Discontinuous Galerkin method for solving the black‐oil problem in porous media

We introduce a new algorithm for solving the three‐component three‐phase flow problem in two‐dimensional and three‐dimensional heterogeneous media. The oil and gas components can be found in the liquid and vapor phases, whereas the aqueous phase is only composed of water component. The numerical scheme employs a sequential implicit formulation discretized with discontinuous finite elements. Capillarity and gravity effects are included. The method is shown to be accurate and robust for several test problems. It has been carefully designed so that calculation of appearance and disappearance of phases does not require additional steps.     

Multiphase transient flow model in wellbore annuli during gas kick in deepwater drilling based on oil-based mud

Transient-state gas and oil-based mud (OBM) two-phase flow in wellbore annuli will occur during gas kick. The phase behavior of influx gas and OBM will make the gas kick during OBM drilling more complicated. There are three possible cases in an annulus: only liquid flow in the entire annulus, gas and liquid two-phase flow in part of the annulus, and gas and liquid two-phase flow in the entire annulus. First, the phase behaviors of gas and OBM in wellbore annuli are studied based on the phase behavior of methane and diesel. A multiphase transient-flow model in annuli during gas kick based on OBM is then established based on gas–liquid two-phase flow theory and on flash theory in annuli. The influences of phase behavior in annuli and annular geometry are taken into account. The local flow parameters are predicted by the hydrodynamic models and the local thermodynamic parameters are predicted by the heat-transfer models in the corresponding flow pattern. The proposed model has a better performance, compared with two other models, against the published experimental data. Finally, the variation of pit gain, well-bottom hole pressure, and gas void fraction are obtained, leading to a better understanding of the occurrence and evolution mechanism of gas kick during deepwater drilling.     

Transient modeling of non-isothermal, dispersed two-phase flow in natural gas pipelines

Unsteady-state or transient two-phase flow, caused by any change in rates, pressures or temperature at any location in a two-phase flow line, may last from a few seconds to several hours. In general, these changes are an order of magnitude longer than the transient encountered during single-phase flow. The primary reason for this phenomenon is that the velocity of wave propagation in a two-phase mixture is significantly slower. Interfacial transfer of mass, momentum and energy further complicate the problem. It is primarily due to the numerical difficulties anticipated in accurately modeling transient two-phase flow that the state of the art in this important area is restricted to a handful of studies with direct applicability to petroleum and gas engineering. A limited amount of information on the subject of two-phase transport phenomena is available in the petroleum engineering literature. Most of the publications for two-phase flow of gas assume that temperature is constant over the entire length of the pipeline.This study is the first effort to simulate the non-isothermal, one-dimensional, transient homogenous two-phase flow gas pipeline system using two-fluid conservation equations. The modified Peng–Robinson equation of state is used to calculate the vapor–liquid equilibrium in multi-component natural gas to find the vapor and liquid compressibility factors. Mass transfer between the gas and the liquid phases is treated rigorously through flash calculation, making the algorithm capable of handling retrograde condensation. The liquid droplets are assumed to be spheres of uniform size, evenly dispersed throughout the gas phase.The method of solution is the fully implicit finite difference method. This method is stable for gas pipeline simulations when using a large time step and therefore minimizes the computation time. The algorithm used to solve the non-linear finite difference thermo-fluid equations for two-phase flow through a pipe is based on the Newton–Raphson method.The results show that the liquid condensate holdup is a strong function of temperature, pressure, mass flow rate, and mixture composition. Also, the fully implicit method has advantages, such as the guaranteed stability for large time step, which is very useful for simulating long-term transients in natural gas pipeline systems.     

