Estimation Equations of Relative Permeabilities Considered Saturation Distribution

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* _a ^m (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.