Modeling of Two-Phase Flow in Oil Wells Using a Simplified Two-Fluid Model

Abstract

In this work, with the idea of finding a simplified, numerically stable, one-dimensional, time-dependent two-fluid mathematical model whose predictions are in agreement with oil wells data, a study of the accumulative terms effect on the numerical stability and predictions of a general two-fluid model, was carried out. The fluids considered in oil wells were water, oil, and gas. The liquid phase in the model is formed by water and oil with pseudoproperties. The model is able to predict pressure, volume fraction, velocity, and temperature for both phases. The numerical solution of the model, which consists of mass, momentum, and energy conservation equations, is based on the finite difference technique in the implicit scheme. The thermodynamic and transport properties of the fluids are estimated by black-oil PVT correlations. It was observed that, a numerically stable model, with acceptable predictions has to take into account the accumulative terms for the liquid volume fraction, gas velocity, and liquid temperature. Numerical results are in agreement with field data and theoretical results reported in literature.     

蒸汽吞吐水平井产液过程井筒传热与传质研究

国内水平井蒸汽吞吐注汽过程井筒的数学模型已经较完善,但对稠油产出过程的井筒温度分布研究涉及不多。应用离散化井筒模型,建立了水平井单轮次蒸汽吞吐单井模型。利用质量守恒、动量定理和能量守恒原理建立了水平井稠油开采过程中井筒压力、温度变化分布以及水平井产液量预测模型,用数值方法对模型进行了求解,编制了相应的计算程序并应用胜利油田现场井例数据验证了该模型的可靠性。该模型为水平井蒸汽吞吐产能预测、生产系统优化设计提供理论依据。     

Mathematical Model For Bubbly Water-Heavy Oil-Gas Flow in Vertical Pipes

Abstract

In this work a unidimensional, time-dependent homogeneous mathematical model is presented. The model is able to predict pressure, temperature and velocity profiles of the flow known as bubbly-gas—bubbly-oil, which can be present when water-heavy oil and gas flow simultaneously in vertical pipes. The mathematical model consists of mass, momentum, and energy conservation equations and its numerical solution is based on the finite difference technique in the implicit scheme. The thermodynamic and transport properties of the fluids are estimated by correlations reported in the literature. The effects of different water-gas and water-oil shear stress correlations on the prediction were evaluated. As a result, some correlations are recommended to simulate the bubbly-gas—bubbly-oil flow. A new correlation for water-heavy oil-gas friction factor is suggested. A comparison of the model with existing experimental data shows a satisfactory agreement.     

Predicting the Distribution of Pressure,Temperature, Velocity,and Density of Three-phase Bubbly Flow in HTHP Wells

A one-dimensional, thermal, steady state mathematical model is presented, which can be used for determining the pressure, temperature, velocity and density distributions of three-phase flow. The numerical solution, which consists of mass, momentum, and energy conservation equations, is based on the four order Runge-Kutta method. Due to the sensitivity of gas holdup, an improved model is performed and makes the result more stable. The average value is adopted to meet the redundancy of model. The data of X Well, 7110 m deep, in Sichuan, China, is used for case calculations and a sensitivity analysis is made for the model.     

高压深井分段改造管柱封隔器间压力预测及应用

针对高压深井分段改造过程中封隔器间环空压力下降造成的改造管柱和封隔器受力状况恶化问题,基于能量守恒原理和井筒传热理论,建立了考虑摩擦生热和对流换热等影响的注入工况井筒温度场二维瞬态预测模型,并分析了井筒温度和压力变化对封隔器间环空体积的影响;然后结合井筒温度瞬态预测模型、环空流体PVT状态方程、油管柱径向变形计算模型和地层瞬态渗流方程,建立了典型高压深井封隔器间环空压力预测模型。最后,以塔里木油田1口高压气井为例开展了封隔器间环空压力预测。分析结果表明:常规设计方法认为安全的管柱,考虑封隔器间环空压力下降后就存在非常大的失效风险,高压深井分段改造管柱设计过程中必须充分考虑该因素。该研究成果为高压深井分段改造管柱的优化设计提供了新思路。     