Modeling of three dimensional thermocapillary flows with evaporation at the interface based on the solutions of a special type of the convection equations

Theoretical and numerical study of the convection processes, which are accompanied by evaporation/condensation, in the framework of new non-standard problem is largely motivated by new physical experiments. One of the principal questions is to understand the character and to evaluate the degree of influence of particular factors or their combined action on the structure of the joint flows of liquid and gas-vapor mixture. The flow topology is determined by four main mechanisms: natural and thermocapillary convection, tangential stresses and mass transfer due to evaporation at the interface. The mathematical modeling of the fluid flows in an infinite channel with a rectangular cross section is carried out on the basis of the solution of a special type of the convection equations. The effects of thermodiffusion and diffusive thermal conductivity in the gas phase and evaporation at the thermocapillary interface are taken into consideration. Numerical investigations are performed for the liquid – gas (ethanol – nitrogen) system under normal and low gravity. The fluid flows are characterized as translational and progressively rotational motions and can be realized in various forms.     

Investigation of Flow Rate Limitation in Open Capillary Channel

A forced liquid flow through an open capillary channel with free liquid surfaces was investigated experimentally under low gravity. Since the free surfaces can only withstand a certain difference between the liquid pressure and the ambient pressure the flow rate in the channel is limited. The maximum flow rate is achieved when the surfaces collapse. The aim of the investigation is to determine the limitation of the flow rate and the corresponding critical flow velocity. The investigations were performed on board the sounding rocket mission TEXUS‐37 providing a reduced gravity environment of 10^‐4 g in all axis for 6 minutes.     

Homogenization of compressible two-phase two-component flow in porous media

The paper is devoted to the homogenization of immiscible compressible two-phase two-component flow in heterogeneous porous media. We consider liquid and gas phases, two-component (water and hydrogen) flow in a porous reservoir with periodic microstructure, modeling the hydrogen migration through engineered and geological barriers for a deep repository for radioactive waste. Phase exchange, capillary effects included by the Darcy–Muskat law and Fickian diffusion are taken into account. The hydrogen in the gas phase is supposed compressible and could be dissolved into the water obeying the Henry law. The flow is then described by the conservation of the mass for each component. The microscopic model is written in terms of the phase formulation, i.e. the liquid saturation phase and the gas pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion–convection equation for the liquid saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem. We rigorously justify this homogenization process for the problem by using the two-scale convergence.     

弱重力场中的平面活塞运动

本文分析了弱重力场中等速活塞运动驱动恒星大气的气体动力学过程.在活塞前面,气体被压缩.压缩气体利用其部分内能,以及有些情况下其动能,以克服外加重力.当逃逸速度与等离子体速度之比值为一小参数时,所有量可对小参数展开,基态解给出均匀流,如同没有重力场的气体动力学所讨论的那样.一阶关系给出外加引力场对流场的影响,即激波强度变化不大而气体内能不断耗散.对于强激波和活塞附近,近似得到的分析解有类似的特征.由于外加重力场在天体物理和大气物理过程中的重要性,这些结果对于恒星和行星大气中瞬变过程的机制会有启发.     

Mach configuration in pseudo-stationary compressible flow

This paper is devoted to studying the local structure of Mach reflection, which occurs in the problem of the shock front hitting a ramp. The compressible flow is described by the full unsteady Euler system of gas dynamics. Because of the special geometry, the motion of the fluid can be described by self-similar coordinates, so that the unsteady flow becomes a pseudo-stationary flow in this coordinate system. When the slope of the ramp is less than a critical value, the Mach reflection occurs. The wave configuration in Mach reflection is composed of three shock fronts and a slip line bearing contact discontinuity. The local existence of a flow field with such a configuration under some assumptions is proved in this paper. Our result confirms the reasonableness of the corresponding physical observations and numerical computations in Mach reflection.

In order to prove the result, we formulate the problem to a free boundary value problem of a pseudo-stationary Euler system. In this problem two unknown shock fronts are the free boundary, and the slip line is also an unknown curve inside the flow field. The proof contains some crucial ingredients. The slip line will be transformed to a fixed straight line by a generalized Lagrange transformation. The whole free boundary value problem will be decomposed to a fixed boundary value problem of the Euler system and a problem to updating the location of the shock front. The Euler system in the subsonic region is an elliptic-hyperbolic composite system, which will be decoupled to the elliptic part and the hyperbolic part at the level of principal parts. Then some sophisticated estimates and a suitable iterative scheme are established. The proof leads to the existence and stability of the local structure of Mach reflection.

