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[a]College of Petroleum Engineering, China University of Petroleum (East China), Qingdao, China.
[b]Directional drilling company, Shengli oilfield of Sinopec, Dongying, China.
*Corresponding author.
Received 20 July 2012; accepted 8 September 2012
Abstract
To give a quantitative description of well control risk, a multi-layer fuzzy comprehensive evaluation based on AHP (analytic hierarchy process) is used. During the evaluation, risk factors and weight are given by Delphi method and AHP method. A multi-level and multi-factor evaluation system is built including four level-one factors of geologic uncertainty, well control equipments, techniques and crew quality, and fourteen level-two factors. Then a calculation is given with an oilfield in West China. The result shows geologic uncertainty is the primary factor leading to well control risks and the grade of well control risk is “higher risk”. The application result indicates that well control risk assessment by fuzzy comprehensive evaluation is feasible.
Key words: Risk assessment; Fuzzy comprehensive evaluation; Analytic hierarchy process; Weight; Risk factor
Gong, P. B., Sun, B. J., Liu, G., & Wang, Y. (2012). Fuzzy Comprehensive Evaluation in Well Control Risk Assessment Based on AHP: A Case Study. Advances in Petroleum Exploration and Development, 4(1),-0. Available from: URL: http://www.cscanada.net/index.php/aped/article/view/j.aped.1925543820120401.758
DOI: http://dx.doi.org/10.3968/j.aped.1925543820120401.758
NOMENCLATURE
A = Target factor in Figure 2
B1, B2, …, B4 = First-level factors in Figure 2
C1, C2, …, C14 = Second-level factors in Figure 2
A = Judgment matrix of the four factors including B1, B2, …, B4
W = Weight of factors including B1, B2, …, B4
W1 = Weight of factors including C1, C2 and C3
W2 = Weight of factors including C4, C5, …, C7
W3 = Weight of factors including C8, C9, …, C11
W4 = Weight of factors including C12, C13 and C14
V = Fuzzy evaluation set
R = Evaluation matrix of factors including B1, B2, …, B4
R1 = Evaluation matrix of factors including C1, C2 and C3
R2 = Evaluation matrix of factors including C4, C5, …, C7
R3 = Evaluation matrix of factors including C8, C9, …, C11
R4 = Evaluation matrix of factors including C12, C13 and C14
D = Total evaluation matrix of the well control risk
D1 = Evaluation matrix of factor B1
D2 = Evaluation matrix of factor B2 D3 = Evaluation matrix of factor B3
D4 = Evaluation matrix of factor B4
INTRODUCTION
With the deep oil exploration and development, the engineering geologic conditions become more and more complex. Drilling equipments are increasingly large, and drilling technology becomes more complex[1,2]. This makes well control operations generate massive complex and uncertain factors, which results in great risk[3]. It plays an important guiding role in the wildcat well drilling to perform a careful risk identification and scientific risk evaluation of well control predrilling. In recent years, fuzzy comprehensive evaluation has been reported in risk assessment of drilling industry[4-7], which is visual with clear thinking and intuitive to understand. Besides, it is a quantitative analysis. At present, hazard operability study (HAZOP) and other qualitative methods are used to make a risk assessment in drilling[8-10]. But a quantitative risk assessment result cannot be obtained easily.
In this paper, we take the oilfield in western China as an example, establishing a multi-layer and multi-factor evaluation system including four level-one factors of geologic uncertainty, well control equipment, techniques and crew quality etc. and fourteen level-two factors through well control risk identification. A multi-layer fuzzy comprehensive evaluation is demonstrated step by step whose risk factor and weight is valued by Delphi method and AHP method. The evaluation result is analyzed and a prediction of well control risk is obtained. Results coincide with the actual drilling process through comparison, so it plays a guiding role to adopt fuzzy comprehensive evaluation to perform well control risk assessment for safe drilling before drilling.
