预测产量及可采储量的广义数学模型

Establishment and application of generalized mathematical models.

数学模型是油藏工程的重要预测工具之一，不但可以全程预测油气田的产量，而且可以预测油气田的可采储量。目前能用于实际预测工作的数学模型有广义翁氏模型、威布尔（Ｗｅｉｂｕｌ）模型，瑞利（Ｒａｙｌｅｉｇｈ）模型、ｔ模型、ＨＣＺ（ＨｕＣｈｅｎＺｈａｎｇ）模型、逻辑推理（Ｌｏｇｉｓｔｉｃ）模型、哈伯特（Ｈｕｂｂｅｒｔ）模型和龚帕兹（Ｃｏｍｐｅｒｔｚ）模型，每种数学模型都有一次线性试差求解法。在对上述８种数学模型的综合理论研究和分析的基础上，建立了２类广义数学模型，并提出了新的二重线性试差求解法，可以大大提高数学模型的实用范围和预测精度。

Mathematical model is an important prediction method in reservoir engineering. It can forecast not only production rate of oil and gas fields during their whole development history, but also their recoverable reserves. Up to now, 8 types of mathematical model have been derived theoretically, which are generalized Weng's model, Weibull model, Rayleigh model, t model, HCZ (Hu Chen Zhang) new model, Logistic model, Hubbert model and Compertz model. Simultaneously, one time linear trial and error method applied to each mathematical model has been put forward. In this paper, by researching comprehensively in theory, 2 types of generalized mathematical model are established and double linear trial and error method is provided based on the above 8 types of mathematical model. These 2 types of model expand the prediction range and improve the precise of prediction.