保温油管海洋采油井筒温度压力计算耦合模型

生产管柱上部采用真空隔热保温油管是海洋油井提高产液温度,防止油井结蜡的有效手段,科学设计保温油管的合理下深则需要准确预测海洋采油井筒温度剖面。将产液视作气液两相流,分别建立了质量守恒、动量守恒和能量守恒模型,模型中考虑了温度和压力对原油、天然气和地层水热物理性质的影响,井斜角对换热和压力降的影响,以及电潜泵机械能损失引起的热源。采用交错网格和全隐式有限体积法离散技术,建立了适合于海洋生产井筒温度场和压力场耦合求解的数值方法,保证了模型求解的稳定和收敛。利用所建立的模型对1口海洋油井进行了井筒温度分析和保温油管下深设计,结果表明,模型预测精度高（相对误差为0.46%）,设计保温油管下深能有效地提高油流温度,避免油井结蜡。     

Coupled thermo-hydro analysis of steam flow in a horizontal wellbore in a heavy oil reservoir

A novel model for dynamic temperature distribution in heavy oil reservoirs is derived from the principle of energy conservation.A difference equation of the model is firstly separated into radial and axial difference equations and then integrated.Taking into account the coupling of temperature and pressure in the reservoir and wellbore,models for calculating distributions of the reservoir temperature,reservoir pressure,and water saturation are also developed.The steam injected into the wellbore has a more significant effect on reservoir pressure than on reservoir temperature.Calculation results indicate that the reservoir temperature and pressure decrease exponentially with increasing distance from the horizontal wellbore.The radial variation range of the pressure field induced by steam is twice as wide as that of the temperature field,and both variation ranges decrease from the wellbore heel to the toe.Variation of water saturation induced by steam is similar to the temperature and pressure fields.The radial variation ranges of the reservoir temperature and pressure increase with steam injection time,but rate of increase diminishes gradually.     

储层石蜡沉积预测技术研究与应用

在油田开发过程中 ,由于油藏温度、压力等条件的变化 ,高含蜡原油在近井带容易产生石蜡沉积 ,堵塞地层孔隙或裂缝 ,严重影响油田开采 ,尤其对于低渗油田 ,伤害特别严重。文中应用理想溶液理论、质量守恒和能量守恒等基本原理 ,建立更符合油田实际情况的油藏中石蜡沉积预测数学模型 ,开发一套方便实用的油藏中石蜡沉积预测软件系统FPOS1 0。在此基础上 ,应用室内实验数据和现场数据对吉林新民油田油井石蜡沉积情况进行预测和现场拟合 ,确定新民油田临界石蜡沉积半径为 2 5m ,快速、准确地为现场清防蜡措施提供理论依据。     

温度、压力对油基钻井液密度的影响规律及数学模型

油基钻井液的密度受温度和压力影响显著,掌握油基钻井液在不同温度和压力条件下密度的变化规律是钻井安全的重要保障。基于现场配方在室内配制了相同组分、不同密度的4种油基钻井液,使用Anton Paar公司的流体高温高压密度测试仪测定了4种油基钻井液的密度在温度范围60～220 ℃、压力范围20～120 MPa内的变化,探究了温度和压力对油基钻井液密度的影响规律,并建立了油基钻井液密度的温压二元数学模型。使用现场不同密度的油基钻井液对模型的准确性进行了验证,结果表明预测值与实测值之间具有较高的一致性,平均预测准确度达97.93%,能够满足现场使用的需要。另外对2种类似配方的油基钻井液进行了密度准确性验证,结果显示平均误差为9.24%,精度较高。      

