A Machine Learning-based Approach For Permeability Prediction Of Porous Media

Image-based modeling techniques have been widely used to characterize flow and transport in porous media with the development of microscopic imaging techniques and numerical modeling methods.As one of the most important hydraulic parameters,permeability can be calculated by simulating flow in porous media with computational fluid dynamics(CFD)techniques.Nevertheless,it is usually computationally expensive and time consuming due to the huge number of discretization grids.Since permeability is solely determined by the pore geometry,it is of interest to develop an efficient prediction method with machine learning algorithms.In this work,an efficient approach was proposed to achieve fast prediction of permeability directly from the three-dimensional structural images of porous media.In this way,the computationally expensive CFD simulations can be avoided.Furthermore,different machine learning techniques were compared.The approach consists of three main parts:(a)Generating stochastic three-dimensional porous structures.(b)Using Lattice Boltzmann method(LBM)to simulate flow in each porous structure;calculating the permeability of each structure according to the hydraulic gradient and average flow velocity,and establishing the data set for machine learning.(c)Using a part of the samples to train the machine learning models and another part to evaluate the accuracy of the model predictions.The models are divided into two categories according to the type of input data.One is based on the characteristic parameters of pore structures,and machine learning algorithms such as multiple linear regression,artificial neural network,support vector machine and random forest are employed to build the models.The other is to directly predict the permeability using convolutional neural network model based on the raw image data.We compared the predictive power of multiple trained machine learning methods using the coefficient of determinant R2 obtained on the test data set.The main conclusions are as follows:(1)When the characteristic parameters of pore geometry were used as the inputs,the determinant coefficient R2 obtained from the test set with the four models were all above 0.90.It was shown that all four models were with good predictive ability,and the nonlinear regression method performed better than the multiple linear regression method.(2)When the raw image data were used as inputs,the R2 value of convolutional neural network on the test set was 0.89.It was shown that the machine learning methods performed very well with the pore characteristic parameters as input,while the convolutional neural network was able to give reasonably accurate and fast predictions.(3)In terms of computational efficiency,all the machine learning methods were faster compared to the traditional LB method.In specific,the convolutional neural networks achieved about 1-2 orders of speed-up.This study demonstrates the promising potential of machine learning methods in fast predicting for permeability.The proposed methods can also be used for fast prediction of other geometry related properties of porous media.