基于拟压力函数的单井气水两相生产数据分析方法  

Transient production analysis of gas-water two-phase flow of gas wells using a pseudo-pressure function based approach

作　　者：王军磊[1] 位云生[1] WANG Junlei;WEI Yunsheng(PetroChina Research Institute of Petroleum Exploration and Development,Beijing 100083,China)

机构地区：[1]中国石油勘探开发研究院,北京100083

出　　处：《中国石油大学学报（自然科学版）》2024年第6期123-131,共9页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：中国石油天然气股份有限公司基础性前瞻性项目(2024DJ86)。

摘　　要：通过推导压力与饱和度间本构关系,定义两相拟压力函数和β因子,实现封闭地层单井气水两相非线性渗流数学模型的线性化,并给出定流压、定产量、阶段变流压等生产制度下的单井全生命周期产能公式;通过Duhamel褶积原理推导变流压/变产量下非稳态/拟稳态的解析解,明确两相物质平衡拟时间适用条件,形成生产数据分析方法。结果表明:积分形式的拟压力和β因子能够表征渗流过程中压力-饱和度的变化路径及相互影响,适用于不同工作制度的产能预测;在拟稳态时期两相物质平衡拟时间对任何工作制度均精确成立,在非稳态阶段对呈阶段性单调递减或连续性变化的生产制度近似渐进;无量纲形式下的规整化产气量和气相物质平衡拟时间对应关系与水相数据相同,通过图版拟合可获取储层物性、单井控制含气/水储量等参数。In order to analyze gas/water two phase flow of gas wells in depletion-driven reservoirs,this work,based on the constitutive relationship between pressure and saturation,proposes the gas/water phase integral transformations including pseudo-pressure andβfactor to linearize the two-phase diffusivity equation for a closed cylindrical reservoir with one vertical well.A pseudo-pressure based approach was described,which can generate the required benchmark analytical solution for single-phase liquid case,and the rescaled well performance equations subject to constant bottomhole pressure(BHP),constant rate,and step-BHP constraints were presented.A rigorous equation for variable BHP/rate constraints was also derived by using the Duhamel convolution,and the application conditions on the use of liquid type curves were studied with the definition of a two-phase material-balance pseudo-time.The results show that the pseudo-pressure based approach andβfactor can account for the change in saturation and gas/water PVT properties with pressure,and capture the path inter-dependency of pressure and saturation throughout the production life of the well.The material balance pseudo-time can convert variable rates/BHPs in gas-water two-phase cases into an equivalent constant rate solution for single-phase liquid case.In a boundary-dominated flow regime,the material-balance pseudo-time is strictly a rigorous solution,regardless of well specification constraints.Nevertheless,the material-balance pseudo-time works fairly well in infinite acting flow regimes,which is an approximate solution for the constraint of step like decline drawdown and continuous non-monotonic drawdown.In a dimensionless way combined with the concepts of pseudo-pressure and material balance pseudo-time,the gas-phase equation has exactly the same form as the water phase,which means the dimensionless gas production data overlay with those of water production.The other unknowns such as formation parameters,original gas in place(OGIP)and original water in place(OWIP

关 键 词：气水两相 非线性渗流 压力-饱和度关系 拟压力 物质平衡拟时间 

分 类 号：TE33[石油与天然气工程—油气田开发工程]