油气井井口装置传热计算新方法

为了对井口装置的温度场和热量场进行精确计算,从质量守恒和能量守恒的基本原理出发,在充分考虑井口装置结构及传热特性的基础上,建立了油气井井口传热数学模型,并求出了该数学模型的解析解。该模型将地表气温和风速等动态因数作为求解条件,能够较准确地描述温度场分布的时变性和非均质特征。建模时为了便于计算,根据传热等效原理对高产气井井口结构进行了简化。X-1井的实例计算结果表明,模型能够对井口装置的温度场和热量场进行精细刻画,其可靠性在试井资料解释中得到了很好的验证。     

Predicting the Distribution of Pressure,Temperature, Velocity,and Density of Transient Flow in HTHP Production Wells by the Finite Difference Method

A one-dimensional, thermal, transient state mathematical model is presented, which can be used for determining the pressure, temperature, velocity, and density distributions of gas flow. The numerical solution, which consists of mass, momentum, energy conservation equation, and gas state equation, is based on the finite difference method. The data of ‘X Well,’ 7,110 m deep, in Sichuan, China, is used for case calculations and a sensitivity analysis is made for the model.     

海上非凝结气与过热蒸汽混注井筒传热特征研究

为了优化海上稠油油藏"非凝结气与过热蒸汽"（简称为"混合汽/气"）混注过程中的注汽参数,根据质量、能量和动量守恒方程,建立了井筒内非等温流动数学模型,结合海水中传热模型、地层内瞬态导热模型,建立了完整的海上稠油油藏注混合汽/气井筒传热模型,利用有限差分法和迭代法计算得到井筒内的压力和温度分布。研究结果表明:海水流动能明显增加井筒热损失,降低混合汽/气的温度;随着非凝结气含量增加,混合汽/气的温度和过热度均下降;随着注汽压力增加,过热度不断下降。海上稠油油藏注混合汽/气井筒传热模型为优选注汽参数和分析海水对井筒热损失的影响提供了理论依据。      

抽油机井节点分析方法及应用

本文根据油田生产的实际情况,对预测油井IPR曲线的Vogel方程和Brown提出的计算泵吸入口压力的公式进行了修正,修正后的数学模型考虑了较多的因素,完善了抽油机井节点分析方法。油田实际资料计算表明:修正后的数学模型比较符合抽油机井的实际生产情况,并且计算结果的精确性较好。     

A Study on the Heat Penetrating Coupling Unsteady State Model of Heavy Oil During Steam Flooding

An unsteady model of temperature field coupled with seepage field during thermal recovery process was derived and the solution method was given. Considering the effects of pressure and temperature during the derivation, the variation laws, with different types of constraints, of temperature and pressure changing with time and space were summarized in the model. The deduced governing equations are applied to oil fields with practical data and the comparison of the results with the numerical results and empirical formula calculation results is basically the same. Examples show that the heat penetrating coupling method can analyze dynamic variation of the formation temperature and pore fluid pressure data near borehole wall quantitatively during thermal production in heavy oil reservoir.     

环空注蒸汽伴热工艺的数学模型及注汽参数优化

环空注蒸汽伴热降黏适用于开采高凝固点、高黏度原油，它对各种类型的稠油能够保证降黏效果，具有较广的使用范围。根据能量守恒原理建立了环空注蒸汽伴热工艺的井筒温度分布数学模型，该模型是具有半隐式边界条件的常微分非线性方程组。在用迭代法求取蒸汽干度为0的深度的基础上，推导出该温度模型的解析解。该解析解形式简单，使用方便，计算快捷准确。另外，以加热能耗最小为目标，以井筒温度不低于拐点温度为约束条件，用带约束的遗传算法对蒸汽注入参数进行了优化设计。以胜利油田滨南采油厂一口环空注蒸汽伴热井为例进行实例验证，结果表明，该温度模型的计算结果与实际符合较好，参数优化设计方法新颖、快速。该模型为准确求解环空注蒸汽温度场分布及快速优化注汽参数提供了新的方法。     

