A Modified Method and Experimental Verification for Estimating Relative Permeability from Resistivity Logging Data
Authors: Bian Huiyuan , Li Kewen , Yang Jinghai , Pei Jianya , Lao Pengcheng , Li Xiaowei 
Published: March 2015

Abstract
The existing method to infer relative permeability from resistivity data was modified by including more parameters such as residual oil saturation. Both oil-water relative permeability and resistivity were measured simultaneously in the same core sample at a room temperature in order to verify the modified model. Altogether 16 core samples in 2 wells from Daqing oil field, China have been tested. The permeability ranged from about 10 to 800 md. The oil-water relative permeability data were measured using a dynamic displacement technique. Oil-water relative permeability data were inferred from the resistivity data measured in the laboratory and logged from the well using the modified model. The model data were then compared to the experimental data. We demonstrated that the relative permeability of both oil and water calculated from the resistivity data measured in the same core samples and logged from the same wells were close to the experimental data measured using a dynamic displacement approach. The modified model had a greater accuracy compared with the existing models. Using the modified model, it would be possible to obtain the different distribution of relative permeability characteristics in different kinds of formations in a reservoir. It may also be feasible to infer relative permeability data while drilling if resistivity well logging is being taken.

Introduction
Relative permeability is one of the important parameters controlling multiphase fluid flow in porous media. These data are traditionally obtained with experimental measurements. However, relative permeability is expensive, difficult, and time-consuming to measure in the laboratory, especially for the rocks from unconventional oil and gas reservoirs such as shale plays, tight sands, and extremely low permeability reservoirs. It is also difficult to maintain exact reservoir conditions in taking a core or a fluid sample from the reservoir and bringing it to surface and it is almost impossible to conduct the measurements in real time. Consequently, there has been a decades-long research effort to develop methods and procedures to infer relative permeability using network modeling. Recently, the industry has been researching new methods to extract relative permeability in-situ including the utilization of specially designed permanent downhole electric resistivity array, pressure, and flow rate measurements.
Relative permeability can also be derived from other parameters such as capillary pressure data. Mahmoud et al. (2013) predicted the capillary pressure from well logging data in carbonate reservoir and sandstone reservoir.
Purcell (1949) reported a mathematical model to calculate the relative permeability from capillary pressure data. From then on, many researchers worked on this area. Li (2005, 2007 and 2010), Li and Horne (2006) and Li and Williams (2006) have made a lot of contribution for estimating the relative permeability using resistivity well logging data.
Based on the reaserch on the interrelation between capillary pressure, resistivity and relative permeability reported by Li (2010), Alex et al. (2012) considered to modify the model in double porosity systems. They developed a method to calculate relative permeability and caplillary pressure from resistivity well logging data in naturally fractured reservoirs.