Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.     

Generating line spectra from experimental responses. Part IV: Application to experimental data

The previously reported algorithms for deriving line spectra (respondance time distributions) from synthetic or smoothed experimental responses is here extended to experimental data. The earlier algorithm was modified to improve performance in the presence of experimental errors. The effect of smoothing the data with the aid of the cubic spline function was examined.The performance of the modified algorithm was studied comprehensively. Auto-predictions and cross-predictions of storage and loss compliances from the generated line spectra were in excellent agreement. In equally good agreement were the line spectra obtained from compliance data and from stress relaxation data obtained on the same material.     

New hybrid Cartesian cut cell/enriched multipoint flux approximation approach for modelling and quantification of structural uncertainties in petroleum reservoirs

Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir rock and fluid properties and its geometrical structure calls for history matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history‐matched models, which might result in different predictions of reservoir performance. Uncertainty quantification narrows down the model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of uncertainty quantification ignore large‐scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more significantly compared with petrophysical uncertainty. Quantification of structural uncertainty has been usually considered impracticable because of the need for global regridding at each step of history matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian cut cell method that decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of history matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of a class of locally conservative flux continuous methods (extended enriched multipoint flux approximation method or extended EMPFA). The robustness and consistency of the proposed hybrid Cartesian cut cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic model of uncertain structures. Copyright © 2015 John Wiley & Sons, Ltd.     

Co-history Matching: A Way Forward for Estimating Representative Saturation Functions

Core-scale experiments and analyses would often lead to estimation of saturation functions (relative permeability and capillary pressure). However, despite previous attempts on developing analytical and numerical methods, the estimated flow functions may not be representative of coreflood experiments when it comes to predicting similar experiments due to non-uniqueness issues of inverse problems. In this work, a novel approach was developed for estimation of relative permeability and capillary pressure simultaneously using the results of “multiple” corefloods together, which is called “co-history matching.” To examine this methodology, a synthetic (numerical) model was considered using core properties obtained from pore network model. The outcome was satisfactorily similar to original saturation functions. Also, two real coreflood experiments were performed where water at high and low rates were injected under reservoir conditions (live fluid systems) using a carbonate reservoir core. The results indicated that the profiles of oil recovery and differential pressure (dP) would be significantly affected by injection rate scenarios in non-water wet systems. The outcome of co-history matching could indicate that, one set of relative permeability and capillary pressure curves can reproduce the experimental data for all corefloods.     

井筒气液两相流对致密气压裂水平井试井的影响

多段压裂水平井技术是目前开采致密气最常用的方法之一,在致密气压裂水平井试井测试中常常伴随着一定的产水量,井筒气液两相流会增加井筒流体的流动阻力,加大井筒流体流动对试井解释的影响.为了明确井筒气液两相流对致密气藏压裂水平井试井的影响,提高产水致密气压裂水平井的试井解释精度,建立了一种井筒气液两相流与地层渗流耦合的试井模型,采用数值方法对模型进行求解,获得了考虑井筒气液两相流的压裂水平井试井理论曲线、压力场分布及裂缝产量分布.研究结果表明:井筒气液两相流会增加试井理论曲线中压力和压力导数值,造成靠近入窗点的压力扩散要快于远离入窗点的压力扩散,引起靠近入窗点的裂缝产量要高于远离入窗点的裂缝产量.现场实例分析进一步说明,不考虑井筒两相流可能会对产水压裂水平井的试井解释结果产生很大误差,主要表现为水平井筒假设为无限大导流能力会使得拟合得到的表皮系数偏大,将测试点视为入窗点会使得拟合得到的原始地层压力偏小.所建立的考虑井筒两相流的压裂水平井试井模型为产水致密气井试井资料的正确解释提供了重要技术保障.      

The analysis of two-phase flow instability in a vertical U-tube evaporator

This paper describes both the experimental and theoretical analysis of two-phase flow instability in a vertical U-tube evaporator. In the experiment investigation the effects of various parameters on flow instability are studied by using Freon-12 as working medium and the influence of flow oscillations on heat transfer deterioration is obtained. The mathematical model to describe flow oscillations occurring in the vertical U-tube with flow stagnation and upward movement of bubbles due to buoyancy in the heated downcomer is developed. The finite differential equations are solved by using a modified two-step iteration technique. The calculated results are in good agreement with the experimental data.     

