致密气自扩散渗流模型

Self-diffusion flow model of tight gas

致密气藏已经开始在世界上大规模开发,但其基本渗流机理尚不明确,现有渗流模型难以对生产数据进行完善的解释。笔者介绍并通过实例对Jin和Chen (2019)提出的新渗流模型及其适用性进行了研究。Jin和Chen从可压缩流体的N-S方程出发,基于Klainerman和Majda(1982)的小马赫数流动理论,利用渐近展开,多尺度分析和体积平均升尺度技巧,得到了时间尺度大于声波时间尺度时致密气藏一次开采油藏尺度下新的渗流方程。新的渗流方程反映了致密气藏一次开采完全是由气体的膨胀性驱动的物理本质,其扩散系数与孔隙度和气体黏度成正比,与气体密度成反比。通过实例对比自扩散模型与目前基于Darcy定律及其修正的渗流模型发现,Darcy渗流以及组合流动模型得到的气体产量仅在生产压差较小时才能与实际生产数据吻合,此时的产量较小;生产压差越大,Darcy渗流模型与实际生产数据偏差越大;而自扩散模型计算的产量能够较好地拟合实际生产数据。

Tight gas reservoirs have begun to be exploitated on a large scale in the world,of which the basic flow mechanism is still unclear.It is difficult to perfectly interpret production data using the existing flow models.Through the comparison of actual cases,this paper introduces and explores the new flow model proposed by Jin and Chen(2019)and its applicability by examples.According to the N-S equation of compressible fluids and based on the theory of Klainerman and Majda(1982)for low Mach num ber flow,Jin and Chen obtained the new flow equation for the primary recovery of tight gas reservoirs on the reservoir scale in the case of time scale greater than the acoustic time scale usingasymptotic expansion,multi-scale analysis and the upscaling technique of volume averaging.The new flow equation reflects the physical nature th at the primary recovery of tight gas reservoirs is driven entirely by the expansibility of gas,and its diffusion coefficient is proportional to porosity and gas viscosity,and inversely proportional to gas density.The comparison by case studies between the self-diffusion model and the current flow model based on the Darcy’s law and its modification shows that the gas yield obtained by the Darcy and combined flow model can only be consistent with the actual production data when the producing pressure drop is sm all,and the gas yield at this time is sm all;the larger the producing pressure drop,the greater the deviation between the Darcy flow model and the actual production data;the gas yield calculated by the self-diffusion model can well fit the actual production data.