianfu 《Acta Geotechnica》2019,14(6):2083-2101

The propagation of hydraulic fracture in elastic rocks has widely been investigated. In the paper, we shall focus on numerical modeling of hydraulic fracturing in a class of porous rocks exhibiting plastic deformation. The plastic strain of porous rocks is described by a non-associated plastic model based on Drucker–Prager criterion. The plastic deformation is coupled with fluid pressure evolution described by the lubrication theory. An extended finite element method is used for modeling the propagation of fracture. The fracture propagation criterion is based on the J-integral. The proposed numerical model is validated by comparisons with numerical and analytical results. The influence of plastic deformation on fracture propagation process is investigated.

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10.
The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

11.
Natural fractures are characterized by rough surfaces and complex fluid flows. A large distribution of apertures (residual voids) within their walls and the presence of contact points (in situ normal loads) produce heterogeneous flows (channeling). The resulting permeabilities, porosities or fluid–rock exchange surfaces cannot be realistically modeled by parallel and smooth plate models. Four natural fractures are sampled at different depths and degrees of alteration in the Soultz sandstone and granite (EPS1 drillhole, Soultz-sous-Forêts, Bas-Rhin, France). The fracture surfaces are measured with mechanical profilometry and maps of asperity heights (XYZ). Resulting local apertures (XYe) are then calculated. A statistical study of the surface profiles (XZ) show that the fractures are more or less rough and tortuous according to the types of alteration. Altered samples are characterized by smoother surfaces of fractures. Such differences imply that (i) the average fracture aperture is not representative for the whole fracture and that (ii) the different local apertures should be integrated in hydraulic and mechanical models. A hydraulic model (finite difference calculations) of fluid flow, taking into account the elastic closure (Hertz contact theory) of fractures with depth, is used. Maps of contact points and relative local loads within the fracture planes are compared to flow maps. They show different channeling of fluid flows. Strongly altered fractures are characterized by homogeneous fluxes despite the presence of numerous contact zones during the closure of fracture. By contrast, fresh fractures develop, increasing fluid flow channels with depth.Fracture closure (increasing normal stress) does not systematically increase the channeling of fluid flow. There is evidence for a general smoothing out of the irregularities of the fracture walls due to precipitation of secondary minerals, indicating that the cubic law can be commonly valid, also at great crustal depth but this validity depends on the degree of fracture alteration. Mineralogical and geochemical observations, thus, should be taken into account to perform more accurate permeability calculations and models of fluid circulation in fracture networks.  相似文献   

12.
Unaltered metasediments of the Mary Kathleen Fold Belt are composed predominantly of layered amphibolite-facies scapolitic calc-silicate rocks in which minimal infiltration of externally derived fluids occurred during regional metamorphism. There were substantial differences in volatile activities between different layers in the layered sequences, in particular: a CO2/a H 2 O inferred from reaction progress estimates and analysis of biotite-clinopyroxene-fluid phase relations; a NaCl/a H 2 O inferred from scapolite compositions; and a HCl/a H 2 O inferred from biotite compositions. In one outcrop in which a clinopyroxene-producing reaction dominated, differences in approximate X CO 2of up to 0.25 occurred between several samples collected over 50 metres. Variations in a H 2 O/a HCl of up to one order of magnitude are inferred at 1 to 50 m scales from biotite-Cl contents, and variations in NaCl contents of scapolite from 0.0 to up to 0.6 Cl atoms in the Cl–CO3–SO4 site reflect a large variation of a NaCl in the coexisting fluid at similar scales. Most calcsilicate layers internally buffered fluid compositions in the H2O–CO2–NaCl–HCl system. Local occurrences of NaCl-rich scapolite suggest that some layers may have been in equilibrium with halite during early prograde metamorphism. At peak metamorphic temperatures, disolution of halite was complete but layers containing high-NaCl scapolite continued to buffer fluid at high values of a NaCl. Fluid immiscibility does not appear to have affected the progress of the devolatilization reactions. Although fluid was predominantly internally buffered, moderate quantities of fluid were released by prograde mineral reactions in many layers, up to 30 cm3 fluid per 100 cm3 rock. Numerous episodes of fluid escape were required, probably via microfractures, such that the released fluid did not obviously influence reaction progress in the layers through which it passed. The anomaly of beautifully preserved internal buffering signatures and the requirement for produced fluid locally to pass across layers in a deforming rock sequence suggest that the escaping fluid did not leave any readily observable tracks. This is explained by rapid rates of fracture propogation and fluid migration therein. This internally buffered system contrasts strongly with adjacent calc-silicate rocks that show evidence for infiltration of externally derived fluids at high fluid/rock ratios, and highlights the broad range of fluid behaviour that can be expected in deforming, heterogeneous rock sequences.  相似文献   

