Post‐synthetic modification (PSM) is an effective approach for the tailored functionalization of metal‐organic architectures, but its generalizability remains challenging. Herein we report a general ...covalent PSM strategy to functionalize PdnL2n metal‐organic cages (MOCs, n=2, 12) through an efficient Diels–Alder cycloaddition between peripheral anthracene substituents and various functional motifs bearing a maleimide group. As expected, the solubility of functionalized Pd12L24 in common solvents can be greatly improved. Interestingly, concentration‐dependent circular dichroism and aggregation‐induced emission are achieved with chiral binaphthol (BINOL)‐ and tetraphenylethylene‐modified Pd12L24, respectively. Furthermore, Pd12L24 can be introduced with two different functional groups (e.g., chiral BINOL and achiral pyrene) through a step‐by‐step PSM route to obtain chirality‐induced circularly polarized luminescence. Moreover, similar results are readily observed with a smaller Pd2L4 system.
Two PdnL2n (n=2, 12) type metal‐organic cages (MOCs) decorated with anthracene groups have been successfully functionalized by a covalent post‐synthetic modification (PSM) approach. This has led to the modified MOCs having new functions compared to the parent MOCs (e.g., concentration‐dependent chirality, aggregation‐induced emission, and chirality‐induced circularly polarized luminescence).
Rock fractures are ubiquitous in geological systems and usually provide dominant pathways for fluid flow in fractured reservoirs. When the flowing fluid is reactive, fracture dissolution expands the ...aperture and forms various dissolution patterns that amplify the pathways. Previous works focused on the dissolution processes in Hele‐Shaw cells (parallel‐plate) and porous media, but the transitions of dissolution patterns in radial rough fractures are not well understood. Here we combine flow‐visualization experiments with theoretical analysis to elucidate the transitions of dissolution patterns under various flow‐rate and reaction‐rate conditions. We observe and quantify three distinct dissolution morphologies as compact, wormhole, and uniform patterns. We show that the critical Péclet numbers, corresponding to the transitions from compact to wormhole and to uniform patterns, increase with the reaction rate. Based on the growth of dissolution channels in the flow and transverse directions, we establish a theoretical model that describes the transitions of these three distinct dissolution patterns. The phase diagram predicted by the model exhibits good agreement with our experimental results and also well captures the pattern transitions reported in the previous studies. This work improves the understanding on how fracture aperture expands in the dissolution processes that lead to various dissolution channels. Our work is also critical for controlling the fluid flow behavior in dissolving natural rock fractures in subsurface flow systems.
Key Points
We visualize and quantify three distinct dissolution patterns in radial rough fractures
We propose a theoretical model to predict the transitions of dissolution patterns affected by the flow rate and the dissolution kinetic
A phase diagram predicted by the model shows good agreement with our experiments and with the existing experiments and simulations
•Three typical nonlinear flow behaviors were identified in deformable rock fractures.•Two empirical equations were proposed for Forchheimer’s nonlinear coefficient.•The effect of fracture roughness ...on the non-Darcy flow behaviors was quantified.•A new criterion was presented for assessing the applicability of Darcy’s law.
This study focuses on experimental evaluation of the Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0MPa to 30.0MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid–water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical equations were proposed for parametric expression of the Forchheimer’s nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy’s law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer’s law incorporated with the single-parameter equation to that predicted by the Darcy’s law. A sensitivity analysis was performed using the double-parameter equation for examining the dependence of the Forchheimer’s nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers.
•3D Fracture geometry was decomposed into primary and secondary roughness with wavelet analysis.•The role of secondary roughness in the nonlinearity of flow through rock fractures was illustrated by ...high-resolution LBM simulations.•The mechanisms of nonlinear flow (eddy flow and back flow) caused by secondary roughness were demonstrated.•The Forchheimer's law proves to well represent the nonlinear flow behaviors in the 3D fractures.
