Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Identifying the enhancement mechanism of Al/MoO_(3) reactive multilayered films on the ignition ability of semiconductor bridge using a one-dimensional gas-solid two-phase flow model

Energetic Semiconductor bridge(ESCB)based on reactive multilayered films(RMFs)has a promising application in the miniature and intelligence of initiator and pyrotechnics device.Understanding the ignition enhancement mechanism of RMFs on semiconductor bridge(SCB)during the ignition process is crucial for the engineering and practical application of advanced initiator and pyrotechnics devices.In this study,a one-dimensional(1D)gas-solid two-phase flow ignition model was established to study the ignition process of ESCB to charge particles based on the reactivity of Al/MoO_(3) RMFs.In order to fully consider the coupled exothermic between the RMFs and the SCB plasma during the ignition process,the heat release of chemical reaction in RMFs was used as an internal heat source in this model.It is found that the exothermal reaction in RMFs improved the ignition performance of SCB.In the process of plasma rapid condensation with heat release,the product of RMFs enhanced the heat transfer process between the gas phase and the solid charge particle,which accelerated the expansion of hot plasma,and heated the solid charge particle as well as gas phase region with low temperature.In addition,it made up for pressure loss in the gas phase.During the plasma dissipation process,the exothermal chemical reaction in RMFs acted as the main heating source to heat the charge particle,making the surface temperature of the charge particle,gas pressure,and gas temperature rise continuously.This result may yield significant advantages in providing a universal ignition model for miniaturized ignition devices.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Modeling of multiphase flow in low permeability porous media:Effect of wettability and pore structure properties

Multiphase flow in low permeability porous media is involved in numerous energy and environmental applications.However,a complete description of this process is challenging due to the limited modeling scale and the effects of complex pore structures and wettability.To address this issue,based on the digital rock of low permeability sandstone,a direct numerical simulation is performed considering the interphase drag and boundary slip to clarify the microscopic water-oil displacement process.In addition,a dual-porosity pore network model(PNM)is constructed to obtain the water-oil relative permeability of the sample.The displacement efficiency as a recovery process is assessed under different wetting and pore structure properties.Results show that microscopic displacement mechanisms explain the corresponding macroscopic relative permeability.The injected water breaks through the outlet earlier with a large mass flow,while thick oil films exist in rough hydrophobic surfaces and poorly connected pores.The variation of water-oil relative permeability is significant,and residual oil saturation is high in the oil-wet system.The flooding is extensive,and the residual oil is trapped in complex pore networks for hydrophilic pore surfaces;thus,water relative permeability is lower in the water-wet system.While the displacement efficiency is the worst in mixed-wetting systems for poor water connectivity.Microporosity negatively correlates with invading oil volume fraction due to strong capillary resistance,and a large microporosity corresponds to low residual oil saturation.This work provides insights into the water-oil flow from different modeling perspectives and helps to optimize the development plan for enhanced recovery.

Liquid-liquid two-phase flow in a wire-embedded concentric microchannel: Flow pattern and mass transfer performance

In this work, flow pattern and mass transfer of liquid-liquid two-phase flow in a wire-embedded concentric microchannel are studied using toluene-water system. Droplet flow, slug flow, oval flow and annular flow are observed in the wire-embedded concentric microchannel. The effects of embedded wires and physical properties on flow patterns are investigated. The embedded wire insert is conducive to the formation of annular flow. The flow pattern distribution regions are distinguished by the Caaq(capillary number)±We_(org)(Weber number) flow pattern map. When Weorg<0.001, slug flow is the main flow pattern, and when Weorg>0.1, annular flow is the main flow pattern. Oval flow and droplet flow are between We_(org)= 0.001-0.1, and oval flow is transformed into droplet flow with the increase of Caaq. The effect of flow rate, phase ratio, initial acetic acid concentration, insert shape and flow patterns on mass transfers are studied. Mass transfer process is enhanced under annular flow conditions, the volumetric mass transfer coefficient is up to 0.36 s^(-1) because of the high interfacial area and interface renewal rate of annular flow.

Comprehensive modeling of frictional pressure drop during carbon dioxide two-phase flow inside channels using intelligent and conventional methods

Environmentally friendly nature of CO_(2),associated with its safety and high efficiency,has made it a widely used working fluid in heat exchangers.Since CO_(2)has strange thermophysical features,specific models are required to estimate its two-phase characteristics,particularly frictional pressure drop(FPD).Herein,a widespread dataset,comprising 1195 experimental samples for two-phase FPD of CO_(2)was adopted from 10 sources to fulfill this requirement.The literature correlations failed to provide satisfactory precisions and exhibited the average absolute relative errors(AAREs)between 29.29% and 67.69% from the analyzed data.By inspiring the theoretical method of Lockhart and Martinelli,three intelligent FPD models were presented,among which the Gaussian process regression approach surpassed the others with AARE and R^(2)values of 5.48% and 98.80%,respectively in the test stage.A novel simple correlation was also derived based on the least square fitting method,which yielded opportune predictions with AARE of 19.76% for all data.The truthfulness of the newly proposed models was assessed through a variety of statistical and visual analyses,and the results affirmed their high reliability over a broad range of conditions,channel sizes and flow patterns.Furthermore,the novel models performed favorably in describing the physical attitudes corresponding to two-phase FPD of CO_(2).Eventually,the importance of operating factors in controlling the FPD was discussed through a sensitivity analysis.

