Effect of Hydrogen Sulfide on Condensation and Flow of Gas Condensate Fluids in Porous Media

Condensation and flow experiments were conducted at subsurface conditions in a glass micromodel using reservoir fluids with and without the hydrogen sulfide component. It has been noted that the formation of the condensing phase as well as modes of condensate flow are similar for both fluids. Furthermore, an additional condensate transport mechanism, termed lamella flow, was observed with the sour fluid. It has been concluded that core flow experiments conducted with sweet reservoir fluid should reproduce the flow of sour fluid to a large extent.     

近井地带凝析油聚集机理研究综述

凝析气藏衰竭开发过程中,当压力降到露点压力以下时,凝析油会在近井地带迅速聚集,严重损害凝析气井的生产能力.从实验和理论上综述凝析油在近井地带的聚集机理,通过研究凝析气藏衰竭开发过程中出现在近井地带的凝析油气流动的不同流型和相态特征,评价近井地带可动凝析油和不可动凝析油对气体流动性的影响.准确认识凝析油气的聚集特征和聚集机理对凝析气藏的高效开发具有重要的指导意义.      

Nonsteady sink and source in a rotating fluid

The effect of the Coriolis force on the nonsteady two-dimensional sink or source flow has been studied theoretically. With the assumptions of incompressibility and invisddity of fluid, the equations governing the flow are still non-linear. However, a set of analytical and exact solutions is obtained for the velocity and pressure distributions. The result shows that no significant vortex flow can be induced by a source flow, the circulation produced there mainly is because the observer is moving with the rotating system; however, a sink will always induce a vortex, the strength of circulation in the sink flow is simply in proportion to the rotating speed of the system and the time integrated sink strength. As the system is under a constant rotating speed, the circulation will vanish only when the time integrated sink strength vanishes. Several special cases of sink strength are examined and their results are presented in this paper. The purpose of this study is mainly to relate the strength of circulation with the strength of sink and source. Consequently, it- can be applied to the weather forecast for hurricanes or tornadoes.     

Zur Kondensation an der Wand dampfdurchströmter Kanäle mit veränderlichem Querschnitt

The flow of pure vapor in channels with variable cross section and cooled walls is considered. The balances for mass, energy and momentum and the transport of heat across the film of condensate are dealt by a finite difference method. Selected examples show that convergent channels improve condensation compared with channels of constant cross section. Excessive temperature drop by acceleration, however, must be avoided. Adversed pressure gradient may cause separation of the condensate film. The influence of the following parameters is discussed: gravity, increased friction, entrainment of condensat, cocurrent and countercurrent flow of the cooling medium and finite resistance of heat of channel wall. The shape of velocity profiles of the condensate is shown as a function of the pressure gradient.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

One-dimensional water vapor expansion with condensation at higher pressures

Numerical calculation of nucleating water vapor flow through a nozzle at high pressure is presented. Contrary to the classical approach which takes into account only latent heat release due to condensation, the vapor phase removal and change of vapor structure has also been taken into account. This more general treatment of condensing vapor is needed when the influence of condensation of vapors at higher pressure on gasdynamic behavior of the flow is considered. At higher pressure the radius of critical droplets can be comparable with the mean free path. This has to be taken into account when the equation of droplets' growth is derived. A modified set of equations using Hertz and Knudsen models for droplet growth is proposed.     

Experimental investigation of flow boiling characteristics in a cross-linked microchannel heat sink