     

川渝裂缝性地层自动压井环空多相压力波速特性研究北大核心CSCD

考虑虚拟质量力、环空沿程压力、气液相间阻力、气体滑脱、环空空隙率等因素,基于小扰动理论,提出了裂缝性地层自动压井环空多相压力波速数学模型,结合半显式差分方法,以彭州PZ-5-3D井(垂深5827 m)为实例,对模型编程求解.结果表明:裂缝性地层出气具有段塞流特点,随空隙率增大,压力波速呈现先减小后增大趋势;空隙率在0%至16%区间,压力波速以液弹为主,压力波速呈急剧下降趋势;空隙率在16%至40%区间,压力波速趋于平缓恒定值;空隙率在42%至100%区间,压力波速呈现增大趋势,压力波速以气弹为主;随环空井深减小,环空空隙率减小,压力波速整体呈现减小趋势;随压井循环排气井口回压增大,压力波速整体呈现增大趋势;环空空隙率在0%至13%区间内,气体滑脱速度对压力波速影响不大;环空空隙率在13%至85%区间内,随气体滑脱速度增大,压力波速呈现减小趋势;节流阀调阀时间间隔与井底压力响应时间具有跟随性,随井底压力响应时间增大,调阀时间间隔增大.     

Numerical simulation two phase flows of casting filling process using SOLA particle level set method

Mould filling process is a typical gas–liquid metal two phase flow phenomenon. Numerical simulation of the two phase flows of mould filling process can be used to properly predicate the back pressure effect, the gas entrapment defects, and better understand the complex motions of the gas phase and the liquid phase. In this paper, a novel sharp interface incompressible two phase numerical model for mould filling process is presented. A simple ghost fluid method like discretization method and a density evaluation method at face centers of finite difference staggered grid are proposed to overcome the difficulties when solving two phase Navier–Stokes equations with large-density ratio and large-viscosity ratio. A new mass conservation particle level set method is developed to capture the gas–liquid metal phase interface. The classical pressure-correction based SOLA algorithm is modified to solve the two phase Navier–Stokes equations. Two numerical tests including the Zalesak disk problem and the broken dam problem are used to demonstrate the accuracy of the present method. The numerical method is then adopted to simulate three mould filling examples including two high speed CCD camera imaging water filling experiments and an in situ X-ray imaging experiment of pure aluminum filling. The simulation results are in good agreement with the experiments.     

Piston Problems of Two-Dimensional Chaplygin Gas

In this paper, the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas. The angle of the piston is allowed to vary in a wide range. The piston can be pushed forward into the static gas, or pulled back from the gas. The global existence of solution to the piston problem with any initial speed is established, and the structures of the global solutions are clearly described. The authors find that for the proceeding piston problem the front shock can be detached, attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston; while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.     

Existence of Neutral Rayleigh Waves in the Hagen–Poiseuille Flow Through a Pipe of Circular Cross Section

The inviscid neutral stability of Hagen–Poiseuille flow through a circular pipe is studied using both analytical and numerical techniques. A zero phase shift is applied across the critical surface to represent the effects of strong nonlinearity. Using a form of Sturm's comparison theorem it is possible to prove that no neutral solutions exist if a combination of the axial and azimuthal wave numbers of the perturbation exceeds a critical value. As a consequence, the physical problem admits only neutral solutions for an azimuthal wave number of unity.     

On Disturbances to a Stratified Mixing Layer

Using a nonlinear critical layer analysis, we examine the behavior of disturbances to the Holmboe model of a stratified shear layer for Richardson numbers 0相似文献   

带激波的一维非定常两相流动的数值模拟

本文将处理带激波的单相气体非定常流动问题的两种高分辨数值方法(随机取样法和二阶GRP有限差分法)推广应用于气固悬浮体(亦称含灰气体)两相情况,计算了含灰气体激波管中两相激波特性、波后流场结构及气固两相流动参数随时间的变化.数值结果表明:这两种方法均能给出带有尖锐间断阵面的两相激波松弛结构.二阶GRP方法在计算精度和机时耗用等方面优于随机取样法.     

