低渗油藏非线性渗流规律数学模型及其应用

中国已探明未动用的2.4×10⁹t低渗透石油地质储量成为石油工业发展的重要潜力。低渗透非线性渗流是开发低渗透油气田所需解决的重要基础问题,也是现代渗流力学的前沿研究方向之一。根据实验结果,首次提出了低渗透非线性渗流规律的连续函数模型,为使低渗透非线性渗流的研究从定性分析到定量分析奠定了基础。基于此模型建立了低渗透非线性定常和非定常渗流数学模型。导出了非线性定常渗流压力分布和产量公式,运用影响半径的概念和平均质量守恒的方法导出了非线性非定常渗流压力分布和影响半径公式。根据实验得到的参数及建立的模型进行了算例分析,得出了非线性定常渗流压力分布、非定常渗流压力分布及影响半径发展的规律,并将其与按线性渗流规律计算的结果进行了对比,结果表明二者差别明显,在进行低渗透油气田开发计算时,应考虑非线性渗流的影响。

MATHEMATICAL MODEL OF NONLINEAR FLOW LAW IN LOW PERMEABILITY POROUS MEDIA AND ITS APPLICATION

Two thousand and four hundred millions tons of proved and undeveloped low permeability reserves are a great potentiality for Chinese petroleum industry to develop.A problem on nonlinear flow in low permeability porous media is a basic one in exploiting low permeability oil and gas fields.It is also one of up to date research fields of modern mechanics of fluids in porous media.It is the first time that a mathematical model expressed in a continuous function for the nonlinear flow was established based on experiments.It lays a foundation of studying the nonlinear flow from qualitative analysis to quantitative one.Nonlinear mathematical models for steady and unsteady flow are given according to the model.Formulas of pressure distributions are presented.A formula of pressure disturbance radius of the unsteady flow is derived by means of average conservation of mass.An example is discussed on the authority of experiments.Pressure distributions and a movement law of the radius for the nonlinear flow,and their comparisons with those for the linear flow are obtained.It is shown that there is much difference between results based on nonlinear flow law and linear flow law.Thus,it is necessary that influence of nonlinear flow on development indexes of the fields be taken into account.