Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 964204, 5 pages
http://dx.doi.org/10.1155/2015/964204

Research Article

Study and Application of Safety Risk Evaluation Model for CO₂ Geological Storage Based on Uncertainty Measure Theory

Hujun He,1,2 Yaning Zhao,³ Xingke Yang,¹ Yaning Gao,¹ and Xu Wu¹

¹School of Earth Science and Resources, Chang’an University, Xi’an 710054, China
²Key Laboratory of Western Mineral Resources and Geological Engineering, Ministry of Education, Chang’an University, Xi’an 710054, China
³The 213th Research Institute of China Ordnance Industry, Xi’an 710061, China

Received 23 September 2015; Accepted 29 November 2015

Academic Editor: Hiroyuki Mino

Copyright © 2015 Hujun He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Analyzing showed that the safety risk evaluation for CO₂ geological storage had important significance. Aimed at the characteristics of CO₂ geological storage safety risk evaluation, drawing on previous research results, rank and order models for safety risk evaluation of CO₂ geological storage were put forward based on information entropy and uncertainty measure theory. In this model, the uncertainty problems in safety risk evaluation of CO₂ geological storage were solved by qualitative analysis and quantitative analysis, respectively; uncertainty measurement functions for the relevant factors were established based on experimental data; information entropy theory was applied to calculate the index weight of factors; safety risk level was judged based on credible degree recognition criterion and ordered. This model was applied in three typical zones of Erdos and Hetao basins. The results show that uncertainty measure method is objective and reasonable and can be used as a new way to evaluate the safety of CO₂ geological storage sites in the future.

1. Introduction

The extensive use of coal, oil, natural gas, and other fossil fuels significantly increases the CO₂ content of the atmosphere. This leads to global warming and poses a serious threat to humans and the sustainable development of our society and economy. CO₂ emissions have become a major problem. At present, scientists agree that CO₂ capture and storage is an important and effective strategy for easing climate change. It can also be effectively, comprehensively, and sustainably applied to resource development, energy utilization, economic growth, and ecological environment protection, among others [1, 2].

A geological implementation of CO₂ storage could safely trap CO₂ in rock cracks in the deep crust of the earth, but this takes a long time. Furthermore, temperatures and pressure changes inside the earth cause sudden geological events such as volcanoes and earthquakes, which trigger tectonic movements. Additionally, human engineering activities such as abandoned wells could lead to CO₂ leaks [3]. Thus, CO₂ geological sequestration technology is a “double-edged sword”; it could effectively alleviate the environmental disaster of climate change, but, at the same time, it could induce geological environmental disasters. It is therefore imperative that the people research methods for geologically storing CO₂ and evaluate the security risks.

Recently, there have been several investigations into evaluating the risks of CO₂ geological storage, and researchers have proposed many risk evaluation methods. However, the proposed standards and methods have mainly been aimed at the storage medium and lack of systemic evaluation weight methods [4–6]. CO₂ geological storage security risk is a comprehensive combination of many internal and external factors, which are random, fuzzy, grey, and uncertain. It is important that the people analyse the uncertainties of this information. In this regard, uncertainty mathematical theory provides a better way. Based on previous CO₂ geological storage security risk evaluation research and referring to the mathematical theory of uncertainty [7, 8], a new method is proposed for evaluating the risks in this paper.

2. Uncertainty Measure

Let be objects in the index space . Each object has single evaluation index spaces; that is, . can be expressed as a -dimensional vector . has evaluation levels, and its evaluation level space is , where indicates the th level. The th level is stronger than the ()th level; that is, . Then, is an ordered partition class in evaluation space .

2.1. Uncertainty Measure for a Single Index

Let indicate that measured value belongs to (the th evaluation level). must satisfy

Equation (2) means meets the “normalization” for evaluation space ; equation (3) means meets the “additivity” for evaluation space . Because it satisfies (1), (2), and (3), is called the uncertainty measure or measure [9–11].

