Self-Similarity in Contamination Transport to a Formation Fluid Tester During Cleanup Production

Sampling hydrocarbon fluids from a reservoir during an early phase of formation testing (typically during interruptions in drilling) represent an important step in formation evaluation targeting the characterization of composition and pressure/volume/temperature (PVT) properties of petroleum reserves required for their efficient development. A sampling job is usually accomplished with a tool, the formation tester, which can be conveyed downhole on a wireline cable, drill-pipe, or tubing. This tool has a probe and a pump allowing for the production of reservoir fluid from a small spot of a borehole wall covered by filtercake or mudcake deposited during drilling. The filtercake is built by the invasion of mud filtrate into the formation under pressure overbalance created by the mud column inside the wellbore. For this reason, after drilling, each wellbore is surrounded by a cylindrical zone saturated with mud filtrate and, prior to obtaining a sample of virgin formation fluid, cleanup production must be initiated to overcome the consequences of invasion. A 3D model of flow and contamination transport during cleanup production is considered in this article. The model assumes a piston-like displacement and no filtrate leakage through mudcake. This model leads to a multiscale problem of flow and transport in porous media with geometrical and hydrodynamic singularities. A full sensitivity analysis of its solutions has been carried out versus the initial depth of filtrate invasion and the viscosity contrast between the formation fluid and invaded mud filtrate. The numerical modeling has revealed two phases of cleanup production. During the early phase, the contamination of produced fluid is predominantly affected by a circumferential contamination transport. During the later phase, the evolution of contamination is controlled mainly by mud-filtrate displacement vertically. In the absence of viscosity contrast, both phases of cleanup can be described by exponential laws for the contamination versus the produced volume with exponents matching the empirical correlation (−5/12) and the far-field pseudospherical flow pattern (−2/3) for the early and late phases of cleanup, respectively. In the presence of viscosity contrast, the far-field asymptote holds whereas the circumferential regime of cleanup is strongly affected by the viscosity ratio. The application of solutions found to the cleanup production monitoring is briefly described.     

Numerical prediction of droplet dynamics in turbulent flow,using the level set method

In the present article, the droplet dynamics in turbulent flow is numerically predicted. The modelling is based on an interfacial marker-level set (IMLS) method, coupled with the Reynolds-averaged Navier–Stokes (RANS) equations to predict the dynamics of turbulent two-phase flow. The governing equations for time-dependent, two-dimensional and incompressible two-phase flow are described in both phases and solved separately using a control volume approach on structured cell-centred collocated grids. The topological changes of the interface are predicted by applying the level set approach. The kinematic and dynamic conditions on the interface separating the two phases are satisfied. The numerical method proposed is validated against a well-known computational fluid dynamics problem. Further, the deformation and breakup of a single droplet either suddenly moved in air or exposed to turbulent stream are numerically investigated. In general, the developed numerical method demonstrates remarkable capability in predicting the characteristics of complex turbulent two-phase flows.     

Lattice-Boltzmann simulations of flow through Fontainebleau sandstone

We report preliminary results from simulations of single-phase and two-phase flow through three-dimensional tomographic reconstructions of Fontainebleau sandstone. The simulations are performed with the lattice-Boltzmann method, a variant of lattice-gas cellular-automation models of fluid mechanics. Simulations of single-phase flow on a sample of linear size 0.2 cm yield a calculated permeability in the range 1.0–1.5 darcys, depending on direction, which compares qualitatively well with a laboratory measurement of 1.3 darcys on a sample approximately an order of magnitude larger. The sensitivity of permeability calculations to sample size, grid resolution, and choice of model parameters is quantified empirically. We also present a qualitative study of immiscible two-phase flow in a sample of linear size 0.05 cm; simulations of both drainage and imbibition are presented.     

Two-phase flow pattern identification using continuous hidden Markov model

This paper presents a new method for identifying two-phase flow regimes from the instantaneous local fluid phase signals using continuous hidden Markov model (CHMM). CHMM is known to be a very strong pattern identifier. Air–water two-phase flows were realized in a transparent vertical tube. The tube length was 2 m, and its inner diameter was 19 mm. The instantaneous local fluid phase signals were collected using a single step index multimode optical fiber probe located at the center and mid-length of the tube. Signal features required in CHMM implementation were extracted using an innovative method. Various aspects of hidden Markov modeling and their effects on the results were studied. The flow pattern results are in very good agreement with photographs of the flow captured during the experiments. In sum, the results show that hidden Markov model has a good potential in identifying two-phase flow patterns.     

Fixed stream-tube method for solving two-phase plane flow problems and its theoretical analysis

The fixed stream-tube method widely adopted in engineering field for giving an approximate solution to the two-dimensional problems of two-phase flow through porous media is summarized and an improvement has been made in this paper. Its core part, i.e., the fluid displacement within a one-dimensional stream tube with variable cross-sectional area under a given pressure difference across the tube is thoroughly studied. The existence and uniqueness of solution are proved, the exact solution, numerical solution and its convergence, stability analyses are given in this paper.     

