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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Investigation of low water recovery based on gas-water two-phase low-velocity Non-Darcy flow model for hydraulically fractured horizontal wells in shale

Various mechanisms are employed to interpret the low water recovery during the shale-gas production period,such as extra-trapped water in the fracture network,water imbibition due to osmotic pressure and capillary pressure.These lead to the difficulty of water flow,which could be described by lowvelocity non-Darcy's law known as threshold pressure gradient(TPG).In this paper we firstly employ the low-velocity non-Darcy's law to describe the water flow and use Darcy flow accounting for slip flow and free molecular flow mechanisms to model gas flow in the shale formation.The sensitive study using numerical simulation shows that the proposed flow model could model the low fracturing liquid recovery and that large pseudo TPG leads to lower fracturing liquid recovery.Thus,the proposed model would give new insight to model the low water recovery in shale formations.

A study of hydrate plug formation in a subsea natural gas pipeline using a novel high-pressure flow loop

The natural gas pipeline from Platform QKI8-1 in the southwest of Bohai Bay to the onshore processing facility is a subsea wet gas pipeline exposed to high pressure and low temperature for a long distance. Blockages in the pipeline occur occasionally. To maintain the natural gas flow in the pipeline, we proposed a method for analyzing blockages and ascribed them to the hydrate formation and agglomeration. A new high-pressure flow loop was developed to investigate hydrate plug formation and hydrate particle size, using a mixture of diesel oil, water, and natural gas as experimental fluids. The influences of pressure and initial flow rate were also studied. Experimental results indicated that when the flow rate was below 850 kg/h, gas hydrates would form and then plug the pipeline, even at a low water content （10%） of a water/oil emulsion. Furthermore, some practical suggestions were made for daily management of the subsea pipeline.

Multibeam water column data research in the Taixinan Basin:Implications for the potential occurrence of natural gas hydrate

A multi beam sonar survey is carried out in the continental slope of the Taixinan Basin to obtain submarine topographic and water column data. The data are processed to obtain water column images. Anomalous water column images, displaying plume characteristics, are found in gas hydrate enriched areas in the Taixinan Basin.This indicates the presence of natural gas resources in the Taixinan Basin. The multibeam sonar system is shown to provide an accurate and effective approach for detecting sub-sea gas hydrate.

Study on gas–liquid flow characteristics in stirred tank with dual-impeller based on CFD-PBM coupled model

Study on gas–liquid flow in stirred tank with two combinations of dual-impeller(six-bent-bladed turbine(6BT)+six-inclined-blade down-pumping turbine(6 ITD),the six-bent-bladed turbine(6BT)+six-inclinedblade up-pumping turbine(6ITU))was conducted using computational fluid dynamics(CFD)and population balance model(PBM)(CFD-PBM)coupled model.The local bubble size was captured by particle image velocimetry(PIV)measurement.The gas holdup,bubble size distribution and gas–liquid interfacial area were explored at different conditions through numerical simulation.The results showed that the 4 mm bubbles accounted for the largest proportion of 33%at the gas flow rates Q=0.76 m^(3)·h^(-1) and 22%at Q=1.52 m^(3)·h^(-1) for combined impeller of 6BT+6ITU,while the bubbles of 4.7 mm and 5.5 mm were the largest proportion for 6BT+6ITD combination,i.e.25%at Q=0.76 m^(3)·h^(-1) and 22%at Q=1.52 m^(3)·h^(-1),respectively,which indicated that 6BT+6ITU could reduce bubble size effectively and promote gas dispersion.In addition,the gas holdup around impellers was increased obviously with the speed compared with gas flow rate.So it was concluded that 6ITU impeller could be more conductive to the bubble dispersion with more uniform bubble size,which embodied the advantages of 6BT+6ITU combination in gas–liquid mixing.

A dynamic managed pressure well-control method for rapid treatment of gas kick in deepwater managed pressure drilling

During deepwater managed pressure drilling(MPD),the gas kick may occur in abnormally high-pressure formations.If the traditional well control method is adopted,the treatment time is long and the advantage of early gas kick detection of MPD is lost.The dynamic managed pressure well-control(MPWC)method can be used to rapidly treat gas kick in deepwater MPD.In this paper,considering the effect of large-variable-diameter annulus and complex wellbore temperature in deepwater drilling,a simplified model of non-isothermal gas-liquid two-phase flow was established for dynamic deepwater MPWC simulation.Using this model,the response characteristics of outlet flow and wellhead backpressure were investigated.The results indicated that the gas fraction,outlet liquid flow rate,pit gain and wellhead backpressure presented complex alternating characteristics when gas moved upwards in the wellbore due to the large-variable-diameter annulus.The outlet liquid flow rate would be lower than the inlet flow rate and the pit gain would decrease before the gas moved to the wellhead.The variation trend of the wellhead backpressure was consistent with that of the pit gain.When the gas-liquid mixture passed through the choke,the expansion or compression of the gas caused part of the choke pressure drop to be supplemented or unloaded,delaying the response rate of the wellhead backpressure.The wellbore temperature,borehole diameter and seawater depth had different effects on outlet flow rate,pit gain and wellhead backpressure.This research could provide a new idea for well control methods in deepwater managed pressure drilling.

Improving Existing Drainage and Gas Recovery Technologies: An Experimental Study on the Wellbore Flow in a Horizontal Well

With the increasing number of horizontal wells with low pressure,low yield,and water production,the phenomenon of water and liquid accumulation in gas wells is becoming progressively more serious.In order to fix these issues,it is necessary to improve existing drainage and gas recovery technologies,increase the fluid carrying capacity of these wells,and ensure that the bottom-hole airflow has enough energy to transport the liquid to the wellhead.Among the many techniques of drainage and gas recovery,the gas lift has recently become a popular method.In the present study,through the simulation of the entire horizontal well,the flow regularity of the whole wellbore during the lift of low-pressure gas has been analyzed.The pressure distribution,liquid holdup rate,flow pattern,and energy loss(including gravity loss and friction loss)have been determined using the Beggs-brill approach.It has been found that the total pressure drop of the wellbore decreases first and increases gradually after reaching a minimum value when gas extraction is carried out via gas lift.Based on the analysis of the influence of the injection volume on wellbore pressure drop and the influence of flow pattern on the lifting efficiency,the optimal gas-lift injection parameters have been determined by taking the minimum pressure loss of wellbore as the judgment criterion.

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.