Hydrodynamic and Thermal Fields in a Porous Medium with Injection of Superheated Steam

The plane one-dimensional and radially symmetric problems of injection of superheated steam into a porous medium saturated with gas are considered. Self-similar solutions are constructed on the assumption that in this case four zones are formed in the porous medium, namely, a gas flow zone, superheated and wet steam zones, and a water slug zone formed due to steam condensation. On the basis of the solution obtained, both the effects of the boundary pressure, mass flow rate, and temperature of the injected superheated steam and the effect of the initial state of the porous medium on the propagation of the hydrodynamic and thermal fields in the porous medium are studied.     

考虑诱导缝多段压裂水平井非均质改造压力动态模型研究

为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化,建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型,耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解,对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性.基于压力导数曲线特征进行流动阶段划分和参数敏感性分析,得到以下结果:和常规压裂水平井井底压力导数曲线相比较,理想模式下,考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝“补充”阶段、储层线性流动阶段和拟边界控制流阶段.诱导缝条数的增加加剧了综合线性流阶段的持续时间,降低了流体渗流阻力,早期阶段压力曲线越低;当诱导缝与压裂裂缝导流能力一定时,裂缝导流能力越大,线性流持续时间越长;当所有压裂裂缝不在一个区域时,沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段,因此,沿井筒方向两端区域渗透率越低,早期阶段压力曲线越高;当所有压裂裂缝在一个区域时,渗透率变化只影响径向流阶段之后压力曲线形态,外区渗透率越低,早期径向流阶段之后压力曲线越高.通过实例验证,表明该模型和方法的实用性和准确性.     

Analytical model of steam zone propagation in porous media

Steam injected into oil-bearing porous media forms a steam zone which propagates in three-dimensional space. The injected steam forms the condensation front bounding the seam zone. Simultaneous mass and the energy transfers take place through this moving boundary, between the rocks and fluids inside and outside the steam zone. The energy transfer is by conduction and convection. A new mathematical model describes the propagation growth of the steam zone subject to initial and boundary conditions, and is applicable in a general case of heterogeneous steam zone of arbitrary geometry. The model is based on the simultaneous analytical solution of the coupled overall mass and energy balance equations for a multi-phase steam zone, and is presented here for the first time. The resulting nonlinear integral equation does not have an analytical solution for a general case. The exact solution is found for a cylindrical homogeneous steam zone. For a special case of a one-dimensional, two phase steam zone, this solution shows excellent agreement with available experimental data.     

Two-front mathematical model of water injection into a steam-saturated geothermal reservoir

A mathematical model of the process of water injection into a high-temperature steam-saturated geothermal reservoir is proposed. In the reservoir there is a zone of co-existence of steam and water which is separated from the steam and water zones by moving interfaces (phase transition fronts) whose location is determined in the process of solving the problem. Within the framework of the proposed model the thermodynamic contradiction that exists in the single-front case for low permeabilities, expressed as supercooling of the steam in the corresponding zone ahead of the interface [1, 2], is not observed. With increase in the permeability the two-front solution obtained goes smoothly over into a noncontradictory single-front solution. Neutral curves separating the domains of existence of the different types of solution in parameter space are constructed. Moscow. e-mail: barmin@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 105–112, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-01042).     

油页岩原位注热开采储层有效热解区变化规律分析

针对油页岩原位注热开采过程中储层有效热解区变化规律不清,实际热解效果无法准确判断难题,采用数值模拟方法,以抚顺油页岩储层为研究对象,建立了油页岩原位注热开采热流固耦合力学模型,与前人结果对比,验证了模型可靠性。重点考察水力压裂裂缝通道短路问题,分析得到了油页岩原位注热开采过程中储层有效热解区、储层有效热解区中地应力、注汽压力及沉降量随注热时间变化规律。结果表明,过热蒸汽沿水力压裂裂缝流动不会出现裂缝通道短路现象,过热蒸汽可通过水力压裂裂缝加速油页岩储层热解;采用过热蒸汽对流加热油页岩储层效率高,只需1年能使96%的油页岩储层达到热解所需温度;油页岩储层有效热解区中部形成应力集中区,最大地应力为21.6 MPa;热解后靠近注热井处岩层发生沉降,热解2年后最大沉降量达0.85 m。所得结论对现场油页岩原位注热开采有参考意义。     

