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• Impacts of water flow on hydrodynamic heat transfer in rock fractures were experimentally elucidated. • Parametric models linking heat transfer behaviors with flow rate and fracture geometry were developed. • Effect of nonlinear flow resistance on the feasibility of heat extraction was quantified. Hydrodynamic heat transfer in rock fractures is crucial for many geophysical processes and engineering activities, notably in harnessing geothermal energy. Despite extensive research, characterizing hydrodynamic heat transfer in rock fractures, complicated by their geometric heterogeneity, remains a formidable challenge. To address this challenge, we experimentally investigated the hydrodynamic heat transfer in rock fractures with diverse geometric features at steady-state elevated temperatures. We found that both heterogeneous fracture geometry and elevated temperatures promote the transition of fracture flow from a linear to nonlinear regime. This flow regime transition enhances the heterogeneity of heat transfer intensity within the fracture and exacerbates the increase in heat transfer efficiency with flow rate. At a fortyfold increase in flow rate, the heat transfer coefficient in the most heterogeneous fracture rises by approximately 72 times, compared to about 28 times in the least heterogeneous one. Leveraging experimental data, we developed parametric models linking heat transfer coefficients, outflow temperature, and heat recovery rate to flow rate and geometric features, yielding a theoretical formulation for the maximal heat recovery rate. By introducing the concept of an energy conversion rate, we quantitatively evaluated the effect of nonlinear flow resistance on heat extraction feasibility, revealing that energy conversion rates in highly heterogeneous fractures can be up to 452 times lower than in less heterogeneous ones. This highlights the pivotal role of flow resistance in heat extraction feasibility. Our findings are instrumental for understanding and predicting the hydrodynamic heat transfer within fractured geothermal reservoirs and analogous hydro-thermal systems. [ABSTRACT FROM AUTHOR]

• Impacts of wall porosity on fracture flow were systematically investigated at pore scale. • Mechanisms governing direction and magnitude of fluid exchange at the fracture-matrix interface were elucidated. • Flux contributions of porous walls to fracture outlet and fracture-matrix interface were functionalized by wall porosity. • Influence of porous walls cannot be equivalently represented by applying slip boundary conditions. This study investigates the influence of porous walls on fluid flow behavior in single rough-walled fractures. A series of direct numerical simulations (DNS) were conducted to examine fluid flow through rough-walled fractures surrounded by porous walls under various hydraulic gradients. The simulation results clearly demonstrate the progressively significant impact of porous walls on flow characteristics as porosity increases. Regression analyses indicate that the Forchheimer's law, which characterizes the nonlinear flow of rock fractures, remains valid in the presence of porous walls. Moreover, increased porosity enhances fluid exchange and leads to an increased ability for single fractures to transmit fluid. Two double-parameter equations were established to quantitatively characterize the effects of porous walls on hydraulic conductivity of the fracture and fluid exchange between porous walls and the fracture. Further analysis revealed that the angle between the fracture profile and main flow direction profoundly influences the inflow/outflow exchange between the fracture and its adjacent porous walls. Moreover, the pore-scale results indicate that it is unreasonable to equate the effect of porous walls with slip boundaries as suggested in previous studies. The results and findings of this study deepen our understanding of flow behavior at the interface between the rough-walled fracture and adjacent porous walls, and they serve as a basis for accurately simulating large-scale fracture networks that consider the hydraulic contribution of fracture walls. [ABSTRACT FROM AUTHOR]

• Flow behaviors are associated with fracture heterogeneity and the filling conditions. • Filling particles result in two competing mechanisms impacting flow regime in fractures. • Fracture walls confining the fluid flow significantly reduce the media permeability. • A semi-empirical model for predicting water flow in filled fractures is proposed. Fluid flow through filled rock fractures is relevant to numerous engineering applications and geophysical processes. However, a proper understanding of the flow behaviors in filled fractures is still far from being completed. To investigate the fluid flow in a rough-walled fracture filled with a porous medium, we systematically compare the micro- and macroscopic flow behaviors within filled fractures and corresponding open fractures and porous media based on a series of pore-scale simulation results. We find that the filling medium has a dual role in altering the flow regime, as the filling particles can not only cut the flow domain into several pore channels and thus limit the generation of large-span eddies, but also force the fluid to flow around them and promote the generation of local eddies. Compared with porous media, the fluid flow within filled fractures is confined by fracture walls, which greatly alters the media permeability and the flow nonlinearity therein. By introducing the hydraulic radius and Darcy-Weisbach equation, we develop a new semi-empirical model to estimate the fluid flow through filled fractures using phenomenological coefficients of corresponding open fractures and porous media. The proposed model, satisfying dimensional consistency, shows high fidelity in predicting water flow through filled fractures. More importantly, this model can be successfully reduced to the typical form of the Forchheimer equation applied to open fractures and porous media. The results and findings are expected to be useful in predicting and evaluating the fluid flow in complex geological setting. [ABSTRACT FROM AUTHOR]