油-气两相流管线系统振动分析及减振控制

针对油-气主管线系统的油-气两相流振动问题,建立了管线系统的动力学模型.分析计算油-气两相流在管道内的动力学特性,判断其流型;根据动量定理得到了管线各处受力的时间历程,从而确定管道系统受到的实际动载荷并求出其振动时间历程响应;分析管线系统的模态和影响振动模态的关键因素,采用合理加强原有支撑刚度和在恰当部位增加新支撑等措施,使管道系统的振动得到控制.分析结果与现场实测数据对比,验证了此振动分析方法的有效性.     

Disturbances to a rotating fluid with a sphere moving along the axis of rotation

I.IntroductionWhenabodyprojectedinthewaterisintranslationalmotionthroughwateritwillcertainlycausesdisturbances.Howtodetectthedisturbancesf'arawayfromthebodyandhowtodetermillebytheintbrlnationobtainedthepositionandvelocityofthebodyandthesiteofprojectionareimportant.Astheprojectedbodyisrotating,thefluidaroundisinauniformlyrotationrelativetothereferenceframerotatinginsynchronismwiththebody,andthisisaquestionofthemotionofabodyinarotatingfluid.SuchproblemswerefirststudiedbyProudman(1916)l']andTay…     

On hindered settling of particles of different sizes

The flow of a non-dilute fluid suspension is considered in which the dispersed phase consists of particles or droplets of different sizes. A phenomenological two-phase flow theory is formulated for both continuous and discrete distributions of particle sizes and illustrated by considering the batch settling of such a mixture. The volume fractions and particle distribution functions are determined, as well as the composition of the sedimentary layer.     

Highlights of two-phase critical flow: On the links between maximum flow rates,sonic velocities,propagation and transfer phenomena in single and two-phase flows

To improve the understanding of two-phase critical flow phenomena, both single- and two-phase flows are studied in parallel. This can be done only if compatible mathematical models are used for both flows. In particular, since the evolution of the fluid or of the mixture is, in fact, a consequence of the transfers at the wall and at the interface, it is more rational to postulate transfer laws than to assume fluid, or mixture, evolutions.It is shown that the mathematical form of the above transfer laws is of primary importance, and it is proposed to allow for the presence, in the transfer terms, of partial derivatives of dependent variables.The critical flow condition is discussed within the above framework. A necessary critical flow criterion is obtained by equating to zero the determinant of the set of equations describing the steady-state flow. This criterion must be complemented by the study of the compatibility conditions of the set.It is verified that a flow is critical when disturbances, initiated downstream of some “critical” section, cannot propagate upstream of this section. A decrease of the outlet pressure has therefore no effect on the flow parameters upstream of the critical section, and the flow rate is maximum.Examples are given to demonstrate the potentialities of the method. It is shown that appropriate assumptions on the transfer laws enable existing models to be discussed.     

Slip and induced magnetic field effects on peristaltic transport of Johnson-Segalman fluid

The peristaltic flow of a Johnson-Segalman fluid in a planar channel is investigated in an induced magnetic field with the slip condition.The symmetric nature of the flow in a channel is utilized.The velocity slip condition in terms of shear stresses is considered.The mathematical formulation is presented,and the equations are solved under long wavelength and low Reynolds number approximations.The perturbation solutions are established for the pressure,the axial velocity,the micro-rotation component,the stream function,the magnetic-force function,the axial induced magnetic field,and the current distribution across the channel.The solution expressions for small Weissenberg numbers are derived.The flow quantities of interest are sketched and analyzed.     

Particle drag in a dilute turbulent two-phase suspension flow

The drag between phases plays an important role in the study of a turbulent two-phase suspension flow and its physical understanding will greatly promote progress in theoretical treatments of a whole range of important industrial and technical problems involving such a flow. The conventional practice of using the results of measurements based on a single particle in a laminar stream for the case of a turbulent flow of a dilute suspension is questioned. An analysis of the results of local measurements of upward turbulent flows of a solid particle-air two-phase suspension leads to the determination of the realistic particle drag coefficient over a wide range of flow conditions. It is established that the particle drag can be described by the simple Stokes law, based on an apparent turbulent viscosity of the fluid for the particles in the suspension flow. A correlation is provided for this apparent turbulent viscosity in terms of the particle size and concentration in the suspension, the local flow turbulence Reynolds number and the particle-to-fluid density ratio.     

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.      

Experimental two-phase flow measurement using ultra fast limited-angle-type electron beam X-ray computed tomography

An experimental evaluation of a novel limited-angle-type ultra fast electron beam X-ray computed tomography approach for the visualization and measurement of a gas–liquid two-phase flow is reported here. With this method, a simple linear electron beam scan is used to produce instantaneous radiographic views of a two-phase flow in a pipe segment of a flow loop. Electron beam scanning can be performed very rapidly, thus a frame rate of 5 kHz is achieved. Radiographic projections are recorded by a very fast detector arc made of zink–cadmium–telluride elements. This detector records the X-ray radiation passing through the object with a sampling rate of 1 MHz. The reconstruction of slice images from the recorded detector data is a limited-angle problem since in our scanning geometry the object’s Radon space is only incompletely sampled. It was investigated here, whether this technology is able to produce accurate gas fraction data from bubbly two-phase flow. Experiments were performed both on a Perspex phantom with known geometry and an experimental flow loop operated under vacuum conditions in an electron beam processing box.     