1. MODEL OF WELL CONTROL RISK EVALUATION AND CALCULATIONS
An oilfield in west China is used to perform the well control risk assessment. This oilfield belongs to piedmont structure. Geologic structure is complicated and the foreseeability of geologic conditions is poor, which may cause serious discrepancy with the actual drilling. It is difficult to observe the sign at the preliminary stage of overflow in drilling. In this area, non-standard phenomenon in well control operation often occurs, which can cause potential well control risk. The overall situation of well control equipments is ordinary and the quality of staff in drilling crew is higher.
We invited twenty experts including five drilling engineers, five drilling safety engineers, five scholars in drilling engineering and five rig managers. They are all experienced drilling workers. Factors of the well control risk should be identified first by all the experts. Then a hierarchical framework of well control risk factors is established in terms of the subordinate relations. After the weight of each hierarchical factor is valued, we make fuzzy evaluation of the bottom level factors first. And its evaluation result is used as the matrix of membership degree for evaluation set as the single factor of the above layer which is gradually evaluated bottom up. As for the analysis of evaluation results, it is from the upper factors to the lower ones. The principle of simple two-level fuzzy comprehensive evaluation method is shown (Figure 1). Calculation of matrix A1 is performed by each row: ,=1,2,…,n. So a new matrix w can be obtained as w. Normalize the matrix w according to the formula (=1,2,…,n). So the characteristic vector of the matrix A1 can be obtained as the vector W =. And the value of w1,w2,..wn also means the weight of factors in matrix A1. The largest eigenvalue of matrix A1 can be calculated according to the formula (A1w)i/nwi. During the calculation, (A1w)i is the i-th factor in vector (A1w).
When the largest eigenvalue of matrix A1 is determined, the judgment of consistency check in mathematics will be performed as the following two formulas[12]:
CI = (λmax-n)/(n-1),CR = CI/RI
In the formula mean random consistency index RI is valued in Table 2. If CR ≤ 0.1, then the coincidence principle can be accepted. If the value of CR is not acceptable, the experts should discuss again. And a recalculation is made.
With regard to the four factors of B1, B2, B3 and B4 in the first level, the experts gives a judgment matrix collectively through discussion at the meeting and the weight of each factor can be obtained by the above calculation process (shown in Table 3).
Table 2
Mean Random Consistency Index RI
Order of matrix 1 2 3 4 5 6 7 8 9
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45
Table 3
Fuzzy Comparison Matrix and Weight of Well Control Risk Factors
Evaluation
matrix A B1 B2 B3 B4 Weight of first level (W) Check procedure
B1 1 2 4 5 0.503 λmax=4.17
CI=0.057
CR=0.063<0.1
B2 1/2 1 4 2 0.283
B3 1/4 1/4 1 2 0.119
B4 1/5 1/2 1/2 1 0.095
In Table 3, judgment matrix of the four factors is given by the experts as follow:
The weight of the factors in first level is calculated by the procedure above. And the weight of the four factors is as follow:
W = (0.503, 0.283, 0.119, 0.095)
Similarly in the second level, factors of C1, C2, C3; C4, C5, C6, C7; C8, C9, C10, C11; C12, C13, C14 are calculated respectively (Table 4). And the results are as follows:
W1 = (0.539, 0.297, 0.164)
W2 = (0.466, 0.095, 0.160, 0.278)
W3 = (0.311, 0.465, 0.072, 0.152)
W4 = (0.163, 0.297, 0.54)
2. WELL CONTROL RISK EVALUATION RESULTS AND ANALYSIS
2.1 Determining the Well Control Evaluation Set and Single Factor’s Evaluation Matrix
Evaluation set is used to divide the single factors into grade. Well control risk fuzzy evaluation set is built as follows.
