气井无因次流入动态曲线的特征函数

CHARACTERISTIC FUNCTION OF DIMENSIONLESS INFLOW-PERFORMANCE RELAT IONSHIP CURVE OF GAS WELL

无因次IPR曲线是实现油气井一点法产能试井和预测流入动态的理论基础。文章论述了气井无因次流入动态 (IPR)方程中的特征参数α的物理意义 ,并首次提出其解析函数α(θ) ,其中无因次自变量θ包含了与气层产能相关的所有物理量。α实质上是气井二项式产能方程中层流项系数的无因次形式 ,它表示在所有非理想流动条件下的最大无阻 (完全敞喷条件下 )总表皮系数中 ,与产量无关的表皮系数所占的份额 ;相应 1-α为无因次湍流系数 ,表示与产量相关的表皮系数占最大总表皮系数的份额 ;α的极限范围为 0～ 1,分别表示气井流入动态完全遵循非达西流动规律和完全遵循达西规律 ;α反映了气体渗流规律的综合特征 ,是控制无因次IPR曲线形状的特征参数。经敏感性分析表明 ,α的主要影响因素是表皮系数、地层压力和气层渗透率 ,且在低渗低压条件下尤为敏感。应用实例证明 ,文章所提出的解析表达式α(θ)完善了气井无因次IPR方程的理论 ,使其较任何经验相关式具有更宽的适用范围。

Dimensionless inflow performance rela tionship (IPR) curve is the theoretical basis of realizing the single point del iverability test and predicting the inflow performance of oil/gas wells.In the paper,the physical significance of the characteristic parameter α in the dimensionless IPR equation of gas well is discussed and its analytical functio n α(θ) is firstly put forward,in which the dimensionless independent var iable θ includes all the physical variables relevant to gas well deliverabi lity.Essentially, α is the dimensionless from of the coefficient of the lam inar flow term in gas well binomial deliverability equation,representing the fra ction of the skin factor independent of production in the total skin factor of m aximum open flow capacity under all non ideal flowing conditions,and 1 α is the dimensionless coefficient of turbulent flow,representing the fraction of the skin factor relevant to production in the maximum total skin factor.The lim it range of α is from 0 to 1,which represents gas well inflow performance's fully following non Darcy's law and Darcy's law respectively. α reflects t he comprehensive characteristics of gas flowing in reservoir,being the character istic parameter of controlling the shape of the dimensionless IPR curve.Through sensitivity analysis,it is indicated that the skin factor,formation pressure and permeability are the main factors of influencing α ,especially under the co nditions of low permeability and low pressure.According to the applied examples, it is proved that the theory of the gas well dimensionless IPR equation has been improved by use of the analytical function α(θ) presented in the paper, which makes the equation being of much wider application range in comparison wit h any empirical correlation.