一维水平自发渗吸无因次模型及其数值解

Dimensionless Model and Numerical Solution for 1D Horizontal Spontaneous Imbibition

对影响渗吸特征的油藏参数进行归整,导出考虑毛细管回压的一维自发渗吸问题无因次模型。该模型选取水相归一化饱和度和无量纲压力作为主未知变量,毛管压力函数只在模型的一个偏微分方程中出现,便于数值求解。在求解该模型的全隐式守恒型差分格式中,对两邻点间饱和度函数取平均饱和度下的值,就可以得到该问题的数值解。通过对幂律型相对渗透率和毛管压力曲线情形下此模型数值解的讨论,指出前人关于一维不可压自发渗吸问题解析解所用的假设条件只对纯逆向渗吸有一定的适用性。通过多个同逆并发渗吸算例,得到油藏参数变化对渗吸动态特征影响的初步认识。

The reservoir parameters affecting imbibition performance are normalized. The dimensionless model for 1 D horizontal spontaneous imbibition in consideration of capillary back pressure is derived. In the model, the normalized water saturation and dimensionless water pressure are chosen as the primary unknown variables. The capillary pressure function only appears in one PDE in the model which is convenient to be solved numerically. The numerical solution can be obtained by the fully implicit and conservative difference scheme with the saturation function value between two adjacent points to be set on the value at the arithmetic average saturation for the two points. The solution of this model with relative permeability and capillary pressure curves matching power law is discussed. The assumption used by prior researchers to obtain the analytical solution for 1 D incompressible spontaneous imbibition problem is pointed out to be only partially applicable for purely countercurrent case. More numerical results for co-current imbibition cases are also obtained and discussed, and some preliminary cognition about the variation of imbibition performance along with reservoir parameters is concluded.