V = (v1, v2, v3, v4, v5) = (higher risk, high risk, average risk, lower risk, low risk) The risk degree of fourteen single factors in the second level is evaluated first. The grade of membership of the single factor Cj attached to the element vm in evaluation set is calculated by the membership formula:
rjm = Mjm/N
rjm - membership to the element vm in evaluation set;
Mjm - number of experts who think factor Cj is corresponding to element vm in evaluation set;
N - total number of experts at the meeting.
So we can obtain the fuzzy evaluation matrix Ri, which is composed of factors’ membership magnitude included in factor Bi (i = 1,2,3,4). The evaluation matrix Ri is listed as the following form.
In this process, the Delphi method is used to evaluate the grade of membership attached to the evaluation set. We send questionnaires to all the experts. Each of them evaluates every single factor (C1, C2, …, C14) by choosing which element they belongs to in the evaluation set V. Then we take back all the questionnaires and make a statistical analysis and calculate the membership with membership formula. The result of the single factor evaluation results are given by the drilling experts (Table 4). From Table 4 we can obtain the fuzzy evaluation matrix of the single factors included in the risk of geologic uncertainty, well control equipment, personal quality and technology and operations. The four evaluation matrixes are R1, R2, R3 and R4 as follows.
Table 4
Weight of Each Level and Single-Factor Evaluation Matrix
First-level factors Weight of first level factors (W) Second level factors Weight of second level factors Grade of risk (evaluation sets)
Higher High Average Low Lower
Geologic uncertainty B1 0.503 C1 W1 0.539 0.500 0.250 0.125 0.125 0
C2 0.297 0.250 0.500 0.125 0.125 0
C3 0.164 0.125 0.250 0.500 0.125 0
Well control equipment B2 0.283 C4 W2 0.466 0.250 0．375 0.250 0.125 0
C5 0.095 0.125 0.500 0.250 0.125 0
C6 0.160 0 0.125 0.375 0.375 0.125
C7 0.278 0.250 0.375 0.250 0.125 0
Techniques & operations B3 0.119 C8 W3 0.311 0.250 0.375 0.250 0.125 0
C9 0.465 0.375 0.250 0.125 0.125 0.125
C10 0.072 0 0.375 0.375 0.125 0.125
C11 0.152 0.125 0.250 0.375 0.125 0.125
Staff quality B4 0.095 C12 W4 0.163 0 0 0.125 0.625 0.250
C13 0.297 0.125 0.250 0.250 0.250 0.125
C14 0.54 0.125 0.250 0.375 0.125 0.125
2.2 Multilevel Fuzzy Comprehensive Evaluation of Well Control Risk The fuzzy comprehensive evaluation adopts fuzzy mathematics algorithm. During the calculation, the multiplication addition and multiplying operation in the ordinary matrix are replaced by taking the bigger and taking the smaller operations respectively[13-15]. After the calculation the second level results are normalized and the evaluation matrix D1, D2, D3 and D4 are obtained.
D1 = W1R1 = (0.460, 0.273, 0.152, 0.115, 0.000)
D2 = W2R2 = (0.216, 0.323, 0.216, 0.138, 0.107)
D3 = W3R3 = (0.316, 0.262, 0.212, 0.105, 0.105)
D4 = W4R4 = (0.116, 0.233, 0.349, 0.151, 0.151)
According to the results of matrix D1, D2, D3 and D4, the first level factors’ fuzzy evaluation set R can be gained.
R = (D1, D2, D3, D4)T
Similarly the first level result of evaluation can be calculated as the following process.
D = WR = (0.460, 0.283, 0.216, 0.138, 0.107)
After normalization, vector D can be noted as the following form.
