Mechanical Analysis and Safety Evaluation of Double-Packer string in a horizontal well

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1 Advances in Intelligent Systems Research (AISR, volume 07 International Conference on Information Technology and Intelligent Manufacturing (ITIM 07 Mechanical Analysis and Safety valuation of ouble-packer string in a horizontal well Yinping Cao, Hao Li and Yihua ou Mechanical ngineering College, Xi'an Shiyou University Abstract uring the hydraulic compression packer setting process, axial stress of the string will be generated, which may affect the safety of the string. In this paper, the double-packer string in a horizontal well is taken as the object. Considering the two packers are seated separately, on the basis of Lame formula, generalized Hooke' s law and bar deformation theory, the equations of axial force and axial stress of the string from the packers, and the deformation of the string without constraint from packers are deduced under wellhead pressure. The results show that, when packer is sealed with wellhead pressure as 0 MPa, the axial stress generated on the string between the bending section and packer is 9.9 MPa. When packer is sealed with wellhead pressure as 5 MPa, the axial stress generated on the string between the bending section and the packer is MPa. The axial stress of the string between packer and packer is reduced to 5.08 MPa and the total axial stress of the string between the bending section and packer is MPa. It can be seen that packer increases the axial stress on the string between the packer and the bending section when it is seated and causes the axial stress of the string between packer and packer reduced. Thus, the dangerous point locates between packer and the curved section of the string. The axial stress near the bottom of the string is reduced and the string tends to be safe. The results can be used to provide references for the selection of horizontal string to ensure its safety. Keywords Mechanical Analysis; string; ouble-packer; Horizontal Well I. INTROUCTION In the process of separate-layer water injection and separate-layer fracturing, the downhole string needs to be connected with multiple packers to achieve separate-layer production of oil and gas well []. ue to the effect of the packer sealing process, the string will deform when the downhole packer is sealed. The axial stress will occur in the string because its deformation is constrained by the sealed packer, which can affect the safety of the string. In order to ensure the safety of the downhole string and tools, it is necessary to analyze the force and length of the strings before and after packer is sealed. In the 960s, Lubinski first analyzed the force and deformation of a string with a single packer. He studied the axial deformation of the single-packer string under the four effects based on Hooke's law and the spiral buckling theory of string []. In the 980s, Hammerlindl further studied the stress and deformation of double-packer string [3~]. In 00, Qindao Li systematically analyzed and discussed the force and deformation of single-packer string [5~6]. There are also many domestic and foreign experts and scholars studied the packer string later, but most of them only focus on the packer string in vertical wells and intubation packers, which is relatively simple [7~0]. In 0, Zhanguo Lv conducted the mechanical analysis of the multi- hydraulic compression packer string in a horizontal well. He only researched the influence on the force and length of the string when each packer was sealed, while ignoring the interaction between the various packers []. Considering the shortage of existing research, in this paper the double-packer string and the hydraulic compression packers in a horizontal well are taken as the object. Considering the influence of the later sealed packer on the force and length of the string and previous sealed packers, the equations of the axial force and axial stress of the string from the packer under wellhead pressure are deduced. Besides that, the deformation of the string without packer is also deduced. II. RSARCH SCOP AN BASIC ASSUMPTIONS A. Research scope In this paper, double-packer string in a horizontal well, hydraulic compression packers and a uniform string are taken as the object. B. Basic assumptions The basic assumptions adopted are: The well is filled with liquid; ignoring the weight of string; ignoring the buckling deformation of string; when the packer is seated, it is pushed by successive steps; the packer is named from the bottom of the well, i.e. packer, packer, respectively. Based on the assumptions, the diagram of double-packer string in a horizontal well is shown in ig.. h is the depth of the wellhead to the horizontal section. The distance between the end of the bending section and packer is L; the distance between packer and packer is L, called the first section string; and the distance between packer and the end of the bending section is L, called the second section string. ig. The diagram of double - packer string in a horizontal well Copyright 07, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license ( 8

