### Abstract

High resolution, 3-D micro-structure images of rocks can be used to compute the transport and elastic properties of those samples using a digital rock physics approach. Those properties are complex functions of the pore size distribution, geometry and morphology, which necessitates the use of accurate 3-D volumes. Because of the limited availability of 3-D micro-structure images of rocks, several attempts to construct 3-D images from 2-D ones have been made. In this study, we propose a new stochastic method to reconstruct a 3-D image of the rock using only a 2-D section of the imaged rock sample. Our method is based on a simple observation that the pores are gradually deformed from one section to the next one. Therefore, the first step is to generate multiple independent realizations by performing Multiple-Point Statistics (MPS) based stochastic simulations. These simulations represent independent 2-D scans through the rock volume. Next, a succession of images is generated spanning two adjacent independent sections. These images consist of gradually morphed features from one section to those in the next independent section. Juxtaposing these 2-D images results in the reconstructed 3-D image. We calculate the spatial connectivity in the 3^{rd} direction and confirmed that the proposed method can retrieve the connectivity in the 3^{rd} direction accurately. We also compute transport and elastic properties from the reconstructed image and from the original image to verify that this method reproduces the appropriate spatial statistics and pore size distribution, geometry and morphology. We also compare the numerical results with laboratory measurements performed on the sample. The results obtained using the reconstructed image reveal that the numerically calculated properties are similar to the measured values. We compare the mismatch of transport and elastic properties with the original measurements with that of the previous reconstruction algorithm. These comparisons show that the proposed simulation method has the same accuracy as previous ones. However, the proposed method is much more computationally efficient than the other algorithms, mainly due to the faster MPS algorithm and the fact that the simulation is being done only for the independent layers instead of all the layers. The proposed methodology is an accurate method to reconstruct a 3-D representative sample of a rock given only one 2-D thin section. The algorithm is computationally efficient and faster than the previously introduced algorithm, and can easily be used to characterize samples for which 3-D images are difficult to obtain in terms of both time and expenses.

Original language | English (US) |
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Title of host publication | Society of Petroleum Engineers - SPE Western Regional Meeting |

Publisher | Society of Petroleum Engineers |

ISBN (Electronic) | 9781613994658 |

State | Published - Jan 1 2016 |

Event | SPE Western Regional Meeting 2016 - Anchorage, United States Duration: May 23 2016 → May 26 2016 |

### Publication series

Name | Society of Petroleum Engineers - SPE Western Regional Meeting |
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### Other

Other | SPE Western Regional Meeting 2016 |
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Country | United States |

City | Anchorage |

Period | 5/23/16 → 5/26/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Energy Engineering and Power Technology

### Cite this

*Society of Petroleum Engineers - SPE Western Regional Meeting*(Society of Petroleum Engineers - SPE Western Regional Meeting). Society of Petroleum Engineers.

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*Society of Petroleum Engineers - SPE Western Regional Meeting.*Society of Petroleum Engineers - SPE Western Regional Meeting, Society of Petroleum Engineers, SPE Western Regional Meeting 2016, Anchorage, United States, 5/23/16.

**3-D reconstruction of porous media from a 2-D section and comparisons of transport and elastic properties.** / Naraghi, Morteza Elahi; Spikes, Kyle; Srinivasan, Sanjay.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - 3-D reconstruction of porous media from a 2-D section and comparisons of transport and elastic properties