The matrix

is the single index evaluation matrix. When constructing it, the single index measure function must be first established. Existing methods for constructing this function include linear, exponential, parabola, and sinusoidal functions. Regardless of its type, the simulation function must be nonnegative, unitary, and additive. Suitable uncertainty measures can be selected according to the characteristics of specific indexes. A linear uncertainty measure is currently the most popular and simple, so it was used in this paper.

2.2. Determining the Index Weight

Let represent the importance of relative to the other indexes, and let be the weight of . The weight of each index is determined using information entropy theory [12–15]. That is,

2.3. Comprehensive Measure for Multiple Indexes

Using the index weights, the multi-index comprehensive measure can be calculated to evaluate . Here, if , , then is known as the uncertainty measure, and is the multi-index comprehensive evaluation measure vector of .

2.4. Recognition Criterion of the Credibility

If , a credibility criterion can be introduced. Let be the degree of credibility, where ; typically use or 0.7. If , then it is considered to belong to .

2.5. Ordering

As well as discriminating ’s evaluation level, sometimes it must be ordered according to its importance. If , the command value of is . Then, , and , where is the uncertainty importance degree of evaluation factor . is called the uncertainty importance vector. is ordered according to the value of .

3. Example Application

The data of 3 typical zones in the Erdos and Hetao basins provided by Wang [16] were taken as the research object. Drawing from the results in [17–20], we set the cover layer lithology, total thickness of the cover layer, seismic safety, presence of drilling and abandoned wells within 25 km² of the site, topography, main wind directions between the CO₂ perfusion site and residents, distance from permanent residents, and distance from surface drinking water sources such as rivers and reservoirs, as evaluation factors. The qualitative parameters such as the cover layer lithology, seismic safety, presence of drilling and abandoned wells within 25 km² of the site, topography, and main wind directions between the CO₂ perfusion site and residents are valued by a semiquantitative method. The grading standards and values are shown in Table 1. The values of the quantitative parameters such as total thickness of the cover layer, distance from permanent residents, and distance from surface drinking water sources such as rivers and reservoirs were valuable measures, as shown in Table 2. Each evaluation index was classified and valued, and the evaluation set is (or high, medium, and low). The basic situations of number 1, number 2, and number 3 target zones are shown in Table 3.

Table 1: Classification criteria of the qualitative indexes.

Grade
Value
Factors

The cover layer lithology
Seismic safety
Presence of drilling and abandoned wells within 25 km² of the site
Topography
Main wind directions between the CO₂ perfusion site and residents

High
3
Shale and compact limestone
Low
Many and not sealed
Lying and complex terrain
Upwind

Medium
2
Mud rocks
Medium
Exist and have been sealed
Broad and shallow terrain
Side wind

Low
1
Evaporating rocks
High
No
High convex open terrain
Downwind

Table 2: Classification criteria of quantitative indexes.

Grade
Factors

Total thickness of the cover layer (m)
Distance from permanent residents (m)
Distance from surface drinking water sources such as rivers and reservoirs (m)

High
<40
<800
<150

Medium
40–80
800±
150±

Low
>80
>800
>150

Table 3: Survey statistics for the evaluation index.

Research zone
The cover layer lithology
Total thickness of the cover layer (m)
Seismic safety
Presence of drilling and abandoned wells within 25 km² of the site
Topography
Main wind directions between the CO₂ perfusion site and residents
Distance from permanent residents (m)
Distance from surface drinking water sources such as rivers and reservoirs (m)

Number 1 target zone
Mud rock
40–80
Medium
No
Complex terrain
Downwind
>800
150±

Number 2 target zone
Mud rock
40–80
High
No
High convex open terrain
Side wind
800±
>150

Number 3 target zone
Mud rock
40–80
Low
No
Broad and shallow terrain
Downwind
>800
<150

3.1. Single Index Measure Function

According to the constructing method of single index measure function, combined with grading standards in Tables 1 and 2, and the specific values in Table 3, single index measure functions are constructed in order to obtain the measured value of each evaluation index. The single index measure functions of qualitative indexes such as the cover layer lithology, seismic safety, presence of drilling and abandoned wells within 25 km² range of the site, topography, and main wind direction between the CO₂ perfusion site and residents are shown in Figure 1. The single index measure functions of quantitative indexes such as total thickness of the cover layer are shown in Figure 2. We used the same method for constructing the single index measure function for distance from permanent residents and distance from surface drinking water sources such as rivers and reservoirs.

