Numerical modelling of reservoir at pore scale: A comprehensive review

Abstract

Pore scale reservoir modelling is carried out to digitally build the inner structure of the reservoir samples using proper mathematical algorithms based on certain priors extracted from training image(s) or laboratory measured data. Although various imaging devices can provide the inner structure of the rock sample directly, numerical modelling methods still has its irreplaceable advantages. Firstly, due to some intrinsic limitations, no imaging device so far can provide a 3D porous structure satisfying both resolution and field of view except for a very few of homogeneous reservoir samples with relatively large pore-throat size, while numerical modelling is an effective approach to improve the resolution of the machine produced images. Secondly, in some cases, where only 2D images (such as the images of drill cuttings) are available, numerical modelling is the only option to reconstruct a 3D porous structure. Thirdly, numerical modelling is a convenient and low-cost technique that makes it widely applicable. This paper presents a comprehensive review of the pore scale reservoir modelling. Pore structure's modelling can be treated as a supervised prediction process with two steps: 1) extraction of descriptors (prior knowledge) from the training image(s) or laboratory measured data; and 2) numerical reconstruction under the supervision of the extracted descriptors. In terms of extraction of descriptors, using multiple-point statistics (MPS) instead of random function models is a great step that made the empirical multivariate distributions inferred from training images can be directly used to reconstruct porous structure. Another great progress is the application of multiple-resolution training images where the image degradation mechanism contained in these different resolution images can be used to supervise the reconstruction. In terms of supervised reconstruction, some mathematical strategies such as Gaussian Random field, simulated annealing are applied to reproduce these descriptors in the reconstructed images. Along with the flourish of deep learning, a convolutional neural networks model is introduced into reconstruction process with an impressive performance.