Comparison of Methods for Drainage Relative Permeability Estimation From Displacement Tests

Abstract

Abstract This paper compares classical and contemporary methods used to obtain relative permeability from dynamic experiments. We apply a variety of analytical, semi-analytical and history matching methods to analyze experimental data of oil-water unsteady-state drainage displacements. The analysis involves two types of error: bias and variance errors. The bias error in the resultant relative permeabilities mainly comes from the smoothening and differentiation of the experimental data while the variance error represents statistical uncertainty in measurements. We elect to use our own experimental data to minimize the variance error. We compare the numerical and functional fitting methods proposed for the differentiation and apply spline and Gaussian functions for fitting production and pressure data, respectively. We use spline fitting improved by time-domain data sampling to achieve a more effective history match. This approach minimizes the effects of non-uniqueness and shape dependency of relative permeability curves. We present a modification of the semi-analytical method of Civan and Donaldson (1989). Comparison of different methods shows that analytical methods are in agreement with each other but differ from the semi-analytical and history matching methods. The modified semi-analytical approach agrees well with the improved history matching. The spline and Gaussian functions for fitting experimental data are capable to preserve the data shape and yield less bias error. The function fitting methods are more effective than numerical methods in differentiation/integration of experimental data, preserving the features of the data and minimizing the errors. Semi-analytical methods provide a better first guess for history matching. Use of the cubic spline curves for relative permeability makes the relative permeability curve more flexible and any shape of the curve can be produced. There is a trade-off between the simplicity of the conventional Corey-type power law function and the accuracy of the cubic splines.