This study investigates the impacts of surface roughness on the nonlinear fluid flow through three-dimensional (3D) self-affine rock fractures, whose original surface roughness is decomposed into primary roughness (i.e. the large-scale waviness of the fracture morphology) and secondary roughness (i.e. the small-scale unevenness) with a wavelet analysis technique. A 3D Lattice Boltzmann method (LBM) is adopted to predict the flow physics in rock fractures numerically created with and without consideration of the secondary roughness, respectively. The simulation results show that the primary roughness mostly controls the pressure distribution and fracture flow paths at a large scale, whereas the secondary roughness determines the nonlinear properties of the fluid flow at a local scale. As the pressure gradient increases, the secondary roughness enhances the local complexity of velocity distribution by generating and expanding the eddy flow and back flow regions in the vicinity of asperities. It was found that the Forchheimer's law characterizes well the nonlinear flow behavior in fractures of varying roughness. The inertial effects induced by the primary roughness differ only marginally in fractures with the roughness exponent varying from 0.5 to 0.8, and it is the secondary roughness that significantly enhances the nonlinear flow and leads to earlier onset of nonlinearity. Further examined were the effects of surface roughness on the transmissivity, hydraulic aperture and the tortuosity of flow paths, demonstrating again the dominant role of the secondary roughness, especially for the apparent transmissivity and the equivalent hydraulic aperture at high pressure gradient or high Reynolds number. The results may enhance our understanding of the role of surface roughness in the nonlinear flow behaviors in natural rock fractures.
The development of energy‐saving technology for the efficient separation of olefin and paraffin is highly important for the chemical industry. Herein, we report a self‐assembled Fe4L6 capsule ...containing a hydrophobic cavity, which can be used to encapsulate and separate propylene/propane. The successful encapsulation of propylene and propane by the Fe4L6 cage in a water solution was documented by NMR spectroscopy. The binding constants K for the Fe4L6 cage toward propylene and propane were determined to be (5.0±0.1)×103 M−1 and (2.1±0.7)×104 M−1 in D2O at 25 °C, respectively. Experiments and theoretical studies revealed that the cage exhibited multiple weak interactions with propylene and propane. The polymer‐grade propylene (>99.5 %) can be obtained from a mixture of propylene and propane by using the Fe4L6 cage as a separation material in a U‐shaped glass tube. This work provides a new strategy for the separation of olefin/paraffin.
A water‐soluble tetrahedral Fe4L6 metal‐organic cage has been successfully used to separate propane and propylene under ambient conditions. Mixed gases of C3H6 and C3H8 were captured by Fe4L6 at the gas‐liquid interface in a U‐shaped glass tube. Governed by the guest binding affinity, C3H6 is released first after transport of the gases to the receiving arm of the tube.
This study experimentally investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0–30.0MPa). Both ...mated granite and unmated sandstone fractures were adopted for water flow tests and the experimental results were well fitted with the Forchheimer equation. The coefficients of viscous and inertial pressure drops experience an enlargement of 2–5 orders of magnitude with the increasing confining pressure. The critical Reynolds number Rec was successfully estimated based on the Forchheimer equation by taking α percentage (usually 10%) of the nonlinear effect as the critical point between the linear and nonlinear flow. The obtained Rec versus confining pressure curves generally display a nonlinear weakening stage (I) in the early stage of confining pressure loading, which is followed by a nonlinear enhancement stage (II) as the confining pressure further increases. A zoning map of fluid flow regimes based on Rec in the full range of the confining pressures (1.0–30.0MPa) was presented. For the first time, an empirical relationship between the nonlinear coefficient B and the hydraulic aperture eh in rock fractures under varying confining pressure was developed based on the laboratory observations. A critical Reynolds number equation was then proposed to quantify the onset of nonlinear flow through rough-walled fractures with varying eh.
•Nonlinear flow in rough fractures under confining pressure up to 30MPa was demonstrated.•The ascending–descending variation of critical Reynolds number with confining pressure was illustrated.•A power-law function between B and eh and a new CRN model were proposed.