D = (0.382, 0.235, 0.179, 0.115, 0.089)
2.3 Calculation Result Analysis
The frequently-used HAZOP method of well control risk assessment is to put the idea of risk analysis into each step of operations during well control. Through the deviation analysis of the technology or the variation of status parameter in well control process, we can identify these changes and deviation’s influences on system and the consequences. Then we can make an analysis of the causes and put forward the effective measures. It can only make a qualitative analysis for a certain well rather than some wells in one block zone. Also it cannot provide quantitative risk value. However, fuzzy comprehensive evaluation method can perform a risk assessment of well control not only for a certain well but also for a block of oilfield wells and can provide a quantitative risk value. We can get the following results from the front fuzzy comprehensive evaluation process of well control risk in western oilfield:
(1) According to the principle of maximum membership degree, from the first-level evaluation result D, we can conclude the overall well control risk of the oilfield is “higher risk” level. The possibility of “higher risk” and “high risk” level accounts for 61.7%. In the initial drilling of several wildcat in this oilfield, such complicated situations as well kick, overflow and leakage often appears, which is consistent with the evaluation.
(2) From Table 3, in the first level of risk factors, geologic uncertainty risk and risk of well control equipment account for 50.3% and 28.3% respectively. From further risk identification of both, we can see the biggest risk points of the second level are respectively the uncertainty of formation pressure and casing deformation. The membership degree of both risk points are respectively “higher risk” and “high risk”. (3) From the analysis process, it is concluded that geologic predicted risk is the most important factor of causing high risk. Therefore, we ought to increase the exploration of this block and enhance the precision of prediction of geologic prospecting. In addition, we still need to improve the reliability of well control equipment and well control process operation in order to reduce well control risk of the block.
CONCLUSIONS AND SUGGESTIONS
(1) Fuzzy comprehensive evaluation method of well control risk, which integrated multilevel well control risks, avoids the limitations of using single index evaluation. This method has combined qualitative study with quantitative study to make the evaluation results more reasonable and accurate.
(2) Though there are subjective influence in experts’ Delphi method and importance judgment of risk factors, experts’ Delphi method is finished collectively, which makes the error reduce. And analytic hierarchy process weakens the subjectivity importance judgment of risk factors.
(3) The following actual drilling process of western oilfield in China shows that using fuzzy comprehensive evaluation method for well control risk assessment based on AHP before drilling is feasible.
(4) According to different situations of each oilfield, it can better instruct on-site construction and enhance drilling safety to establish risk system to do fuzzy comprehensive evaluation. This requires a further identification of well control risk factors, which makes risk system structure more reasonable.
REFERENCES
[1] Zang, Y.B., Wang, R.H., & Zhang, R. (2010). The Method and Expert System for Risk Assessment of Drilling in High-Sulfur Gas Field. Paper SPE 134115, presented at SPE Asia Pacific Oil and Gas Conference and Exhibition, Queensland, Australia, Oct. 18-20, 2010.
[2] Nilsen, T., & Karlsen, H. C. (2008). Risk Based Decision Support for the Planning of a Challenging HPHT Drilling Operation. Paper SPE 12526, presented at the International Petroleum Technology Conference, Kuala Lumpur, Malaysia, Dec. 3-5, 2008.
[3] Lian, Z.L., Zhou, Y.C., & Shen, R.C. (2009). A Discussion on Technology of No Drilling Surprise(NDC). Oil Drilling & Production Technology, 31(1), 90-94.
[4] Ke, K., Guan, Z.C., & Zhang, J.Y. (2009). Affecting Factors Research on the Risks of Deep Water Drilling Operation in West Africa. Oil Drilling & Production Technology, 31(5), 5-10.
[5] Qian, X.D., & Liu, Z.D. (2009). Risk Fuzzy Comprehensive Evaluation of Offshore Drilling Based on AHP. Safety and Environmental Engineering, 16(4), 78-81. [6] Yan, T.H., Zhou, G.Q., & Wang, Y.M. (2009). Assessment of the Status of Equipment of Well-Drilling Team Based on Fuzzy Comprehensive Evaluation Method. Oil Field Equipment, 38(7), 5-9.