AU - Naraghi, Morteza Elahi

AU - Spikes, Kyle

AU - Srinivasan, Sanjay

PY - 2016/1/1

Y1 - 2016/1/1

N2 - High resolution, 3-D micro-structure images of rocks can be used to compute the transport and elastic properties of those samples using a digital rock physics approach. Those properties are complex functions of the pore size distribution, geometry and morphology, which necessitates the use of accurate 3-D volumes. Because of the limited availability of 3-D micro-structure images of rocks, several attempts to construct 3-D images from 2-D ones have been made. In this study, we propose a new stochastic method to reconstruct a 3-D image of the rock using only a 2-D section of the imaged rock sample. Our method is based on a simple observation that the pores are gradually deformed from one section to the next one. Therefore, the first step is to generate multiple independent realizations by performing Multiple-Point Statistics (MPS) based stochastic simulations. These simulations represent independent 2-D scans through the rock volume. Next, a succession of images is generated spanning two adjacent independent sections. These images consist of gradually morphed features from one section to those in the next independent section. Juxtaposing these 2-D images results in the reconstructed 3-D image. We calculate the spatial connectivity in the 3rd direction and confirmed that the proposed method can retrieve the connectivity in the 3rd direction accurately. We also compute transport and elastic properties from the reconstructed image and from the original image to verify that this method reproduces the appropriate spatial statistics and pore size distribution, geometry and morphology. We also compare the numerical results with laboratory measurements performed on the sample. The results obtained using the reconstructed image reveal that the numerically calculated properties are similar to the measured values. We compare the mismatch of transport and elastic properties with the original measurements with that of the previous reconstruction algorithm. These comparisons show that the proposed simulation method has the same accuracy as previous ones. However, the proposed method is much more computationally efficient than the other algorithms, mainly due to the faster MPS algorithm and the fact that the simulation is being done only for the independent layers instead of all the layers. The proposed methodology is an accurate method to reconstruct a 3-D representative sample of a rock given only one 2-D thin section. The algorithm is computationally efficient and faster than the previously introduced algorithm, and can easily be used to characterize samples for which 3-D images are difficult to obtain in terms of both time and expenses.

AB - High resolution, 3-D micro-structure images of rocks can be used to compute the transport and elastic properties of those samples using a digital rock physics approach. Those properties are complex functions of the pore size distribution, geometry and morphology, which necessitates the use of accurate 3-D volumes. Because of the limited availability of 3-D micro-structure images of rocks, several attempts to construct 3-D images from 2-D ones have been made. In this study, we propose a new stochastic method to reconstruct a 3-D image of the rock using only a 2-D section of the imaged rock sample. Our method is based on a simple observation that the pores are gradually deformed from one section to the next one. Therefore, the first step is to generate multiple independent realizations by performing Multiple-Point Statistics (MPS) based stochastic simulations. These simulations represent independent 2-D scans through the rock volume. Next, a succession of images is generated spanning two adjacent independent sections. These images consist of gradually morphed features from one section to those in the next independent section. Juxtaposing these 2-D images results in the reconstructed 3-D image. We calculate the spatial connectivity in the 3rd direction and confirmed that the proposed method can retrieve the connectivity in the 3rd direction accurately. We also compute transport and elastic properties from the reconstructed image and from the original image to verify that this method reproduces the appropriate spatial statistics and pore size distribution, geometry and morphology. We also compare the numerical results with laboratory measurements performed on the sample. The results obtained using the reconstructed image reveal that the numerically calculated properties are similar to the measured values. We compare the mismatch of transport and elastic properties with the original measurements with that of the previous reconstruction algorithm. These comparisons show that the proposed simulation method has the same accuracy as previous ones. However, the proposed method is much more computationally efficient than the other algorithms, mainly due to the faster MPS algorithm and the fact that the simulation is being done only for the independent layers instead of all the layers. The proposed methodology is an accurate method to reconstruct a 3-D representative sample of a rock given only one 2-D thin section. The algorithm is computationally efficient and faster than the previously introduced algorithm, and can easily be used to characterize samples for which 3-D images are difficult to obtain in terms of both time and expenses.

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M3 - Conference contribution

AN - SCOPUS:84978473781

T3 - Society of Petroleum Engineers - SPE Western Regional Meeting

BT - Society of Petroleum Engineers - SPE Western Regional Meeting

PB - Society of Petroleum Engineers

ER -