An efficient method for the prediction of the motion of individual bubbles

We present a method for the simulation of two-phase flows which can be applied to problems characterised by the presence of up to several hundreds of gas bubbles. The bubble model is kept simple, requiring only six parameters to describe the shape of a single bubble. The model is coupled to a conventional time discrete finite-volume scheme for the solution of the Navier–Stokes equations by the density field which is calculated on basis of the information on the positions and the shapes of the bubbles before each time step. The motion of the bubbles is in turn calculated from an analysis of the computed flow field. Systematical errors due to simplifications are eliminated by the introduction of correction factors. For a selection of fluid dynamical problems, the results of simulations using the method are compared to experimental data. Good quantitative agreement could be found.     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

Hybrid stress analysis of vibrating plates using holographic interferometry and finite elements

The work reported herein is concerned with an investigation of the potential of mating time-average holography and static-finite-element analysis (a ‘hybrid’ stress-analysis technique) in solving dynamic problems. The model studied is a vibrating thin rectangular cantilever plate. Realtime holography was used to locate natural vibrating modes of the plate. Experimental data were smoothed to remove scatter using a spline-like procedure in one or two dimensions, as applicable. Two methods of smoothing the experimental displacement data used in the hybrid procedure were considered. The first involved preprocessing (smoothing) the data before they were incorporated into the numerical model, while the second involved smoothing the data as part of the solution process. In both instances the amount of smoothing was specified by the user. The first and fourth vibrational modes were investigated. The results were compared to a NASTRAN dynamic solution and to a Ritz method series solution with very good results.     

Anisotropic hardening and non-associated flow in proportional loading of sheet metals

Conventional isotropic hardening models constrain the shape of the yield function to remain fixed throughout plastic deformation. However, experiments show that hardening is only approximately isotropic under conditions of proportional loading, giving rise to systematic errors in calculation of stresses based on models that impose the constraint. Five different material data for aluminum and stainless steel alloys are used to calibrate and evaluate five material models, ranging in complexity from a von Mises’ model based on isotropic hardening to a non- associated flow rule (AFR) model based on anisotropic hardening. A new model is described in which four stress–strain functions are explicitly integrated into the yield criterion in closed form definition of the yield condition. The model is based on a non-AFR so that this integration does not affect the accuracy of the plastic strain components defined by the gradient of a separate plastic potential function. The model not only enables the elimination of systematic errors for loading along the four loading conditions, but also leads to a significant reduction of systematic errors in other loading conditions to no higher than 1.5% of the magnitude of the predicted stresses, far less that errors obtained under isotropic hardening, and at a level comparable to experimental uncertainty in the stress measurement. The model is expected to lead to a significant improvement in stress prediction under conditions dominated by proportional loading, and this is expected to directly improve the accuracy of springback, tearing, and earing predictions for these processes. In addition, it is shown that there is no consequence on MK necking localization due to the saturation of the yield surface in pure shear that occurs with the aluminum alloys using the present model.     

High-Order Vibrations’ Dynamic Scaling Laws of Distorted Scaled Models of Thin-Walled Short Cylindrical Shells

In this study, we investigate the dynamic scaling laws of geometrically distorted models for predicting dynamic characteristics of thin-walled short cylindrical shells. Approximate and accurate analysis methods for obtaining the scaling laws are introduced. Two coefficient functions are established in deriving high-order scaling laws for a narrow range distorted model. Then a modified function is obtained by using numerical analysis, in order to modify the errors of wide range distorted models. The general form of the high-order scaling laws of thin-walled short cylindrical shells is also developed. To be practical, a process of detecting scaling laws by experimental operation is summarized, and the applicability of scaling laws is validated by using experimental data. Although there are some limitations in practice, the scaling laws of the thin-walled short cylindrical shell still have the ability to predict the prototype with good accuracy.     

An Uncertainty Estimator for Slitting Method Residual Stress Measurements Including the Influence of Regularization

This paper describes the development of a new uncertainty estimator for slitting method residual stress measurements. The new uncertainty estimator accounts for uncertainty in the regularization-based smoothing included in the residual stress calculation procedure, which is called regularization uncertainty. The work describes a means to quantify regularization uncertainty and then, in the context of a numerical experiment, compares estimated uncertainty to known errors. The paper further compares a first-order uncertainty estimate, established by a repeatability experiment, to the new uncertainty estimator and finds good correlation between the two estimates of precision. Furthermore, the work establishes a procedure for automated determination of the regularization parameter value that minimizes total uncertainty. In summary, the work shows that uncertainty in the regularization parameter is a significant contributor to the total uncertainty in slitting method measurements and that the new uncertainty estimator provides a reasonable estimate of single measurement uncertainty.

