A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Mechanisms of fracture propagation from multi-cluster using a phase field based HMD coupling model in fractured reservoir

Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recognized as significant factors affecting hydraulic fracture(HF)propagation,the combined influence of these factors remains poorly understood.To address this knowledge gap,a novel coupled hydromechanical-damage(HMD)model based on the phase field method is developed to investigate the propagation of multi-cluster HFs in fractured reservoirs.The comprehensive energy functional and control functions are established,while incorporating dynamic fluid distribution between multiple perforation clusters and refined changes in rock mechanical parameters during hydraulic fracturing.The HMD coupled multi-cluster HF propagation model investigates various scenarios,including single HF and single NF,reservoir heterogeneity,single HF and NF clusters,and multi-cluster HFs with NF clusters.The results show that the HMD coupling model can accurately capture the impact of approach angle(θ),stress difference and cementation strength on the interaction of HF and NF.The criterion of the open and cross zones is not fixed.The NF angle(a)is not a decisive parameter to discriminate the interaction.According to the relationship between approach angle(θ)and NF angle(a),the contact relationship of HF can be divided into three categories(θ=a,θ<a,andθ>a).The connected NF can increase the complexity of HF by inducing it to form branch fracture,resulting in a fractal dimension of HF as high as2.1280 at angles of±45°.Inter-fracture interference from the heel to the toe of HF shows the phenomenon of no,strong and weak interference.Interestingly,under the influence of NFs,distant HFs from the injection can become dominant fractures.However,as a gradually increases,inter-fracture stress interference becomes the primary factor influencing HF propagation,gradually superseding the dominance of NF induced fractures.

Two-way coupling of unsaturated-saturated flow by integrating the SWAT and MODFLOW models with application in an irrigation district in arid region of West China

This paper presents the realization of two-way coupling of the unsaturated-saturated flow interactions of the SWAT2000 and MODFLOW96 models on the basis of the integrated surface/groundwater model SWATMOD99, and its application in Hetao Irrigation District （HID）, Inner Mongolia, China. Major revisions and enhancements were made to the SWAT2000 and MODFLOW models for simulating the detailed hydrologic budget and coupled unsaturated and saturated interactions, and irrigation canal hydrology for the HID. The simulation results of seasonal groundwater recharge to and evaporate from the shallow groundwater, and the annual water budget over the district are presented and discussed. The results implied the necessity of two-way coupling of the unsaturated-saturated interactions when groundwater is shallow, and the feasibility of making comprehensive use of the information coming from both the surface water and groundwater models to make a more physically-based assessment of the coupled interactions.

A model for coupling reservoir inflow and wellbore flow in fishbone wells

A coupling model is proposed in this paper by using the Green Function and Newman＇s product principle, and the solution method is provided here as well. This model can be used to describe the reservoir inflow and wellbore flow for fishbone wells in an unsteady flow or pseudo-steady flow state. A case study indicates that the bottom hole pressure declines quickly in the unsteady flow period which is very short. The pressure drop per unit time remains unchanged under the pseudo-steady flow conditions. The distribution of flow rate along the main wellbore shows a wave shape under the unsteady flow condition, and the flow rate distribution in each branch is similar. The flow rate distribution along the main wellbore is irregular ＂U＂ shaped under the pseudo-steady flow condition, and the space-symmetrical branches have the same flow distribution pattern. In the initial production period, the flow rate increases significantly as the length of branches and the angle between branches and the main wellbore increase. As the production continues, the length and angle of branches have only a slight effect on the flow in fishbone wells.

A Regional-Scale Method of Forecasting Debris Flow Events Based on Water-Soil Coupling Mechanism

A debris flow forecast model based on a water-soil coupling mechanism that takes the debrisflow watershed as a basic forecast unit was established here for the prediction of disasters at the watershed scale.This was achieved through advances in our understanding of the formation mechanism of debris flow.To expand the applicable spatial scale of this forecasting model,a method of identifying potential debris flow watersheds was used to locate areas vulnerable to debris flow within a forecast region.Using these watersheds as forecasting units and a prediction method based on the water-soil coupling mechanism,a new forecasting method of debris flow at the regional scale was established.In order to test the prediction ability of this new forecasting method,the Sichuan province,China was selected as a study zone and the large-scale debris flow disasters attributable to heavy rainfall in this region on July 9,2013 were taken as the study case.According to debris flow disaster data on July 9,2013 which were provided by the geo-environmental monitoring station of Sichuan province,there were 252 watersheds in which debris flow events actually occurred.The current model predicted that 265 watersheds were likely to experience a debris flow event.Among these,43 towns including 204 debrisflow watersheds were successfully forecasted and 24 towns including 48 watersheds failed.The false prediction rate and failure prediction rate of thisforecast model were 23% and 19%,respectively.The results show that this method is more accurate and more applicable than traditional methods.