This paper experimentally investigates flow boiling characteristics in a cross-linked microchannel heat sink at low mass fluxes and high heat fluxes. The heat sink consists of 45 straight microchannels each with a hydraulic diameter of 248 μm and heated length of 16 mm. Three cross-links, of width 500 μm, are introduced in the present microchannel heat sink to achieve better temperature uniformity and to avoid flow mal-distribution. Flow visualization, flow instability, two-phase pressure drop, and two-phase heat transfer measurements are conducted using the dielectric coolant FC-72 over a range of heat flux from 7.2 to 104.2 kW/m², mass flux from 99 to 290 kg/m² s, and exit quality from 0.01 to 0.71. Thermochromic liquid crystals are used in the present study as full-field surface temperature sensors to map the temperature distribution on the heat sink surface. Flow visualization studies indicate that the observed flow regime is primarily slug. Visual observations of flow patterns in the cross-links demonstrate that bubbles nucleate and grow rapidly on the surface of the cross-links and in the tangential direction at the microchannels’ entrance due to the effect of circulations generated in those regions. The two-phase pressure drop strongly increases with the exit quality, at x_e,o < 0.3, and the two-phase frictional pressure drop increases by a factor of 1.6–2 compared to the straight microchannel heat sink. The flow boiling heat transfer coefficient increases with increasing exit quality at a constant mass flux, which is caused by the dominance of the nucleation boiling mechanism in the cross-link region.     

Positive Effect of Flow Velocity on Gas–Condensate Relative Permeability: Network Modelling and Comparison with Experimental Results

Positive velocity dependency of relative permeability of gas–condensate systems, which has been observed in many different core experiments, is now well acknowledged. The above behaviour, which is due to two-phase flow coupling in condensing systems at low interfacial tension (IFT) conditions, was simulated using a 3D pore network model. The steady-dynamic bond network model developed for this purpose was also equipped with a novel anchoring technique, which was based on the equivalent hydraulic length concept adopted from fluid flow through pipes. The available rock data on the co-ordination number, capillary pressure, absolute permeability, porosity and one set of measured relative permeability curves were utilised to anchor the capillary, volumetric and flow characteristics of the constructed network model to those properties of the real core sample. Then the model was used to predict the effective permeability values at other IFT and velocity levels. There is a reasonable quantitative agreement between the predicted and measured relative permeability values affected by the coupling rate effect.     

MODELLING OF RELEASE OF GAS FROM HIGH-PRESSURE PIPELINES

The problem investigated is the break of a high-pressure pipeline carrying natural single-phase gas which may condensate (retrograde) when the pressure drops. Single-phase non-ideal gas is assumed using a general- ized equation of state. Taking advantage of the choked massflow condition, the break is split into a pipe flow problem and a dispersion flow problem, both solved using a finite difference control volume scheme. The transient flow field from the pipeline break location is expanded analytically, using an approximation of the governing equations, until ambient pressure is reached and matched to the corresponding gas dispersion flow field using as subgrid model a jet box with a time-varying equivalent nozzle area as an internal boundary of the dispersion domain. The turbulence models used for the pipe and dispersion flow fields are an empirical model of Reichard and the k–ϵ model for buoyant flow respectively. The pipe flow simulations indicate that the flow from the pipeline might include dispersed condensate which will affect quantitatively the mass flow rate from the pipeline and qualitatively the gas dispersion if the condensate rains out. The transient dispersion simulation shows that an entrainment flow field develops and mixes supersaturated gas with ambient warmer air to an unsaturated mixture. Because of the inertia of the ambient air, it takes time to develop the entrainment flow field. As a consequence of this and the decay of the mass flow with time, the lower flammability limit of the gas–air mixture reaches its most remote downstream position relatively early in the simulation (about 15 s) and withdraws closer to the break location.     

Network Modeling of Non-Darcy Flow Through Porous Media

Darcy's law is inadequate for describing high-velocity gas flow in porous media, which occurs in the near well-bore region of high capacity gas and condensate reservoirs. This study is directed at understanding the non-Darcy flow behavior. A pore-level network model has been developed to describe high velocity flow. The inputs to the model are pore size distributions and network coordination numbers. The outputs are permeability, non-Darcy coefficient, tortuousity and porosity. The additional pressure gradient term is found to be proportional to the square of the velocity in accordance with the Forchheimer's equation. The correlation between the non-Darcy coefficient and other flow properties (the permeability, the porosity and the tortuousity) is found to depend on the morphological parameters being changed. General correlations are derived between these flow properties.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (Ⅰ)

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications,some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

First,the notions of the measure of noncompactnees and condensing set- valued mappings are introduced in locally FC-uniform spaces without convexity struc- ture.A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces.As applications, some new equilibrium existence theorems of generalized game involving condensing map- pings are established in locally FC-uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.     