     

基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象,采用颜色模型模拟出口处粘弹流体和空气的两相流动,通过重新标色获得两种流体的界面,并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较,发现格子Boltzmann两相模型结果与解析解和实验结果相吻合,相比于单相模型,收敛速度更快,解的稳定性更高．研究了流道尺寸对胀大率的影响,并对挤出胀大的内在机理进行了分析．     

Some peculiarities of two-phase flow in nozzles

Calculations are conducted for unidimensional two-phase flow in nozzles for a wide range of particle concentrations and dimensions. It is established that there exists a maximum in loss of specific momentum due to a lag in particle velocity and temperature relative to the gas. The results obtained are compared with calculations using linearized theory as well as with experimental data. The agreement between calculation and experiment is noted. Equilibrium flow of a two-phase mixture with solidification of liquid particles is considered. The presence of an anomalous flow region is established, where in the model of an ideal unidimensional equilibrium flow in a nozzle with discharge into a vacuum the presence of two successively located minimum sections is necessary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–57, May–June, 1973.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

A tomographic PIV resolution study based on homogeneous isotropic turbulence DNS data

In order to accurately assess measurement resolution and measurement uncertainty in DPIV and TPIV measurements, a series of simulations were conducted based on the flow field from a homogeneous isotropic turbulence data set (Re _λ = 141). The effect of noise and spatial resolution was quantified by examining the local and global errors in the velocity, vorticity and dissipation fields in addition to other properties of interest such as the flow divergence, topological invariants and energy spectra. In order to accurately capture the instantaneous gradient fields and calculate sensitive quantities such as the dissipation rate, a minimum resolution of x/η = 3 is required, with smoothing recommended for the TPIV results to control the inherently higher noise levels. Comparing these results with experimental data showed that while the attenuation of velocity and gradient quantities was predicted well, higher noise levels in the experimental data led increased divergence.     

An adaptive multigrid finite-volume scheme for incompressible Navier–Stokes equations

An algorithm for the solutions of the two-dimensional incompressible Navier–Stokes equations is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. It is based on an artificial compressibility method and uses higher-order upwind finite-volume techniques for the convective terms and a second-order finite-volume technique for the viscous terms. Three upwind schemes for discretizing convective terms are proposed here. An interesting result is that the solutions computed by one of them is not sensitive to the value of the artificial compressibility parameter. A second-order, two-step Runge–Kutta integration coupling with an implicit residual smoothing and with a multigrid method is used for achieving fast convergence for both steady- and unsteady-state problems. The numerical results agree well with experimental and other numerical data. A comparison with an analytically exact solution is performed to verify the space and time accuracy of the algorithm.     

MODELLING TWO-PHASE FLOW-EXCITED DAMPING AND FLUIDELASTIC INSTABILITY IN TUBE ARRAYS

This paper reports the results of an experimental study of the flow-induced vibration of a heat exchanger tube array subjected to two-phase cross-flow of refrigerant 11. The primary concern of the research was to develop a methodology for predicting the critical flow velocities for fluidelastic instability which better characterize the physics of two-phase flows. A new method is proposed for calculating the average fluid density and equivalent flow velocity of the two-phase fluid, using a newly developed void fraction model to account for the difference in velocity between the gas and liquid phases. Additionally, damping measurements in two-phase flow were made and compared with the data of other researchers who used a variety of modelling fluids. The results show that the two-phase damping follows a similar trend with respect to homogeneous void fraction, and when normalized, agree well with the data in the literature. The fluidelastic threshold data of several researchers who used a variety of fluids, is re-examined using the proposed void fraction model, and the results show a remarkable change in trend with flow regime. The data corresponding to the bubbly flow regime shows no significant deviation from the trend established by Connors' theory. However, the data corresponding to the intermittent flow regime show a significant decrease in stability which is nearly independent of the mass-damping parameter. It is believed that the velocity fluctuations that are inherent in the intermittent flow regime are responsible for tripping the instability, causing lower than expected stability of the bundle.     

Mathematical Modeling of Two-Phase Convective Flows with Fine Particles

A two-phase convective flow with convection caused by a nonuniform distribution of solid particles is considered. The use of the mathematical model proposed is illustrated by an example of a two-phase flow in a shutter sedimentation reservoir.