一种利用岩块特征长度估算二维渗吸量的新方法

A New Method for Approximate Evaluation of Two-Dimensional Oil-Water Imbibition Based on Block Characteristic Length

对于存在大量亲水疏油岩块的天然裂缝性油藏,自发渗吸是基质岩块和裂缝系统油水交换的重要驱动机制.对于一维渗吸问题,前期存在自相似解析解,后期可以用近似解析解描述,从而可以很方便地估算出岩块剩余油饱和度和岩块出油速率.本文研究了二维矩形岩块在不同边界条件下渗吸过程的近似解析解,通过引入特征长度,将二维岩块渗吸问题等效为一维,从而可以有效利用一维近似解析解来估算出二维岩块渗吸过程中剩余油饱和度和岩块出油速率随时间的变化.本文提出了一个新的混合特征长度,在渗吸前期取岩块面积与岩块开放边界长度之比;在渗吸后期,特征长度根据前期特征长度和Ma等提出的特征长度按饱和度插值确定.通过数值检验比较了几种常见的特征长度取法和本文提出的混合特征长度取法,结果表明新的混合特征长度总体性能优于其他已有的特征长度取法,并且适用于本文列举的所有边界条件.

Spontaneous imbibition is an important driving mechanism for oil-water transfer flow between matrix blocks and fractures in naturally fractured reservoirs. For the one-dimensional imbibition problem, the remaining oil saturation and the oil production rate can be easily estimated by the self-similar analytic solution at the early stage and the approximate analytical description at the later stage. In this paper, the approximate solution of the imbibition process under different boundary conditions is studied for two-dimensional rectangular matrix block. The two-dimensional imbibition problem is equivalent to the one-dimensional problem with the help of the defined characteristic length, so that the remaining oil saturation and the oil production rate from the matrix block can be easily estimated according to the approximate one-dimensional analytical solution. A new mixed characteristic length is proposed, with its early stage value given by the ratio of the area of rock block to the length of open boundary, and its late stage value given by the interpolation of the early stage value and Ma’s characteristic length according to the saturation. The performance of the proposed mixed characteristic length is compared with those of the existing ones. Numerical tests show that the overall performance of the proposed mixed characteristic length is better than the existing ones. In addition, it is suitable for all the boundary conditions listed in this paper.