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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 is widely used in petroleum geology research, oil field development index forecasting and other fields. For the Logistic model, it is difficult to give a suitable initial iteration value, and it is easy to converge to the local minima. In order to reduce the difficulty of solving and speed up calculation, the idea of “reducing dimension” will need to solve the three-dimensional optimization problem Simplifies to solve the problem of univariate nonlinear equations, and proposes a solution to the univariate solution interval search algorithm and dichotomy algorithm. The proposed algorithm has the advantages of stable calculation process and good performance, which overcomes the defects that the general numerical optimization algorithm is difficult to give suitable initial values and easily converges to local minima in the parameter estimation of Logistic model. The algorithm was used to establish the prediction model of the cumulative yield of the Weiyan Oilfield. According to the results of model fitting, the maximum relative error between annual oil production history data of Peiyan Well is only 0.15%. The ultimate cumulative yield of Peiyan well field is 127.8425 × 104t, and the remaining output is 31.2 × 104t. The algorithm of this paper can be applied to the practical problems such as the prediction of petroleum geological reserves and the analysis of oilfield production trends.