A Novel Empirical Equation for Relative Permeability in Low Permeability Reservoirs

In this paper, a novel empirical equation is proposed to calculate the relative permeability of low permeability reservoir. An improved item is introduced on the basis of Rose empirical formula and Al-Fattah empirical formula, with one simple model to describe oil/water relative permeability. The position displacement idea of bare bones particle swarm optimization is applied to change the mutation operator to improve the RNA genetic algorithm. The parameters of the new empirical equation are optimized with the hybrid RNA genetic algorithm (HRGA) based on the experimental data. The data is obtained from a typical low permeability reservoir well 54 core 27-1 in GuDong by unsteady method. We carry out matlab programming simulation with HRGA. The comparison and error analysis show that the empirical equation proposed is more accurate than the Rose empirical formula and the exponential model. The generalization of the empirical equation is also verified.

Graphical abstractFig. 3 shows the curve of water phase relative permeability. Parameters of our empirical equation, exponential model and Rose empirical formula are optimized by HRGA method. Fig. 5 is the error analysis for water phase. In Fig. 5, the straight line is Y = X, with the computational data equal to experimental data. So the nearer the data points to this curve, the closer the calculating data to the real data. From these two figures, the empirical equation in this paper is much better than the exponential model and Rose empirical formula, while exponential model is better than Rose empirical formula.Figure optionsDownload full-size imageDownload as PowerPoint slide