同时预测油井中压力和温度剖面方法的改进

根据油气在井筒中流动的特点，在前人研究的基础上，将分别计算压力和温度的公式组合成为一个同时含有压力梯度和温度梯度的计算型，采用数值算法进行双重迭代，即可较准确而迅速地同时预测井筒中的压力和温度分布。文中用取自江汉、南阳油田40口油井的实测资料，对所述方法进行了验算，井与国际上比较流行的几种单独计算压力和温度梯度方法所得的结果作了比较。结果表明：该方法计算的压力平均百分误差为1．75％，标准偏差为3．14％，优于原型的Aziz法；温度平均百分误差为2．83％，标准偏差为9．23％，明显优于美国的Shiu法和苏联经验法。图4表3参7     

变形介质油藏油井产能预测研究

对于变形介质油藏油井产能预测问题,传统的研究方法均假设地层岩石的变形系数为常数,这导致了目前的变形介质油藏产能预测模型不能准确地反映出油井产能的变化趋势,尤其在生产压差较大的情况下,误差较大。文中研究了变形系数与产能的关系,考虑了生产压差对变形系数的影响,从而改进了变形介质油藏油井产能预测模型。改进后的模型从理论上解释了变形介质油藏矿场系统试井中,油井流入动态曲线在井底压力高于饱和压力时即向压力轴偏转,并出现最大产量点的现象,并对最大产量点出现的原因进行了分析。文中还提出了变形介质油藏油井井底最低合理流动压力,为油井确定合理的工作制度提供技术支持,从而更有效地分析及预测油井产能的变化。     

气井生产过程中碳钢管柱CO2腐蚀规律

掌握气井稳态生产过程中CO₂对碳钢管柱沿井深方向的腐蚀规律才能更好地确定油气田开发和实施方案,预防和降低管柱腐蚀失效事故。根据质量守恒、动量守恒、能量守恒以及非理想气体状态方程建立了地面稳态生产条件下管柱内热流耦合计算模型,并与实测结果进行了对比研究。以Norsok模型为基础,根据实际生产用管材等建立了相应的修正表达式,并进行了实例验证。研究了CO₂摩尔分数、井筒总体传热系数,管柱内半径和日产量对管柱腐蚀速率的影响。研究表明,建立的热流耦合模型和腐蚀预测模型计算精度满足工程需要;地面日产量越大,井深方向管柱内天然气密度、速度、温度越高,而压力越低;增加CO₂摩尔分数和地面日产气量、降低井筒总体传热系数和管柱内径均可引起管柱最大腐蚀速率出现的位置向井口方向移动,并且日产气量和井筒总体传热系数的影响更为明显;沿井深方向上,管柱腐蚀速率变化分为4个阶段,且不同影响参数变化时,腐蚀速率的影响规律不尽相同。     

不同含水和压力条件下的油井流入动态

根据多相渗流理论推导出适合于不同含水、流压和静压条件下的油井流入动态预测公式,并用埕北油田30套系统试井资料对该方法和其他方法进行了对比验证,该方法的预测精度可达到-0.1％;同时指出,P_(wf)=2/3 P_b是油井的临界流压;当P_(wf)<2/3 P_b时,油井产量随流压的降低而大幅度降低。临界流压是地层的特征参数,不随地层压力发生变化。     

苏里格南区气井速度管柱适用条件分析

在气井管理及气井动态分析中,井筒压力、温度是重要的参数。基于质量守恒、动量守恒、能量守恒和传热学原理,综合考虑压力和温度之间的相互影响,建立了气井井筒压力温度耦合模型,应用四阶龙格-库塔算法数值求解。通过气井实测数据对模型进行验证,算例表明模型计算结果可靠,可以满足工程计算要求。速度管柱是苏里格南区重要的排水采气措施,针对速度管柱选井缺乏定量标准的问题,在井筒压力温度预测基础上,评价了速度管柱气井在不同条件下的水合物生成风险、携液临界流量和冲蚀产量,给出了速度管柱气井满足携液和安全的产量范围,提出了适用速度管柱新井的试气无阻流量界限,为苏里格南区速度管柱的下入时机和选井提供了理论基础和指导意见。