西南石油大学学报(自然科学版) ›› 2000, Vol. 22 ›› Issue (3): 37-40.DOI: 10.3863/j.issn.1000-2634.2000.03.010
• 石油工程 • 上一篇 下一篇
何炳全 向开理
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HE Bing-quan XIANG Kai-li
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摘要： 将非线性的分形理论应用于渗流力学,在考虑井筒续流,表皮效应的影响下,建立了分形油藏不稳定渗流的有效井径数学模型。在该数学模型中通过引入双参数(df,θ)来描述油藏的分形特征。分形维数df反映了分形体的几何特征,是分形体复杂程度的重要标志;分形指数θ描述了分形网络的连通情况(与谱维数有关)。用拉普拉斯变换求出了此数学模型的解析解及长、短时渐近解,分析了压力动态特征和参数的影响。
关键词: 分形油藏, 数学模型, 压力动态特征
Abstract: With wellbore after-flow and skin effect taken into con-sideration, an effective well radius mathematical model is pro-posed for unsteady flow of fluids in fractal reservoirs. Nonlinear fractal geometric theory is applied to the dynamics of flow in the model. Features of the fractal reservoir are described with towfractal parameters (df,θ), where df describes the geometric fea-tures andθdepicts the connectivity of the fractal network of the reservoir. Laplace transform is used to obtain the analytical so-lutions and long-time/short-time asymptotic solutions of the model. And analyses are made on the character and effects of pressure behavior and the parameters.
Key words: fractal reservoir, mathematical model, ana-lytical solution, pressure behavior
中图分类号:
TE312
何炳全 向开理. 分形油藏不稳定渗流有效井径数学模型的解析解 [J]. 西南石油大学学报(自然科学版), 2000, 22(3): 37-40.
HE Bing-quan XIANG Kai-li. ANALYTICAL SOLUTIONS OF EFFECTIVE WELL RADIUS MODEL OF UNSTEADY FLOW IN FRACTAL RESERVOIRS[J]. 西南石油大学学报(自然科学版), 2000, 22(3): 37-40.
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