摘要
用非稳态法进行驱替实验来获得原始实验数据，对数据计算处理后进行曲线拟合，根据拟合曲线求导后得到相对渗透率值，其值的精确程度与选取什么样的数学模型作为拟合函数及曲线拟合时拟合程度是否高密切相关。采用琼斯所作的恒速水驱油试验数据和胜利油田具有代表性的某一岩心试验数据，论证平均含水饱和度与无因次累积注水量的关系为单调上升函数，平均有效粘度与无因次累积注水量的关系为单调下降函数，说明对这２类函数关系的拟合函数的要求是曲线光滑。目前普遍使用多项式进行拟合。高阶多项式拟合函数拐点多，波动严重，据此计算出来的相对渗透率值误差大，在相渗曲线图上表现为曲线出现振荡，不光滑。低阶多项式的拟合系数又太小，据此求得的相对渗透率值不精确。若试验数据完全呈单调性或只有个别数据点形成拐点，可以对拐点或剔除或调整，以保证曲线的单调光滑，再采用三次样条函数进行曲线拟合。这种拟合函数通过绝大多数数据点，拟合程度最高，从而保证了相对渗透率值的精确性。对拐点多、波动剧烈的试验数据，应该从对数函数和指数函数中选取拟合程度最高的函数作为拟合函数，以保证求取的相对渗透率值精确。图３表１参４（郭海莉摘）
Generally unsteady state laboratory displacement experiment is employed to obtain raw data of two phase fluid. Curve fit is performed based on the points which are obtained from raw data and then the relative permeability is calculated from curve fit. The accuracy of relative permeability depend on what mathematical models are used to act as fit function and whether curve fit is reasonable. The raw data came from Jones' and Shengli's experiments are used to demonstrate that the function of S w vs. Q i (average water saturation vs. dimensionless accumulative injected water volume) is increasing monotonously and the function of λ -1 vs. Q i (average effective viscosity vs. dimensionless accumulative injected water volume) is decreasing monotonously. These demand that the fit function's curve should be smooth. At present polynomials are always used to act as fit function. Higher order of polynomials can result in oscillations and non monotonic derivatives which cause unpleasant kinds in the relative permeability curve. Accordingly, the error of relative permeability will be large. Lower order of polynomials can result in weak curve fit and accordingly the relative permeability is not accurate. Spline function is employed to fit curve when the points are monotonous or few points are deviated. The deviated points can be distinguished and therefore be eliminated or adjusted to keep curve smooth and monotonous. One of the logarithm function and exponential function whose coefficient of fit is the biggest should be used to assure the accuracy of relative permeability when the points exert oscillations seriously.
出处
《石油勘探与开发》
SCIE
EI
CAS
CSCD
北大核心
1998年第6期63-66,共4页
Petroleum Exploration and Development
关键词
油水两相流
相对渗透率
水驱
油田开发
Displacement test, Relative permeability, Curve fit, Calculation method
