Estimation of the Water–Oil Relative Permeability Curve from Radial Displacement Experiments. Part 1: Numerical Inversion Method

Abstract

The water–oil relative permeability curve is mainly obtained from linear displacement experiments. Few radial displacement experiments have been carried out. In the process of linear displacement experiments, the flow properties of the water–oil two phase are linear. Nevertheless, it is radial near the bottom holes of an actual reservoir. With regard to both kinds of displacement experiments, the flow characteristics are various, which may result in great deviation to apply the linear calculation theory of the relative permeability curve to an actual reservoir. As a result of the above-mentioned problems, on the basis of radial displacement experiments, using the Levenberg–Marquardt algorithm for automatic history matching, this paper performs optimization of production performance and relative permeability representation models. Finally, a novel numerical inversion method for the radial water–oil relative permeability curve is established. A test based on the basic data of a radial laboratory displacement experiment is performed to verify the effect of the proposed method. The results show that oil relative permeability is more sensitive to the cumulative production data, while water relative permeability is more sensitive to the bottomhole pressure data of the producers. It also indicates that the cubic B-spline model (CBM) is far more general and flexible and has the advantage of local fitting compared to the power law model (PM). In addition, the numerical inversion method proposed for the radial water–oil relative permeability curve is reliable and can meet the engineering requirement, which provides a basic calculation theory for the estimation of the water–oil relative permeability curve.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

“…However, due to the inherent limitations confronted by the relative permeability representation model, no significant recognitions were achieved (Li et al 2012;Chen and Reynolds 2015). Using the Levenberg-Marquardt (LM) algorithm for automatic history matching, Hou et al addressed the optimization of production performance and relative permeability representation models and finally proposed a numerical inversion method for estimation of the radial water-oil relative permeability curve, which attracts great interest by researchers in petroleum engineering (Hou et al 2012a(Hou et al , b, 2015.…”

Estimation of relative permeability curves using an improved Levenberg-Marquardt method with simultaneous perturbation Jacobian approximation

“…In order to ensure the cubic B-spline model to be monotonic, many researchers use log transformation for the original controlling knots. Following Hou et al (2012b), the pseudo-controlling knots are written as:…”

“…The secant version of the LM method is intended for this problem. The most widely used method is to 3 replace the elements of original Jacobian by finite difference approximations (Hou et al, 2012a(Hou et al, , 2012b. For simplicity, the LM method with finite difference Jacobian approximation is denoted as the LM-FD method.…”

Prediction of carbon dioxide separation from gas mixtures in petroleum industries using the Levenberg–Marquardt algorithm

“…In this case, some investigations can be considered. Hou et al (2012) presented a model for the estimation of the water-oil relative permeability from radial displacement experiments by using LM algorithm to optimize the model. Ghiasi (2012) presented a new empirical correlation for estimation of hydrate formation temperature of sweet natural gas.…”