Deterministic single factor of safety method cannot explicitly account for the influences of various sources of uncertainties (e.g., spatial variability of geomaterials, measurement and ...transformation uncertainties) in stability design of slopes. Many probabilistic methods have been applied to the reliability‐based design (RBD) of slopes, but they typically require performing numerous deterministic slope stability analyses. In this paper, an efficient reliability‐based design method for spatially varying slopes based on field data is proposed. Here, the RBD of a slope angle is concerned. Reliability‐based design is implemented using an inverse First Order Reliability Method (inverse FORM ‐ IFORM). A sandy slope and a cohesive slope are investigated as examples, respectively, to illustrate the proposed method. The results indicate that the proposed method can quickly obtain rational design schemes of slope angles accounting for the spatial variability of soil properties, measurement and transformation uncertainties based on the field data. It can act as a practical and effective tool for the RBD of slopes in two‐dimensional spatially variable soils. Additionally, it is found that the random field mesh size affects the RBD results significantly, while the probability distribution and horizontal autocorrelation of soil parameters have slight influences on the RBD results.
•A simplified approach for generating conditional random field is proposed.•Analytical posterior statistics can be derived using the proposed approach.•The proposed approach is more efficient and ...accurate than adaptive Bayesian updating with structural reliability methods.•The actual spatial variation can be well characterized by conditional random field.•Borehole layout scheme affects the probability of slope failure significantly.
Conditional random field model can make best use of limited site investigation data to properly characterize the spatial variation of soil properties. This paper aims to propose a simplified approach for generating conditional random fields of soil undrained shear strength. A numerical method is adopted to validate the effectiveness of the proposed approach. With the proposed approach, the analytical posterior statistics of spatially varying undrained shear strength conditioned on the known values at measurement locations can be obtained. The conditional random field model of undrained shear strength is constructed using the field vane shear test data at a site of the west side highway in New York and the probability of slope failure is estimated by subset simulation. A clay slope under undrained conditions is investigated as an example to illustrate the proposed approach. The effects of borehole location and borehole layout scheme on the slope reliability are addressed. The results indicate that the proposed approach not only can well incorporate the limited site investigation data into modelling of the actual spatial variation of soil parameters by conditional random fields, but also can capture the depth-dependent nature of soil properties. The realizations of conditional random fields generated by the proposed approach can be well constrained to the site investigation data.
High‐pressure packer test (HPPT) is an enhanced constant head packer test for characterizing the permeability of fractured rocks under high‐pressure groundwater flow conditions. The interpretation of ...the HPPT data, however, remains difficult due to the transition of flow conditions in the conducting structures and the hydraulic fracturing‐induced permeability enhancement in the tested rocks. In this study, a number of HPPTs were performed in the sedimentary and intrusive rocks located at 450 m depth in central Hainan Island. The obtained Q‐P curves were divided into a laminar flow phase (I), a non‐Darcy flow phase (II), and a hydraulic fracturing phase (III). The critical Reynolds number for the deviation of flow from linearity into phase II was 25−66. The flow of phase III occurred in sparsely to moderately fractured rocks, and was absent at the test intervals of perfect or poor intactness. The threshold fluid pressure between phases II and III was correlated with RQD and the confining stress. An Izbash's law‐based analytical model was employed to calculate the hydraulic conductivity of the tested rocks in different flow conditions. It was demonstrated that the estimated hydraulic conductivity values in phases I and II are basically the same, and are weakly dependent on the injection fluid pressure, but it becomes strongly pressure dependent as a result of hydraulic fracturing in phase III. The hydraulic conductivity at different test intervals of a borehole is remarkably enhanced at highly fractured zone or contact zone, but within a rock unit of weak heterogeneity, it decreases with the increase of depth.
Key Points:
The Q‐P curves by HPPTs were divided into Darcy, non‐Darcy, and fracking phases
The characteristics of Q‐P curves were correlated with the intactness of rocks
The permeability in different phases was evaluated with an analytical model