Figure 1: Single index measure function for the cover layer lithology, seismic safety, presence of drilling and abandoned wells within 25 km² range of the site, topography, and main wind direction between the CO₂ perfusion site and residents.

Figure 2: Single index measure function for total thickness of the cover layer.

According to single index measure function mentioned above and combined with the actual data in Table 3, the single index evaluation matrix of 3 target zones can be calculated. For example, the single index evaluation matrix for number 1 target zone was

3.2. Calculating the Multiple Index Measures Evaluation Matrix

Formula (5) determines the weight of each index. The weights of the evaluation indexes for number 1 target zone were , . Using the single index measure matrix and the multiple index calculation formula, the multiple index vector was .

3.3. Degree of Credibility

We set the degree of credibility to and used the multiple index comprehensive evaluation measure vector and credibility formula to calculate that . Then, the grade of number 1 target zone was “medium.” The other two target zones are evaluated in a similar way. The results are shown in Table 4. Our evaluations of the safety risk grade of each target zone match well with the results obtained by Wang [16] using fuzzy comprehensive evaluation method.

Table 4: Evaluation results comparing the uncertainty measure models and the fuzzy comprehensive evaluation results from Wang [16].

Research zone
General uncertainty measure
Evaluation results of uncertainty measure model
Evaluation results of fuzzy comprehensive evaluation

Number 1
0.125
0.5
0.375
II
II

Number 2
0
0.5
0.5
III
III

Number 3
0.25
0.375
0.375
II
II

3.4. Ordering of the Safety Risk Grades

According to order formula, because , we can take , where , so that . Ordering the CO₂ geological storage safety risk grade of 3 target zones, we see that the risk is highest in number 3 target zone, followed by number 1 target zone and then number 2 target zone.

4. Conclusions

(1) According to the random, fuzzy, grey, and uncertainty characteristics of CO₂ geological storage safety risk evaluation, an evaluation method of CO₂ geological storage safety risk based on uncertainty measure theory was put forward, and the evaluation model of CO₂ geological storage safety risk was established based on uncertainty measure theory.

(2) The index weights were objectively calculated based on information entropy theory. The safety risk of CO₂ geological storage was evaluated using credibility measurements, and the risk grades were ranked. This method is objective and reasonable and provides a new way to evaluate the safety risk of CO₂ geological storage.

(3) The method was applied to data from 3 typical zones in Erdos and Hetao basins. The results matched well with those obtained by the fuzzy comprehensive evaluation method in Wang [16].

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work was financially supported by CO₂ geological storage integrated research in China (12121210004) and the special fund for basic scientific research of central colleges (310827151056 and 310827153408).

References

S. Sun, “Geological problems of CO₂ underground storage and its significance on the mitigation of climate change,” China Basic Science, no. 3, pp. 17–22, 2006.

S. Q. Zhang, J. Q. Guo, X. F. Li, J. J. Fan, and Y. J. Diao, Geological Foundation of Carbon Dioxide Geological Storage and Site Geological Evaluation in China, Geology Press, Beijing, China, 2011.

Z. G. Xu, D. Z. Chen, R. S. Zeng, K. Guo, and Y. P. Li, “Technologies for monitoring subsurface CO₂ distribution and local environmental effects of CO₂ geological storage,” Advances in Climate Change Research, vol. 4, no. 6, pp. 363–368, 2008.

J. Xu, J. Y. Zhang, X. Pan, and C. G. Zheng, “Current status of carbon dioxide storage technologies,” Coal Conversion, vol. 28, no. 3, pp. 80–86, 2005.

