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.

Application of Two-dimensional Viscous CE/SE Method in Calculation of Two-phase Detonation

The method of two-dimensional viscous space-time conservation element and solution element (CE/SE) can be used to calculate the gas-liquid two-phase interior flow field in pulse detonation engine (PDE). In this paper, the evolution of the detonation wave and the distribution of its physical parameters were analyzed. The numerical results show that the change of axial velocity of gas is the same as that of detonation pressure. The larger the liquid droplet radius is, the longer the time to get stable detonation wave is. The calculated results coincide with the experimented results better.

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.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

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.

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.

Reconstructing bubble profiles from gas-liquid two-phase flow data using agglomerative hierarchical clustering method

The knowledge of bubble profiles in gas-liquid two-phase flows is crucial for analyzing the kinetic processes such as heat and mass transfer, and this knowledge is contained in field data obtained by surface-resolved computational fluid dynamics (CFD) simulations. To obtain this information, an efficient bubble profile reconstruction method based on an improved agglomerative hierarchical clustering (AHC) algorithm is proposed in this paper. The reconstruction method is featured by the implementations of a binary space division preprocessing, which aims to reduce the computational complexity, an adaptive linkage criterion, which guarantees the applicability of the AHC algorithm when dealing with datasets involving either non-uniform or distorted grids, and a stepwise execution strategy, which enables the separation of attached bubbles. To illustrate and verify this method, it was applied to dealing with 3 datasets, 2 of them with pre-specified spherical bubbles and the other obtained by a surface-resolved CFD simulation. Application results indicate that the proposed method is effective even when the data include some non-uniform and distortion.

NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA

By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.

Two-phase Method without Any Artificial Variable

A method is provided to achieve an initial basic feasible solution of a linear programming in this paper. This method dose not need introducing any artificial variable, but needs only solving an auxiliary linear programming. Compared with the traditional two-phase method, it has advantages of saving the memories and reducing the computational efforts.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

Numerical Method for Determination of Composition of Weak Acid Mixtures by Potentiometric Titration

An equation describing the state of weak acid mixtures was derived from the relationships between mole balance and charge balance. The equation was solved with numerical method and the compositions of the acid mixtures were determined. The advantages of this treatment were demonstrated by analyzing binary mixtures of chloroacetic, formic and acetic acids.

CHARACTERISTIC DIFFERENCE METHODS FOR TWO-PHASE DISPLACEMENT IN NATURALLY FRACTURED RESERVOIRS

In this paper we shall give the characteristic difference methods for two phase displace meat problem in naturally fractured reservoirs.We shall prove the existence,uniqueness of the ap proximate solution and a priori discrete L2-error estimates.

Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow

We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

In this paper, an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface, where the surface tension is implemented. The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid, an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface, and an indicator function is introduced to update the fluid properties accurately. The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points, and then the surface tension is directly computed by using the normal vector and curvature of the interface. Two benchmark problems, including Laplace＇s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation. Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.

Gradient-augmented hybrid interface capturing method for incompressible two-phase flow

Motivated by inconveniences of present hybrid methods,a gradient-augmented hybrid interface capturing method（GAHM） is presented for incompressible two-phase flow.A front tracking method（FTM） is used as the skeleton of the GAHM for low mass loss and resources.Smooth eulerian level set values are calculated from the FTM interface,and are used for a local interface reconstruction.The reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology change.The cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial cell.The performance of the GAHM is carefully evaluated in a benchmark test.Results show significant improvements of mass loss,clear subgrid structures,highly accurate derivatives（normals and curvatures） and low cost.The GAHM is further coupled with an incompressible multiphase flow solver,Super CE/SE,for more complex and practical applications.The updated solver is evaluated through comparison with an early droplet research.

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.

THE SOLUTION FOR TRANSIENT TWO-PHASE FLOW BY SPLIT FLUX VECTOR METHOD

In this paper the transient two-phase flow equations and their eigenvalues are first introduced. The flux vector is then split into subvectors which just contain a specially signed eigenvalue. Using one-sided spatial difference operators finite difference equations and their solutions are obtained. Finally comparison with experiment shows the predicted results produce good agreement with experimental data.

QUANTITATIVE ANALYSIS OF VERY WEAK ACID AND BASE BY pH-FIXED TITRATION METHOD

pH-fixed titration method for the determination of weak acids and bases has been studied in this paper.It is not necessary to know the ionization constant of weak acid or base and the concentration of titrant. This method had been applied to determine phenol,4-aminoantipyrine and glycine,whose ionization constants range from 10^(-10)to 10^(-12).The results were satisfactory.

Titration Method Validation of Live Vaccines against Infectious Bursal Disease

Validating a method of analysis goes through different steps, which aims at testing the normality of measurements distribution, estimating the uncertainty of the components of a measurement （i.e., accuracy and correctness）, and finally, define the control tests of non degradation of the method performances. This paper outlines the steps for validating a biological method of analysis. It involves the construction of an experimental design, a statistical model, and the preparation of an interne laboratory reference material （pilot vaccine）. The latter is used to study the impact of deviation and variation factors, in order to, optimize the analytical method, to evaluate the bias （random error）, and to calculate the uncertainty of measurement, and make the control charts. This method is applied in the titration of live viral vaccines of Gumboro disease on chicken＇s embryos fibroblasts. The experimental results show that potential influence factors related to the titration method had no significant influence on the obtained results. Taking into account these results, an operating mode has been elaborated. The finalized method proved to be faithful to standard deviation of repeatability and reproducibility of 0.21 and 0.22, respectively, with a confidence level of 95%. The calculated uncertainty of measurement is equal to 0.2, which represents the average error level of a titer. A homogeneous stock of interne laboratory reference vaccine （MRIL）, with an average titer of 5.9 log DIT 50, was produced and the control chart set in away to provide the laboratory with an important tool of control and monitoring of the viral titers evolution in time, as well as, the mastery of the validated titration method performances.

Liquid-Gas Two-Phase Flow Simulation in Mold Filling Process with Level Set Method

Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.