A numerical algorithm for flame propagation in premixed gases

The propagation speed of a premixed laminar flame or a weak deflagration wave is not uniquely determined in the hyperbolic theory of reactive gas flow. In this paper, we take a hyperbolic system of conservation laws as a governing system of equations for reacting gases and propose an algorithm to determine a wave propagation speed uniquely. The wave speed and states around a flame are computed through solving a Riemann problem near a flame in the phase space. The Riemann problem can be solved by combining the information from the internal wave structure, which is ignored in the hyperbolic approximation, and characteristic information. Therefore, the wave speed comes to depend on the internal variables such as viscosity and diffusion. This method can be used to track a premixed laminar flame when combined with any front tracking method. Some computational results are also presented.     

Transport and Reaction Processes in Concrete at High Temperatures

Simulating processes in concrete at high temperatures requires coupled formulation of transport and reaction. Transport can be formulated using balance equations for mass and heat as well as constitutive equations. The equations have to be valid in the whole temperature range from 293 K up to 1000 K. Instantaneous thermodynamic equilibrium is assumed for the gas and liquid phase of water substance. Above the critical point of water, only its gas phase exist. This requires a combined mass balance, which contains vapour balance as well as the mass balance of liquid water. Rapid evaporation of water and degradation of cement minerals leads to an enormous pressure increase in the gas phase. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self-similar time-varying flows of an ideal gas with a change in the adiabatic exponent in a “reflected” shock wave

Self-similar one-dimensional time-varying problems are considered under the assumption that there is a change in the adiabatic exponent in a shock wave (SW) running (“reflected”) from a centre or axis of symmetry (later from a centre of symmetry, CS) or from a plane. The medium is an ideal (inviscid and non-heat-conducting) perfect gas with constant heat capacities. In problems with strong SW, the change in the adiabatic exponent in a gas approximately simulates physicochemical processes such as dissociation and ionization and, in the problem of the collapse of a spherical cavity in a liquid, the conversion of liquid into vapour. In both cases, the adiabatic exponent decreases on passing across a reflected SW. Problems of the collapse of a spherical cavity, the reflection of a strong SW from a centre of symmetry and a simpler problem with a self-similarity index of one are examined. When it is assumed that there is an increase in the adiabatic exponent, the self-similar solutions of the first two problems are rejected due to the decrease in entropy from the instant when the SW is reflected. When it is assumed that there is a decrease in the adiabatic exponent, the solutions of these problems only become unsuitable after a finite time has elapsed for the same reason. Up to this time when the decrease in the adiabatic exponent has not reached a certain threshold, the structure of the self-similar solution does not undergo qualitative changes. When the above-mentioned threshold is exceeded, a self-similar solution is possible if a cylindrical or spherical piston expands according to a special law from the instant of SW reflection from the CS. When there is no piston, the flow behind the reflected wave becomes non-self- similar. In the case of the deceleration of a plane flow, conditions are possible with the joining of SW from different sides to a centred rarefaction wave.     

The excitation mechanism of a shear stress induced rotary wave

The free surface flow in a vertical, cylindrical, rotating container will be considered when axis-symmetric angular and radial shear stress distributions are applied on the free surface. It is well known that in the inviscid case a rotary wave which can be described by a flow potential exists. We want to determine the stability limit of the axis-symmetric base state with respect to the rotary wave for small Ekman and Froude numbers. Under the above assumption, the critical flow conditions can be determined analytically. The results can be verified experimentally using a vertical, cylindrical container partially filled with water where the top lid rotates with a given angular velocity. Thus, the induced air flow will exert shear stresses in the angular and radial direction onto the water surface. Above a certain threshold, rotary waves can be observed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

ON INTERACTION OF SHOCK AND SOUND WAVE （I）

This paper studies the interaction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged dormain, By using the method of constructing asymptotic solutions and Newton‘siteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will he given in the following paper.