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.

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.

Ultrasonic method for measuring water holdup of low velocity and high-water-cut oil-water two-phase flow

Oil reservoirs with low permeability and porosity that are in the middle and late exploitation periods in China＇s onshore oil fields are mostly in the high-water-cut production stage.This stage is associated with severely non-uniform local-velocity flow profiles and dispersed-phase concentration（of oil droplets） in oil-water two-phase flow,which makes it difficult to measure water holdup in oil wells.In this study,we use an ultrasonic method based on a transmission-type sensor in oil-water two-phase flow to measure water holdup in lowvelocity and high water-cut conditions.First,we optimize the excitation frequency of the ultrasonic sensor by calculating the sensitivity of the ultrasonic field using the finite element method for multiphysics coupling.Then we calculate the change trend of sound pressure level attenuation ratio with the increase in oil holdup to verify the feasibility of the employed diameter for the ultrasonic sensor.Based on the results,we then investigate the effects of oildroplet diameter and distribution on the ultrasonic field.To further understand the measurement characteristics of the ultrasonic sensor,we perform a flow loop test on vertical upward oilwater two-phase flow and measure the responses of the optimized ultrasonic sensor.The results show that the ultrasonic sensor yields poor resolution for a dispersed oil slug in water flow（D OS/W flow）,but the resolution is favorable for dispersed oil in water flow（D O/W flow） and very fine dispersed oil in water flow（VFD O/W flow）.This research demonstrates the potential application of a pulsed-transmission ultrasonic method for measuring the fraction of individual components in oil-water two-phase flow with a low mixture velocity and high water cut.

Optimizing Two-Phase Flow Heat Transfer:DCS Hybrid Modeling and Automation in Coal-Fired Power Plant Boilers

In response to escalating challenges in energy conservation and emission reduction,this study delves into the complexities of heat transfer in two-phase flows and adjustments to combustion processes within coal-fired boilers.Utilizing a fusion of hybrid modeling and automation technologies,we develop soft measurement models for key combustion parameters,such as the net calorific value of coal,flue gas oxygen content,and fly ash carbon content,within theDistributedControl System(DCS).Validated with performance test data,thesemodels exhibit controlled root mean square error(RMSE)and maximum absolute error(MAXE)values,both within the range of 0.203.Integrated into their respective automatic control systems,thesemodels optimize two-phase flow heat transfer,finetune combustion conditions,and mitigate incomplete combustion.Furthermore,this paper conducts an in-depth exploration of the generationmechanismof nitrogen oxides(NOx)and low oxygen emission reduction technology in coal-fired boilers,demonstrating a substantial reduction in furnace exit NOx generation by 30%to 40%and the power supply coal consumption decreased by 1.62 g/(kW h).The research outcomes highlight the model’s rapid responsiveness,enabling prompt reflection of transient variations in various economic indicator parameters.This provides a more effective means for real-time monitoring of crucial variables in coal-fired boilers and facilitates timely combustion adjustments,underscoring notable achievements in boiler combustion.The research not only provides valuable and practical insights into the intricacies of two-phase flow heat transfer and heat exchange but also establishes a pioneering methodology for tackling industry challenges.

Liquid holdup measurement with double helix capacitance sensor in horizontal oil-water two-phase flow pipes

This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil–water two-phase flow. The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented. Then, a horizontal oil–water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor, in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes. The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

An analytical model for water-oil two-phase flow in inorganic nanopores in shale oil reservoirs

The existence of water phase occupies oil flow area and impacts the confined oil flow behavior at the solid substrate in inorganic nanopores of shale oil reservoirs,resulting in a completely different flow pattern when compared with the single oil phase flow.This study proposes an analytical model to describe the water-oil two-phase flow.In this model,water slippage at the solid substrate is considered while oil slip is introduced to calculate the oil movement at the solid-oil boundary in dry conditions.It is proven that the oil flow profiles of both the two-phase model and single-phase model show parabolic shapes,but the oil flow capacity drops when water takes up the flow space and the impact of water is more significant when the pore dimension is smaller than 30 nm.Also,the oil flow velocity at a pore center is found to drop linearly given a larger water saturation in wet conditions.The effects of surface wettability and oil properties on water-oil flow are also discussed.Compared with the existing singlephase models,this model describes oil flow pattern in the wet condition with the incorporation of the influence of nanopore properties,which better predicts the oil transport in actual reservoir conditions.Water-oil relative permeability curves are also obtained to improve oil yield.

TWO-PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

This paper examines the two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection by means of a fixed streamlinemodel,The mathematical model of the verical two-dimensional flow or oil-water for a horizontal well in a medium with double-porosity is established ,and whose accuratesolutions are obtained by using the characteristic method .The saturation distributionsin the fractured system and the matrix system as well as the formula of the time of water free production are presented .All these results provide a theoretical basis and a computing method for oil displacement by edge water from naturally fracturedreservirs.