Simulation of gas–liquid two-phase flow in a flow-focusing microchannel with the lattice Boltzmann method

A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, surface tension,wetting properties, and rheological characteristics of the fluid on the two-phase flow are analyzed. The results indicate that the flow pattern transfers from slug flow to dry-plug flow with a sufficiently small capillary number. Due to the presence of three-phase contact lines, the contact angle has a more significant effect on the dry-plug flow pattern than on the slug flow pattern. The deformation of the front and rear meniscus of a bubble in the shear-thinning fluid can be explained by the variation of the capillary number. The reduced viscosity and increased contact angle are beneficial for the drag reduction in a microchannel. It also demonstrates the effectiveness of the current method to simulate the gas–liquid two-phase flow in a microchannel.

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.

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 1–Turbulence properties and particle chord time and length

This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.

Experimental Investigation of Regular or Wavy Two-Phase Flow in a Manifold

An experimental study was conducted to investigate the properties of stratified regular or wavy two-phase flow in two parallel separators located after a manifold.A total of 103 experiments with various gas and liquid velocity combinations in three inlet pipes were conducted,including 77 groups of outlet pipe resistance symmetry and 26 groups of outlet pipe resistance asymmetry trials.The experimental results have revealed that when the gas-liquid flow rate is low,the degree of uneven splitting is high,and“extreme”conditions are attained.When the superficial gas velocity is greater than that established in the extreme case,the direction of the liquid-phase displacement is reversed,while that of the gas remains unchanged.Thus,the degree of gas phase bias tends to be mitigated with an increase in the gas velocity,while the uneven splitting degree of liquid approaches 10%.Finally,varying the gas-phase outlet pipe resistance is shown to effectively change the gas-liquid two-phase flow distribution.

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 2–Bubble clustering

A survey on bubble clustering in air–water flow processes may provide significant insights into turbulent two-phaseflow.These processes have been studied in plunging jets,dropshafts,and hydraulic jumps on a smooth bed.As a first attempt,this study examined the bubble clustering process in hydraulic jumps on a pebbled rough bed using experimental data for 1.70<Fr_(1)<2.84(with Fr_(1) denoting the inflow Froude number).The basic properties of particle grouping and clustering,including the number of clusters,the dimensionless number of clusters per second,the percentage of clustered bubbles,and the number of bubbles per cluster,were analyzed based on two criteria.For both criteria,the maximum cluster count rate was greater on the rough bed than on the smooth bed,suggesting greater interactions between turbulence and bubbly flow on the rough bed.The results were consistent with the longitudinal distribution of the interfacial velocity using one of the criteria.In addition,the clustering process was analyzed using a different approach:the interparticle arrival time of bubbles.The comparison showed that the bubbly flow structure had a greater density of bubbles per unitflux on the rough bed than on the smooth bed.Bed roughness was the dominant parameter close to the jump toe.Further downstream,Fr_(1) predominated.Thus,the rate of bubble density decreased more rapidly for the hydraulic jump with the lowest Fr_(1).

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.

Transient pressure analysis of polymer flooding fractured wells with oil-water two-phase flow

The oil-water two-phase flow pressure-transient analysis model for polymer flooding fractured well is established by considering the comprehensive effects of polymer shear thinning,shear thickening,convection,diffusion,adsorption retention,inaccessible pore volume and effective permeability reduction.The finite volume difference and Newton iteration methods are applied to solve the model,and the effects of fracture conductivity coefficient,injected polymer mass concentration,initial polymer mass concentration and water saturation on the well-test type curves of polymer flooding fractured wells are discussed.The results show that with the increase of fracture conductivity coefficient,the pressure conduction becomes faster and the pressure drop becomes smaller,so the pressure curve of transitional flow goes downward,the duration of bilinear flow becomes shorter,and the linear flow appears earlier and lasts longer.As the injected polymer mass concentration increases,the effective water phase viscosity increases,and the pressure loss increases,so the pressure and pressure derivative curves go upward,and the bilinear flow segment becomes shorter.As the initial polymer mass concentration increases,the effective water phase viscosity increases,so the pressure curve after the wellbore storage segment moves upward as a whole.As the water saturation increases,the relative permeability of water increases,the relative permeability of oil decreases,the total oil-water two-phase mobility becomes larger,and the pressure loss is reduced,so the pressure curve after the wellbore storage segment moves downward as a whole.The reliability and practicability of this new model are verified by the comparison of the results from simplified model and commercial well test software,and the actual well test data.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.

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.

Determination of dynamic capillary effect on two-phase flow in porous media: A perspective from various methods

The relationship between capillary pressure and saturation plays a critical role in the characterization of two-phase flow and transport in aquifers and oil reservoirs. This relationship is usually determined under the static condition, where capillary pressure is the only function of saturation. However,considerable experiments have suggested that the dependence of capillary pressure on desaturation rate is under the dynamic condition. Thus, a more general description of capillary pressure that includes dynamic capillary effect has been approved widely. A comprehensive understanding of the dynamic capillary effect is needed for the investigation of the two-phase flow in porous media by various methods. In general, dynamic capillary effect in porous media can be studied through the laboratory experiment, pore-to macro-scale modeling, and artificial neural network. Here, main principle and research procedures of each method are reviewed in detail. Then, research progress, disadvantages and advantages are discussed, respectively. In addition, upscaling study from pore-to macro-scale are introduced, which explains the difference between laboratory experiment and pore-scale modeling. At last, several future perspectives and recommendations for optimal solution of dynamic capillary effect are presented.

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.