Displacement Pattern And Relative Permeability Model For Two-phase Flow In Rough Fractures

Two-phase flow in rock fractures is one of the key scientific issues in the fields of enhanced oil/gas recovery,geological CO₂ sequestration,and prevention and control of groundwater pollution.Controlled by factors such as fracture geometry,fluid properties and flow conditions,the interfacial instability always occurs,which results in a complex displacement patterns and challenges the developments of the macro-constitutive model for the two-phase flow in fractured media.Although laboratory experiments have played an irreplaceable role in studying the mechanism of fracture two-phase flow,there are still technical difficulties in visualizing the pressure distributions and local flow fields.Computational fluid dynamics（CFD）provides an important tool for studying the characteristics of two-phase flow in fractures,but direct numerical simulation for fluid-fluid displacements in 3D rough fractures and the validation with experiments were rarely reported,and the understanding of how the fracture roughness and wettability affect the displacement pattern and the macro-constitutive relationship of two-phase flow is not deep enough.This thesis takes rough fractures as the research object,uses numerical simulation as the main method,and takes the influence mechanism of roughness and wettability on the two-phase flow of rough fractures as the core issue.Carry out research on the applicability of direct numerical simulation of two-phase flow in rough fractures,and the displacement pattern and macroscopic characterization model of the two-phase flow of rough fractures are studied.The major achievements obtained in this thesis are summarized below:（1）We conducted 3D numerical simulations of water displacing silicon oil in a rough fracture to demonstrate the applicability of the direct numerical simulation.The numerical simulations can capture two-phase flow behaviors in the fracture at both the sample scale and microscale,overcoming the limitations of laboratory experiment that cannot visualize the local 3D flow field.Numerical simulations revealed the key role of capillary force and viscous force on the displacement direction of two-phase flow in rough fracture.At present,although few studies on the direct numerical simulation of two-phase displacement in 3D rough fractures have been reported,it is still not clear whether the numerical simulation can accurately reproduce the interface morphology of two-phase flow at sample scale and accurately describe the displacement behaviors at the microscale.To this end,based on the numerical method for directly solving the Navier-Stokes equations,we perform 3D numerical simulations for two-phase displacement in a real rough fracture with capillary number log₁₀Ca ranging from-3 to-5.Comparison between visual experiments and simulations shows that the simulated results can not only reproduce the dynamic invasion morphologies at the scale of fracture,but also describe the classic Haines jump events at the microscale and the 3D flow field characteristics at the tip of the two-phase flow interface,which verified the applicability and reliability of the direct numerical simulation method,and made up for the limitations of the laboratory experiment that it is difficult to observe the local 3D flow field.Statistical analysis of the numerical simulation results shows that with the increase of the capillary number,the velocity vector of the flow field tends to the macroscopic flow direction,thus revealing the microscopic mechanism that the enhanced viscous effect promotes the interface to drive in the direction of the macroscopic hydraulic gradient.（2）We investigated how the roughness and wettability impact the invasion morphologies of two-phase flow in rough fractures.We established the relationship between interface area and saturation considering the key factors such as roughness and wettability,and the relationship between the flow characteristics of two-phase flow and energy dissipation was illustrated.Fracture roughness and wettability have important effects on the two-phase flow displacement pattern.However,because it is difficult to prepare the roughness and wettability of rock fractures as required in laboratory experiments,the research on the effects of roughness and wettability on the two-phase flow of fractures is not yet thorough enough.Therefore,based on the above two-phase flow numerical simulation technology,we constructed 3D self-affine rough fracture models to study the important effects of roughness and wettability on the morphological characteristics of two-phase flow interface in 3D fractures,which revealed that the rule of increasing the roughness or weakening the hydrophilicity leading to the narrowing of the finger width and the increase of the instability of the two-phase flow interface,expounded the influence of interface morphology characteristics on the interface area and saturation,and established the relationship between interface area and saturation considering the key factors such as roughness and wettability.We further studied the conversion relationship between surface energy,kinetic energy,dissipated energy and external work during the two-phase flow of rough fractures under different roughness and wettability conditions,and founded that the kinetic energy and surface energy of the system gradually increased with increasing roughness and decreasing hydrophilicity respectively,clarified the law of increased energy dissipation due to the increased interface instability,and revealed the internal relationship between the two-phase flow characteristics and energy dissipation.（3）Based on the dynamic characteristics of the flow field during the two-phase displacement process,a method for predicting the relative permeability of two-phase flow in rough fractures was developed,and a relative permeability model that considered the effects of roughness and wettability was established,revealing the effects of roughness and wettability on the macroscopic characteristics of two-phase flow in rough fractures.Based on the dynamic characteristics of the two-phase flow field,the unsteady JBN method is widely used to determine the relative permeability of two-phase fluid,but the traditional unsteady JBN method has some defects such as too small prediction range of relative permeability and obvious capillary end effect under high viscosity ratio.In this regard,this thesis developed an improved JBN method that can additionally acquire the relative permeability data of the fracture profile location,which overcome the above-mentioned defects of the traditional JBN method.On this basis,according to the numerical simulation results of the 3D flow field of the fractures,the optimal fitting function relations between saturation and water injection multiple,ratio of pressure drop to water injection multiple and inverse of water injection multiple are obtained by using the improved JBN method.Furthermore,the Corey type oil-water relative permeability curve model considering the effects of roughness and wettability was established,and the rule that the isotonic point of the relative permeability curve of the two-phase flow moved to the left as the hydrophilicity weakened or the roughness increased.The above research results demonstrate the applicability of numerical simulation to the study of the two-phase flow mechanism of rough fractures,and deepen the understanding of the two-phase flow displacement pattern and macroscopic seepage characteristics of fractured media.It has broad application prospects in hydrogeological evaluation of non-saturated water zone,enhanced oil/gas recovery,geological CO₂ sequestration.