2 Advances in Intelligent Systems Research (AISR, volume III. MCHANICAL ANALYSIS O STRING WHN PACKR IS SAT uring the process of packer setting, a smaller ball is put from the wellhead into the balloon of packer and then wellhead pressure p is applied. rom the Lame formula, the radial stress and circumferential stress in the horizontal section string from the wellhead pressure are []: ( p d p ( p p d i o i o r d ( d di ( p d p ( p p d i o i o d ( d di ( ( Where, p 0 is the outside pressure of the string at the bottom, MPa; is the outside diameter of the string, m; d is the inside diameter of the string, m; d i is the diameter in an arbitrary place of the string, m; p i is the downhole pressure caused by wellhead pressure, which can be calculated as follows: p p gh (3 i Where, i is the density of the liquid in the string, kg/m 3. Because of the above two stresses, the string will conduct radial deformation, which will arise axial deformation. According to the generalized Hooke 's law, the axial strain of the horizontal section string is [3]: z z r i ( ( Where, is the elastic modulus of the string, MPa; is the Poisson's ratio of the string; z is the axial stress of horizontal section string, MPa. The axial deformation is: L ( (5 L zl z r Assuming that the horizontal section string has no constraint from packer, that is, the string is not subjected to axial force, then the string will be free to deform. At this time the axial stress z of the string is zero. Substituting zero in (5 for z, we can obtain: ( r L ( p id p0 L L zl (6 ( d Because of the bending friction and the packer constrained each ends of the horizontal section string, the axial deformation of the horizontal section string was limited, so that the axial restraining force was generated on the string from the packer. This axial force makes the deformation of the string is zero, i.e. L=0. Substituting zero in (5 for L, we can obtain: ( p id po z ( r d (7 The corresponding axial force is: z As ( p id po (8 Where, A s is the cross-sectional area of the string, m. IV. MCHANICAL ANALYSIS O STRING WHN PACKR IS SAT uring the process of packer setting, a larger ball is put from the wellhead into the balloon of the packer and then the wellhead pressure p is applied. Also, the radial stress r and circumferential stress in the second section string will be generated. Because of the above two stresses, the second section string will conduct radial deformation, which will arise axial deformation. According to the generalized Hooke 's law, the axial strain of the second section string is: z z ( r (9 Where, z is the axial stress of the second section string, MPa. The axial deformation is: L L zl z ( r (0 Because of the bending friction and the packer constrained each ends of the second section string, the axial deformation of the string was limited, so that the axial restraining force was generated on the string from the packer. This axial force makes the deformation of the second section string is zero, i.e. L =0. Substituting zero in (0 for L, we can obtain: ( pid po z ( r d ( Where, p i is the downhole pressure caused by wellhead pressure p, MPa, which can be obtained when substituting p in (3 for p. The corresponding axial force is: z As ( pid po ( The horizontal section string with two packers is now simplified as a simple beam, as shown in ig.. In the figure, the first constraint from left to right is the bending friction on the string, the second constraint is the packer to the string, and the third constraint is the packer. 9

3 Advances in Intelligent Systems Research (AISR, volume ig. The simplified diagram of the horizontal segment packer string If the constraints from the packers and are removed, the second section string will be free to deform under the action of the wellhead pressure p. At this time the axial stress z of the second section string is zero. Substituting zero in (0 for z, we can obtain: ( r L ( pid p0 L L zl (3 ( d If the constraint from the intermediate packer is removed without removing the constraint from the packer, the length of the horizontal section string will remain constant under two constraints from the bending section and the packer when the wellhead pressure p is applied, but the axial deformation will be generated on the second section string, assuming the deformation is shortening and the size is L ', as a result the first section string will elongate, assuming the deformation is L '. rom the above analysis, it can be seen that a "virtual axial force" which has the same size as and opposite to is generated on the position of packer when the constraint from the packer is removed. The force shortens the second section string and elongates the first section string, and the deformation is L ' and L ', respectively, as shown in ig. 3. ig.3 The diagram of removing the packer constraint In the figure above, the axial force is generated from the bending section, and the axial force is generated from the packer. Assuming the rightward axial force is positive, then by the static balance of the conditions, we can obtain: 0 ( Because of the above equation has one known force and two unknown forces and, the simple beam structure is a statically indeterminate structure. According to the above analysis, we can obtain the deformation coordination equation is: And physical equation: L ' L ' 0 (5 L L ' (6 As L L ' (7 As Substituting (6 and (7 into (5, we obtain: L L 0 (8 Simultaneous ( and (8, we can obtain: L L L L L L (9 (0 It can be seen that the axial restraining forces from the bending section and the packer are and respectively, but all opposite to the direction shown in ig. 3 when the constraint from the packer is present. rom the above analysis, it can be seen that a leftward axial force is generated on the string from the packer when the packer is seated, so that the axial force generated on the horizontal section string from the packer is changed. We can obtain: ' ( V. SATY VALUATION It can be seen from the above analysis, when the two packers are sealed, the axial stress of the string between the end of the bending section and the packer is: ' ( z z z The axial stress of the string between the packer and packer is: L ' z z z L L (3 Using the fourth strength theory of material mechanics to check: z z r r ( When check the first section string, the axial stress in ( is obtained from (3, and the radial stress and the circumferential stress in ( are obtained from ( and (, respectively. When check the second section string, the axial stress in ( is obtained from (, and the radial stress and the circumferential stress in ( can be obtained by substituting p i in ( and ( for p i. 30

