GPU-accelerated 3D reconstruction of porous media using multiple-point statisticsComput Geosci


Ting Zhang, Yi Du, Tao Huang, Xue Li
Computational Theory and Mathematics / Computer Science Applications / Computational Mathematics / Computers in Earth Sciences


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Comput Geosci

DOI 10.1007/s10596-014-9452-9


GPU-accelerated 3D reconstruction of porous media using multiple-point statistics

Ting Zhang · Yi Du · Tao Huang · Xue Li

Received: 13 December 2013 / Accepted: 7 October 2014 © Springer International Publishing Switzerland 2014

Abstract It is very important for the study of predicting fluid transport properties or mechanisms of fluid flow in porous media that the characteristics of porous media can be extracted in relatively smaller scales and then are copied in a larger or even arbitrary region to reconstruct virtual 3D porous media that have similar structures with the real porous media. One of multiple-point statistics (MPS) method, the single normal equation simulation algorithm (SNESIM), has been widely used in reconstructing 3D porous media recently. However, owing to its large CPU cost and rigid memory demand, the application of SNESIM has been limited in some cases. To overcome this disadvantage, parallelization of SNESIM is performed on the compute unified device architecture (CUDA) kernels in the graphic processing unit (GPU) to reconstruct each node on simulation grids, combined with choosing the optimal size of data templates based on the entropy calculation towards the training image (TI) to acquire high-quality reconstruction with a low CPU cost; meanwhile, the integration of hard data and soft data is also included in the processing of CUDA kernels to improve the accuracy. Representative

T . Zhang

College of Computer Science and Technology, Shanghai

University of Electric Power, 2588 Changyang Road, Shanghai 200090, People’s Republic of China

Y. Du ()

School of Computer and Information, Shanghai Second

Polytechnic University, 2360 Jinhai Road, Shanghai 201209,

People’s Republic of China e-mail:

Y. Du · T. Huang · X. Li

Department of Modern Mechanics, University of Science and

Technology of China, 96 Jinzhai Road, Hefei 230027,

People’s Republic of China elementary volumes (REVs) for porosity, variogram, and entropy are analyzed to guarantee that the scale of observation is large enough and parameters of concern are constant.

This parallel GPU-version 3D porous media reconstruction only requires relatively small size memory and benefits from the tremendous calculating power given by CUDA kernels to shorten the CPU time, showing its high efficiency for the reconstruction of porous media.

Keywords Porous media · Graphic processing unit ·

Parallel · Multiple-point statistics · Soft data ·

Representative elementary volume

Mathematics Subject Classifications (2010) 76S05 · 86A32 · 68W10 · 94A08 1 Introduction

The flow properties in porous media have been widely studied not only in petroleum engineering, but also in hydrology, environmental engineering, and some other related fields.

The structural information of porous media is necessary prior to predicting the flow properties and describing the physical relationship between rock grains and fluids. Hence, the reconstruction of porous media is of great significance when the internal structure of porous media in large scales cannot be easily acquired [1–5].

The research on the reconstruction of porous media has been developing rapidly in recent decades [2, 3]. Fatt [6] pioneered the pore network model based on hypothetical pore structure to study the characteristics of some flow properties. The Voronoi networks and Delaunay triangulations were used by Blunt and King [7, 8] to improve the pore network models. Some researchers presented some typical

Comput Geosci models like the sphere-packing model afterwards [9]. However, because the pore spaces in a rock represented by a network of pores (corresponding to the larger void spaces) and throats (the narrow openings connecting the pores) are usually mimicked by simplified shapes, they cannot accurately describe the complicated topological structures of porous media.

At the same time, the structure of porous media can currently be acquired by 2D or 3D imaging directly owing to the fast development of imaging techniques including focused ion beam, laser scanning confocal microscopy, Xray computed tomography (CT), and so on [2, 10, 11].

Based on real images of porous media, the process-based method [12] and some statistical methods were developed to realize 3D reconstruction of porous media [13].

One typical widely used statistical method for extraction of statistical information is multiple-point statistics (MPS) introduced by the seminar work of Guardiano and

Srivastava [14]. Actually, using MPS in the reconstruction of porous media was started by the pioneering work of

Okabe and Blunt [2, 3], who used a 2D CT-scanned image of porous media as a training image (TI) containing the intrinsic features to build 3D pore spaces. Afterwards, some other researchers similarly built 3D pore spaces with the resolution of microns [15, 16].

The single normal equation simulation (SNESIM) algorithm [17, 18] was used in the above reconstruction methods to acquire the conditional probability distribution function (cpdf) of TIs, which were actually pseudo-3D images constructed by a few 2D thin CT-scanned cross sections to reduce CPU cost [2, 3, 15, 16]. For example, Okabe and

Blunt [2, 3] aggregated the statistical information by rotating a 2D thin cross section of porous media to reproduce 3D pore spaces. Comunian et al. [15] developed a method that relies on merging the probabilities obtained by 2D crosssection images in three directions. Hajizadeh et al. [16] proposed a technique relying on stacking a series of successive 2D MPS simulated images coupled to a conditioning data extraction procedure. Xu et al. [19] revised the memory storage method from the search tree to array structure to reduce memory demand using 2D TIs.

In the above research work, combined 2D CT-scanned images of porous media were directly or indirectly used as a pseudo-3D TI to build 3D pore spaces with the resolution of several microns. Because there are only two states, pore spaces and grains, existing in porous media, it is appropriate to simulate the categorical variables using an MPS method such as SNESIM which is actually used to acquire cpdfs of 3D structures in the above methods [2, 3, 15, 16, 19].