[7] Liu, H.C., Qi, M.X., & Zhao, N., et al. (2009). Application of Fuzzy Comprehensive Evaluation in Petroleum Drilling Rig Assessment. Oil Field Equipment, 38(5), 18-21.
[8] Schubert, J.J., Juvkam, H.C., & Weddle, C.E. (2002). HAZOP of Well Control Procedures Provides Assurance of the Safety of the Subsea MudLift Drilling System. Paper SPE 74482, presented at IADC/SPE drilling conference, Dallas, Texas, Feb. 26-28, 2002.
[9] Fu, J.M., & Zheng, X.Y. (2005). HAZOP Analysis on Well Control Operation. Safety, Health & Environment, 5(11), 3-45.
[10] Fanning, E.F. (2002). Risk Management for Emergency Operations. Paper SPE 02-708, presented at ASSE Professional Development Conference and Exposition, Nashville, Tennessee, Jun. 9-12, 2002.
[11] Niven, K., & Jong, G.D. (2008). Health Risk Assessment: Improving Quality and Cost Effectiveness by Leveraging People, Processes, and Tools. Paper SPE 111728, presented at SPE International Conference on Health, Safety, and Environment in Oil and Gas Exploration and Production, Nice, France, Apr. 15-17, 2008.
[12] Chen, S.L., Li, J.G., & Wang, X.G. (2005). Fuzzy Set Theory and Application. Beijing: Science Press.
[13] Zinmerman, H.J., & Zysoo, P. (1980). Latent Connectives in Hum an Decision Making. Fuzzy Sets and Systems, 4(1), 37-51.
[14] Lee, E.S., & Li, R.J. (1993). Fuzzy Multiple Objective Programming and Compromise Programming with Pare to Optimum. Fuzzy Sets and Systems, 53(2), 275-288.
[15] Chen, H.K., & Chou, H.W. (1996). Solving Multiobjective Liner Programming-a Generic Approach. Fuzzy Sets and Systems, 82(1), 35-38.
[b]Directional drilling company, Shengli oilfield of Sinopec, Dongying, China.
*Corresponding author.
Received 20 July 2012; accepted 8 September 2012
Abstract
To give a quantitative description of well control risk, a multi-layer fuzzy comprehensive evaluation based on AHP (analytic hierarchy process) is used. During the evaluation, risk factors and weight are given by Delphi method and AHP method. A multi-level and multi-factor evaluation system is built including four level-one factors of geologic uncertainty, well control equipments, techniques and crew quality, and fourteen level-two factors. Then a calculation is given with an oilfield in West China. The result shows geologic uncertainty is the primary factor leading to well control risks and the grade of well control risk is “higher risk”. The application result indicates that well control risk assessment by fuzzy comprehensive evaluation is feasible.
Key words: Risk assessment; Fuzzy comprehensive evaluation; Analytic hierarchy process; Weight; Risk factor
Gong, P. B., Sun, B. J., Liu, G., & Wang, Y. (2012). Fuzzy Comprehensive Evaluation in Well Control Risk Assessment Based on AHP: A Case Study. Advances in Petroleum Exploration and Development, 4(1),
DOI: http://dx.doi.org/10.3968/j.aped.1925543820120401.758
NOMENCLATURE
A = Target factor in Figure 2
B1, B2, …, B4 = First-level factors in Figure 2
C1, C2, …, C14 = Second-level factors in Figure 2
A = Judgment matrix of the four factors including B1, B2, …, B4
W = Weight of factors including B1, B2, …, B4
W1 = Weight of factors including C1, C2 and C3
W2 = Weight of factors including C4, C5, …, C7
W3 = Weight of factors including C8, C9, …, C11
W4 = Weight of factors including C12, C13 and C14
V = Fuzzy evaluation set
R = Evaluation matrix of factors including B1, B2, …, B4
R1 = Evaluation matrix of factors including C1, C2 and C3
R2 = Evaluation matrix of factors including C4, C5, …, C7
R3 = Evaluation matrix of factors including C8, C9, …, C11
R4 = Evaluation matrix of factors including C12, C13 and C14
D = Total evaluation matrix of the well control risk
D1 = Evaluation matrix of factor B1
D2 = Evaluation matrix of factor B2 D3 = Evaluation matrix of factor B3
D4 = Evaluation matrix of factor B4
INTRODUCTION
With the deep oil exploration and development, the engineering geologic conditions become more and more complex. Drilling equipments are increasingly large, and drilling technology becomes more complex[1,2]. This makes well control operations generate massive complex and uncertain factors, which results in great risk[3]. It plays an important guiding role in the wildcat well drilling to perform a careful risk identification and scientific risk evaluation of well control predrilling. In recent years, fuzzy comprehensive evaluation has been reported in risk assessment of drilling industry[4-7], which is visual with clear thinking and intuitive to understand. Besides, it is a quantitative analysis. At present, hazard operability study (HAZOP) and other qualitative methods are used to make a risk assessment in drilling[8-10]. But a quantitative risk assessment result cannot be obtained easily.
