石油产量预测的麦克斯韦模型

使用广义翁氏模型研究石油产量预测问题时，常采用线性试差法进行模型参数估计，该方法因需要预先设定1个参数值，并在此条件下求得另2个参数，所以受到的人为影响因素较多。基于统计学中的麦克斯韦分布，建立了两参数的麦克斯韦模型，提出了非线性最优化、一元多项式回归、二元线性回归这3种参数估计法求解麦克斯韦模型中的2个参数。依据1971-2016年挪威石油产量数据，对比了3种方法的求解过程及计算结果，并分析了3种方法的优缺点。结果表明：3种方法的计算结果与实际数据均非常吻合，由此证明了麦克斯韦模型的适用性及其参数估计方法的准确性；回归方法所得均方差极小，说明该方法具有较高的精度，而非线性最优化方法拟合的最高产量发生时间更为准确。这一研究为油气田的产量预测提供了新的模型和有效的模型参数估计方法。

Maxwell model of oil production forecasting

When using generalized Weng's model to study the prediction of oil production,linear trial and error method is often used to estimate the parameters of the model. This method needs to set one parameter value beforehand and obtain the other two parameters under this condition,which is easy to be influenced by some artificial factors. Based on Maxwell distribution in statistics,a two-parameter Maxwell model was established. Furthermore, three different parameter estimation methods,such as nonlinear optimization,univariate polynomial regression and binary linear regression,were proposed to solve two parameters in the Maxwell model. Taking oil production from 1971 to 2016 in Norway as training data set,the solving processes and calculation results of the three methods were compared,and the advantages and disadvantages of the three methods were analyzed. The results show that the oil production data obtained by the three methods are in good agreement with the actual data, which proves the applicability of the Maxwell model and the accuracy of the parameter estimation method. In addition,the mean square deviations obtained by two regression methods are very small,which shows that the precisions of regression modeling methods are higher,and the maximum production year fitted by non-linear optimization method is more accurate. This study provides a new model and an effective parameter estimation method for oil and gas field production prediction.