海洋天然气水合物降压开采地层井壁力学稳定性分析

降压开采天然气水合物使其分解会导致储层孔隙度、渗透率、孔隙压力和岩层骨架有效应力发生改变, 同时降低沉积物的胶结程度, 使地层的抗剪强度和承载能力降低, 从而引起井壁失稳、海底滑坡、海底面沉降等工程问题. 为此, 在地下多相非等温数值模拟软件TOUGH+Hydrate框架内, 基于扩展的三维Biot固结理论, 考虑水合物分解相变、传热(T)、流动(H)、岩土体变形(M)等过程及其相互耦合作用, 建立了新的水合物开采传热-流动-力学(THM)耦合数学模型, 并开发有限元程序对其进行数值求解. 以中国南海神狐海域GMGS1航次SH2站位水合物储层条件为研究对象, 构建了垂直井降压开采THM耦合地层井壁稳定性分析模型, 预测了水合物开采过程中储层温-压-力场和水合物分解区的演化规律, 揭示了地层优势出砂区域和海底面沉降趋势. 结果表明: 储层降压导致地层有效应力增大, 进而引起井周地层发生沉降, 且地层的沉降主要发生在降压开采前期, 最大沉降位置位于井壁周围, 向储层内部延伸地层沉降量快速减小; 水合物分解导致井周地层力学强度降低, 加剧了储层的沉降; 井筒降压造成射孔段井壁应力集中最为明显, 从而造成井壁破坏的潜在风险, 这些区域正是水合物开采出砂防治的关键区域.      

污染区对部分打开井井底压力响应的影响

钻井造成的污染区对部分打开井的影响不同于裸眼井. 为了分析污染区对部分打开井井底压力响应的影响,建立了一种部分打开井的二维轴对称渗流模型,模型考虑了真实的污染区以及储层渗透率各向异性特征.利用有限元数值方法对模型进行求解,获得了部分打开井的井底压力响应及储层压力分布. 根据压力响应及压力分布特征,将部分打开井的压力响应过程划分为5 个流动阶段,其中早期局部径向流动和椭球流动是该类井最典型的特征. 对污染区的影响分析表明:传统方法中的表皮系数S 并不等于污染区引起的机械表皮系数S_d;无量纲井筒储存系数不能与机械表皮系数组合. 修正了传统方法中部分打开井的井底压力公式,验证了部分打开井的总表皮计算公式,为该类井的井底压力响应解释及产能预测提供理论指导.      

An experimental and numerical study into turbulent condensing steam jets in air

 Temperatures, velocities, and droplet sizes are measured in turbulent condensing steam jets produced by a facial sauna, for varying nozzle diameters and varying initial velocities (Re=3,600–9,200). The release of latent heat due to droplet condensation causes the temperature in the two-phase jet to be significantly higher than in a single-phase jet. At some distance from the nozzle, droplets reach a maximum size and start to evaporate again, which results in a change in sign of latent heat release. The distance of maximum size is determined from droplet size measurements. The experimental results are compared with semi-analytical expressions and with a fully coupled numerical model of the turbulent condensing steam jet. The increase in centreline temperature due to droplet condensation is successfully predicted. Received: 5 April 2000 / Accepted: 15 November 2000     

Mathematical model of water-steam phase transitions in hydrothermal reservoirs

The problem of steam production from a water-saturated hydrothermal reservoir is considered. It is shown that the introduction of a evaporation surface separating the gas and liquid phases leads to superheating of the water in a zone ahead of the front. This contradiction is removed by introducing of an extended phase transitions zone between the single-phase zones. In this case the problem contains two unknown moving boundaries considered as surfaces of discontinuity of the moisture content.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 98–105, November–December, 1994.     

Direct contact condensation of steam on a horizontal surface of water

A study of direct contact condensation of stagnant saturated and superheated steam on slowly moving subcooled water has been performed with reference to a horizontal flat geometry. Inlet water mass flowrate and temperature together with inlet steam temperature and superheating have been investigated as experimental variables. Their influence on direct contact condensation heat transfer coefficient is shown. A theoretical model for direct contact condensation prediction is proposed, in the frame of the present geometry.     

Condensation induced water hammer: Numerical prediction

Contact of steam and subcooled water in a pipe or a pressurized vessel leads to intensive condensation accompanied by a pressure drop in the volume of condensing steam and an acceleration of the surrounding water mass towards the steam volume, which can result in a severe water hammer and plant damage. This phenomenon is known as the condensation induced water hammer (CIWH). A one-fluid model is developed for the prediction of pressure surges during CIWH. It is shown that the reliable prediction of pressure surges strongly depends on the calculation of the condensation rate, transient friction and the water column–steam interface tracking. Due to the lack of the CIWH condensation models, a new approach is derived. The one-fluid model predictions of pressure surges are compared with available measured data from a CIWH experimental facility and acceptable agreements are obtained. In addition, the ability of the developed model to simulate the water cannon event, which takes place during the steam drainage into the pool of subcooled water, is demonstrated. Experimentally observed considerable scattering of test data under the same conditions is related to the condensation rate and its dependence on the entrained droplets–steam interfacial area concentration in the vicinity of the water column head.     