In this paper, we take the oilfield in western China as an example, establishing a multi-layer and multi-factor evaluation system including four level-one factors of geologic uncertainty, well control equipment, techniques and crew quality etc. and fourteen level-two factors through well control risk identification. A multi-layer fuzzy comprehensive evaluation is demonstrated step by step whose risk factor and weight is valued by Delphi method and AHP method. The evaluation result is analyzed and a prediction of well control risk is obtained. Results coincide with the actual drilling process through comparison, so it plays a guiding role to adopt fuzzy comprehensive evaluation to perform well control risk assessment for safe drilling before drilling.
1. MODEL OF WELL CONTROL RISK EVALUATION AND CALCULATIONS
An oilfield in west China is used to perform the well control risk assessment. This oilfield belongs to piedmont structure. Geologic structure is complicated and the foreseeability of geologic conditions is poor, which may cause serious discrepancy with the actual drilling. It is difficult to observe the sign at the preliminary stage of overflow in drilling. In this area, non-standard phenomenon in well control operation often occurs, which can cause potential well control risk. The overall situation of well control equipments is ordinary and the quality of staff in drilling crew is higher.
We invited twenty experts including five drilling engineers, five drilling safety engineers, five scholars in drilling engineering and five rig managers. They are all experienced drilling workers. Factors of the well control risk should be identified first by all the experts. Then a hierarchical framework of well control risk factors is established in terms of the subordinate relations. After the weight of each hierarchical factor is valued, we make fuzzy evaluation of the bottom level factors first. And its evaluation result is used as the matrix of membership degree for evaluation set as the single factor of the above layer which is gradually evaluated bottom up. As for the analysis of evaluation results, it is from the upper factors to the lower ones. The principle of simple two-level fuzzy comprehensive evaluation method is shown (Figure 1). Calculation of matrix A1 is performed by each row: ,=1,2,…,n. So a new matrix w can be obtained as w. Normalize the matrix w according to the formula (=1,2,…,n). So the characteristic vector of the matrix A1 can be obtained as the vector W =. And the value of w1,w2,..wn also means the weight of factors in matrix A1. The largest eigenvalue of matrix A1 can be calculated according to the formula (A1w)i/nwi. During the calculation, (A1w)i is the i-th factor in vector (A1w).
When the largest eigenvalue of matrix A1 is determined, the judgment of consistency check in mathematics will be performed as the following two formulas[12]:
CI = (λmax-n)/(n-1),CR = CI/RI
In the formula mean random consistency index RI is valued in Table 2. If CR ≤ 0.1, then the coincidence principle can be accepted. If the value of CR is not acceptable, the experts should discuss again. And a recalculation is made.
With regard to the four factors of B1, B2, B3 and B4 in the first level, the experts gives a judgment matrix collectively through discussion at the meeting and the weight of each factor can be obtained by the above calculation process (shown in Table 3).