W. Zhang and Y. L. Li, “Research status and prospects of carbon dioxide sequestration technique,” Environmental Pollution & Control, vol. 28, no. 12, pp. 950–953, 2006.

H. J. He, X. K. Yang, H. X. Chao, and W. G. Zhang, “Creation of CO₂ geological storage suitability model in coal-accumulating basin based on AHP and fuzzy comprehensive evaluation,” Disaster Advances, vol. 6, no. 5, pp. 24–30, 2013.

G. Y. Wang, “Uncertainty information and its mathematical treatment,” Journal of Harbin Architecture and Engineering Institute, vol. 23, no. 4, pp. 52–58, 1990.

K. D. Liu, H. Q. Wu, and Y. J. Pang, Mathematics Treatment and Application of Uncertainty Information, Science Press, Beijing, China, 1999.

F. Q. Gong, X. B. Li, L. J. Dong, and X. L. Liu, “Underground goaf risk evaluation based on uncertainty measurement theory,” Chinese Journal of Rock Mechanics and Engineering, vol. 27, no. 2, pp. 323–330, 2008.

H. J. He, S. R. Su, X. J. Wang, and P. Li, “Evaluation on activity of active faults based on uncertainty measure theory,” Disaster Advances, vol. 5, no. 4, pp. 1281–1286, 2012.

H. J. He, S. R. Su, X. J. Wang, and P. Li, “Study and application on comprehensive evaluation model of landslide hazard based on uncertainty measure theory,” Journal of Central South University (Science and Technology), vol. 44, no. 4, pp. 1564–1570, 2013.

H. J. He, Y. M. Yan, C. X. Qu, and Y. Fan, “Study and application on stability classification of tunnel surrounding rock based on uncertainty measure theory,” Mathematical Problems in Engineering, vol. 2014, Article ID 626527, 5 pages, 2014.

W. Q. Li, L. N. Zhang, and W. Q. Meng, “Comprehensive evaluation on MIS based on information entropy and unascertained measure model,” Journal of Hebei Institute of Architectural Science and Technology, vol. 22, no. 1, pp. 49–52, 2005.

S. G. Li, C. Ma, and G. Q. Wang, “Colliery ventilation safety evaluation on the basis of the unascertained measure,” Journal of University of Science and Technology Beijing, vol. 28, no. 2, pp. 101–103, 2006.

W. L. Cai and Y. S. Huang, “Study on supply chain evaluation index reduction based on information entropy research,” Science and Technology Innovation Herald, no. 36, pp. 174–176, 2007.

C. Q. Wang, Study on Evaluation Method for Safety Risk of CO₂ Geological Storage, North China Electric Power University, Baoding, China, 2012.

Y.-J. Diao, S.-Q. Zhang, J.-Q. Guo, X.-F. Li, and H. Zhang, “Geological safety evaluation method for CO₂ geological storage in deep saline aquifer,” Geology in China, vol. 38, no. 3, pp. 786–792, 2011.

J. Q. Guo, S. Q. Zhang, Y. J. Diao, X. F. Li, H. Zhang, and J. J. Fan, “Site selection method of CO₂ geological storage in deep saline aquifers,” Journal of Jilin University (Earth Science Edition), vol. 41, no. 4, pp. 1084–1091, 2011.

G. Q. Yang, X. S. Su, S. H. Du, W. Xu, J. Y. Meng, and D. Y. Gao, “Suitability assessment of geological sequestration of CO₂ in Songliao Basin,” Acta Geoscientica Sinica, vol. 32, no. 5, pp. 570–580, 2011.

P. Y. Xu, C. Q. Wang, F. C. Zhang, X. F. Li, and X. F. Jia, “Study on the safety risk evaluation indexes system for CO₂ geological storage in the deep saline aquifer,” Safety and Environmental Engineering, vol. 19, no. 4, pp. 62–65, 2012.