关键词: 自发渗吸, 无因次模型, 数值求解, 毛管回压

Abstract:

The reservoir parameters affecting imbibition performance are normalized. The dimensionless model for 1D 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 1D 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.

Key words: spontaneous imbibition, dimensionless model, numerical solution, capillary back pressure