13.
程万  蒋国盛  周治东  魏子俊  张宇  王炳红  赵林 《岩土力学》2018,39(12):4448-4456
水平井中多条水力裂缝间的应力干扰行为,造成了压裂液排量的非均匀分配,影响了水力裂缝的几何形态。采用边界元法研究岩体在压裂液作用下的变形程度,以幂律流体泊肃叶平板流动方程来研究水力裂缝内部的压裂液流场,考虑了多条裂缝间应力干扰和压裂液流量分配,建立了流-固耦合的水平井多条水力裂缝同步扩展模型。模型可模拟水平井多条水力裂缝几何形态、应力干扰情况和压裂液排量的分配情况,可解释水力裂缝之间的竞争机制。多条裂缝同步扩展时,压裂液排量并非均等地分配到各个裂缝之中,进入到内部裂缝的压裂液流量最小,内部裂缝宽度最小;内部的水力裂缝增长一定长度后,停止增长,并且在应力干扰下逐渐闭合。  相似文献   

14.
This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.  相似文献   

15.
A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

16.
A four‐node plane parametric element AQGβ6‐I is constructed on the basis of the quadrilateral area coordinate, the generalized conforming principle and the projection technique with a penalty factor β within an interval of 0–1. When β = 0, the element has excellent bending performance. When β = 1, the element can pass patch test strictly; its performance is as good as many famous elements. When β value is between 0 and 1, such as β = 0.5, the element can arrive at a compromise between (relatively) low sensitivity to mesh distortion and perfect convergence. The work provides an illuminating method to alleviate a difficult problem in finite element modelling using the four‐node quadrilateral element, which can pass the strict patch test, but has poor performance in bending dominated problem; on the contrary, it has excellent performance in bending dominated problem but cannot pass the strong patch test. The AQGβ6‐I with the convergence formulation (β = 1) is then applied to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials. The computational examples are carried out to demonstrate that the AQGβ6‐I (β = 1) element is not only stable, reliable and efficient but also of high accuracy. The present study provides a good applicable element for finite element simulations of solid‐deformation/fluid‐flow for porous geomaterials. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

17.
随着扩展有限元理论的深入研究,利用扩展有限元方法模拟水力压裂具有了一定的可操作性。相比于常规有限元方法,XFEM方法具有计算结果精度高和计算量小的优点。但是,如何模拟射孔孔眼、如何模拟流体与岩石相互作用以及分析水力裂缝的扩展规律仍然是难题。以研究水力压裂裂缝扩展规律为目的,建立了岩石多孔介质应力平衡方程、流体渗流连续性方程和边界条件。通过有限元离散化方法对耦合方程矩阵进行处理。通过富集函数定义初始裂缝(射孔孔眼),选择最大主应力及损伤变量D分别作为裂缝起裂和扩展判定准则,利用水平集方法模拟水力裂缝扩展过程。数值模拟结果显示:增加射孔方位角、压裂液排量和减小水平地应力差,起裂压力上升;黏度对起裂压力无明显影响。增加射孔方位角、压裂液排量、黏度和减小水平地应力差值有助于裂缝宽度的增加。增加水平地应力差值、压裂液排量和减小射孔方位角以及压裂液黏度有助于裂缝长度增加,反之亦然。基于ABAQUS的水力裂缝扩展有限元法可对不同井型和诸多储层物性参数及压裂施工参数进行分析,且裂缝形态逼真,裂缝面凹凸程度清晰,结果准确。此研究可作为一种简便有效研究水力压裂裂缝扩展规律的方法为油田水力压裂设计与施工提供参考与依据。  相似文献   

