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

Authors: Hujun He; Yaning Zhao; Xingke Yang; Yaning Gao; Xu Wu
Journal: Mathematical Problems in Engineering
 (2015)

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## 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.


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## Body

## 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

Letx1,x2,…,xn be n objects in the index space X=x1,x2,…,xn. Each object has m single evaluation index spaces; that is, I=I1,I2,…,In. xi can be expressed as a m-dimensional vector xi=xi1,xi2,…,xim. xi has p evaluation levels, and its evaluation level space is U=C1,C2,…,Cp, where Ck indicates the kth level. The kth level is stronger than the (k+1)th level; that is, Ck>Ck+1. Then, C1,C2,…,Cp is an ordered partition class in evaluation space U.


### 2.1. Uncertainty Measure for a Single Index

Letμijk=μ(xij∈Ck) indicate that measured value xij belongs to Ck (the kth evaluation level). μ must satisfy(1)0≤μxij∈Ck≤1i=1,2,…,n;j=1,2,…,m;k=1,2,…,p,(2)μxij∈U=1i=1,2,…,n;j=1,2,…,m,(3)μxij∈⋃l=1kCl=∑l=1kμxi∈Clk=1,2,…,p.Equation (2) means μ meets the “normalization” for evaluation space U; equation (3) means μ meets the “additivity” for evaluation space U. Because it satisfies (1), (2), and (3), μ is called the uncertainty measure or measure [9–11].The matrix(4)μijkm×p=μi11μi12⋯μi1pμi21μi22⋯μi2p⋮⋮⋮⋮μim1μim2⋯μimpis 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

Letwij(0≤wij≤1,∑j=1mwij=1) represent the importance of Ij relative to the other indexes, and let wij be the weight of Ij(j=1,2,…,m). The weight of each index is determined using information entropy theory [12–15]. That is,(5)vij=1+1lg⁡p∑i=1pμijklg⁡μijk,wj=vij∑i=1nvij.


### 2.3. Comprehensive Measure for Multiple Indexes

Using the index weights, the multi-index comprehensive measure can be calculated to evaluateμik=∑j=1mwijμijk(i=1,2,…,n;j=1,2,…,m;k=1,2,…,p). Here, if 0≤μk≤1, ∑k=1pμik=1, then μik is known as the uncertainty measure, and μi1,μi2,…,μip is the multi-index comprehensive evaluation measure vector of xi.


### 2.4. Recognition Criterion of the Credibility

IfC1>C2>⋯>Cp, a credibility criterion can be introduced. Let λ be the degree of credibility, where λ≥0.5; typically use λ=0.6 or 0.7. If k0=mink:∑l=1kpμil≥λ,1≤l≤k, then it is considered to belong to Ck0.


### 2.5. Ordering

As well as discriminatingxi’s evaluation level, sometimes it must be ordered according to its importance. If C1>C2>⋯>Cp, the command value of Cl0 is nl0. Then, nl0>nl+1, and qxi=∑l=1pnlμil, where qxi is the uncertainty importance degree of evaluation factor xi. q=qx1,qx2,…,qxp is called the uncertainty importance vector. xi is ordered according to the value of qxi.


## 2.1. Uncertainty Measure for a Single Index

Letμijk=μ(xij∈Ck) indicate that measured value xij belongs to Ck (the kth evaluation level). μ must satisfy(1)0≤μxij∈Ck≤1i=1,2,…,n;j=1,2,…,m;k=1,2,…,p,(2)μxij∈U=1i=1,2,…,n;j=1,2,…,m,(3)μxij∈⋃l=1kCl=∑l=1kμxi∈Clk=1,2,…,p.Equation (2) means μ meets the “normalization” for evaluation space U; equation (3) means μ meets the “additivity” for evaluation space U. Because it satisfies (1), (2), and (3), μ is called the uncertainty measure or measure [9–11].The matrix(4)μijkm×p=μi11μi12⋯μi1pμi21μi22⋯μi2p⋮⋮⋮⋮μim1μim2⋯μimpis 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

Letwij(0≤wij≤1,∑j=1mwij=1) represent the importance of Ij relative to the other indexes, and let wij be the weight of Ij(j=1,2,…,m). The weight of each index is determined using information entropy theory [12–15]. That is,(5)vij=1+1lg⁡p∑i=1pμijklg⁡μijk,wj=vij∑i=1nvij.


## 2.3. Comprehensive Measure for Multiple Indexes

Using the index weights, the multi-index comprehensive measure can be calculated to evaluateμik=∑j=1mwijμijk(i=1,2,…,n;j=1,2,…,m;k=1,2,…,p). Here, if 0≤μk≤1, ∑k=1pμik=1, then μik is known as the uncertainty measure, and μi1,μi2,…,μip is the multi-index comprehensive evaluation measure vector of xi.


## 2.4. Recognition Criterion of the Credibility

IfC1>C2>⋯>Cp, a credibility criterion can be introduced. Let λ be the degree of credibility, where λ≥0.5; typically use λ=0.6 or 0.7. If k0=mink:∑l=1kpμil≥λ,1≤l≤k, then it is considered to belong to Ck0.


## 2.5. Ordering

As well as discriminatingxi’s evaluation level, sometimes it must be ordered according to its importance. If C1>C2>⋯>Cp, the command value of Cl0 is nl0. Then, nl0>nl+1, and qxi=∑l=1pnlμil, where qxi is the uncertainty importance degree of evaluation factor xi. q=qx1,qx2,…,qxp is called the uncertainty importance vector. xi is ordered according to the value of qxi.


## 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 C1,C2,C3 (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
DownwindTable 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
>150Table 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 Tables1 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 Table3, 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(6)μA1=010010010001100001001010.


### 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 w1,w2,w3,w4,w5,…,w8={0.125,0.125,0.125,0.125,0.125,0.125, 0.125,0.125}. Using the single index measure matrix and the multiple index calculation formula, the multiple index vector was μ1=ϖ1·μA1=0.125,0.5,0.375.


### 3.3. Degree of Credibility

We set the degree of credibility toλ=0.6 and used the multiple index comprehensive evaluation measure vector and credibility formula to calculate that k0=0.625>0.5. 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
C
1
C
2
C
3
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, becauseC1>C2>C3, we can take nl=8-2q, where 1≤q≤3, so that q=q1q2q3=3.5,3,3.75. 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.


## 3.1. Single Index Measure Function

According to the constructing method of single index measure function, combined with grading standards in Tables1 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 Table3, 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(6)μA1=010010010001100001001010.


## 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 w1,w2,w3,w4,w5,…,w8={0.125,0.125,0.125,0.125,0.125,0.125, 0.125,0.125}. Using the single index measure matrix and the multiple index calculation formula, the multiple index vector was μ1=ϖ1·μA1=0.125,0.5,0.375.


## 3.3. Degree of Credibility

We set the degree of credibility toλ=0.6 and used the multiple index comprehensive evaluation measure vector and credibility formula to calculate that k0=0.625>0.5. 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
C
1
C
2
C
3
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, becauseC1>C2>C3, we can take nl=8-2q, where 1≤q≤3, so that q=q1q2q3=3.5,3,3.75. 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].



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