Table 2
Mean Random Consistency Index RI
Order of matrix 1 2 3 4 5 6 7 8 9
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45
Table 3
Fuzzy Comparison Matrix and Weight of Well Control Risk Factors
Evaluation
matrix A B1 B2 B3 B4 Weight of first level (W) Check procedure
B1 1 2 4 5 0.503 λmax=4.17
CI=0.057
CR=0.063<0.1
B2 1/2 1 4 2 0.283
B3 1/4 1/4 1 2 0.119
B4 1/5 1/2 1/2 1 0.095
In Table 3, judgment matrix of the four factors is given by the experts as follow:
The weight of the factors in first level is calculated by the procedure above. And the weight of the four factors is as follow:
W = (0.503, 0.283, 0.119, 0.095)
Similarly in the second level, factors of C1, C2, C3; C4, C5, C6, C7; C8, C9, C10, C11; C12, C13, C14 are calculated respectively (Table 4). And the results are as follows:
W1 = (0.539, 0.297, 0.164)
W2 = (0.466, 0.095, 0.160, 0.278)
W3 = (0.311, 0.465, 0.072, 0.152)
W4 = (0.163, 0.297, 0.54)
2. WELL CONTROL RISK EVALUATION RESULTS AND ANALYSIS
2.1 Determining the Well Control Evaluation Set and Single Factor’s Evaluation Matrix
Evaluation set is used to divide the single factors into grade. Well control risk fuzzy evaluation set is built as follows.
V = (v1, v2, v3, v4, v5) = (higher risk, high risk, average risk, lower risk, low risk) The risk degree of fourteen single factors in the second level is evaluated first. The grade of membership of the single factor Cj attached to the element vm in evaluation set is calculated by the membership formula:
rjm = Mjm/N
rjm - membership to the element vm in evaluation set;
Mjm - number of experts who think factor Cj is corresponding to element vm in evaluation set;
N - total number of experts at the meeting.
So we can obtain the fuzzy evaluation matrix Ri, which is composed of factors’ membership magnitude included in factor Bi (i = 1,2,3,4). The evaluation matrix Ri is listed as the following form.
In this process, the Delphi method is used to evaluate the grade of membership attached to the evaluation set. We send questionnaires to all the experts. Each of them evaluates every single factor (C1, C2, …, C14) by choosing which element they belongs to in the evaluation set V. Then we take back all the questionnaires and make a statistical analysis and calculate the membership with membership formula. The result of the single factor evaluation results are given by the drilling experts (Table 4). From Table 4 we can obtain the fuzzy evaluation matrix of the single factors included in the risk of geologic uncertainty, well control equipment, personal quality and technology and operations. The four evaluation matrixes are R1, R2, R3 and R4 as follows.
Table 4
Weight of Each Level and Single-Factor Evaluation Matrix
First-level factors Weight of first level factors (W) Second level factors Weight of second level factors Grade of risk (evaluation sets)
Higher High Average Low Lower
Geologic uncertainty B1 0.503 C1 W1 0.539 0.500 0.250 0.125 0.125 0
C2 0.297 0.250 0.500 0.125 0.125 0
C3 0.164 0.125 0.250 0.500 0.125 0
Well control equipment B2 0.283 C4 W2 0.466 0.250 0．375 0.250 0.125 0
C5 0.095 0.125 0.500 0.250 0.125 0
C6 0.160 0 0.125 0.375 0.375 0.125
C7 0.278 0.250 0.375 0.250 0.125 0
Techniques & operations B3 0.119 C8 W3 0.311 0.250 0.375 0.250 0.125 0
C9 0.465 0.375 0.250 0.125 0.125 0.125
C10 0.072 0 0.375 0.375 0.125 0.125
C11 0.152 0.125 0.250 0.375 0.125 0.125
Staff quality B4 0.095 C12 W4 0.163 0 0 0.125 0.625 0.250
C13 0.297 0.125 0.250 0.250 0.250 0.125
C14 0.54 0.125 0.250 0.375 0.125 0.125
2.2 Multilevel Fuzzy Comprehensive Evaluation of Well Control Risk The fuzzy comprehensive evaluation adopts fuzzy mathematics algorithm. During the calculation, the multiplication addition and multiplying operation in the ordinary matrix are replaced by taking the bigger and taking the smaller operations respectively[13-15]. After the calculation the second level results are normalized and the evaluation matrix D1, D2, D3 and D4 are obtained.
