Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

Numerical simulation of the gas-solid two-phase flow inside the multi-channel nozzle for the surface nanocrystallization induced by the ultrasonic particulate peening

Using a gas-solid two-phase model(a discrete phase model),the authors investigated the flow field inside the multi-channel nozzle for surface nanocrystallization(SNC)induced by the ultrasonic particulate peening(USPP).By computation,the velocity fields of both the gas and the solid phases were simulated and the track of the solid phase was analyzed in detail.It can be found that the velocities of the two phases are able to reach an ultrasonic level;meanwhile,the dispersion width of the solid phase at the nozzle exit is less than that of the gas phase.When particle diameters are less than 5 μm,there is a decreasing trend in the dispersion width of the solid phase with an increase in particle diameters.The trend becomes stable as the particle diameters are greater than 5 μm;in the meantime,the distribution of solid particles is near the axis of the jet flow.The optimal standoff distance between the nozzle and the substrate in the process of USPP is about 120 mm.Simulation results can help improve the design of mass-production-oriented multi-channel nozzles for SNC induced by USPP.

Simulation of Gas-Water Two-Phase Flow in Tight Gas Reservoirs Considering the Gas Slip Effect

A mathematical model for the gas-water two-phase flow in tight gas reservoirs is elaborated.The model can account for the gas slip effect,stress sensitivity,and high-speed non-Darcy factors.The related equations are solved in the framework of a finite element method.The results are validated against those obtained by using the commercial software CMG(Computer Modeling Group software for advanced recovery process simulation).It is shown that the proposed method is reliable.It can capture the fracture rejection characteristics of tight gas reservoirs better than the CMG.A sensitivity analysis of various control factors(initial water saturation,reservoir parameters,and fracturing parameters)affecting the production in tight gas wells is conducted accordingly.Finally,a series of theoretical arguments are provided for a rational and effective development/exploitation of tight sandstone gas reservoirs.

A COUPLED MODEL FOR MUILTIPHASE FLUID FLOW AND SEDIMENTATION DEFORMATION IN OIL RESERVOIR AND ITS NUMERICAL SIMULATION

A mathematical model for coupled multiphase fluid flow and sedi- mentation deformation is developed based on fluid-solid interaction mechanism.A finite difference-finite element numerical approach is presented.The results of an example show that the fluid-solid coupled effect has great influence on multiphase fluid flow and reservoir recovery performances,and the coupled model has practical significance for oilfield development.

Lubrication properties of Nitinol 60 alloy used as high-speed rolling bearing and numerical simulation of flow pattern of oil-air lubrication

The friction and wear tests were performed using Nitinol 60 alloy pin sliding over GCr15 steel disk in a pin-on-disk tribometer system under PAO oil lubrication conditions. It was found that Nitinol 60 alloy can be lubricated well and has shown remarkable tribological performance. Average coefficient of friction （COF） of Nitinol 60 is 0.6 under dry friction; however, average COF decreases to 0.1 under PAO oil lubrication. SEM image of the worn surface shows that Nitinol 60 exhibits excellent wear resistance and the wear mechanism is mainly adhesive wear. Flow pattern of oil-air flow in oil pipe was simulated by FLUENT software with VOF model for acquiring working performance of oil-air lubrication. The optimum velocity of oil and air at the inlet was achieved, which provides the great proposal for the design of experiment of oil-air lubrication of Nitinol 60 alloy. The simulation results showed that the optimum annular flow of flow pattern was obtained when air velocity is 10 m/s and oil velocity is 0.05 m/s. The formation mechanism of annular flow was also discussed in the present study.

Numerical simulation on electrolyte flow field in 156 kA drained aluminum reduction cells

Based on the commercial CFD software CFX-4.3, two-phase flow of electrolyte in 156 kA drained aluminum reduction cells with a new structure was numerically simulated by multi-fluid model and k-ε turbulence model. The results show that the electrolyte flow in the drained cells is more even than in the conventional cells. Corresponding to center point feeding, the electrolyte flow in the drained cells is more advantageous to the release of anode gas, the dissolution and diffusion of alumina, and the gradient reduction of the electrolyte density and temperature. The average velocity of the electrolyte is 8.3 cm/s, and the maximum velocity is 59.5 cm/s. The average and maximum velocities of the gas are 23.2 cm/s and 61.1 cm/s, respectively. The cathode drained slope and anode cathode distance have certain effects on the electrolyte flow.

Two-dimensional Dynamics Simulation of Two-phase Debris Flow

To investigate the movement mechanism of debris flow, a two-dimensional, two-phase, depthintegrated model is introduced. The model uses Mohr-Coulomb plasticity for the solid rheology, and the fluid stress is modeled as a Newtonian fluid. The interaction between solid and liquid phases, which plays a major role in debris flow movement, is assumed to consist of drag and buoyancy forces. The applicability of drag force formulas is discussed. Considering the complex interaction between debris flow and the bed surface, a combined friction boundary condition is imposed on the bottom, and this is also discussed. To solve the complex model equations, a numerical method with second-order accuracy based on the finite volume method is proposed. Several numerical experiments are performed to verify the feasibilities of model and numerical schemes. Numerical results demonstrate that different solid volume fractions substantially affect debris flow movement.

A Numerical Sirnulation of Gas-Particle Two-Phase Flow in a Suspension Bed Using DifFusion Flux Model

A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.