Numerical investigation on permeability evolution behavior of rock by an improved flow-coupling algorithm in particle flow code

Permeability is a vital property of rock mass, which is highly affected by tectonic stress and human engineering activities. A comprehensive monitoring of pore pressure and flow rate distributions inside the rock mass is very important to elucidate the permeability evolution mechanisms, which is difficult to realize in laboratory, but easy to be achieved in numerical simulations. Therefore, the particle flow code （PFC）, a discrete element method, is used to simulate permeability behaviors of rock materials in this study. Owe to the limitation of the existed solid-fluid coupling algorithm in PFC, an improved flow-coupling algorithm is presented to better reflect the preferential flow in rock fractures. The comparative analysis is conducted between original and improved algorithm when simulating rock permeability evolution during triaxial compression, showing that the improved algorithm can better describe the experimental phenomenon. Furthermore, the evolution of pore pressure and flow rate distribution during the flow process are analyzed by using the improved algorithm. It is concluded that during the steady flow process in the fractured specimen, the pore pressure and flow rate both prefer transmitting through the fractures rather than rock matrix. Based on the results, fractures are divided into the following three types： I） fractures link to both the inlet and outlet, II） fractures only link to the inlet, and III） fractures only link to the outlet. The type I fracture is always the preferential propagating path for both the pore pressure and flow rate. For type II fractures, the pore pressure increases and then becomes steady. However, the flow rate increases first and begins to decrease after the flow reaches the stop end of the fracture and finally vanishes. There is no obvious pore pressure or flow rate concentration within type III fractures.

Simulation of dilatancy-controlled gas migration processes in saturated bentonite using a coupled multiphase flow and elastoplastic H2 M model

Dilatancy-controlled gas flow in preferential pathways plays a key role in the safety analysis of radioactive waste repositories.This is particularly the case for bentonite,an often-preferred barrier material.Gas flow in preferential pathways is characterized by localization and spontaneous behavior,which is challenging to simulate in numerical models due to strong hydro-mechanical coupling.To analyze a laboratory experiment in the framework of the DECOVALEX-2023 project,this study introduced a new approach of combining continuous modelling methods with spatial material properties derived from material heterogeneities and experimental observations.The proposed model utilized hydro-mechanical spatial distributions,namely Young’s modulus and gas entry pressure,and elastoplasticity combined with a linear swelling model.A conceptual strain-dependent permeability approach simulated dilatancycontrolled gas flow based on hydro-mechanical coupling.To test the effectiveness of the presented approach,a gas injection test in a compacted,saturated bentonite sample was simulated using the opensource code OpenGeoSys 5.8 and compared with experimental observations.The presented methodology is capable of simulating localized gas flow in preferential pathways.The spatial distributions of Young’s modulus and gas entry pressure affect the swelling pressure,relative permeability and,in combination with the strain-dependent permeability model,also the intrinsic permeability.

Numerical analysis of flow-thermal coupling in micro-plasma welding pool of thin-wall part

The formed characteristics of thin-wall part is studied when it is in the process of MPAW. Finite element method is used to sinmlate the temperature field coupling flow field in the welding of thin-wall part. It is found that because of the obvious effect of heat accumution in cross-section, where the distribution of temperature field area presents trapezoidal inverted approximately in the molten pool and the non-molten pool area presents level. The surface tension, the electromagnetic force and buoyancy are considered for analyzing the effects on the fluid flow of welding-pool. It can be obtained that the surface tension is the main driving force in the welding pool, which is far greater than electromagnetic force and buoyancy.

Effects of fracture evolution and non-Darcy flow on the thermal performance of enhanced geothermal system in 3D complex fractured rock

In fractured geothermal reservoirs,the fracture networks and internal fluid flow behaviors can significantly impact the thermal performance.In this study,we proposed a non-Darcy rough discrete fracture network(NR-DFN)model that can simultaneously consider the fracture evolution and non-Darcy flow dynamics in studying the thermo-hydro-mechanical(THM)coupling processes for heat extraction in geothermal reservoir.We further employed the model on the Habanero enhanced geothermal systems(EGS)project located in Australia.First,our findings illustrate a clear spatial-temporal variation in the thermal stress and pressure perturbations,as well as uneven spatial distribution of shear failure in 3D fracture networks.Activated shear failure is mainly concentrated in the first fracture cluster.Secondly,channeling flow have also been observed in DFNs during heat extraction and are further intensified by the expansion of fractures driven by thermal stresses.Moreover,the combined effect of non-Darcy flow and fracture evolution triggers a rapid decline in the resulting heat rate and temperature.The NR-DFN model framework and the Habanero EGS's results illustrate the importance of both fracture evolution and non-Darcy flow on the efficiency of EGS production and have the potential to promote the development of more sustainable and efficient EGS operations for stakeholders.