• Influencing factors of infiltration modes were systematically investigated. • A semi-analytical model for three infiltration scenarios was established. • Evolution features of water head and stratified wetting zone were revealed. The classic GA model assumes a constant-head ponded water and with a saturated water content above the wetting zone, which limits its application. This study investigated a semi-analytical method for predicting rainwater infiltration into an inclined soil interlayer considering time-varying head and stratified water content. An evolving wetting profile and a half-parabolic wetting profile of transient zone were observed during infiltration process based on numerical simulations. The water head in the fissure showed a linearly-increasing characteristic before the soil interlayer was fully saturated, while showed an exponentially-increasing feature after the soil interlayer was fully saturated. A semi-analytical model was subsequently established for predicting the variables (time-dependent water head and the length of the stratified wetting zone) based on the classical GA equation, Darcy's law, and mass conversation law, as well as the numerical simulation calibration. This semi-analytical model describes three specific infiltration scenarios (scenarios I, II, and III) involving two infiltration modes (i.e., rainfall infiltration and constant-head infiltration), which were comprehensively shaped by fissure height, rain intensity, and duration. This model has a concise expression satisfying dimensional consistency and can be successfully reduced to the classic GA model. The validity of this semi-empirical model was further confirmed by numerical simulations, which showed good performance by capturing the evolving trends of the water head, saturated, transitional, and wetting zones in the inclined soil interlayer. The results and findings deepen the understanding of transient infiltration in rock slopes with inclined soil interlayer, and are helpfully for assessing the evolving slope stability during rainfall. [ABSTRACT FROM AUTHOR]

• Influencing factors of infiltration modes were systematically investigated. • A semi-analytical model for three infiltration scenarios was established. • Evolution features of water head and stratified wetting zone were revealed. The classic GA model assumes a constant-head ponded water and with a saturated water content above the wetting zone, which limits its application. This study investigated a semi-analytical method for predicting rainwater infiltration into an inclined soil interlayer considering time-varying head and stratified water content. An evolving wetting profile and a half-parabolic wetting profile of transient zone were observed during infiltration process based on numerical simulations. The water head in the fissure showed a linearly-increasing characteristic before the soil interlayer was fully saturated, while showed an exponentially-increasing feature after the soil interlayer was fully saturated. A semi-analytical model was subsequently established for predicting the variables (time-dependent water head and the length of the stratified wetting zone) based on the classical GA equation, Darcy's law, and mass conversation law, as well as the numerical simulation calibration. This semi-analytical model describes three specific infiltration scenarios (scenarios I, II, and III) involving two infiltration modes (i.e., rainfall infiltration and constant-head infiltration), which were comprehensively shaped by fissure height, rain intensity, and duration. This model has a concise expression satisfying dimensional consistency and can be successfully reduced to the classic GA model. The validity of this semi-empirical model was further confirmed by numerical simulations, which showed good performance by capturing the evolving trends of the water head, saturated, transitional, and wetting zones in the inclined soil interlayer. The results and findings deepen the understanding of transient infiltration in rock slopes with inclined soil interlayer, and are helpfully for assessing the evolving slope stability during rainfall. [ABSTRACT FROM AUTHOR]

• Solute transport in fractures with slip BC was studied by pore-scale simulations. • Effect of slip BC on solute transport was manifested over the entire flow regime. • Influencing mechanisms of slip BC were elucidated under different flow regimes. Fundamental understanding of solute transport behaviors in rock fractures is of great importance to many hydrogeological processes. The fate of fluid-borne solutes is inherently linked to fluid flow process in rock fractures, which is usually theoretically and numerically analyzed under the assumption of classic no-slip boundary condition. However, fluid slippage at rock surfaces is possibly present in some geological environments, such as hydrophilicity change in rock surfaces exposed to organic substances, or the immobile wetting film covering rock surfaces. These situations would induce a non-zero velocity at the boundary walls for flowing fluid, i.e., fluid slippage, which leads to a violation of the no-slip assumption. Nonetheless, the effect of slippery boundary on fluid-borne solute transport is poorly understood for rock fractures. This study systematically investigated the slippery boundary effect on solute transport in rough-walled rock fractures under different flow regimes. A series of pore-scale simulation results showed that the slippery boundary has a profound influence on both microscale and macroscale solute transport behaviors in rock fractures. Such an influence became more significant with increasing hydraulic gradient, accompanied by the flow regime transitioning from Darcy to non-Darcian. For Darcy flow regime, the slippery boundary exerted its influence on solute transport by altering velocity distribution pattern in rock fracture; while for non-Darcian flow regime, the enlarged eddy volume and promoted mass transfer process by the slippery boundary profoundly affected solute transport behaviors. Further discussion indicated that the predictive models with parameters estimated from the conventional no-slip boundary condition cannot directly apply to the slip one. Moreover, the effect of slippery boundary would possibly have an impact on larger-scale fractured rock aquifers which requires further verification. The results and findings enrich the understanding of solute transport in fractured rocks where the slippery boundary is prevalently present, and contribute to developing predictive models for complex geological environments. [ABSTRACT FROM AUTHOR]