NUMERICAL MODELING OF 3-D TURBULENT TWO-PHASE FLOW AND COAL COMBUSTION IN A PULVERIZED-COAL COMBUSTOR

In the present paper, a multifluid model of two-phase flows with pulverized-coal combustion, based on a continuum-trajectory model with reacting particle phase, is developed and employed to simulate the 3-D turbulent two-phase hows and combustion in a new type of pulverized-coal combustor with one primary-air jet placed along the wall of the combustor. The results show that: (1) this continuum-trajectory model with reacting particle phase can be used in practical engineering to qualitatively predict the flame stability, concentrations of gas species, possibilities of slag formation and soot deposition, etc.; (2) large recirculation zones can be created in the combustor, which is favorable to the ignition and flame stabilization.

Application of numerical simulation to flow induced corrosion in flowing seawater system

An established model was presented as a new kind of means for investigating flow induced corrosion. In this method the near-wall hydrodynamic parameters including wall shear stress τ and mass transfer coefficient k near the wall of materials can be numerically calculated, and combining corrosive kinetics tested by experiments, the corrosion rates can be also calculated accurately. The flow induced corrosion mechanism was further verified by numerical results in this model, and the various corrosion phenomena were explained. The modelled results also show that the ability to accurately utilize numerical method to study flow induced corrosion strongly to some extent depends on material corrosive kinetics processes tested by experiments.

NUMERICAL SIMULATION FOR AIR AND AIR-PM FLOW IN WALL FLOW DIESEL PARTICULATE FILTERS

Numerical simulations are performed both for the single airflow and air-PMtwo-phase flow in wall flow diesel participate filters (DPF) for the first time. The calculationdomain is divided into two regions. In. the inlet and outlet flow channels, the simulations areperformed for the steady and laminar flow; In the porous filtration walls, the calculation model forflow in porous media is used. The Lagrange two-phase flow model is used to calculate the air-PMflow in DPF, for the dispersed phase (PM), its flow tracks are obtained by the integrating of theLagrange kinetic equation. The calculated velocity, pressure distribution and PM flow tracks in DPFare obtained, which exhibits the main flow characteristics in wall flow DPF and will be help for theoptimal design and performance prediction of wall flow DPF.

Gas-solid flow field numerical simulation of different feeding and returning formations of flue-gas circulating fluidized bed

3D Euler double-fluid model was applied and three different feedstocks and reverts formations were simulated. By calculating and analyzing the state of gas and solid fluxion in absorber using three different methods of the feedstocks and reverts in recirculating fluidized bed, described the behavior of gas and solid through the gas-phase velocity, turbulence intensity, gas-solid sliding velocity, and density of particles. The results show that the feedstocks and reverts enters into absorption tower through two symmetrical feedings and are mixed with flue gas. Based on the respective analysis of each model and the com- parison analysis of the three models, this paper drew conclusions. The turbulence intensity of absorption tower is high, gas-solid sliding speed is big, and granule concentration near the axis is high, which has advantages for desulfurization and im- proving the utilization rate of absorbent.

Numerical simulation of a self-absorbing microbubble generator for a cyclonic-static microbubble flotation column

The Cyclonic-Static Microbubble Flotation Column (FCSMC) is currently a widely used, novel type of flotation device. The self-absorbing microbubble generator is the core component of this device. The structure of the microbubble generator directly influences flotation column performance by affecting bubble size and distribution as well as gas holdup in the column. However, the complicated flow inside the generator results in high R&D costs and difficulty in testing. Thus, the CFD software, FLUENT, was used to simulate the gas-liquid two-phase flow inside a self-absorbing microbubble generator. The effect of area ratio, a key structural parameter, was studied in detail. Critical flow-field parameters including velocity, turbulent kinetic energy, minimum static pressure and gas holdup were obtained. The simulation results demonstrate that the optimum area ratio is 3.

Numerical simulation of mould filling process for pressure plate and valve handle in LFC

In lost foam casting (LFC), the distribution of polymer beads during the bead filling process is not uniform, and the collision between polymer beads determines the distribution of two-phase flow of gas and solid. The interaction between the gas and solid phases reveals as coupling effect of the force that gas exerts on particles or vice versa, or that among particles. The gas-solid flow in filling process is nonlinearity, which makes the coupling effect an essential point to carry out a simulation properly. Therefore, information of each particle's motion is important for acquiring the law of filling process. In bead filling process, compressed air is pressed into mold cavity, and discharged from gas vent, creating a pressure difference between outer and inner space near the gas vent. This pressure difference directly changes the spatial distribution and motion trace of gas and solid phases. In this paper, Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) are employed to simulate the fluid dynamic character based on Newton's Third Law of Motion. The simulation results of some casting products such as pressure plate and valve handle are compared with the result obtained from practical experiment in order to test the feasibility of DEM. The comparison shows that this DEM method can be a very promising tool in the mould filling simulation of beads' movement.

NUMERICAL SIMULATION OF CASTING PROCESS

In this paper, the development status of casting numerical simulation technology is introduced. In additional, mathematical model, solution method, initial condition, boundary condition and defect predicting scheme of foundry process are also analyzed, which include the mold filling process, solidification process and the process coupling fluid flow with heat transfer. Finally, a practical casting is taken out to show how to predict defects and optimize foundry process with numerical simulation technology.

NUMERICAL SIMULATION OF MOLTEN POOL AND CONTROL STRATEGY OF KISS POINT IN A TWIN-ROLL STRIP CASTING PROCESS

Coupled turbulent flow, temperature fields of the twin-roll casting strip process were simulated by three-dimensional finite element method. Based on the heat balance calculation and using inverse methods between the simulations and real experiments, the relational models among casting speed, location, and coefficient of heat transfer between molten metal and rolls in different regions are given. In the simulation, the calculated surface temperatures are in good agreement with the measured values. An on-line model of kiss point is derived by simulations and the geometry of molten pool, corresponding control strategy is also proposed.