Numerical modeling of influence of thermal flow coupling on flow characteristics of molten steel

Using the equation of continuity and the double equation of Navier-Stokes and k-ε, numerical modeling on a single outlet continuous casting tundish has been carried out during the process of non-thermal flow coupling. The flow field distribution inside the tundish was calculated and the viscosity response time was calculated with the mass transfer equation based on the flow field distribution. The flow characteristics of the molten steel inside the tundish were analyzed, with the results of the numerical modeling compared to the hydraulic modeling. The results showed that the Resident Time Distribution （RTD） curves in the latter anatomosed comparatively better. This certified the validity established by the mathematical model. Numerical modeling was carried out on both large and small tundishes during the processes of thermal flow coupling and also thermal non-flow coupling. The results showed that in regards to large tundishes with relatively simple flow processes, using numerical modeling for thermal flow coupling is necessary.

Flow-Noise Calculation Using the Mutual Coupling Between Vulcanized Rubber and the Flow Around in Water

A vulcanized rubber layer is usually used on the head of an axisymmetric body to keep it streamlined and watertight.The elastic boundary condition is considered when the flow noise of an axisymmetric body is calculated,and we employ the mutual coupling method between the vulcanized rubber layer and the How around to solve the flow-noise field for an axisymmetric body in water.The results show that the deformation of the vulcanized rubber layer is reduced with the increase in Young's modulus.The Young's modulus of the rubber material should be large enough to keep it streamlined,and the noise power levels in the peak of the axisymmetric body are smaller than the other positions,which provides us with important theoretical support for laying acoustic arrays on the head of the body.

Modeling of the Coupling of the Lightning Shock Wave Flow Circuit in the High Voltage Electrical Network

This article focuses on the aggression of lightning overload on the equipment of the electrical network of sites where storm activity is very dense;and the electrocution of people located in the direct environment of the high-voltage substation during the flow of lightning current to the ground through the ground socket. The modeling of the flow circuit of the shock wave consisting of guard wire, lightning arrester and ground socket couple to the transformer of the high voltage substations, thanks to the approach of a servo block, led to the synthesis of a PID regulator (corrector) whose action is to reject the effects of the overvoltage on the network equipment and to significantly reduce or even cancel the effects of the step or touch voltage due to the distribution of the potential around the ground socket;and thus improve the quality of service of the high-voltage transmission and distribution electricity network, especially in stormy times.

FEM-BEM Coupling for the MHD Pipe Flow in an Exterior Region

In this study, the magnetohydrodynamic (MHD) flow through a circular pipe under the influence of a transverse mag- netic field when the outside medium is also electrically conducting is solved numerically by using FEM-BEM coupling approach. The coupled partial differential equations defined for the interior medium are transformed into homogenous modified Helmholtz equations. For the exterior medium on an infinite region, the Laplace equation is considered for the exterior magnetic field. Unknowns in the equations are also related with the corresponding Dirichlet and Neumann type coupled boundary conditions. Unknown values of the magnetic field on the boundary and for the exterior region are obtained by using BEM, and the unknown velocity and magnetic field inside the pipe are obtained by using SUPG type stabilized FEM. Computations are carried for very high values of magnetic Reynolds numbers Rm1, Reynolds number Re and magnetic pressure Rh of the fluid. The results show that using stabilized method enables us to get stable and accurate numerical approximations consistent with the physical configuration of the problem over rough mesh which also results a cheap computational cost.

A Study of Thermal Response and Flow Field Coupling Simulation around Hayabusa Capsule Loaded with Light-Weight Ablator

The numerical simulation of flow field around Hayabusa capsule loaded with light-weight ablator thermal response coupled with pyrolysis gas flow inside the ablator was carried out. In addition, the radiation from high temperature gas around the capsule was coupled with flow field. Hayabusa capsule reentered the atmosphere about 12 km/sec in velocity and Mach number about 30. During such an atmospheric entry, space vehicle is exposed to very savior aerodynamic heating due to convection and radiation. In this study, Hayabusa capsule was treated as a typical model of the atmospheric entry spacecraft. The light-weight ablator had porous structure, and permeability was an important parameter to analyze flow inside ablator. In this study, permeability was a variable parameter dependent on density of ablator. It is found that the effect of permeability of light-weight ablator was important with this analysis.