18.
The interaction of an advancing hydraulically loaded crack and in situ fracture network can yield highly complex patterns. We model the connectivity of cells in a finite element domain and in a fracture network by a simplicial complex data structure. The complete adjacency information between cells is determined by one level down facet and one level up cofacet neighborhood information. Combined with a disjoint set data structure, explicit algorithms are derived to efficiently track network connectivity and load transfer between independent fracture sets. We also propose an approach to regularize the application of hydraulic load to newly intersected in situ cracks to smoothen the transition of pressure on intersected cracks from ambient to hydraulic pressure and to avoid the sudden loading of the entire length of these cracks. Numerical results demonstrate the performance of crack connectivity and load transfer models and the effect of regularization model. The results show that as the angle between an incoming hydraulically loaded crack and an in situ crack increases, the effect of in situ crack shifts from slight realignment to diversion/offsetting of the loaded crack. As the angle difference approaches the normal angle, the loaded crack tends to penetrate through the in situ crack. The proposed schemes are also used for transient simulation of 2D reservoirs with multiple perforations surrounded by in situ cracks with and without a bias in the distribution of their orientation. It was shown that from 2 perforations with angles closer to in situ cracks at low loading rates to all perforations at higher loading rates can result in active hydraulic crack propagation. The h‐adaptive method of asynchronous space‐time discontinuous Galerkin method is used to exactly track complex fracture patterns in these dynamic fracture simulations.  相似文献   

19.
Similarity solutions are derived for wedge-shaped hydraulic fractures driven by a constant inlet pressure P0 into a permeable medium under a uniform confining stress σ. These results describe the seepage-dominated regime in which most of the injected fluid is lost into the permeable walls of the fracture; they complement previous results for the capacitance-dominated regime in which seepage is negligible. Fracture propagation velocity is obtained as an analytical function of fracture length, driving pressure, confining stress, material properties and a single separation constant or eigenvalue which is determined numerically. Self-similar profiles of pressure, opening displacement and fluid velocity along the fracture are presented, together with the self-similar isobars of the two-dimensional pressure field within the permeable medium. Comprehensive results are reported for laminar or turbulent flow of a constant-compressibility liquid or an ideal gas driven by overpressures (P0?σ)/σ ranging from 10?2 to 102.  相似文献   

20.
Halite traps inclusions of the mother fluid when precipitating. When unchanged, the density of these fluid inclusions (FIs) records the water temperature Tf at the time of crystal formation. As halite is ubiquitous on Earth and geological time, its FIs possess a high potential as temperature archives. However, the use of FIs in halite as an accurate palaeothermometer has been hampered due to limitations of microthermometry, the most commonly used analytical method. Here, we show how Brillouin spectroscopy in halite FIs bypasses these limitations and allows recovering Tf to within 1 °C or less. To demonstrate this, we measured samples synthesised at 24.6 ± 0.5 °C and 33 ± 1 °C, and obtained 24.8 ± 0.4 °C and 31.9 ± 0.4 °C, respectively. This novel approach thus provides an accurate palaeothermometer for lacustrine and marine environments. Moreover, Brillouin spectroscopy solves the long‐standing debate on damage of halite fluid inclusions through quantifying the acceptable temperature excursion for preserving elastic behaviour: [l/(1 µm)]?0.64 × (90 °C), where l is the FI size. This threshold is lower for FIs close to the surface of the host crystal or to another FI. We also list ‘best practices’ for applying both microthermometry and Brillouin thermometry.  相似文献   

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