Logistic模型参数估计的新方法

New Method of Estimation of Logistic Model Parameter

Logistic模型在石油地质研究、油田开发指标预测等领域应用广泛。针对Logistic模型存在难以给定合适的初始迭代值、容易收敛到局部极小点等方面的局限,遵循旨在降低求解难度、提高计算速度的"降维"思路,将需要求解三维优化问题简化成求解一元非线性方程问题,并提出了求解该一元方程的解区间搜索算法和二分法求解算法。该算法具有计算过程稳定、熟练性能好等特点,克服了一般数值优化算法应用在Logistic模型参数估计问题中难以给定合适初始值和容易收敛于局部极小点等缺陷。采用该算法建立了摆宴井油田累积产量预测模型。根据模型拟合的结果与摆宴井油田年产油历史数据最大相对误差仅为0.15%。通过求极限得摆宴井油田最终累积产量为127.8425×104t,剩余产量为31.2×104t。本文算法可应用于石油地质储量预测、油田产量趋势分析等实际问题中。

Logistic model has wide application on the fields of research on petroleum geology and prediction on oilfield development index.The Logistic model has the limitations of being difficult to give suitable primary iteration value and easy to converge to the local minimum point.Followed by the thinking of dimension descent on lower computing difficulty and higher computing velocity,3D optimization problem needs to be solved may be simplified into nonlinear equation with one known,and search algorithm of solution interval and dichotomy algorithm for this equation are put forward.This algorithm has the features of stable computing process and good facility,which overcomes the limitations of the application of normal numerical optimization algorithm on the parameter estimation of the Logistic model.Forecasting model of cumulative oil production in Baiyanjing oilfield is established by using this algorithm.Maximum relative error is only 0.15% between matching results of the model and historical data of yearly oil production in Baiyanjing oilfield.Through limit finding,we know that ultimate cumulative oil production in the Baiyanjing oilfield is 127.8425×104t and remaining oil production is 31.2×104t.It can be applied in some actual problems such as forecasting of oil in place and analysis of oil production in oilfield.