Estimation Equations of Relative Permeabilities Considered Saturation Distribution

Abstract

The authors have investigated effects of distribution of saturation in a geothermal reservoir on relative permeabilities. Because the grid cells in a numerical calculation of reservoir simulation are not so small that the distributions of saturation in the cells are not assumed to be uniform. This paper proposes a model of saturation distribution, using a probability density function. The model, based on the Bernoulli trials, gives the following relation between the average value of the relative permeability for water phase, k_rwa and the arithmetical mean of the normalized water saturation, S_w^*_a : k_rwa= S_w^*_a, ^m (1≤m≤4). Also, the relative permeability of the steam phase, k_rga is as follows: k_rga=1-2S_w^*_a+2S_w^*_a^(2m+1)/3-S_w^*_am(1≤m≤4), where m is an index representing the non-uniformity of saturation. When m equals 4, k_rwa and k_rga each agree with the, so-called, Corey's equations. Then, the saturation is assumed to be distributed uniformly in the grid cell. On the other hand, when m=1, the flow of each phase is isolated one another . The proposed correlation equations are investigated through some experimental data already reported by the authors. The equations agree quite well with the experimental results of mass transfer in water-steam flow with boiling in a porous medium.