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.     

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.      

Effect of homogeneous condensation on the dynamics of a hot vapor bubble in a cold liquid jet

The problem of initiating cavitation bubbles in a cold liquid jet by injecting hot steam into high-pressure zone specially organized at the nozzle outlet is considered. Previously, in [1], a plane flowfield in which vapor bubbles were formed at the cusp of the cavity (high-pressure zone) and propagated together with the liquid along the axis of symmetry was considered. In certain cases, in the bubble expansion process the vapor temperature drops below the saturation temperature. In the present paper, vapor condensation in the bubble volume (homogeneous condensation) is also taken into account.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 56–61, November–December, 1996.     

汽油机燃烧室内温度场测量的激光剪切干涉法

采用激光剪切干涉法测量了汽油机燃烧室内的温度场,并分析了剪切干涉法测温的基本原理,推导出利用干涉条纹图求解温度分布的关系式。在一台二冲程火花点火发动机上设置石英窗和信号同步系统,建立了适合高速摄影的激光剪切干涉测量装置。通过改变剪切干涉量,测取发动机燃烧室内干涉条纹图,从而获得缸内燃烧的二维温度场。结果表明,激光剪切干涉法抗振性强,光路简单可靠,可以进行高速摄像,是研究内燃机燃烧过程的有效方法。从温度场可以看出,燃烧过程中缸内大致可分为三个区,即已燃区、未燃区和燃烧区,具有不同的温度分布和温度梯度。燃烧区温度最高,温度梯度大;已燃区温度次之,梯度较小;未燃区温度最低,但梯度较大。     

The intersection of a slip-plane and a stress-free boundary: Application to inhomogeneous yielding

An analysis is presented for the stable formation of a localized yield-zone within an elasticallydeformed material. The interaction of the yield zone, the stress-free boundary from which this zone originates, and the far-field stress gradient in the elastic body is discussed. A distribution of edge dislocations on a slip-plane is employed as a model for the yield zone. The results of the analysis are compared to four-point bend-test data from mild steel bars. In the analysis, upper and lower yield-point data are used as the controlling parameter values for the formation of this zone. The predicted length of the yield region and the stress distribution around the region are in agreement with the experimental data. From the results of the analysis, a location for the formation of a second yield-zone is suggested. The distance between yield zones is obtained and compared to the observed separation distance in the experiment.     

缝洞型油藏三维离散缝洞数值试井模型

缝洞型碳酸盐岩油藏发育着大尺度的溶洞和裂缝,非均质性极强,缝洞型碳酸盐岩油藏问题的研究成为了世界级难题之一.由于大尺度溶洞和裂缝对储层的流体流动起主导作用,因此,基于连续介质理论的双重介质或三重介质模型已不适合其中流体流动的描述.根据大型缝洞分布地质特征,探索性地提出了一种板块组合的复合架构离散缝洞模型描述该类油藏中的流体流动,将三维空间大裂缝用板块描述,溶洞用高渗透率和高孔隙度不规则多面体团块描述.将裂缝面用二维三角形单元离散, 溶洞和基质用三维四面体离散, 利用三维混合单元有限元法对建立的不定常渗流模型进行求解,得到了三维渗流条件下的试井理论曲线及压力场分布.通过对试井理论曲线特征的分析, 获得了各敏感参数对试井曲线的影响规律.通过对1口井的实际测试资料解释结果的分析,并与实际地震反射资料及生产实际资料的对比,发现本文所建立的模型可以较好地反映裂缝和溶洞的地质动态状况,并与实际生产状况具有较好的一致性.这一结果说明了所建模型的正确性以及测试资料分析结果的可靠性.      

Heat transfer in horizontal tubes during two phase natural circulation with presence of noncondensing gas

 The condensation process of steam inside horizontal tubes during natural circulation gains in importance regarding the reactor safety research for existing and future nuclear power plants. Experimental investigations due to the condensation process were realized with the rig HORUS to study the behaviour of water-steam-gas mixtures in horizontal tubes. The paper includes statements regarding the flow and heat transfer conditions inside the tube and the temperature distribution inside the small tube wall. The experiments showed a blockade of the heat transfer area with Nitrogen which is connected with an increasing primary pressure followed by a compression of the Nitrogen and a reentry of steam into the tube. The experiments serve for the creation of an experimental data base. A model development for calculation of the heat transfer is described. The model was implemented in the German thermal-hydraulic code ATHLET. The comparison of calculated data and the measured parameters of HORUS rig show the code improvement for the simulation of noncondensing gases. Received on 17 January 2000