Exact solutions for nonlinear transient flow model including a quadratic gradient term

The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform.Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.     

A Well in a ??Target?? Stratum of a Two-Layered Formation: The Muskat?CRiesenkampf Solution Revisited

Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a ??target?? layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the ??target?? layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.     

Near-Critical Gas–Liquid Flow in Porous Media: Monovariant Model, Analytical Solutions and Convective Mass Exchange Effects

We examine a class of hydrocarbon reservoirs whose thermodynamic state remains close to the critical point during the all period of reservoir exploitation. Such a situation is typical for the so-called gas–condensate systems, in which the liquid phase is formed from gas when pressure decreases. Due to proximity to critical point, the mixture contains many components which are neutral with respect to the phase state. This determines a low thermodynamic degree of freedom of the system. As the results, the mathematical flow model allows a significant reduction in the number of conservation equations, whatever the number of chemical components. In the vicinity of a well, the system may be reduced to one transport equation for saturation. This nonlinear model yields exact analytical solutions when the flow is self-similar. In more general case of flow, we develop partially linearized solutions which are shown to be sufficiently exact. The spectrum of examined cases covers the flow in a medium with a sharp heterogeneity and a sharp variation in the flow rate. A significant relative gas flow past liquid gives rise to a convective mass exchange phenomenon which appears highly different from that observed in static. In the case of a medium discontinuity, the convective mass exchange gives rise to a phenomenon of condensate saturation billow formation. A sharp variation in the flow rate leads to a hysteretic behavior of the saturation field.     

One dimensional numerical simulation for steady annular condensation flow in rectangular microchannels

A one dimensional model for steady annular condensation flow in rectangular microchannels is developed and numerically solved under constant heat flux condition. The results indicate that the annular condensation length is determined by the contact angle, heat flux, vapor pressure, hydraulic diameter and aspect ratio of rectangular microchannels. A larger inlet vapor pressure and hydraulic diameter or a smaller heat flux and contact angle can all result in a longer annular condensation length. In addition, the simulation results of steady annular condensation flow in rectangular microchannels are compared with that in triangular microchannels. The differences in curvature radius, condensate pressure and velocity, vapor velocity distributions in rectangular and triangular microchannels under the same conditions verify the considerable influence of cross-section shape on micro flow condensation.     

Film thickness measurement with an ultrasonic transducer

A technique for measuring condensate film thickness using an ultrasonic transducer is described. In the experiment, the condensate film thickness with R-113 and FC-72 (a fluorinert compound developed by the 3M Company) condensing on the horizontal lower surface of a rectangular duct was measured at several locations. From the measured values a power law relation between the condensate film thickness and the axial distance from the leading edge of the condensing surface was derived by regression analysis. Assuming a linear temperature profile in the condensate film, local and average heat transfer coefficients were computed from the condensate film thickness. The average heat transfer coefficients were compared with the values obtained by measuring the heat transfer rate to the coolant. The two values were within ±12% of each other. As yet there is no satisfactory analytical model to predict the local heat transfer coefficient even in the annular condensation regime. One of the main difficulties in modeling the condensation is the lack of a suitable model to predict the interfacial shear stress. With the measurement of the film thickness it is possible to determine the interfacial shear stress. It is hoped that the shear stresses so determined will lead to the development of a satisfactory model for interfacial shear stress with condensation.     

An equation set for non-equilibrium two phase flow,and an analysis of some aspects of choking,acoustic propagation,and losses in low pressure wet steam

An equation set for multidimensional, time variant, inviscid flow of a condensing vapour is presented. The equations include the effects of relative motion between the primary gas phase and the suspended liquid droplets. They have been formulated with steam turbine applications in mind but are also relevant to problems of gas-particle and liquid bubble flow.It is shown that the critical velocity in one dimensional choking of low pressure wet steam is identical with the “frozen” speed of acoustic propagation, and the variation of choking mass flow with respect to equilibrium based calculations is described. Results obtained with two different models of droplet growth are compared, and simple formulae for calculating limiting values of choking flow are given. A generalised loss coefficient including the effects of thermodynamic and kinematic non-equilibrium is introduced.     

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.