D1 = W1R1 = (0.460, 0.273, 0.152, 0.115, 0.000)
D2 = W2R2 = (0.216, 0.323, 0.216, 0.138, 0.107)
D3 = W3R3 = (0.316, 0.262, 0.212, 0.105, 0.105)
D4 = W4R4 = (0.116, 0.233, 0.349, 0.151, 0.151)
According to the results of matrix D1, D2, D3 and D4, the first level factors’ fuzzy evaluation set R can be gained.
R = (D1, D2, D3, D4)T
Similarly the first level result of evaluation can be calculated as the following process.
D = WR = (0.460, 0.283, 0.216, 0.138, 0.107)
After normalization, vector D can be noted as the following form.
D = (0.382, 0.235, 0.179, 0.115, 0.089)
2.3 Calculation Result Analysis
The frequently-used HAZOP method of well control risk assessment is to put the idea of risk analysis into each step of operations during well control. Through the deviation analysis of the technology or the variation of status parameter in well control process, we can identify these changes and deviation’s influences on system and the consequences. Then we can make an analysis of the causes and put forward the effective measures. It can only make a qualitative analysis for a certain well rather than some wells in one block zone. Also it cannot provide quantitative risk value. However, fuzzy comprehensive evaluation method can perform a risk assessment of well control not only for a certain well but also for a block of oilfield wells and can provide a quantitative risk value. We can get the following results from the front fuzzy comprehensive evaluation process of well control risk in western oilfield:
(1) According to the principle of maximum membership degree, from the first-level evaluation result D, we can conclude the overall well control risk of the oilfield is “higher risk” level. The possibility of “higher risk” and “high risk” level accounts for 61.7%. In the initial drilling of several wildcat in this oilfield, such complicated situations as well kick, overflow and leakage often appears, which is consistent with the evaluation.
(2) From Table 3, in the first level of risk factors, geologic uncertainty risk and risk of well control equipment account for 50.3% and 28.3% respectively. From further risk identification of both, we can see the biggest risk points of the second level are respectively the uncertainty of formation pressure and casing deformation. The membership degree of both risk points are respectively “higher risk” and “high risk”. (3) From the analysis process, it is concluded that geologic predicted risk is the most important factor of causing high risk. Therefore, we ought to increase the exploration of this block and enhance the precision of prediction of geologic prospecting. In addition, we still need to improve the reliability of well control equipment and well control process operation in order to reduce well control risk of the block.
CONCLUSIONS AND SUGGESTIONS
(1) Fuzzy comprehensive evaluation method of well control risk, which integrated multilevel well control risks, avoids the limitations of using single index evaluation. This method has combined qualitative study with quantitative study to make the evaluation results more reasonable and accurate.
(2) Though there are subjective influence in experts’ Delphi method and importance judgment of risk factors, experts’ Delphi method is finished collectively, which makes the error reduce. And analytic hierarchy process weakens the subjectivity importance judgment of risk factors.
(3) The following actual drilling process of western oilfield in China shows that using fuzzy comprehensive evaluation method for well control risk assessment based on AHP before drilling is feasible.
(4) According to different situations of each oilfield, it can better instruct on-site construction and enhance drilling safety to establish risk system to do fuzzy comprehensive evaluation. This requires a further identification of well control risk factors, which makes risk system structure more reasonable.
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