• Tunnel inflow and influence radius were investigated considering non-Darcian effect. • Semi-empirical models were developed to estimate tunnel inflow and influence radius. • Established models were compared with existing models and applied to real tunnels. How to accurately predict water inflow and relevant groundwater influence of a tunnel are classical scientific issues in the field of hydrogeology, which are also of great significance to the construction and operation of underground engineering. This issue is usually investigated based on the assumption of the linear Darcy's law. However, the tunnel inflow is usually featured by high velocities or high pressures, especially in karst regions, which allows the flow regime to easily develop into non-Darcian flow regime. The impact of the non-Darcian effect on predicting water inflow and influence radius of a tunnel has not yet been systematically examined. Here, we numerically investigated the prediction of stable water inflow and influence radius under non-Darcian flow regime. By numerically solving the continuity equation of seepage flow incorporating the nonlinear Forchheimer law, a series of numerical simulations were conducted for stable water inflow into a tunnel by varying key controlling parameters. The quantitative dependencies of stable water inflow on these parameters were figured out, based on which a semi-empirical stable water inflow model was developed considering the non-Darcian effect. Meanwhile, the magnitude of the influence radius was investigated by statistical analysis of 59 actual engineering cases and estimated using existing empirical formulas. Based on these preliminary explorations, a semi-empirical model for estimating influence radius was concluded from massive simulations. The validities of our proposed semi-empirical models for stable water inflow and influence radius were further numerically verified. Comparative study and application in a real engineering case showed that compared with our proposed models, most existing empirical methods predicted a larger stable water inflow and a smaller influence range of groundwater. Besides, comparative results of proposed models with omitting non-Darcian term indicated that neglecting non-Darcian effect would overestimate both the stable water inflow and influence radius. These findings and established models would be useful for assessing stable water inflow and influence radius of a tunnel under non-Darcian flow regime. [ABSTRACT FROM AUTHOR]

• Water inflow into a tunnel under non-Darcian flow regime is numerically investigated. • A semi-empirical model for predicting tunnel inflow is proposed based on Forchheimer law. • Necessity of considering non-Darcian effect for tunnel inflow is proven in a large number of engineering cases. Water inflow into a tunnel is usually estimated by assuming that the flow follows the linear Darcy's law. However, fluid flow in fractured-rock aquifers is prone to deviation from Darcy's law and gives rise to nonlinear flow phenomena due to significant inertial losses. This non-Darcian effect is seldom considered when evaluating water inflow into the tunnel in a fractured-rock aquifer. In this study, we investigated an analytical method for predicting water inflow into a tunnel considering the non-Darcian effect. A series of numerical simulations for water inflow into a tunnel were conducted with different combinations of parameters, where non-Darcian flow was considered and characterized by the Forchheimer's law. Based on the numerical results and an ingenious parameter integration method, a semi-empirical model was developed to analytically predict water inflow into a tunnel where the flow is under non-Darcian flow regime. The semi-empirical model includes the classic theoretical formula for predicting water inflow and the Forchheimer equation for describing non-Darcian flow. In this context, the non-Darcian effect on water inflow into a tunnel can be quantitatively estimated. This developed model has a concise expression satisfying dimensional consistency with the parameters having sound physical meanings, and it can be successfully reduced to the classic formula under the Darcy flow regime. The validity of this semi-empirical model was confirmed by numerical results, showing a high fidelity in predicting water inflow into a tunnel. By means of this proposed model, the error induced by neglecting non-Darcian effect was estimated for a large number of real engineering cases, which rapidly increased as a power function with the magnitude of water inflow into the tunnel. The necessity of considering the non-Darcian effect when calculating water inflow was thus proven, especially for massive tunnel gushing. The proposed model and the method used in this study can provide guidance for accurately predicting water inflow into a tunnel under a complex non-Darcian flow regime. [ABSTRACT FROM AUTHOR]

• The microscale and macroscale non-Darcian flow behaviors for rock fracture with fluid slippage were numerically investigated. • Two competing mechanisms impacting the apparent fracture permeability due to fluid slippage were revealed. • The slippery fluid flow behavior was tested to be sensitive to the slip length. Fluid flow in rock fractures is usually theoretically and numerically investigated on the premise of no-slip boundary condition (BC). However, fluid slippage at rock surface is naturally present in some circumstances that might lead to a violation of no-slip BC. How and to what extent slip BC affects non-Darcian fracture flow remains poorly constrained. This study systematically investigated the slippery flow behaviors in rock fractures under sequentially-increasing pressure gradients. Two competing mechanisms impacting the apparent permeability (k) due to fluid slippage were revealed: k was not only enhanced by fluid slippage at fracture walls but also was reduced by the accelerated eddy growth due to enhanced velocity field. The increment in k caused by slip velocity initially dominated over the decrement caused by eddy growth during this competing process, but this dominant situation could reverse given a sufficiently large pressure gradient with fully-developed eddies. Moreover, the slippery fluid flow behavior was tested to be very sensitive to the slip length based on our sensitivity analysis. Therefore, a reasonable estimation of the slip length would be crucial to accurately determine the effects of fluid slippage. This study deepens our understanding of fluid flow in rock fractures when slip BC is present, and might provide theoretical guidance for organic pollution remediation, oil recovery, and geological carbon sequestration in fractured reservoirs. [ABSTRACT FROM AUTHOR]