4 Advances in Intelligent Systems Research (AISR, volume VI. CALCULATION XAMPL The depth h of the horizontal well is 000 m, the distance L between the end of the bending section and the packer is 600 m, the distance L between the packers and is 00 m, the outside diameter of the string is 88.9 mm, the inside diameter d of the string is 76 mm, the Poisson's ratio is 0.3, the elastic modulus is. 0 Pa, the permissible stress is 758 MPa, the completion fluid density is. 0 3 kg/m 3, the pressure p 0 outside the string at the bottom is 0 MPa, the wellhead pressure when the packers and are seated is 0 MPa and 5 MPa, respectively. A. Calculations of force and deformation of string when the packer is sealed rom the (6, when there is no constraint from packer, the axial deformation of the horizontal section string is: is: is: ( p id p0 L L 0. ( d rom the (7, the axial stress of the horizontal section string ( p id po z d 9.9 m MPa rom the (8, the axial force of the horizontal section string ( p id po KN irection to the right. B. Calculations of force and deformation of string when the packer is sealed rom the (3, when there are no constraints from packers and, the axial deformation of the horizontal section string is: ( pid p0 L L 0.7 ( d rom the (, the axial stress of the second section string is: ( pid po z d MPa rom the (, the axial force that is generated from the packer is: ( pid po KN irection to the right. rom the (0, the axial force that is generated from the packer is: irection to the left. L L L 58. KN m rom the (, when the packer is seated, the total axial force generated on the horizontal section string from the packer is: C. Strength check ' 5.8 KN Strength check of the first section string rom the ( and (, the radial stress and the circumferential stress is: r MPa, 03. MPa rom the (3, the axial stress of the string is: ' 5.08 z MPa rom the (, the equivalent stress of the string is: =8.65 MPa It is less than the permissible stress of 758 Mpa, thus the first section string is safety. Strength check of the second section string rom the ( and (, the radial stress and the circumferential stress is: r 38.99MPa, 3.9 MPa rom the (, the axial stress of the string is: ' z MPa rom the (, the equivalent stress of the string is: =35.38MPa It is less than the permissible stress of 758 Mpa, thus the second section string is safety. VII. CONCLUSIONS (uring the hydraulic compression packer setting process, the radial stress and the circumferential stress on the string will be generated, resulting in axial deformation of the string is generated. (Because of the packer constrains the string, limits the axial deformation of the string, the axial deformation is converted into the axial restraining force on the string from the packer, resulting in axial stress of the string is generated. (3The later sealed packer increases the axial stress on the string between the packer and the bending section when it is seated and causes the axial stress of the string between the packer and previous sealed packer reduced. Thus, the dangerous point locates between the later sealed packer and the curved section of the string. The axial stress near the bottom of the string is reduced and the string tends to be safe. ACKNOWLGMNT The paper is supported by Chinese National Natural Science oundation (5098 and Natural Science oundation of Shaanxi Province, China (0JQ789. 3

5 Advances in Intelligent Systems Research (AISR, volume RRNCS [] LiPing Zhang, Cen Gao, Qingjiang Gu. Technical Measures for Increasing Production of Oilfield [J]. China Petroleum and Chemical Standards and Quality, 03, 39(8: [] Lubinski A, Althouse W S. Helical Buckling of Tubing Sealed in Packers[J]. Journal of Petroleum Technology, 96, (6: [3] Hammerlindl J. Movement, orces, and Stresses Associated With Combination Tubing Strings Sealed in Packers[J]. Journal of Petroleum Technology, 977, 9(: [] Hammerlindl J. Packer-to-Tubing orces for Intermediate Packers[J]. Journal of Petroleum Technology, 980, 3(3: [5] Qingdao Li, Guangping Xie, Juan Zhang. Calculation Analysis of Initial Amount of Compression of Test String The Third iscussion of orce Analsis System of Packer String[J]. rilling & Production Technology, 00, (6:8-5. [6] Qingdao Li, Guangping Xie, Juan Zhang. orce Analysis of Permanent Packer String The ifth iscussion of orce Analsis System of Packer String[J]. rilling & Production Technology, 00, 5(:6-65. [7] Yihua ou, uxiang Zhang. Mechanical Analysis of Well Testing ownhole String in eep Well With HTHP and Its Application[J]. rilling & Production Technology, 007,(05: [8] Qi Liu, Jianxun Jiang, Qing Shi. Calculation Analysis on orce eformation of Packer String with ree Movement[J]. ault Block Oil and Gas ield, 007, (:6-63. [9] Pengbo ong, Yihua ou. Analysis of Buckling Configuration and Restraint orces of Tubular Strings Sealed in Parkers[J]. Oil ield quipment, 007, 36(0:-7. [0] Yuhua Liao, Bin Yang, Ming Li. Mechanic Model Analyses on Packer Pipe String ffect[j]. Mechanical, 0(s:0-3. [] Zhanguo Lv. Mechanics and Safety Analysis of Multi - packer String in Horizontal Wells[]. Xi'an Shiyou University, 0. [] Zhilun Xu. Simple Teaching of lasticity[m]. Higher ducation Press, 03. [3] Hongwen Liu, Jianxin Lin, Manling Cao. Material Mechanics[M]. Higher ducation Press, 0. 3

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