COUPLING MODEL OF TWO PHASE FLOW IN A FRACTURE-ROCK MATRIX SYSTEM AND ITS STOCHASTIC FEATURE ANALYSIS

This study is concerned with developing a two-dimensional two-phase model that simulate the movement of non-aqueous phase liquid (NAPL) in a fracture-rock matrix system. The intrinsic permeability and the fracture aperture are represented in the model via its KarhunenLoeve expansion. Other parameters and the nodal unknowns, water saturations and water pressures, are represented by their stochastic spectral expansions. The errors resulting from truncation of Karhunen - Loeve and polynomial chaos expansions to a finite number of terms are analyzed. The eigenvalues of stochastic process is found out for any point in the special domain of the problem at any instant in time.

A well test analysis model of generalized tube flow and seepage coupling

"Generalized mobility"is used to realize the unification of tube flow and seepage in form and the unification of commonly used linear and nonlinear flow laws in form,which makes it possible to use the same form of motion equations to construct unified governing equations for reservoirs of different scales in different regions.Firstly,by defining the generalized mobility under different flow conditions,the basic equation governing fluid flow in reservoir coupling generalized tube flow and seepage is established.Secondly,two typical well test analysis models for coupling tube flow and seepage flow are given,namely,pipe-shaped composite reservoir model and partially open cylindrical reservoir model.The log-log pressure draw-down type-curve of composite pipe-shaped reservoir model can show characteristics of two sets of linear flow.The log-log pressure drawdown plot of partially opened cylindrical reservoir model can show the characteristics of spherical flow and linear flow,as well as spherical flow and radial flow.The pressure build-up derivative curves of the two models basically coincide with their respective pressure drawdown derivative curves in the early stage,pulling down features in the late stage,and the shorter the production time is,the earlier the pulling down feature appears.Finally,the practicability and reliability of the models presented in this paper are verified by three application examples.

Numerical Simulation of Bidirectional Flow and Solid Coupling of Single Pile and Single Row Pile Column and Wave

The three-dimensional model of the wave and pile structure was established by using Ansysworkbench software. The bidirectional fluid-structure interaction between the pile and wave was simulated by using Stokes wave theory and the Volume of Fluid Method. The pressure distribution diagram of the fluid-structure interface and the pile structure were observed and analyzed. The maximum equivalent stress on the pile was studied and its variation range was obtained. Compared with Von Mises yield criterion, it was concluded that the pile was stable under such wave conditions.

Mathematical Modeling and Control Algorithm Development for Bidirectional Power Flow in CCS-CNT System

As the demand for more efficient and adaptable power distribution systems intensifies, especially in rural areas, innovative solutions like the Capacitor-Coupled Substation with a Controllable Network Transformer (CCS-CNT) are becoming increasingly critical. Traditional power distribution networks, often limited by unidirectional flow capabilities and inflexibility, struggle to meet the complex demands of modern energy systems. The CCS-CNT system offers a transformative approach by enabling bidirectional power flow between high-voltage transmission lines and local distribution networks, a feature that is essential for integrating renewable energy sources and ensuring reliable electrification in underserved regions. This paper presents a detailed mathematical representation of power flow within the CCS-CNT system, emphasizing the control of both active and reactive power through the adjustment of voltage levels and phase angles. A control algorithm is developed to dynamically manage power flow, ensuring optimal performance by minimizing losses and maintaining voltage stability across the network. The proposed CCS-CNT system demonstrates significant potential in enhancing the efficiency and reliability of power distribution, making it particularly suited for rural electrification and other applications where traditional methods fall short. The findings underscore the system's capability to adapt to varying operational conditions, offering a robust solution for modern power distribution challenges.

A New Magnetic Sealless Coupling Axial Flow Blood Pump

For rotating blood pump, the sealing problem is a very important one to solve. In this paper, it was introduced that we designed and made a small axial flow pump, applying the magnetic coupling method. The pump consisted of two pump housings, a brushless DC motor, an impeller with five wanes, a pair of magnetic discs, a spacer, an inlet and an outlet areas , bearings, a support frame, and etc. The pump is made of titanium and is 125 mm length, 147 ml volume, total 380g of weight. Performances of outputting, sealing, heat creating and damage to blood by the pump were investigated in vitro experiment. Results showed for external experiment that: (1)The pressure created by the pump was 90 mmHg, the flow rates were 1.2 L/min, 4 L/min, 5.9 L/min and 7.8 L/min correspondingly to 5000 rpm, 6000 rpm, 7000 rpm and 8000rpm rotation speeds. The hydrodynamic performance of the axial flow blood pump was enough to meet a patient need when the blood pump was used as a left ventricular assistant device. (2)The hemolysis test was studied by the normalized index of hemolysis(NIH). The NIH result of the axial flow pump was 0.08 g/100 L. (3)The outside temperature of the pump didnt change obviously in 120 hours of rotation, and the sealing function was very well.