NUMERICAL MODELING OF TURBULENTEVAPORATING GAS-DROPLET TWO-PHASE FLOWS IN AN AFTERBURNER DIFFUSOR OF TURBO-FAN JET ENGINES

The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.

SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

Inter-layer interference for multi-layered tight gas reservoir in the absence and presence of movable water

Due to the dissimilarity among different producing layers,the influences of inter-layer interference on the production performance of a multi-layer gas reservoir are possible.However,systematic studies of inter-layer interference for tight gas reservoirs are really limited,especially for those reservoirs in the presence of water.In this work,five types of possible inter-layer interferences,including both absence and presence of water,are identified for commingled production of tight gas reservoirs.Subsequently,a series of reservoir-scale and pore-scale numerical simulations are conducted to quantify the degree of influence of each type of interference.Consistent field evidence from the Yan'an tight gas reservoir(Ordos Basin,China)is found to support the simulation results.Additionally,suggestions are proposed to mitigate the potential inter-layer interferences.The results indicate that,in the absence of water,commingled production is favorable in two situations:when there is a difference in physical properties and when there is a difference in the pressure system of each layer.For reservoirs with a multi-pressure system,the backflow phenomenon,which significantly influences the production performance,only occurs under extreme conditions(such as very low production rates or well shut-in periods).When water is introduced into the multi-layer system,inter-layer interference becomes nearly inevitable.Perforating both the gas-rich layer and water-rich layer for commingled production is not desirable,as it can trigger water invasion from the water-rich layer into the gas-rich layer.The gas-rich layer might also be interfered with by water from the neighboring unperforated water-rich layer,where the water might break the barrier(eg weak joint surface,cement in fractures)between the two layers and migrate into the gas-rich layer.Additionally,the gas-rich layer could possibly be interfered with by water that accumulates at the bottom of the wellbore due to gravitational differentiation during shut-in operations.

Prediction of Flowing Bottomhole Pressures for Two-Phase Coalbed Methane Wells

A method is proposed to predict the flowing bottomhole pressures （FBHPs） for two-phase coalbed methane （CBM） wells. The mathematical models for both gas column pressure and two-phase fluid column pressure were developed based on the well liquid flow equation. FBHPs during the production were predicted by considering the effect of entrained liquid on gravitational gradients. Comparison of calculated BHPs by Cullender-Smith and proposed method was also studied. The results show that the proposed algorithm gives the desired accuracy of calculating BHPs in the low- productivity and low-pressure CBM wells. FBHP is resulted from the combined action of wellhead pressure, gas column pressure and fluid column pressure. Variation of kinetic energy term, compressibility and friction factors with depth increments and liquid holdup with velocity should be considered to simulate the real BHPs adequately. BHP is a function of depth of each column segment. The small errors of less than 1.5% between the calculated and measured values are obtained with each segment within 25 m. Adjusting BHPs can effectively increase production pressure drop, which is beneficial to CBM desorption and enhances reservoir productivity. The increment of pressure drop from 5.37 MPa2 to 8.66 MPa2 leads to an increase of CBM production from 3270 m3/d to 6700 m3/d and is attributed to a decrease in BHP from 2.25 MPa to 1.33 MPa.

Mechanism of gas-water flow at pore-level in aquifer gas storage

By means of the pore-level simulation, the characteristics of gas-water flow and gas-water distribution during the alternative displacement of gas and water were observed directly from etched-glass micromodel. The results show that gas-water distribution styles are divided into continuous phase type and separate phase type. The water lock exists in pore and throat during the process of gas-water displacement, and it reduces the gas flow-rate and has some effects on the recovery efficiency during the operation of gas storage. According to the experimental results of aquifer gas storage in X area, the differences in available extent among reservoirs are significant, and the availability of pore space is 33% 45%.

Two-Phase Flow in Porous Electrodes of Proton Exchange Membrane Fuel Cell

Water management in porous electrodes bears significance due to its strong potential in determining the performance of proton exchange membrane fuel cell.In terms of porous electrodes,internal water distribution and removal process have extensively attracted attention in both experimental and numerical studies.However,the structural difference among the catalyst layer(CL),microporous layer(MPL),and gas diffusion layer(GDL)leads to significant challenges in studying the two-phase flow behavior.Given the different porosities and pore scales of the CL,MPL,and GDL,the model scales in simulating each component are inconsistent.This review emphasizes the numerical simulation related to porous electrodes in the water transport process and evaluates the effectiveness and weakness of the conventional methods used during the investigation.The limitations of existing models include the following:(i)The reconstruction of geometric models is difficult to achieve when using the real characteristics of the components;(ii)the computational domain size is limited due to massive computational loads in three-dimensional(3 D)simulations;(iii)numerical associations among 3 D models are lacking because of the separate studies for each component;(iv)the effects of vapor condensation and heat transfer on the two-phase flow are disregarded;(v)compressive deformation during assembly and vibration in road conditions should be considered in two-phase flow studies given the real operating conditions.Therefore,this review is aimed at critical research gaps which need further investigation.Insightful potential research directions are also suggested for future improvements.

Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity.Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging.This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water.By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water,gas,and high stress sensitivity,the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudotime.The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs,such as original gas-in-place,fracture half-length,reservoir permeability,and well drainage radius.This facilitates the analysis of production dynamics of fractured wells and well-controlled areas,subsequently aiding in locating residual gas and guiding the configuration of well patterns.The specific evaluation processes are detailed.Additionally,a numerical simulation mechanism model was constructed to verify the reliability of the developed methods.The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Permeability evolution and gas flow in wet coal under non-equilibrium state:Considering both water swelling and process-based gas swelling

Accurate knowledge of gas flow within the reservoir and related controlling factors will be important for enhancing the production of coal bed methane.At present,most studies focused on the permeability evolution of dry coal under gas adsorption equilibrium,gas flow and gas diffusion within wet coal under the generally non-equilibrium state are often ignored in the process of gas recovery.In this study,an improved apparent permeability model is proposed which accommodates the water and gas adsorption,stress dependence,water film thickness and gas flow regimes.In the process of modeling,the water adsorption is only affected by water content while the gas adsorption is time and water content dependent;based on poroelastic mechanics,the effective fracture aperture and effective pore radius are derived;and then the variation in water film thickness for different pore types under the effect of water content,stress and adsorption swelling are modeled;the flow regimes are considered based on Beskok’s model.Further,after validation with experimental data,the proposed model was applied to numerical simulations to investigate the evolution of permeability-related factors under the effect of different water contents.The gas flow in wet coal under the non-equilibrium state is explicitly revealed.

Numerical Simulation of a Two-Phase Flow with Low Permeability anda Start-Up Pressure Gradient

A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.

Near-source characteristics of two-phase gas-solid outbursts in roadways

Coal and gas outbursts compromise two-phase gas-solid mixtures as they propagate as shock waves and flows from their sources.Propagation is influenced by the form of the outburst,proximity to source,the structure and form of the transmitting roadways and the influence of obstacles.The following characterizes the propagation of coal and gas outbursts as two-phase gas-solid flows proximal to source where the coupled effects of pulverized coal and gas flows dominate behavior.The characteristics of shock wave propagation and attenuation were systematically examined for varied roadway geometries using experiments and numerical models.The results demonstrate that the geometry of roadway obstructions is significant and may result in partial compression and sometimes secondary overpressurization in blocked and small comer roadways leading to significant attenuation of outburst shock waves.The shock waves attenuate slowly in both straight and abruptly expanding roadways and more significantly in T-shaped roadways.The most significant attenuation appears in small angle comers and bifurcations in roadways with the largest attenuation occurring in blocked roadways.These results provide basic parameters for simplifying transport in complex roadway networks in the far-field,and guidance for the design of coal and gas outburst prevention facilities and emergency rescue.

Multi-scale complexity entropy causality plane: An intrinsic measure for indicating two-phase flow structures

We extend the complexity entropy causality plane（CECP） to propose a multi-scale complexity entropy causality plane（MS-CECP） and further use the proposed method to discriminate the deterministic characteristics of different oil-in-water flows. We first take several typical time series for example to investigate the characteristic of the MS-CECP and find that the MS-CECP not only describes the continuous loss of dynamical structure with the increase of scale, but also reflects the determinacy of the system. Then we calculate the MS-CECP for the conductance fluctuating signals measured from oil–water two-phase flow loop test facility. The results indicate that the MS-CECP could be an intrinsic measure for indicating oil-in-water two-phase flow structures.

Quantitative research of the liquid film characteristics in upward vertical gas, oil and water flows

The study of liquid film characteristics in multiphase flow is a very important research topic, however,the characteristics of the liquid film around Taylor bubble structure in gas, oil and water three-phase flow are not clear. In the present study, a novel liquid film sensor is applied to measure the distributed signals of the liquid film in three-phase flow. Based on the liquid film signals, the liquid film characteristics including the structural characteristics and the nonlinear dynamics characteristics in three-phase flows are investigated for the first time. The structural characteristics including the proportion, the appearance frequency and the thickness of the liquid film are obtained and the influences of the liquid and gas superficial velocities and the oil content on them are investigated. To investigate the nonlinear dynamics characteristics of the liquid film with the changing flow conditions, the entropy analysis is introduced to successfully uncover and quantify the dynamic complexity of the liquid film behavior.