On Barenblatt's Model of Spontaneous Countercurrent Imbibition

Water imbibition is a critical mechanism of secondary oil recovery from fractured reservoirs. Spontaneous imbibition also plays a significant role in storage of liquid waste by controlling the extent of rock invasion. In the present paper, we extend a model of countercurrent imbibition based on Barenblatt's theory of non-equilibrium two-phase flow by allowing the model's relaxation time to be a function of the wetting fluid saturation. We obtain two asymptotic self-similar solutions, valid at early and late times, respectively. At a very early stage, the time scale characterizing the cumulative volume of imbibed (and expelled) fluid is a power function with exponent between 1.5 and 1. At a later stage, the time scaling for this volume approaches asymptotically classical square root of time, whereas the saturation profile asymptotically converges to Ryzhik's self-similar solution. Our conclusions are verified against experiments. By fitting the laboratory data, we estimate the characteristic relaxation times for different pairs of liquids.     

Method of Negative Saturations for Modeling Two-phase Compositional Flow with Oversaturated Zones

We examine the two-phase flow through porous media of multicomponent partially miscible fluids. The composition of both the phases is variable in space and time and is assumed to be in local thermodynamic equilibrium. One of the basic problems in modeling such systems is related to the appearance of single-phase zones occupied by the fluid which is over- (or under-) saturated, i.e., it is significantly remote from the equilibrium two-phase region. In an oversaturated zone, the two-phase flow equations degenerate and can no longer be used, which provokes serious numerical problems. We propose to describe the two-phase and oversaturated single-phase zone by a uniform system of classic two-phase equations while extending the concept of the phase saturation so that it may be negative and higher than one. Physically this means that we consider the oversaturated single-phase states as the pseudo two-phase states which are characterized by a negative saturation of the imaginary phase. Such an extension of the concept of the phase saturation requires the development of some consistence conditions that ensure the equivalence between the pseudo two-phase equations and the true single-phase flow model in the oversaturated zones. This method allows using the existing numerical simulators of two-phase flow for modeling single-phase zones by adding a simple plug-in with no modification of the structure of the simulators. The method is illustrated by several examples of hydrogene-water flow in a waste radioactive storage and of CO₂ injection in an oil reservoir.     

泥石流研究述评

泥石流这一特殊的二相流体是山区常见的一种自然灾害,一般可分为稀性泥石流(颗粒碰撞及离散力起主导作用)和粘性泥石流(粘性力起主导作用)两大类。本文概略地评述了泥石流的几个问题,即泥石流形成学、分类学、动力学等,指出急需解决的问题有泥石流汇流理论、泥石流阻力规律等。文中还根据近年来的动态和趋向,推断更加深入的理论研究和以数学模型为核心的泥石流流域管理模式将会成为泥石流学科发展的主要方向。      

Simulation of gas absorption into string-of-beads liquid flow with chemical reaction

This study is an attempt to investigate the chemical absorption of CO₂ in aqueous monoethanolamine (MEA) solution in a wetted-wire column consisting of one wire. Computational fluid dynamics method along with volume of fluid model was employed for modeling of two-phase flow, mass transfer and chemical reaction inside the column. The modeling results were compared with available experimental data and very good agreement was achieved. The simulation results showed that the diameter and intervals of liquid beads increases by increasing the gas and liquid flow rates. The beads velocity increases by increasing the liquid flow rate and decreasing mass fraction of MEA in the liquid phase. Also, mass transfer resistance in the liquid phase reduces by formation of the beads. It was concluded that the developed model is capable to predict the effect of operating and physical parameters on the investigated chemical absorption process.     

Casson流体在旋转圆盘上的流动

本文研究Casson流体在旋转圆盘上的涂层流动特性,得到基本流动的速度分布,并且用Runge-Kutta法进行数值计算,得到薄膜厚度随时间和流态参数的变化规律,还用能量法检验了流动稳定性。     

Fluid Sampling From Porous Rock to Determine Filtrate Contamination Profiles Around a Well Bore

Drilling fluid filtrate invades the pores of rock surrounding a well bore during drilling of the well, and contaminates the pore fluid originally within the rock pores. Models for the flow of contaminated pore fluid towards a sampling tool within the well bore are investigated, assuming that the filtrate has the same viscosity as the original pore fluid and that the wellbore radius is small compared to the depth of filtrate invasion. If the filtrate contamination in the fluid withdrawn from the rock is monitored as a function of the volume withdrawn, then it is shown that results can be inverted to give the radial distribution of filtrate around the well bore. A new generation of guarded sampling probes is then considered, and it is shown that the radial distribution of filtrate can be obtained by means of such a probe if the fraction of flow entering the central sampling region of the probe is small compared to that entering the concentric annular guard probe. The effects of dispersion, non-zero wellbore radius and anisotropic hydraulic permeability of the rock are also studied, and numerical simulations are used to give some indication of the effect of the ratio of the filtrate viscosity to that of the original pore fluid.