An Artificial Neural Network Based Relative Permeability Predictor
Authors: Guler B. , Ertekin T. , Grader A.S. 
Published: March 2010

Abstract
Relative permeabilities are complex and important rock-fluid properties of reservoirs in which multi-phase flow conditions prevail. Measuring relative permeabilities in the laboratory using cores obtained from a reservoir is a complicated, time demanding, and labour-intensive task. There has been limited success in mathematical modelling of relative permeabilities based on rocks and fluid properties due to our inability to simulate the non-linear controlling mechanisms in place. Artificial neural networks (ANNs) promise a potential avenue for implicitly incorporating the controlling mechanisms and parameters into a model that can be utilized as an effective tool for relative permeability predictions.
The methodology described in this paper exploits the unique topology of ANNs for determining the two-phase (oil-water) relative permeabilities. The ANN is a universal approximator that performs non-linear, multi-dimensional interpolations. In the development stage of the ANN model, a large number of oil-water relative permeability data sets were collected from the literature. These data sets were used to train the model. In composing the architecture of the ANN, only the readily available rock and fluid properties (end-point saturations, porosity, permeability, viscosity, and interfacial tension) have been explicitly incorporated. The predictive ability of the model was tested using experimental data sets that were not used during the training stage. The results are in good agreement with the experimentally reported data. The proposed model exhibits sensitivity to several reservoir properties. The proposed ANN model has a dynamic training base that can be expanded as new data become available.

Introduction
Relative permeabilities quantify multi-phase flow through porous media. Generating an accurate relative permeability vs. saturation relationship for each phase is essential for evaluating the performance of a reservoir during primary, secondary, and tertiary production periods. Relative permeability-saturation relationships vary between reservoirs and within a given reservoir. They are non-linear functions of reservoir rock and fluid properties such as phase saturations, formation types, depositional environment, shale content, heterogeneity, porosity, permeability, interconnectivity of pores, pore geometry, interfacial tensions between flowing phases, phase viscosities, phase densities, and rock wettability.
Experimental and modelling methods are used for assigning relative permeabilities to a reservoir. Although laboratory measurements of relative permeabilities are difficult, they are still the preferred method. Laboratory measurements are technically difficult and require skillful personnel, expensive equipment, and are lengthy to perform. Therefore, estimation of relative permeabilities with mathematical models has always been an attractive goal. Relative permeability models are commonly used only as estimation tools. Mathematical models for relative permeability can be classified under four main categories: capillary, statistical, empirical, and network models. These models require some rock and fluid properties such as end-point saturation values, porosity, absolute permeability, interfacial tensions, and viscosity of phases, and incorporate important assumptions. The models are restricted by their assumptions, are not universally applicable, and may be difficult to update for different systems. Empirical models and pore-network models are frequently used and are the most successful in estimating relative permeabilities. Predicting the relative permeability values using mathematical models is essential for reservoir simulation applications.